Minor docs change

Add methods to Quaternion for consistency with getYaw and setYaw

.github/workflows/build.yml

@@ -5,6 +5,7 @@ on:
     branches: [ '*' ]
   pull_request:
     branches: [ master ]
+  workflow_dispatch:
 
 jobs:
   build_linux:
@@ -14,7 +15,16 @@ jobs:
     - name: Install Arduino CLI
       run: curl -fsSL https://raw.githubusercontent.com/arduino/arduino-cli/master/install.sh | BINDIR=/usr/local/bin sh
     - name: Build firmware
+      env:
+        ARDUINO_SKETCH_ALWAYS_EXPORT_BINARIES: 1
       run: make
+    - name: Upload binaries
+      uses: actions/upload-artifact@v4
+      with:
+        name: firmware-binary
+        path: flix/build
+    - name: Build firmware without Wi-Fi
+      run: sed -i 's/^#define WIFI_ENABLED 1$/#define WIFI_ENABLED 0/' flix/flix.ino && make
     - name: Check c_cpp_properties.json
       run: tools/check_c_cpp_properties.py
 
@@ -43,7 +53,7 @@ jobs:
       run: python3 tools/check_c_cpp_properties.py
 
   build_simulator:
-    runs-on: ubuntu-latest
+    runs-on: ubuntu-22.04
     steps:
     - name: Install Arduino CLI
       uses: arduino/setup-arduino-cli@v1.1.1
@@ -54,28 +64,29 @@ jobs:
       run: sudo apt-get install libsdl2-dev
     - name: Build simulator
       run: make build_simulator
-    - uses: actions/upload-artifact@v3
+    - uses: actions/upload-artifact@v4
       with:
         name: gazebo-plugin-binary
         path: gazebo/build/*.so
         retention-days: 1
 
-#  build_simulator_macos:
-#    runs-on: macos-latest
-#    steps:
-#    - name: Install Arduino CLI
-#      run: brew install arduino-cli
-#    - uses: actions/checkout@v4
-#    - name: Clean up python binaries # Workaround for https://github.com/actions/setup-python/issues/577
-#      run: |
-#        rm -f /usr/local/bin/2to3*
-#        rm -f /usr/local/bin/idle3*
-#        rm -f /usr/local/bin/pydoc3*
-#        rm -f /usr/local/bin/python3*
-#        rm -f /usr/local/bin/python3*-config
-#    - name: Install Gazebo
-#      run: brew update && brew tap osrf/simulation && brew install gazebo11
-#    - name: Install SDL2
-#      run: brew install sdl2
-#    - name: Build simulator
-#      run: make build_simulator
+  build_simulator_macos:
+    runs-on: macos-latest
+    if: github.event_name == 'workflow_dispatch'
+    steps:
+    - name: Install Arduino CLI
+      run: brew install arduino-cli
+    - uses: actions/checkout@v4
+    - name: Clean up python binaries # Workaround for https://github.com/actions/setup-python/issues/577
+      run: |
+        rm -f /usr/local/bin/2to3*
+        rm -f /usr/local/bin/idle3*
+        rm -f /usr/local/bin/pydoc3*
+        rm -f /usr/local/bin/python3*
+        rm -f /usr/local/bin/python3*-config
+    - name: Install Gazebo
+      run: brew update && brew tap osrf/simulation && brew install gazebo11
+    - name: Install SDL2
+      run: brew install sdl2
+    - name: Build simulator
+      run: make build_simulator

.github/workflows/tools.yml

@@ -19,6 +19,21 @@ jobs:
         echo -e "t,x,y,z\n0,1,2,3\n1,4,5,6" > log.csv
         ./csv_to_ulog log.csv
         test $(stat -c %s log.ulg) -eq 196
+  pyflix:
+    runs-on: ubuntu-latest
+    steps:
+    - uses: actions/checkout@v4
+    - name: Install Python build tools
+      run: pip install build
+    - name: Build pyflix
+      run: python3 -m build tools
+    - name: Upload artifacts
+      uses: actions/upload-artifact@v4
+      with:
+        name: pyflix
+        path: |
+          tools/dist/pyflix-*.tar.gz
+          tools/dist/pyflix-*.whl
   python_tools:
     runs-on: ubuntu-latest
     steps:

.gitignore

@@ -2,6 +2,8 @@
 *.elf
 build/
 tools/log/
+tools/dist/
+*.egg-info/
 .dependencies
 .vscode/*
 !.vscode/settings.json

.markdownlint.json

@@ -34,6 +34,7 @@
 			"MPU-6050",
 			"MPU-9250",
 			"GY-91",
+			"GY-521",
 			"ICM-20948",
 			"Linux",
 			"Windows",

.vscode/c_cpp_properties.json

@@ -5,18 +5,18 @@
 			"includePath": [
 				"${workspaceFolder}/flix",
 				"${workspaceFolder}/gazebo",
-				"~/.arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32",
-				"~/.arduino15/packages/esp32/hardware/esp32/3.0.7/libraries/**",
-				"~/.arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32",
-				"~/.arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/**",
-				"~/.arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/dio_qspi/include",
+				"~/.arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32",
+				"~/.arduino15/packages/esp32/hardware/esp32/3.2.0/libraries/**",
+				"~/.arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32",
+				"~/.arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/**",
+				"~/.arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/dio_qspi/include",
 				"~/Arduino/libraries/**",
 				"/usr/include/**"
 			],
 			"forcedInclude": [
 				"${workspaceFolder}/.vscode/intellisense.h",
-				"~/.arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32/Arduino.h",
-				"~/.arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32/pins_arduino.h",
+				"~/.arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32/Arduino.h",
+				"~/.arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32/pins_arduino.h",
 				"${workspaceFolder}/flix/cli.ino",
 				"${workspaceFolder}/flix/control.ino",
 				"${workspaceFolder}/flix/estimate.ino",
@@ -28,11 +28,10 @@
 				"${workspaceFolder}/flix/motors.ino",
 				"${workspaceFolder}/flix/rc.ino",
 				"${workspaceFolder}/flix/time.ino",
-				"${workspaceFolder}/flix/util.ino",
 				"${workspaceFolder}/flix/wifi.ino",
 				"${workspaceFolder}/flix/parameters.ino"
 			],
-			"compilerPath": "~/.arduino15/packages/esp32/tools/esp-x32/2302/bin/xtensa-esp32-elf-g++",
+			"compilerPath": "~/.arduino15/packages/esp32/tools/esp-x32/2411/bin/xtensa-esp32-elf-g++",
 			"cStandard": "c11",
 			"cppStandard": "c++17",
 			"defines": [
@@ -52,19 +51,19 @@
 			"name": "Mac",
 			"includePath": [
 				"${workspaceFolder}/flix",
-				"${workspaceFolder}/gazebo",
-				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32",
-				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.0.7/libraries/**",
-				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32",
-				"~/Library/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/include/**",
-				"~/Library/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/dio_qspi/include",
+				// "${workspaceFolder}/gazebo",
+				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32",
+				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.2.0/libraries/**",
+				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32",
+				"~/Library/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/include/**",
+				"~/Library/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/dio_qspi/include",
 				"~/Documents/Arduino/libraries/**",
 				"/opt/homebrew/include/**"
 			],
 			"forcedInclude": [
 				"${workspaceFolder}/.vscode/intellisense.h",
-				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32/Arduino.h",
-				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32/pins_arduino.h",
+				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32/Arduino.h",
+				"~/Library/Arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32/pins_arduino.h",
 				"${workspaceFolder}/flix/flix.ino",
 				"${workspaceFolder}/flix/cli.ino",
 				"${workspaceFolder}/flix/control.ino",
@@ -76,11 +75,10 @@
 				"${workspaceFolder}/flix/motors.ino",
 				"${workspaceFolder}/flix/rc.ino",
 				"${workspaceFolder}/flix/time.ino",
-				"${workspaceFolder}/flix/util.ino",
 				"${workspaceFolder}/flix/wifi.ino",
 				"${workspaceFolder}/flix/parameters.ino"
 			],
-			"compilerPath": "~/Library/Arduino15/packages/esp32/tools/esp-x32/2302/bin/xtensa-esp32-elf-g++",
+			"compilerPath": "~/Library/Arduino15/packages/esp32/tools/esp-x32/2411/bin/xtensa-esp32-elf-g++",
 			"cStandard": "c11",
 			"cppStandard": "c++17",
 			"defines": [
@@ -102,17 +100,17 @@
 			"includePath": [
 				"${workspaceFolder}/flix",
 				"${workspaceFolder}/gazebo",
-				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32",
-				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.0.7/libraries/**",
-				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32",
-				"~/AppData/Local/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/**",
-				"~/AppData/Local/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.1-632e0c2a/esp32/dio_qspi/include",
+				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32",
+				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.2.0/libraries/**",
+				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32",
+				"~/AppData/Local/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/**",
+				"~/AppData/Local/Arduino15/packages/esp32/tools/esp32-arduino-libs/idf-release_v5.4-2f7dcd86-v1/esp32/dio_qspi/include",
 				"~/Documents/Arduino/libraries/**"
 			],
 			"forcedInclude": [
 				"${workspaceFolder}/.vscode/intellisense.h",
-				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.0.7/cores/esp32/Arduino.h",
-				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.0.7/variants/d1_mini32/pins_arduino.h",
+				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.2.0/cores/esp32/Arduino.h",
+				"~/AppData/Local/Arduino15/packages/esp32/hardware/esp32/3.2.0/variants/d1_mini32/pins_arduino.h",
 				"${workspaceFolder}/flix/cli.ino",
 				"${workspaceFolder}/flix/control.ino",
 				"${workspaceFolder}/flix/estimate.ino",
@@ -124,11 +122,10 @@
 				"${workspaceFolder}/flix/motors.ino",
 				"${workspaceFolder}/flix/rc.ino",
 				"${workspaceFolder}/flix/time.ino",
-				"${workspaceFolder}/flix/util.ino",
 				"${workspaceFolder}/flix/wifi.ino",
 				"${workspaceFolder}/flix/parameters.ino"
 			],
-			"compilerPath": "~/AppData/Local/Arduino15/packages/esp32/tools/esp-x32/2302/bin/xtensa-esp32-elf-g++.exe",
+			"compilerPath": "~/AppData/Local/Arduino15/packages/esp32/tools/esp-x32/2411/bin/xtensa-esp32-elf-g++.exe",
 			"cStandard": "c11",
 			"cppStandard": "c++17",
 			"defines": [

.vscode/extensions.json

@@ -2,7 +2,6 @@
 	// See https://go.microsoft.com/fwlink/?LinkId=827846 to learn about workspace recommendations.
 	"recommendations": [
 		"ms-vscode.cpptools",
-		"twxs.cmake",
 		"ms-vscode.cmake-tools",
 		"ms-python.python"
 	],

Makefile

@@ -13,10 +13,10 @@ monitor:
 
 dependencies .dependencies:
 	arduino-cli core update-index --config-file arduino-cli.yaml
-	arduino-cli core install esp32:esp32@3.0.7 --config-file arduino-cli.yaml
+	arduino-cli core install esp32:esp32@3.2.0 --config-file arduino-cli.yaml
 	arduino-cli lib update-index
 	arduino-cli lib install "FlixPeriph"
-	arduino-cli lib install "MAVLink"@2.0.12
+	arduino-cli lib install "MAVLink"@2.0.16
 	touch .dependencies
 
 gazebo/build cmake: gazebo/CMakeLists.txt

README.md

@@ -4,76 +4,89 @@
 
 <table>
   <tr>
-    <td align=center><strong>Version 1</strong> (3D-printed frame)</td>
+    <td align=center><strong>Version 1.1</strong> (3D-printed frame)</td>
     <td align=center><strong>Version 0</strong></td>
   </tr>
   <tr>
-    <td><img src="docs/img/flix1.jpg" width=500 alt="Flix quadcopter"></td>
+    <td><img src="docs/img/flix1.1.jpg" width=500 alt="Flix quadcopter"></td>
     <td><img src="docs/img/flix.jpg" width=500 alt="Flix quadcopter"></td>
   </tr>
 </table>
 
 ## Features
 
-* Simple and clean Arduino based source code.
-* Acro and Stabilized flight using remote control.
-* Precise simulation using Gazebo.
-* [In-RAM logging](docs/log.md).
-* Command line interface through USB port.
-* Wi-Fi support.
-* MAVLink support.
-* Control using mobile phone (with QGroundControl app).
-* Completely 3D-printed frame.
-* Textbook for students on writing a flight controller ([in development](https://quadcopter.dev)).
-* *Position control and autonomous flights using external camera¹*.
-* [Building and running instructions](docs/build.md).
+* Dedicated for education and research.
+* Made from general-purpose components.
+* Simple and clean source code in Arduino.
+* Control using remote control or smartphone.
+* Precise simulation with Gazebo.
+* Wi-Fi and MAVLink support.
+* Wireless command line interface and analyzing.
+* Python library.
+* Textbook on flight control theory and practice ([in development](https://quadcopter.dev)).
+* *Position control (using external camera) and autonomous flights¹*.
 
 *¹ — planned.*
 
 ## It actually flies
 
-See detailed demo video (for version 0): https://youtu.be/8GzzIQ3C6DQ.
+See detailed demo video: https://youtu.be/hT46CZ1CgC4.
+
+<a href="https://youtu.be/hT46CZ1CgC4"><img width=500 src="https://i3.ytimg.com/vi/hT46CZ1CgC4/maxresdefault.jpg"></a>
+
+Version 0 demo video: https://youtu.be/8GzzIQ3C6DQ.
 
 <a href="https://youtu.be/8GzzIQ3C6DQ"><img width=500 src="https://i3.ytimg.com/vi/8GzzIQ3C6DQ/maxresdefault.jpg"></a>
 
-Version 1 test flight: https://t.me/opensourcequadcopter/42.
+See the [user builds gallery](docs/user.md).
 
-<a href="https://t.me/opensourcequadcopter/42"><img width=500 src="docs/img/flight-video.jpg"></a>
+<a href="docs/user.md"><img src="docs/img/user/user.jpg" width=500></a>
 
 ## Simulation
 
 The simulator is implemented using Gazebo and runs the original Arduino code:
 
-<img src="docs/img/simulator.png" width=500 alt="Flix simulator">
+<img src="docs/img/simulator1.png" width=500 alt="Flix simulator">
 
-See [instructions on running the simulation](docs/build.md).
+## Articles
 
-## Components (version 1)
+* [Assembly instructions](docs/assembly.md).
+* [Building and running the code](docs/build.md).
+* [Troubleshooting](docs/troubleshooting.md).
+* [Firmware architecture overview](docs/firmware.md).
+* [Python library tutorial](tools/pyflix/README.md).
+* [Log analysis](docs/log.md).
+* [User builds gallery](docs/user.md).
+
+## Components
 
 |Type|Part|Image|Quantity|
 |-|-|:-:|:-:|
 |Microcontroller board|ESP32 Mini|<img src="docs/img/esp32.jpg" width=100>|1|
-|IMU (and barometer²) board|GY‑91 (or other MPU‑9250/MPU‑6500 board), ICM‑20948³|<img src="docs/img/gy-91.jpg" width=90 align=center><img src="docs/img/icm-20948.jpg" width=100>|1|
-|Motor|8520 3.7V brushed motor (**shaft 0.8mm!**)|<img src="docs/img/motor.jpeg" width=100>|4|
+|IMU (and barometer²) board|GY‑91, MPU-9265 (or other MPU‑9250/MPU‑6500 board)<br>ICM20948V2 (ICM‑20948)³<br>GY-521 (MPU-6050)³⁻¹|<img src="docs/img/gy-91.jpg" width=90 align=center><br><img src="docs/img/icm-20948.jpg" width=100><br><img src="docs/img/gy-521.jpg" width=100>|1|
+|<span style="background:yellow">Buck-boost converter</span> (recommended)|To be determined, output 5V or 3.3V, see [user-contributed schematics](https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764612179508274&cot=14)|<img src="docs/img/buck-boost.jpg" width=100>|1|
+|Motor|8520 3.7V brushed motor (shaft 0.8mm).<br>Motor with exact 3.7V voltage is needed, not ranged working voltage (3.7V — 6V).|<img src="docs/img/motor.jpeg" width=100>|4|
 |Propeller|Hubsan 55 mm|<img src="docs/img/prop.jpg" width=100>|4|
 |MOSFET (transistor)|100N03A or [analog](https://t.me/opensourcequadcopter/33)|<img src="docs/img/100n03a.jpg" width=100>|4|
 |Pull-down resistor|10 kΩ|<img src="docs/img/resistor10k.jpg" width=100>|4|
 |3.7V Li-Po battery|LW 952540 (or any compatible by the size)|<img src="docs/img/battery.jpg" width=100>|1|
+|Battery connector cable|MX2.0 2P female|<img src="docs/img/mx.png" width=100>|1|
 |Li-Po Battery charger|Any|<img src="docs/img/charger.jpg" width=100>|1|
 |Screws for IMU board mounting|M3x5|<img src="docs/img/screw-m3.jpg" width=100>|2|
 |Screws for frame assembly|M1.4x5|<img src="docs/img/screw-m1.4.jpg" height=30 align=center>|4|
-|Frame bottom part|3D printed⁴:<br>[`flix-frame.stl`](docs/assets/flix-frame.stl) [`flix-frame.step`](docs/assets/flix-frame.step)|<img src="docs/img/frame1.jpg" width=100>|1|
+|Frame main part|3D printed⁴:<br>[`flix-frame-1.1.stl`](docs/assets/flix-frame-1.1.stl) [`flix-frame-1.1.step`](docs/assets/flix-frame-1.1.step)<br>Recommended settings: layer 0.2 mm, line 0.4 mm, infill 100%.|<img src="docs/img/frame1.jpg" width=100>|1|
 |Frame top part|3D printed:<br>[`esp32-holder.stl`](docs/assets/esp32-holder.stl) [`esp32-holder.step`](docs/assets/esp32-holder.step)|<img src="docs/img/esp32-holder.jpg" width=100>|1|
-|Washer for IMU board mounting|3D printed:<br>[`washer-m3.stl`](docs/assets/washer-m3.stl) [`washer-m3.step`](docs/assets/washer-m3.step)|<img src="docs/img/washer-m3.jpg" width=100>|1|
-|*RC transmitter (optional)*|*KINGKONG TINY X8 or other⁵*|<img src="docs/img/tx.jpg" width=100>|1|
+|Washer for IMU board mounting|3D printed:<br>[`washer-m3.stl`](docs/assets/washer-m3.stl) [`washer-m3.step`](docs/assets/washer-m3.step)|<img src="docs/img/washer-m3.jpg" width=100>|2|
+|RC transmitter (recommended)|BetaFPV LiteRadio (CC2500) — with USB support (can control via Wi-Fi).<br>KINGKONG TINY X8 — warning: lacks USB support.<br>Or other⁵|<img src="docs/img/tx.jpg" width=100>|1|
 |*RC receiver (optional)*|*DF500 or other⁵*|<img src="docs/img/rx.jpg" width=100>|1|
 |Wires|28 AWG recommended|<img src="docs/img/wire-28awg.jpg" width=100>||
 |Tape, double-sided tape||||
 
 *² — barometer is not used for now.*<br>
 *³ — change `MPU9250` to `ICM20948` in `imu.ino` file if using ICM-20948 board.*<br>
+*³⁻¹ — MPU-6050 supports I²C interface only (not recommended). To use it change IMU declaration to `MPU6050 IMU(Wire)`.*<br>
 *⁴ — this frame is optimized for GY-91 board, if using other, the board mount holes positions should be modified.*<br>
-*⁵ — you may use any transmitter-receiver pair with SBUS interface.*
+*⁵ — you may use any transmitter-receiver pair with SBUS interface, or any transmitter with USB support*
 
 Tools required for assembly:
 
@@ -85,7 +98,7 @@ Tools required for assembly:
 
 Feel free to modify the design and or code, and create your own improved versions of Flix! Send your results to the [official Telegram chat](https://t.me/opensourcequadcopterchat), or directly to the author ([E-mail](mailto:okalachev@gmail.com), [Telegram](https://t.me/okalachev)).
 
-## Schematics (version 1)
+## Schematics
 
 ### Simplified connection diagram
 
@@ -95,7 +108,9 @@ Motor connection scheme:
 
 <img src="docs/img/mosfet-connection.png" height=400 alt="MOSFET connection scheme">
 
-Complete diagram is Work-in-Progress.
+You can see a user-contributed [variant of complete circuit diagram](https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764612338222067&cot=14) of the drone.
+
+See [assembly guide](docs/assembly.md) for instructions on assembling the drone.
 
 ### Notes
 
@@ -116,10 +131,10 @@ Complete diagram is Work-in-Progress.
 
   |Motor|Position|Direction|Wires|GPIO|
   |-|-|-|-|-|
-  |Motor 0|Rear left|Counter-clockwise|Black & White|GPIO12|
-  |Motor 1|Rear right|Clockwise|Blue & Red|GPIO13|
-  |Motor 2|Front right|Counter-clockwise|Black & White|GPIO14|
-  |Motor 3|Front left|Clockwise|Blue & Red|GPIO15|
+  |Motor 0|Rear left|Counter-clockwise|Black & White|GPIO12 (*TDI*)|
+  |Motor 1|Rear right|Clockwise|Blue & Red|GPIO13 (*TCK*)|
+  |Motor 2|Front right|Counter-clockwise|Black & White|GPIO14 (*TMS*)|
+  |Motor 3|Front left|Clockwise|Blue & Red|GPIO15 (*TD0*)|
 
   Counter-clockwise motors have black and white wires and clockwise motors have blue and red wires.
 
@@ -128,8 +143,8 @@ Complete diagram is Work-in-Progress.
   |Receiver pin|ESP32 pin|
   |-|-|
   |GND|GND|
-  |VIN|VC (or 3.3V depending on the receiver)|
-  |Signal|GPIO4⁶|
+  |VIN|VCC (or 3.3V depending on the receiver)|
+  |Signal (TX)|GPIO4⁶|
 
 *⁶ — UART2 RX pin was [changed](https://docs.espressif.com/projects/arduino-esp32/en/latest/migration_guides/2.x_to_3.0.html#id14) to GPIO4 in Arduino ESP32 core 3.0.*
 
@@ -143,10 +158,6 @@ In case of using other IMU orientation, modify the `rotateIMU` function in the `
 
 See [FlixPeriph documentation](https://github.com/okalachev/flixperiph?tab=readme-ov-file#imu-axes-orientation) to learn axis orientation of other IMU boards.
 
-## Version 0
-
-See the information on the obsolete version 0 in the [corresponding article](docs/version0.md).
-
 ## Materials
 
 Subscribe to the Telegram channel on developing the drone and the flight controller (in Russian): https://t.me/opensourcequadcopter.
@@ -154,3 +165,11 @@ Subscribe to the Telegram channel on developing the drone and the flight control
 Join the official Telegram chat: https://t.me/opensourcequadcopterchat.
 
 Detailed article on Habr.com about the development of the drone (in Russian): https://habr.com/ru/articles/814127/.
+
+See the information on the obsolete version 0 in the [corresponding article](docs/version0.md).
+
+## Disclaimer
+
+This is a fun DIY project, and I hope you find it interesting and useful. However, it's not easy to assemble and set up, and it's provided "as is" without any warranties. There’s no guarantee that it will work perfectly — or even work at all.
+
+⚠️ The author is not responsible for any damage, injury, or loss resulting from the use of this project. Use at your own risk!

arduino-cli.yaml

@@ -1,3 +1,5 @@
 board_manager:
   additional_urls:
     - https://raw.githubusercontent.com/espressif/arduino-esp32/gh-pages/package_esp32_index.json
+network:
+  connection_timeout: 1h

docs/assembly.md

@@ -0,0 +1,29 @@
+# Brief assembly guide
+
+Soldered components ([schematics variant](https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764612338222067&cot=14)):
+
+<img src="img/assembly/1.jpg" width=600>
+
+<br>Use double-sided tape to attach ESP32 to the top frame part (ESP32 holder):
+
+<img src="img/assembly/2.jpg" width=600>
+
+<br>Use two washers to screw the IMU board to the frame:
+
+<img src="img/assembly/3.jpg" width=600>
+
+<br>Screw the IMU with M3x5 screws as shown:
+
+<img src="img/assembly/4.jpg" width=600>
+
+<br>Install the motors, attach MOSFETs to the frame using tape:
+
+<img src="img/assembly/5.jpg" width=600>
+
+<br>Screw the ESP32 holder with M1.4x5 screws to the frame:
+
+<img src="img/assembly/6.jpg" width=600>
+
+<br>Assembled drone:
+
+<img src="img/assembly/7.jpg" width=600>

docs/book.css

@@ -53,6 +53,12 @@ footer a.telegram, footer a.github {
 	border: 1px solid #c9c9c9;
 }
 
+@media (max-width: 600px) {
+	.MathJax_Display {
+		overflow-x: auto;
+	}
+}
+
 .firmware {
 	position: relative;
 	margin: 20px 0;

docs/book.toml

@@ -10,7 +10,7 @@ description = "Учебник по разработке полетного ко
 build-dir = "build"
 
 [output.html]
-additional-css = ["book.css", "zoom.css"]
+additional-css = ["book.css", "zoom.css", "rotation.css"]
 additional-js = ["zoom.js", "js.js"]
 edit-url-template = "https://github.com/okalachev/flix/blob/master/docs/{path}?plain=1"
 mathjax-support = true

docs/book/README.md

@@ -3,7 +3,7 @@
 > [!IMPORTANT]
 > Flix — это проект по созданию открытого квадрокоптера на базе ESP32 с нуля и учебника по разработке полетных контроллеров.
 
-<img src="img/flix1.jpg" class="border" width=500 alt="Flix quadcopter">
+<img src="img/flix1.1.jpg" class="border" width=500 alt="Flix quadcopter">
 
 <p class="github">GitHub:&nbsp;<a href="https://github.com/okalachev/flix">github.com/okalachev/flix</a>.</p>
 

docs/book/SUMMARY.md

@@ -11,8 +11,9 @@
 * [Светодиод]()
 * [Моторы]()
 * [Радиоуправление]()
+* [Вектор, кватернион](geometry.md)
 * [Гироскоп](gyro.md)
-* [Акселерометр]()s
+* [Акселерометр]()
 * [Оценка состояния]()
 * [PID-регулятор]()
 * [Режим ACRO]()

docs/book/firmware.md

@@ -10,8 +10,8 @@
 * `acc` *(Vector)* — данные с акселерометра, *м/с<sup>2</sup>*.
 * `rates` *(Vector)* — отфильтрованные угловые скорости, *рад/с*.
 * `attitude` *(Quaternion)* — оценка ориентации (положения) дрона.
-* `controls` *(float[])* — пользовательские управляющие сигналы с пульта, нормализованные в диапазоне [-1, 1].
-* `motors` *(float[])* — выходные сигналы на моторы, нормализованные в диапазоне [-1, 1] (возможно вращение в обратную сторону).
+* `controlRoll`, `controlPitch`, ... *(float[])* — команды управления от пилота, в диапазоне [-1, 1].
+* `motors` *(float[])* — выходные сигналы на моторы, в диапазоне [0, 1].
 
 ## Исходные файлы
 
@@ -27,6 +27,6 @@
 
 Вспомогательные файлы включают:
 
-* [`vector.h`](https://github.com/okalachev/flix/blob/canonical/flix/vector.h), [`quaternion.h`](https://github.com/okalachev/flix/blob/canonical/flix/quaternion.h) — реализация библиотек векторов и кватернионов проекта.
+* [`vector.h`](https://github.com/okalachev/flix/blob/canonical/flix/vector.h), [`quaternion.h`](https://github.com/okalachev/flix/blob/canonical/flix/quaternion.h) — реализация библиотек векторов и кватернионов.
 * [`pid.h`](https://github.com/okalachev/flix/blob/canonical/flix/pid.h) — реализация общего ПИД-регулятора.
 * [`lpf.h`](https://github.com/okalachev/flix/blob/canonical/flix/lpf.h) — реализация общего фильтра нижних частот.

docs/book/geometry.md

@@ -0,0 +1,309 @@
+# Вектор, кватернион
+
+В алгоритме управления квадрокоптером широко применяются геометрические (и алгебраические) объекты, такие как **векторы** и **кватернионы**. Они позволяют упростить математические вычисления и улучшить читаемость кода. В этой главе мы рассмотрим именно те геометрические объекты, которые используются в алгоритме управления квадрокоптером Flix, причем акцент будет сделан на практических аспектах их использования.
+
+## Система координат
+
+### Оси координат
+
+Для работы с объектами в трехмерном пространстве необходимо определить *систему координат*. Как известно, система координат задается тремя взаимно перпендикулярными осями, которые обозначаются как *X*, *Y* и *Z*. Порядок обозначения этих осей зависит от того, какую систему координат мы выбрали — *левую* или *правую*:
+
+|Левая система координат|Правая система координат|
+|-----------------------|------------------------|
+|<img src="img/left-axes.svg" alt="Левая система координат" width="200">|<img src="img/right-axes.svg" alt="Правая система координат" width="200">|
+
+В Flix для всех математических расчетов используется **правая система координат**, что является стандартом в робототехнике и авиации.
+
+Также необходимо выбрать направление осей — в Flix они выбраны в соответствии со стандартом [REP-103](https://www.ros.org/reps/rep-0103.html). Для величин, заданных в подвижной системе координат, связанной с корпусом дрона, применяется порядок <abbr title="Forward Left Up">FLU</abbr>:
+
+* ось X — направлена **вперед**;
+* ось Y — направлена **влево**;
+* ось Z — направлена **вверх**.
+
+Для величин, заданных в *мировой* системе координат (относительно фиксированной точки в пространстве) — <abbr title="East North Up">ENU</abbr>:
+
+* ось X — направлена на **восток** (условный);
+* ось Y — направлена на **север** (условный);
+* ось Z — направлена **вверх**.
+
+> [!NOTE]
+> Для системы ENU важно только взаимное направление осей. Если доступен магнитометр, то используются реальные восток и север, но если нет — то произвольно выбранные.
+
+Углы и угловые скорости определяются в соответствии с правилами математики: значения увеличиваются против часовой стрелки, если смотреть в сторону начала координат. Общий вид системы координат:
+
+<img src="img/axes-rotation.svg" alt="Система координат" width="200">
+
+> [!TIP]
+> Оси координат <i>X</i>, <i>Y</i> и <i>Z</i> часто обозначаются красными, зелеными и синими цветами соответственно. Запомнить это можно с помощью сокращения <abbr title="Red Green Blue">RGB</abbr>.
+
+## Вектор
+
+<div class="firmware">
+	<strong>Файл прошивки:</strong>
+	<a href="https://github.com/okalachev/flix/blob/master/flix/vector.h"><code>vector.h</code></a>.<br>
+</div>
+
+**Вектор** — простой геометрический объект, который содержит три значения, соответствующие координатам *X*, *Y* и *Z*. Эти значения называются *компонентами вектора*. Вектор может описывать точку в пространстве, направление или ось вращения, скорость, ускорение, угловые скорости и другие физические величины. В Flix векторы задаются объектами `Vector` из библиотеки `vector.h`:
+
+```cpp
+Vector v(1, 2, 3);
+v.x = 5;
+v.y = 10;
+v.z = 15;
+```
+
+> [!TIP]
+> Не следует путать геометрический вектор — <code>vector</code> и динамический массив в стандартной библиотеке C++ — <code>std::vector</code>.
+
+В прошивке в виде векторов представлены, например:
+
+* `acc` собственное ускорение с акселерометра.
+* `gyro` — угловые скорости с гироскопа.
+* `rates` — рассчитанная угловая скорость дрона.
+* `accBias`, `accScale`, `gyroBias` — параметры калибровки IMU.
+
+### Операции с векторами
+
+**Длина вектора** рассчитывается при помощи теоремы Пифагора; в прошивке используется метод `norm()`:
+
+```cpp
+Vector v(3, 4, 5);
+float length = v.norm(); // 7.071
+```
+
+Любой вектор можно привести к **единичному вектору** (сохранить направление, но сделать длину равной 1) при помощи метода `normalize()`:
+
+```cpp
+Vector v(3, 4, 5);
+v.normalize(); // 0.424, 0.566, 0.707
+```
+
+**Сложение и вычитание** векторов реализуется через простое покомпонентное сложение и вычитание. Геометрически сумма векторов представляет собой вектор, который соединяет начало первого вектора с концом второго. Разность векторов представляет собой вектор, который соединяет конец первого вектора с концом второго. Это удобно для расчета относительных позиций, суммарных скоростей и решения других задач. В коде эти операции интуитивно понятны:
+
+```cpp
+Vector a(1, 2, 3);
+Vector b(4, 5, 6);
+Vector sum = a + b; // 5, 7, 9
+Vector diff = a - b; // -3, -3, -3
+```
+
+Операция **умножения на число** `n` увеличивает (или уменьшает) длину вектора в `n` раз (сохраняя направление):
+
+```cpp
+Vector a(1, 2, 3);
+Vector b = a * 2; // 2, 4, 6
+```
+
+В некоторых случаях полезна операция **покомпонентного умножения** (или деления) векторов. Например, для применения коэффициентов калибровки к данным с IMU. В разных библиотеках эта операция обозначается по разному, но в библиотеке `vector.h` используется простые знаки `*` и `/`:
+
+```cpp
+acc = acc / accScale;
+```
+
+**Угол между векторами** можно найти при помощи статического метода `Vector::angleBetween()`:
+
+```cpp
+Vector a(1, 0, 0);
+Vector b(0, 1, 0);
+float angle = Vector::angleBetween(a, b); // 1.57 (90 градусов)
+```
+
+#### Скалярное произведение
+
+Скалярное произведение векторов (*dot product*) — это произведение длин двух векторов на косинус угла между ними. В математике оно обозначается знаком `·` или слитным написанием векторов. Интуитивно, результат скалярного произведения показывает, насколько два вектора *сонаправлены*.
+
+В Flix используется статический метод `Vector::dot()`:
+
+```cpp
+Vector a(1, 2, 3);
+Vector b(4, 5, 6);
+float dotProduct = Vector::dot(a, b); // 32
+```
+
+Операция скалярного произведения может помочь, например, при расчете проекции одного вектора на другой.
+
+#### Векторное произведение
+
+Векторное произведение (*cross product*) позволяет найти вектор, перпендикулярный двум другим векторам. В математике оно обозначается знаком `×`, а в прошивке используется статический метод `Vector::cross()`:
+
+```cpp
+Vector a(1, 2, 3);
+Vector b(4, 5, 6);
+Vector crossProduct = Vector::cross(a, b); // -3, 6, -3
+```
+
+## Кватернион
+
+### Ориентация в трехмерном пространстве
+
+В отличие от позиции и скорости, у ориентации в трехмерном пространстве нет универсального для всех случаев способа представления. В зависимости от задачи ориентация может быть представлена в виде *углов Эйлера*, *матрицы поворота*, *вектора вращения* или *кватерниона*. Рассмотрим используемые в полетной прошивке способы представления ориентации.
+
+### Углы Эйлера
+
+**Углы Эйлера** — *крен*, *тангаж* и *рыскание* — это наиболее «естественный» для человека способ представления ориентации. Они описывают последовательные вращения объекта вокруг трех осей координат.
+
+В прошивке углы Эйлера сохраняются в обычный объект `Vector` (хоть и, строго говоря, не являются вектором):
+
+* Угол по крену (*roll*) — `vector.x`.
+* Угол по тангажу (*pitch*) — `vector.y`.
+* Угол по рысканию (*yaw*) — `vector.z`.
+
+Особенности углов Эйлера:
+
+1. Углы Эйлера зависят от порядка применения вращений, то есть существует 6 типов углов Эйлера. Порядок вращений, принятый в Flix (и в роботехнике в целом) — рыскание, тангаж, крен (ZYX).
+2. Для некоторых ориентаций углы Эйлера «вырождаются». Так, если объект «смотрит» строго вниз, то угол по рысканию и угол по крену становятся неразличимыми. Эта ситуация называется *gimbal lock* — потеря одной степени свободы.
+
+Ввиду этих особенности для углов Эйлера не существует общих формул для самых базовых задач с ориентациями, таких как применение одного вращения (ориентации) к другому, расчет разницы между ориентациями и подобных. Поэтому в основном углы Эйлера применяются в пользовательском интерфейсе, но редко используются в математических расчетах.
+
+> [!IMPORTANT]
+> Для углов Эйлера не существует общих формул для самых базовых операций с ориентациями.
+
+### Axis-angle
+
+Помимо углов Эйлера, любую ориентацию в трехмерном пространстве можно представить в виде вращения вокруг некоторой оси на некоторый угол. В геометрии это доказывается, как **теорема вращения Эйлера**. В таком представлении ориентация задается двумя величинами:
+
+* **Ось вращения** (*axis*) — единичный вектор, определяющий ось вращения.
+* **Угол поворота** (*angle* или *θ*) — угол, на который нужно повернуть объект вокруг этой оси.
+
+В Flix ось вращения задается объектом `Vector`, а угол поворота — числом типа `float` в радианах:
+
+```cpp
+// Вращение на 45 градусов вокруг оси (1, 2, 3)
+Vector axis(1, 2, 3);
+float angle = radians(45);
+```
+
+Этот способ более удобен для расчетов, чем углы Эйлера, но все еще не является оптимальным.
+
+### Вектор вращения
+
+Если умножить вектор *axis* на угол поворота *θ*, то получится **вектор вращения** (*rotation vector*). Этот вектор играет важную роль в алгоритмах управления ориентацией летательного аппарата.
+
+Вектор вращения обладает замечательным свойством: если угловые скорости объекта (в собственной системе координат) в каждый момент времени совпадают с компонентами этого вектора, то за единичное время объект придет к заданной этим вектором ориентации. Это свойство позволяет использовать вектор вращения для управления ориентацией объекта посредством управления угловыми скоростями.
+
+> [!IMPORTANT]
+> Чтобы за единичное время прийти к заданной ориентации, собственные угловые скорости объекта должны быть равны компонентам вектора вращения.
+
+Вектора вращения в Flix представляются в виде объектов `Vector`:
+
+```cpp
+// Вращение на 45 градусов вокруг оси (1, 2, 3)
+Vector rotation = radians(45) * Vector(1, 2, 3);
+```
+
+### Кватернион
+
+<div class="firmware">
+	<strong>Файл прошивки:</strong>
+	<a href="https://github.com/okalachev/flix/blob/master/flix/quaternion.h"><code>quaternion.h</code></a>.<br>
+</div>
+
+Вектор вращения удобен, но еще удобнее использовать **кватернион**. В Flix кватернионы задаются объектами `Quaternion` из библиотеки `quaternion.h`. Кватернион состоит из четырех значений: *w*, *x*, *y*, *z* и рассчитывается из вектора оси вращения (*axis*) и угла поворота (*θ*) по формуле:
+
+\\[ q = \left( \begin{array}{c} w \\\\ x \\\\ y \\\\ z \end{array} \right) = \left( \begin{array}{c} \cos\left(\frac{\theta}{2}\right) \\\\ axis\_x \cdot \sin\left(\frac{\theta}{2}\right) \\\\ axis\_y \cdot \sin\left(\frac{\theta}{2}\right) \\\\ axis\_z \cdot \sin\left(\frac{\theta}{2}\right) \end{array} \right) \\]
+
+На практике оказывается, что **именно такое представление наиболее удобно для математических расчетов**.
+
+Проиллюстрируем кватернион и описанные выше способы представления ориентации на интерактивной визуализации. Изменяйте угол поворота *θ* с помощью ползунка (ось вращения константна) и изучите, как меняется ориентация объекта, вектор вращения и кватернион:
+
+<div id="rotation-diagram" class="diagram">
+	<p>
+		<label class="angle" for="angle-range"></label>
+		<input type="range" name="angle" id="angle-range" min="0" max="360" value="0" step="1">
+	</p>
+	<p class="axis"></p>
+	<p class="rotation-vector"></p>
+	<p class="quaternion"></p>
+	<p class="euler"></p>
+</div>
+
+<script type="importmap">
+{
+	"imports": {
+		"three": "https://cdn.jsdelivr.net/npm/three@0.176.0/build/three.module.js",
+		"three/addons/": "https://cdn.jsdelivr.net/npm/three@0.176.0/examples/jsm/"
+	}
+}
+</script>
+<script type="module" src="js/rotation.js"></script>
+
+> [!IMPORTANT]
+> В контексте управляющих алгоритмов кватернион — это оптимизированный для расчетов аналог вектора вращения.
+
+Кватернион это наиболее часто используемый способ представления ориентации в алгоритмах. Кроме этого, у кватерниона есть большое значение в теории чисел и алгебре, как у расширения понятия комплексного числа, но рассмотрение этого аспекта выходит за рамки описания работы с вращениями с практической точки зрения.
+
+В прошивке в виде кватернионов представлены, например:
+
+* `attitude` — текущая ориентация квадрокоптера.
+* `attitudeTarget` — целевая ориентация квадрокоптера.
+
+### Операции с кватернионами
+
+Кватернион создается напрямую из четырех его компонент:
+
+```cpp
+// Кватернион, представляющий нулевую (исходную) ориентацию
+Quaternion q(1, 0, 0, 0);
+```
+
+Кватернион можно создать из оси вращения и угла поворота, вектора вращения или углов Эйлера:
+
+```cpp
+Quaternion q1 = Quaternion::fromAxisAngle(axis, angle);
+Quaternion q2 = Quaternion::fromRotationVector(rotation);
+Quaternion q3 = Quaternion::fromEuler(Vector(roll, pitch, yaw));
+```
+
+И наоборот:
+
+```cpp
+q1.toAxisAngle(axis, angle);
+Vector rotation = q2.toRotationVector();
+Vector euler = q3.toEuler();
+```
+
+Возможно рассчитать вращение между двумя обычными векторами:
+
+```cpp
+Quaternion q = Quaternion::fromBetweenVectors(v1, v2); // в виде кватерниона
+Vector rotation = Vector::rotationVectorBetween(v1, v2); // в виде вектора вращения
+```
+
+Шорткаты для работы с углом Эйлера по рысканью (удобно для алгоритмов управления полетом):
+
+```cpp
+float yaw = q.getYaw();
+q.setYaw(yaw);
+```
+
+#### Применения вращений
+
+Чтобы применить вращение, выраженное в кватернионе, к другому кватерниону, в математике используется операция **умножения кватернионов**. При использовании этой операции, необходимо учитывать, что она не является коммутативной, то есть порядок операндов имеет значение. Формула умножения кватернионов выглядит так:
+
+\\[ q_1 \times q_2 = \left( \begin{array}{c} w_1 \\\\ x_1 \\\\ y_1 \\\\ z_1 \end{array} \right) \times \left( \begin{array}{c} w_2 \\\\ x_2 \\\\ y_2 \\\\ z_2 \end{array} \right) = \left( \begin{array}{c} w_1 w_2 - x_1 x_2 - y_1 y_2 - z_1 z_2 \\\\ w_1 x_2 + x_1 w_2 + y_1 z_2 - z_1 y_2 \\\\ w_1 y_2 - x_1 z_2 + y_1 w_2 + z_1 x_2 \\\\ w_1 z_2 + x_1 y_2 - y_1 x_2 + z_1 w_2 \end{array} \right) \\]
+
+В библиотеке `quaternion.h` для этой операции используется статический метод `Quaternion::rotate()`:
+
+```cpp
+// Композиция вращений q1 и q2
+Quaternion result = Quaternion::rotate(q1, q2);
+```
+
+Также полезной является операция применения вращения к вектору, которая делается похожим образом:
+
+```cpp
+// Вращение вектора v кватернионом q
+Vector result = Quaternion::rotateVector(v, q);
+```
+
+Для расчета разницы между двумя ориентациями используется метод `Quaternion::between()`:
+
+```cpp
+// Расчет вращения от q1 к q2
+Quaternion q = Quaternion::between(q1, q2);
+```
+
+## Дополнительные материалы
+
+* [Интерактивный учебник по кватернионам](https://eater.net/quaternions).
+* [Визуализация вращения вектора с помощью кватернионов](https://quaternions.online).

docs/book/gyro.md

@@ -1,7 +1,7 @@
 # Гироскоп
 
 <div class="firmware">
-	<strong>Файл прошивки Flix:</strong>
+	<strong>Файл прошивки:</strong>
 	<a href="https://github.com/okalachev/flix/blob/canonical/flix/imu.ino"><code>imu.ino</code></a> <small>(каноничная версия)</small>.<br>
 	Текущая версия: <a href="https://github.com/okalachev/flix/blob/master/flix/imu.ino"><code>imu.ino</code></a>.
 </div>
@@ -100,7 +100,7 @@ void setup() {
 
 Для однократного считывания данных используется метод `read()`. Затем данные с гироскопа получаются при помощи метода `getGyro(x, y, z)`. Этот метод записывает в переменные `x`, `y` и `z` угловые скорости вокруг соответствующих осей в радианах в секунду.
 
-Если нужно гарантировать, что будут считаны новые данные, можно использовать метод `waitForData()`. Этот метод блокирует выполнение программы до тех пор, пока в IMU не появятся новые данные. Метод `waitForData()` позволяет привязать частоту главного цикла `loop` к частоте обновления данных IMU. Это удобно для организации главного цикла управления квадрокоптером.
+Если нужно гарантировать, что будут считаны новые данные, можно использовать метод `waitForData()`. Этот метод блокирует выполнение программы до тех пор, пока в IMU не появятся новые данные. Метод `waitForData()` позволяет привязать частоту главного цикла `loop` к частоте обновления данных IMU. Это удобно для организации главного цикла управления квадрокоптером.
 
 Программа для чтения данных с гироскопа и вывода их в консоль для построения графиков в Serial Plotter выглядит так:
 
@@ -139,7 +139,7 @@ void loop() {
 
 ### Частота сэмплов
 
-Большинство IMU могут обновлять данные с разной частотой. В полетных контроллерах обычно используется частота обновления от 500 Гц до 8 кГц. Чем выше частота сэмплов, тем выше точность управления полетом, но и больше нагрузка на микроконтроллер. В Flix используется частота сэмплов 1 кГц.
+Большинство IMU могут обновлять данные с разной частотой. В полетных контроллерах обычно используется частота обновления от 500 Гц до 8 кГц. Чем выше частота сэмплов, тем выше точность управления полетом, но и больше нагрузка на микроконтроллер.
 
 Частота сэмплов устанавливается методом `setSampleRate()`. В Flix используется частота 1 кГц:
 
@@ -153,7 +153,7 @@ IMU.setRate(IMU.RATE_1KHZ_APPROX);
 
 * `RATE_MIN` — минимальная частота сэмплов для конкретного IMU.
 * `RATE_50HZ_APPROX` — значение, близкое к 50 Гц.
-* `RATE_1KHZ_APPROX`  — значение, близкое к 1 кГц.
+* `RATE_1KHZ_APPROX` — значение, близкое к 1 кГц.
 * `RATE_8KHZ_APPROX` — значение, близкое к 8 кГц.
 * `RATE_MAX` — максимальная частота сэмплов для конкретного IMU.
 

docs/book/js/rotation.js

@@ -0,0 +1,262 @@
+import * as THREE from 'three';
+import { SVGRenderer, SVGObject } from 'three/addons/renderers/SVGRenderer.js';
+import { OrbitControls } from 'three/addons/controls/OrbitControls.js';
+
+const diagramEl = document.getElementById('rotation-diagram');
+
+const scene = new THREE.Scene();
+scene.background = new THREE.Color(0xffffff);
+
+const camera = new THREE.OrthographicCamera();
+
+camera.position.set(9, 26, 20);
+camera.up.set(0, 0, 1);
+camera.lookAt(0, 0, 0);
+
+const renderer = new SVGRenderer();
+diagramEl.prepend(renderer.domElement);
+
+const controls = new OrbitControls(camera, renderer.domElement);
+controls.enableZoom = false;
+
+const LINE_WIDTH = 4;
+
+function createLabel(text, x, y, z, min = false) {
+	const label = document.createElementNS('http://www.w3.org/2000/svg', 'text');
+	label.setAttribute('class', 'label' + (min ? ' min' : ''));
+	label.textContent = text;
+	label.setAttribute('y', -15);
+	const object = new SVGObject(label);
+	object.position.x = x;
+	object.position.y = y;
+	object.position.z = z;
+	return object;
+}
+
+function createLine(x1, y1, z1, x2, y2, z2, color) {
+	const geometry = new THREE.BufferGeometry().setFromPoints([
+		new THREE.Vector3(x1, y1, z1),
+		new THREE.Vector3(x2, y2, z2)
+	]);
+	const material = new THREE.LineBasicMaterial({ color: color, linewidth: LINE_WIDTH, transparent: true, opacity: 0.8 });
+	const line = new THREE.Line(geometry, material);
+	scene.add(line);
+	return line;
+}
+
+function changeLine(line, x1, y1, z1, x2, y2, z2) {
+	line.geometry.setFromPoints([new THREE.Vector3(x1, y1, z1), new THREE.Vector3(x2, y2, z2)]);
+	return line;
+}
+
+function createVector(x1, y1, z1, x2, y2, z2, color, label = '') {
+	const HEAD_LENGTH = 1;
+	const HEAD_WIDTH = 0.2;
+
+	const group = new THREE.Group();
+	const direction = new THREE.Vector3(x2 - x1, y2 - y1, z2 - z1).normalize();
+	const norm = new THREE.Vector3(x2 - x1, y2 - y1, z2 - z1).length();
+	let end = new THREE.Vector3(x2, y2, z2);
+
+	if (norm > HEAD_LENGTH) {
+		end = new THREE.Vector3(x2 - direction.x * HEAD_LENGTH / 2, y2 - direction.y * HEAD_LENGTH / 2, z2 - direction.z * HEAD_LENGTH / 2);
+	}
+
+	// create line
+	const geometry = new THREE.BufferGeometry().setFromPoints([new THREE.Vector3(x1, y1, z1), end]);
+	const material = new THREE.LineBasicMaterial({ color: color, linewidth: LINE_WIDTH, transparent: true, opacity: 0.8 });
+	const line = new THREE.Line(geometry, material);
+	group.add(line);
+
+	if (norm > HEAD_LENGTH) {
+		// Create arrow
+		const arrowGeometry = new THREE.ConeGeometry(HEAD_WIDTH, HEAD_LENGTH, 16);
+		const arrowMaterial = new THREE.MeshBasicMaterial({ color: color });
+		const arrow = new THREE.Mesh(arrowGeometry, arrowMaterial);
+		arrow.position.set(x2 - direction.x * HEAD_LENGTH / 2, y2 - direction.y * HEAD_LENGTH / 2, z2 - direction.z * HEAD_LENGTH / 2);
+		arrow.lookAt(new THREE.Vector3(x1, y1, z1));
+		arrow.rotateX(-Math.PI / 2);
+		group.add(arrow);
+	}
+
+	// create label
+	if (label) group.add(createLabel(label, x2, y2, z2));
+	scene.add(group);
+	return group;
+}
+
+function changeVector(vector, x1, y1, z1, x2, y2, z2, color, label = '') {
+	vector.removeFromParent();
+	return createVector(x1, y1, z1, x2, y2, z2, color, label);
+}
+
+function createDrone(x, y, z) {
+	const group = new THREE.Group();
+
+	// Fuselage and wing triangle (main body)
+	const fuselageGeometry = new THREE.BufferGeometry();
+	const fuselageVertices = new Float32Array([
+		1, 0, 0,
+		-1, 0.6, 0,
+		-1, -0.6, 0
+	]);
+	fuselageGeometry.setAttribute('position', new THREE.BufferAttribute(fuselageVertices, 3));
+	const fuselageMaterial = new THREE.MeshBasicMaterial({ color: 0xb3b3b3, side: THREE.DoubleSide, transparent: true, opacity: 0.8 });
+	const fuselage = new THREE.Mesh(fuselageGeometry, fuselageMaterial);
+	group.add(fuselage);
+
+	// Tail triangle
+	const tailGeometry = new THREE.BufferGeometry();
+	const tailVertices = new Float32Array([
+		-0.2, 0, 0,
+		-1, 0, 0,
+		-1, 0, 0.5,
+	]);
+	tailGeometry.setAttribute('position', new THREE.BufferAttribute(tailVertices, 3));
+	const tailMaterial = new THREE.MeshBasicMaterial({ color: 0xd80100, side: THREE.DoubleSide, transparent: true, opacity: 0.9 });
+	const tail = new THREE.Mesh(tailGeometry, tailMaterial);
+	group.add(tail);
+
+	group.position.set(x, y, z);
+	group.scale.set(2, 2, 2);
+	scene.add(group);
+	return group;
+}
+
+// Create axes
+const AXES_LENGTH = 10;
+createVector(0, 0, 0, AXES_LENGTH, 0, 0, 0xd80100, 'x');
+createVector(0, 0, 0, 0, AXES_LENGTH, 0, 0x0076ba, 'y');
+createVector(0, 0, 0, 0, 0, AXES_LENGTH, 0x57ed00, 'z');
+
+// Rotation values
+const rotationAxisSrc = new THREE.Vector3(2, 1, 3);
+let rotationAngle = 0;
+let rotationAxis = rotationAxisSrc.clone().normalize();
+let rotationVector = new THREE.Vector3(rotationAxis.x * rotationAngle, rotationAxis.y * rotationAngle, rotationAxis.z * rotationAngle);
+
+let rotationVectorObj = createVector(0, 0, 0, rotationVector.x, rotationVector.y, rotationVector.z, 0xff9900);
+let axisObj = createLine(0, 0, 0, rotationAxis.x * AXES_LENGTH, rotationAxis.y * AXES_LENGTH, rotationAxis.z * AXES_LENGTH, 0xe8e8e8);
+
+const drone = createDrone(0, 0, 0);
+
+// UI
+const angleInput = diagramEl.querySelector('input[name=angle]');
+const rotationVectorEl = diagramEl.querySelector('.rotation-vector');
+const angleEl = diagramEl.querySelector('.angle');
+const quaternionEl = diagramEl.querySelector('.quaternion');
+const eulerEl = diagramEl.querySelector('.euler');
+diagramEl.querySelector('.axis').innerHTML = `<b style='color:#b6b6b6'>Ось вращения:</b> (${rotationAxisSrc.x}, ${rotationAxisSrc.y}, ${rotationAxisSrc.z}) ∥ (${rotationAxis.x.toFixed(1)}, ${rotationAxis.y.toFixed(1)}, ${rotationAxis.z.toFixed(1)})`;
+
+function updateScene() {
+	rotationAngle = parseFloat(angleInput.value) * Math.PI / 180;
+	rotationVector.set(rotationAxis.x * rotationAngle, rotationAxis.y * rotationAngle, rotationAxis.z * rotationAngle);
+	rotationVectorObj = changeVector(rotationVectorObj, 0, 0, 0, rotationVector.x, rotationVector.y, rotationVector.z, 0xff9900);
+
+	// rotate drone
+	drone.rotation.set(0, 0, 0);
+	drone.rotateOnAxis(rotationAxis, rotationAngle);
+
+	// update labels
+	angleEl.innerHTML = `<b>Угол вращения:</b> ${parseFloat(angleInput.value).toFixed(0)}° = ${(rotationAngle).toFixed(2)} рад`;
+	rotationVectorEl.innerHTML = `<b style='color:#e49a44'>Вектор вращения:</b> (${rotationVector.x.toFixed(1)}, ${rotationVector.y.toFixed(1)}, ${rotationVector.z.toFixed(1)}) рад`;
+
+	let quaternion = new THREE.Quaternion();
+	quaternion.setFromAxisAngle(rotationAxis, rotationAngle);
+
+	quaternionEl.innerHTML = `<b>Кватернион:</b>
+		<math xmlns="http://www.w3.org/1998/Math/MathML">
+			<mrow>
+				<mo>(</mo>
+				<mrow>
+					<mi>cos</mi>
+					<mo>(</mo>
+					<mfrac>
+						<mi>${rotationAngle.toFixed(2)}</mi>
+						<mn>2</mn>
+					</mfrac>
+					<mo>)</mo>
+				</mrow>
+				<mo>, </mo>
+				<mrow>
+					<mi>${rotationAxis.x.toFixed(1)}</mi>
+					<mo>·</mo>
+					<mi>sin</mi>
+					<mo>(</mo>
+					<mfrac>
+						<mi>${rotationAngle.toFixed(2)}</mi>
+						<mn>2</mn>
+					</mfrac>
+					<mo>)</mo>
+				</mrow>
+				<mo>, </mo>
+				<mrow>
+					<mi>${rotationAxis.y.toFixed(1)}</mi>
+					<mo>·</mo>
+					<mi>sin</mi>
+					<mo>(</mo>
+					<mfrac>
+						<mi>${rotationAngle.toFixed(2)}</mi>
+						<mn>2</mn>
+					</mfrac>
+					<mo>)</mo>
+				</mrow>
+				<mo>,</mo>
+				<mrow>
+					<mi>${rotationAxis.z.toFixed(1)}</mi>
+					<mo>·</mo>
+					<mi>sin</mi>
+					<mo>(</mo>
+					<mfrac>
+						<mi>${rotationAngle.toFixed(2)}</mi>
+						<mn>2</mn>
+					</mfrac>
+					<mo>)</mo>
+				</mrow>
+				<mo>)</mo>
+			</mrow>
+		</math>
+		= (${quaternion.w.toFixed(1)}, ${(quaternion.x).toFixed(1)}, ${(quaternion.y).toFixed(1)}, ${(quaternion.z).toFixed(1)})`;
+
+	eulerEl.innerHTML = `<b>Углы Эйлера:</b> крен ${(drone.rotation.x * 180 / Math.PI).toFixed(0)}°,
+		 тангаж ${(drone.rotation.y * 180 / Math.PI).toFixed(0)}°, рыскание ${(drone.rotation.z * 180 / Math.PI).toFixed(0)}°`;
+}
+
+function updateCamera() {
+	const RANGE = 8;
+	const VERT_SHIFT = 2;
+	const HOR_SHIFT = -2;
+	const width = renderer.domElement.clientWidth;
+	const height = renderer.domElement.clientHeight;
+	const ratio = width / height;
+	if (ratio > 1) {
+		camera.left = -RANGE * ratio;
+		camera.right = RANGE * ratio;
+		camera.top = RANGE + VERT_SHIFT;
+		camera.bottom = -RANGE + VERT_SHIFT;
+	} else {
+		camera.left = -RANGE + HOR_SHIFT;
+		camera.right = RANGE + HOR_SHIFT;
+		camera.top = RANGE / ratio + VERT_SHIFT;
+		camera.bottom = -RANGE / ratio + VERT_SHIFT;
+	}
+	camera.updateProjectionMatrix();
+	renderer.setSize(width, height);
+}
+
+function update() {
+	// requestAnimationFrame(update);
+	updateCamera();
+	updateScene();
+	controls.update();
+	renderer.render(scene, camera);
+}
+update();
+
+window.addEventListener('resize', update);
+angleInput.addEventListener('input', update);
+angleInput.addEventListener('change', update);
+diagramEl.addEventListener('mousemove', update);
+diagramEl.addEventListener('touchmove', update);
+diagramEl.addEventListener('scroll', update);
+diagramEl.addEventListener('wheel', update);

docs/build.md

@@ -9,9 +9,9 @@ cd flix
 
 ## Simulation
 
-### Ubuntu 20.04
+### Ubuntu
 
-The latest version of Ubuntu supported by Gazebo 11 simulator is 20.04. If you have a newer version, consider using a virtual machine.
+The latest version of Ubuntu supported by Gazebo 11 simulator is 22.04. If you have a newer version, consider using a virtual machine.
 
 1. Install Arduino CLI:
 
@@ -84,7 +84,7 @@ The latest version of Ubuntu supported by Gazebo 11 simulator is 20.04. If you h
 
 #### Control with smartphone
 
-1. Install [QGroundControl mobile app](https://docs.qgroundcontrol.com/master/en/qgc-user-guide/getting_started/download_and_install.html#android) on your smartphone.
+1. Install [QGroundControl mobile app](https://docs.qgroundcontrol.com/master/en/qgc-user-guide/getting_started/download_and_install.html#android) on your smartphone. For **iOS**, use [QGroundControl build from TAJISOFT](https://apps.apple.com/ru/app/qgc-from-tajisoft/id1618653051).
 2. Connect your smartphone to the same Wi-Fi network as the machine running the simulator.
 3. If you're using a virtual machine, make sure that its network is set to the **bridged** mode with Wi-Fi adapter selected.
 4. Run the simulation.
@@ -105,17 +105,26 @@ The latest version of Ubuntu supported by Gazebo 11 simulator is 20.04. If you h
 ### Arduino IDE (Windows, Linux, macOS)
 
 1. Install [Arduino IDE](https://www.arduino.cc/en/software) (version 2 is recommended).
-2. Install ESP32 core, version 3.0.7 (version 2.x is not supported). See the [official Espressif's instructions](https://docs.espressif.com/projects/arduino-esp32/en/latest/installing.html#installing-using-arduino-ide) on installing ESP32 Core in Arduino IDE.
-3. Install the following libraries using [Library Manager](https://docs.arduino.cc/software/ide-v2/tutorials/ide-v2-installing-a-library):
+2. Windows users might need to install [USB to UART bridge driver from Silicon Labs](https://www.silabs.com/developers/usb-to-uart-bridge-vcp-drivers).
+3. Install ESP32 core, version 3.2.0. See the [official Espressif's instructions](https://docs.espressif.com/projects/arduino-esp32/en/latest/installing.html#installing-using-arduino-ide) on installing ESP32 Core in Arduino IDE.
+4. Install the following libraries using [Library Manager](https://docs.arduino.cc/software/ide-v2/tutorials/ide-v2-installing-a-library):
    * `FlixPeriph`, the latest version.
-   * `MAVLink`, version 2.0.12.
-4. Clone the project using git or [download the source code as a ZIP archive](https://codeload.github.com/okalachev/flix/zip/refs/heads/master).
-5. Open the downloaded Arduino sketch `flix/flix.ino` in Arduino IDE.
-6. [Build and upload](https://docs.arduino.cc/software/ide-v2/tutorials/getting-started/ide-v2-uploading-a-sketch) the firmware using Arduino IDE.
+   * `MAVLink`, version 2.0.16.
+5. Clone the project using git or [download the source code as a ZIP archive](https://codeload.github.com/okalachev/flix/zip/refs/heads/master).
+6. Open the downloaded Arduino sketch `flix/flix.ino` in Arduino IDE.
+7. Connect your ESP32 board to the computer and choose correct board type in Arduino IDE (*WEMOS D1 MINI ESP32* for ESP32 Mini) and the port.
+8. [Build and upload](https://docs.arduino.cc/software/ide-v2/tutorials/getting-started/ide-v2-uploading-a-sketch) the firmware using Arduino IDE.
 
 ### Command line (Windows, Linux, macOS)
 
 1. [Install Arduino CLI](https://arduino.github.io/arduino-cli/installation/).
+
+   On Linux, use:
+
+   ```bash
+   curl -fsSL https://raw.githubusercontent.com/arduino/arduino-cli/master/install.sh | BINDIR=~/.local/bin sh
+   ```
+
 2. Windows users might need to install [USB to UART bridge driver from Silicon Labs](https://www.silabs.com/developers/usb-to-uart-bridge-vcp-drivers).
 3. Compile the firmware using `make`. Arduino dependencies will be installed automatically:
 
@@ -137,18 +146,21 @@ The latest version of Ubuntu supported by Gazebo 11 simulator is 20.04. If you h
 
 See other available Make commands in the [Makefile](../Makefile).
 
+> [!TIP]
+> You can test the firmware on a bare ESP32 board without connecting IMU and other peripherals. The Wi-Fi network `flix` should appear and all the basic functionality including CLI and QGroundControl connection should work.
+
 ### Setup and flight
 
 Before flight you need to calibrate the accelerometer:
 
-1. Open Serial Monitor in Arduino IDE (use use `make monitor` command in the command line).
+1. Open Serial Monitor in Arduino IDE (or use `make monitor` command in the command line).
 2. Type `ca` command there and follow the instructions.
 
 #### Control with smartphone
 
 1. Install [QGroundControl mobile app](https://docs.qgroundcontrol.com/master/en/qgc-user-guide/getting_started/download_and_install.html#android) on your smartphone.
 2. Power the drone using the battery.
-3. Connect your smartphone to the appeared `flix` Wi-Fi network.
+3. Connect your smartphone to the appeared `flix` Wi-Fi network (password: `flixwifi`).
 4. Open QGroundControl app. It should connect and begin showing the drone's telemetry automatically.
 5. Go to the settings and enable *Virtual Joystick*. *Auto-Center Throttle* setting **should be disabled**.
 6. Use the virtual joystick to fly the drone!
@@ -157,10 +169,33 @@ Before flight you need to calibrate the accelerometer:
 
 Before flight using remote control, you need to calibrate it:
 
-1. Open Serial Monitor in Arduino IDE (use use `make monitor` command in the command line).
+1. Open Serial Monitor in Arduino IDE (or use `make monitor` command in the command line).
 2. Type `cr` command there and follow the instructions.
+3. Use the remote control to fly the drone!
 
-Then you can use your remote control to fly the drone!
+#### Control with USB remote control
+
+If your drone doesn't have RC receiver installed, you can use USB remote control and QGroundControl app to fly it.
+
+1. Install [QGroundControl](https://docs.qgroundcontrol.com/master/en/qgc-user-guide/getting_started/download_and_install.html) app on your computer.
+2. Connect your USB remote control to the computer.
+3. Power up the drone.
+4. Connect your computer to the appeared `flix` Wi-Fi network (password: `flixwifi`).
+5. Launch QGroundControl app. It should connect and begin showing the drone's telemetry automatically.
+6. Go the the QGroundControl menu ⇒ *Vehicle Setup* ⇒ *Joystick*. Calibrate you USB remote control there.
+7. Use the USB remote control to fly the drone!
+
+#### Adjusting parameters
+
+You can adjust some of the drone's parameters (include PID coefficients) in QGroundControl app. In order to do that, go to the QGroundControl menu ⇒ *Vehicle Setup* ⇒ *Parameters*.
+
+<img src="img/parameters.png" width="400">
+
+#### CLI access
+
+In addition to accessing the drone's command line interface (CLI) using the serial port, you can also access it with QGroundControl using Wi-Fi connection. To do that, go to the QGroundControl menu ⇒ *Vehicle Setup* ⇒ *Analyze Tools* ⇒ *MAVLink Console*.
+
+<img src="img/cli.png" width="400">
 
 > [!NOTE]
 > If something goes wrong, go to the [Troubleshooting](troubleshooting.md) article.

docs/firmware.md

@@ -1,19 +1,21 @@
 # Firmware overview
 
+The firmware is a regular Arduino sketch, and follows the classic Arduino one-threaded design. The initialization code is in the `setup()` function, and the main loop is in the `loop()` function. The sketch includes multiple files, each responsible for a specific part of the system.
+
 ## Dataflow
 
 <img src="img/dataflow.svg" width=800 alt="Firmware dataflow diagram">
 
 The main loop is running at 1000 Hz. All the dataflow is happening through global variables (for simplicity):
 
-* `t` *(float)* — current step time, *s*.
+* `t` *(double)* — current step time, *s*.
 * `dt` *(float)* — time delta between the current and previous steps, *s*.
 * `gyro` *(Vector)* — data from the gyroscope, *rad/s*.
 * `acc` *(Vector)* — acceleration data from the accelerometer, *m/s<sup>2</sup>*.
 * `rates` *(Vector)* — filtered angular rates, *rad/s*.
 * `attitude` *(Quaternion)* — estimated attitude (orientation) of drone.
-* `controls` *(float[])* — user control inputs from the RC, normalized to [-1, 1] range.
-* `motors` *(float[])* — motor outputs, normalized to [-1, 1] range; reverse rotation is possible.
+* `controlRoll`, `controlPitch`, ... *(float[])* — pilot's control inputs, range [-1, 1].
+* `motors` *(float[])* — motor outputs, range [0, 1].
 
 ## Source files
 
@@ -28,7 +30,7 @@ Firmware source files are located in `flix` directory. The key files are:
 
 Utility files include:
 
-* [`vector.h`](../flix/vector.h), [`quaternion.h`](../flix/quaternion.h) — project's vector and quaternion libraries implementation.
+* [`vector.h`](../flix/vector.h), [`quaternion.h`](../flix/quaternion.h) — vector and quaternion libraries implementation.
 * [`pid.h`](../flix/pid.h) — generic PID controller implementation.
 * [`lpf.h`](../flix/lpf.h) — generic low-pass filter implementation.
 

docs/img/axes-rotation.svg

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docs/img/left-axes.svg

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docs/img/right-axes.svg

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+        fill: none;
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+        fill: #0076ba;
+      }
+
+      .h {
+        font-size: 50px;
+        font-family: Tahoma;
+      }
+    </style>
+  </defs>
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+  </g>
+</svg>

docs/rotation.css

@@ -0,0 +1,29 @@
+.diagram svg {
+	display: block;
+	width: 100%;
+	height: 400px;
+}
+.diagram .label {
+	font-family: Arial, sans-serif;
+	font-size: 20px;
+	pointer-events: none;
+	color: black;
+	opacity: 0.8;
+	user-select: none;
+}
+.diagram label {
+	display: block;
+}
+@media (min-width: 800px) {
+	.diagram b {
+		width: 200px;
+		display: inline-block;
+	}
+}
+.diagram p.quaternion {
+	overflow-x: auto;
+}
+.diagram input {
+	text-align: center;
+	width: 100%;
+}

docs/theme/index.hbs

@@ -118,7 +118,7 @@
                     <a href="https://t.me/opensourcequadcopter" class="telegram">Telegram-канал</a>
                     💰 Поддержать проект:
                     <iframe style="margin-top: 0.4em;" src="https://yoomoney.ru/quickpay/fundraise/button?billNumber=16U9OH2S4IT.241205&" width="330" height="50" frameborder="0" allowtransparency="true" scrolling="no"></iframe>​
-                    &copy; 2024 Олег Калачев
+                    &copy; 2025 Олег Калачев
                 </footer>
             </mdbook-sidebar-scrollbox>
             <noscript>

docs/troubleshooting.md

@@ -6,6 +6,7 @@ Do the following:
 
 * **Check ESP32 core is installed**. Check if the version matches the one used in the [tutorial](build.md#firmware).
 * **Check libraries**. Install all the required libraries from the tutorial. Make sure there are no MPU9250 or other peripherals libraries that may conflict with the ones used in the tutorial.
+* **Check the chosen board**. The correct board to choose in Arduino IDE for ESP32 Mini is *WEMOS D1 MINI ESP32*.
 
 ## The drone doesn't fly
 
@@ -13,15 +14,19 @@ Do the following:
 
 * **Check the battery voltage**. Use a multimeter to measure the battery voltage. It should be in range of 3.7-4.2 V.
 * **Check if there are some startup errors**. Connect the ESP32 to the computer and check the Serial Monitor output. Use the Reset button to make sure you see the whole ESP32 output.
+* **Check the baudrate is correct**. If you see garbage characters in the Serial Monitor, make sure the baudrate is set to 115200.
 * **Make sure correct IMU model is chosen**. If using ICM-20948 board, change `MPU9250` to `ICM20948` everywhere in the `imu.ino` file.
-* **Check if the CLI is working**. Perform `help` command in Serial Monitor. You should see the list of available commands.
+* **Check if the CLI is working**. Perform `help` command in Serial Monitor. You should see the list of available commands. You can also access the CLI using QGroundControl (*Vehicle Setup* ⇒ *Analyze Tools* ⇒ *MAVLink Console*).
 * **Configure QGroundControl correctly before connecting to the drone** if you use it to control the drone. Go to the settings and enable *Virtual Joystick*. *Auto-Center Throttle* setting **should be disabled**.
-* **Make sure you're not moving the drone several seconds after the power on**. The drone calibrates its gyroscope on the start so it should stay still for a while.
-* **Check the IMU sample rate**. Perform `imu` command. The `rate` field should be about 1000 (Hz).
-* **Check the IMU data**. Perform `imu` command, check raw accelerometer and gyro output. The output should change as you move the drone.
+* **If QGroundControl doesn't connect**, you might need to disable the firewall and/or VPN on your computer.
+* **Check the IMU is working**. Perform `imu` command and check its output:
+  * The `status` field should be `OK`.
+  * The `rate` field should be about 1000 (Hz).
+  * The `accel` and `gyro` fields should change as you move the drone.
 * **Calibrate the accelerometer.** if is wasn't done before. Type `ca` command in Serial Monitor and follow the instructions.
 * **Check the attitude estimation**. Connect to the drone using QGroundControl. Rotate the drone in different orientations and check if the attitude estimation shown in QGroundControl is correct.
 * **Check the IMU orientation is set correctly**. If the attitude estimation is rotated, make sure `rotateIMU` function is defined correctly in `imu.ino` file.
+* **Check the motors type**. Motors with exact 3.7V voltage are needed, not ranged working voltage (3.7V — 6V).
 * **Check the motors**. Perform the following commands using Serial Monitor:
   * `mfr` — should rotate front right motor (counter-clockwise).
   * `mfl` — should rotate front left motor (clockwise).

docs/user.md

@@ -0,0 +1,141 @@
+# Hall of fame
+
+This page contains user-built drones based on the Flix project. Publish your projects into the official Telegram-chat: [@opensourcequadcopterchat](https://t.me/opensourcequadcopterchat) or send materials as a pull request.
+
+---
+
+## RoboCamp
+
+Author: RoboCamp participants.<br>
+Description: 3D-printed and wooden frames, ESP32 Mini, DC-DC buck-boost converters. BetaFPV LiteRadio 3 to control the drones via Wi-Fi connection.<br>
+Features: altitude hold, obstacle avoidance, autonomous flight elements.
+
+RoboCamp took place in July 2025, Saint Petersburg, where 9 participants designed and built their own drones using the Flix project, and then modified the firmware to complete specific flight tasks.
+
+See the detailed video about the event:
+
+<a href="https://youtu.be/Wd3yaorjTx0"><img width=500 src="https://img.youtube.com/vi/Wd3yaorjTx0/sddefault.jpg"></a>
+
+Built drones:
+
+<img src="img/user/robocamp/1.jpg" width=500>
+
+---
+
+Author: chkroko.<br>
+Description: the first Flix drone built with **brushless motors** (DShot interface).<br>
+Features: SpeedyBee BLS 35A Mini V2 ESC, ESP32-S3 board, EMAX ECO 2 2207 1700kv motors, ICM20948V2 IMU, INA226 power monitor and Bluetooth gamepad for control.<br>
+Patch for DShot ESC: https://github.com/Krokodilushka/flix/commit/568345a45ca7ed5b458a11a9d0a9f4c8a91e70ac.
+
+**Flight video:**
+
+<a href="https://drive.google.com/file/d/1GFRanASxKmXINi70fxS5RuzV3LJp7f3m/view?usp=share_link"><img height=300 src="img/user/chkroko-bldc/video.jpg"></a>
+
+<img src="img/user/chkroko-bldc/1.jpg" height=150> <img src="img/user/chkroko-bldc/2.jpg" height=150> <img src="img/user/chkroko-bldc/3.jpg" height=150>
+
+---
+
+Author: chkroko.<br>
+Modification: Control using Bluetooth with **Flydigi Vader 3** gamepad. Source code: https://github.com/Krokodilushka/flix/tree/dev.<br>
+Features: ESP32-C3 SuperMini, BMP580 barometer, INA226 power monitor, IRLZ44N MOSFETs.<br>
+Full description: https://telegra.ph/Flix-dron-06-13.
+
+**Flight video:**
+
+<a href="https://drive.google.com/file/d/1orVKA_-gsezDTns2Xt8xW1BCWPcyPitR/view?usp=sharing"><img height=300 src="img/user/chkroko/video.jpg"></a>
+
+<img src="img/user/chkroko/1.jpg" height=150> <img src="img/user/chkroko/2.jpg" height=150>
+
+---
+
+Author: chkroko.<br>
+Features: ESP32-C3 SuperMini board, INA226 power monitor, IRLZ44N MOSFETs, MPU-6500 IMU.
+
+**Flight video:**
+
+<a href="https://drive.google.com/file/d/1-4ciDsj8slTEaxxRl1-QAkx0cUDkb8iy/view?usp=sharing"><img height=300 src="img/user/cryptokobans/video.jpg"></a>
+
+<img src="img/user/cryptokobans/1.jpg" height=150> <img src="img/user/cryptokobans/2.jpg" height=150>
+
+---
+
+Author: [@jeka_chex](https://t.me/jeka_chex).<br>
+Features: custom frame, FPV camera, 3-blade 31 mm propellers.<br>
+Motor drivers: AON7410 MOSFET + capacitors.<br>
+Custom frame files: https://drive.google.com/drive/folders/1QCIc-_YYFxJN4cMhVLjL5SflqegvCowm?usp=share_link.<br>
+
+**Flight video:**
+
+<a href="https://drive.google.com/file/d/1VnWI5YVPojfqsfpyLX4v2V9zHi9adwcd/view?usp=sharing"><img height=300 src="img/user/jeka_chex/video.jpg"></a>
+
+**FPV flight video:**
+
+<a href="https://drive.google.com/file/d/1RSU6VWs9omsge4hGloH5NQqnxvLyhMKB/view?usp=sharing"><img height=300 src="img/user/jeka_chex/video-fpv.jpg"></a>
+
+<img src="img/user/jeka_chex/1.jpg" height=150> <img src="img/user/jeka_chex/2.jpg" height=150> <img src="img/user/jeka_chex/3.jpg" height=150> <img src="img/user/jeka_chex/4.jpg" height=150> <img src="img/user/jeka_chex/5.jpg" height=150>
+
+---
+
+Author: [@fisheyeu](https://t.me/fisheyeu).<br>
+[Video](https://drive.google.com/file/d/1IT4eMmWPZpmaZR_qsIRmNJ52hYkFB_0q/view?usp=share_link).
+
+<img src="img/user/fisheyeu/1.jpg" height=300> <img src="img/user/fisheyeu/2.jpg" height=300>
+
+---
+
+Author: [@p_kabakov](https://t.me/p_kabakov).<br>
+Custom propellers guard 3D-model: https://drive.google.com/file/d/1TKnzwvrZYzYuRTLLERNmnKH71H9n4Xj_/view?usp=share_link.<br>
+Features: ESP32-C3 microcontroller is used.<br>
+[Video](https://drive.google.com/file/d/1B0NMcsk0fgwUgNr9XuLOdR2yYCuaj008/view?usp=share_link).
+
+<img src="img/user/p_kabakov/1.jpg" width=150> <img src="img/user/p_kabakov/2.jpg" width=150> <img src="img/user/p_kabakov/3.jpg" width=150>
+
+**Custom Wi-Fi RC control:**
+
+<a href="https://github.com/pavelkabakov/flix/blob/master/rc_control_v1/IMG_20250221_195756.jpg"><img height=300 src="img/user/p_kabakov/wifirc.jpg"></a>
+
+See source and description (in Russian): https://github.com/pavelkabakov/flix/tree/master/rc_control_v1.
+
+---
+
+Author: [@yi_lun](https://t.me/yi_lun).<br>
+[Video](https://drive.google.com/file/d/1TkSuvHQ_0qQPFUpY5XjJzmhnpX_07cTg/view?usp=share_link).
+
+<img src="img/user/yi_lun/1.jpg" width=300> <img src="img/user/yi_lun/2.jpg" width=300>
+
+---
+
+Author: [@peter_ukhov](https://t.me/peter_ukhov).<br>
+Features: customized ESP32 holder, GY-ICM20948V2 IMU board, boost-converter for powering the ESP32.<br>
+Files for 3D-printing: https://drive.google.com/file/d/1Sma-FEzFBj2HA5ixJtUyH0uWixvr6vdK/view?usp=share_link.<br>
+Schematics: https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764612179508274&cot=14.<br>
+
+<a href="https://www.youtube.com/watch?v=wi4w_hOmKcQ"><img width=500 src="img/user/peter_ukhov-2/video.jpg"></a>
+
+<img src="img/user/peter_ukhov-2/1.jpg" width=300> <img src="img/user/peter_ukhov-2/2.jpg" width=300>
+
+---
+
+Author: [@Alexey_Karakash](https://t.me/Alexey_Karakash).<br>
+Files for 3D printing of the custom frame: https://drive.google.com/file/d/1tkNmujrHrKpTMVtsRH3mor2zdAM0JHum/view?usp=share_link.<br>
+
+<a href="https://t.me/opensourcequadcopter/61"><img width=500 src="img/user/alexey_karakash/video.jpg"></a>
+
+<img src="img/user/alexey_karakash/1.jpg" height=150> <img src="img/user/alexey_karakash/2.jpg" height=150> <img src="img/user/alexey_karakash/3.jpg" height=150> <img src="img/user/alexey_karakash/4.jpg" height=150> <img src="img/user/alexey_karakash/5.jpg" height=150>
+
+---
+
+Author: [@rudpa](https://t.me/rudpa).<br>
+
+<a href="https://t.me/opensourcequadcopter/46"><img width=500 src="img/user/rudpa/video.jpg"></a>
+
+<img src="img/user/rudpa/1.jpg" height=150> <img src="img/user/rudpa/2.jpg" height=150> <img src="img/user/rudpa/3.jpg" height=150>
+
+---
+
+Author: [@peter_ukhov](https://t.me/peter_ukhov).<br>
+Schematics: https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764612338222067&cot=14.<br>
+
+<a href="https://t.me/opensourcequadcopter/24"><img width=500 src="img/user/peter_ukhov/video.jpg"></a>
+
+<img src="img/user/peter_ukhov/1.jpg" height=150> <img src="img/user/peter_ukhov/2.jpg" height=150> <img src="img/user/peter_ukhov/3.jpg" height=150>

docs/version0.md

@@ -27,4 +27,4 @@ Flix version 0 (obsolete):
 
 <img src="img/schematics.svg" width=800 alt="Flix schematics">
 
-You can also check a user contributed [variant of complete circuit diagram](https://miro.com/app/board/uXjVN-dTjoo=/) of the drone.
+You can also check a user contributed [variant of complete circuit diagram](https://miro.com/app/board/uXjVN-dTjoo=/?moveToWidget=3458764574482511443&cot=14) of the drone.

flix/cli.ino

@@ -5,9 +5,13 @@
 
 #include "pid.h"
 #include "vector.h"
+#include "util.h"
 
-extern PID rollRatePID, pitchRatePID, yawRatePID, rollPID, pitchPID;
-extern LowPassFilter<Vector> ratesFilter;
+extern const int MOTOR_REAR_LEFT, MOTOR_REAR_RIGHT, MOTOR_FRONT_RIGHT, MOTOR_FRONT_LEFT;
+extern float loopRate, dt;
+extern double t;
+extern uint16_t channels[16];
+extern float controlRoll, controlPitch, controlThrottle, controlYaw, controlArmed, controlMode;
 
 const char* motd =
 "\nWelcome to\n"
@@ -23,6 +27,7 @@ const char* motd =
 "p <name> - show parameter\n"
 "p <name> <value> - set parameter\n"
 "preset - reset parameters\n"
+"time - show time info\n"
 "ps - show pitch/roll/yaw\n"
 "psq - show attitude quaternion\n"
 "imu - show IMU data\n"
@@ -30,66 +35,124 @@ const char* motd =
 "mot - show motor output\n"
 "log - dump in-RAM log\n"
 "cr - calibrate RC\n"
-"cg - calibrate gyro\n"
 "ca - calibrate accel\n"
 "mfr, mfl, mrr, mrl - test motor (remove props)\n"
+"sys - show system info\n"
 "reset - reset drone's state\n"
 "reboot - reboot the drone\n";
 
-void doCommand(String& command, String& arg0, String& arg1) {
+void print(const char* format, ...) {
+	char buf[1000];
+	va_list args;
+	va_start(args, format);
+	vsnprintf(buf, sizeof(buf), format, args);
+	va_end(args);
+	Serial.print(buf);
+#if WIFI_ENABLED
+	mavlinkPrint(buf);
+#endif
+}
+
+void pause(float duration) {
+	double start = t;
+	while (t - start < duration) {
+		step();
+		handleInput();
+#if WIFI_ENABLED
+		processMavlink();
+#endif
+		delay(50);
+	}
+}
+
+void doCommand(String str, bool echo = false) {
+	// parse command
+	String command, arg0, arg1;
+	splitString(str, command, arg0, arg1);
+
+	// echo command
+	if (echo && !command.isEmpty()) {
+		print("> %s\n", str.c_str());
+	}
+
+	command.toLowerCase();
+
+	// execute command
 	if (command == "help" || command == "motd") {
-		Serial.println(motd);
+		print("%s\n", motd);
 	} else if (command == "p" && arg0 == "") {
 		printParameters();
 	} else if (command == "p" && arg0 != "" && arg1 == "") {
-		Serial.printf("%s = %g\n", arg0.c_str(), getParameter(arg0.c_str()));
+		print("%s = %g\n", arg0.c_str(), getParameter(arg0.c_str()));
 	} else if (command == "p") {
 		bool success = setParameter(arg0.c_str(), arg1.toFloat());
 		if (success) {
-			Serial.printf("%s = %g\n", arg0.c_str(), arg1.toFloat());
+			print("%s = %g\n", arg0.c_str(), arg1.toFloat());
 		} else {
-			Serial.printf("Parameter not found: %s\n", arg0.c_str());
+			print("Parameter not found: %s\n", arg0.c_str());
 		}
 	} else if (command == "preset") {
 		resetParameters();
+	} else if (command == "time") {
+		print("Time: %f\n", t);
+		print("Loop rate: %.0f\n", loopRate);
+		print("dt: %f\n", dt);
 	} else if (command == "ps") {
-		Vector a = attitude.toEulerZYX();
-		Serial.printf("roll: %f pitch: %f yaw: %f\n", a.x * RAD_TO_DEG, a.y * RAD_TO_DEG, a.z * RAD_TO_DEG);
+		Vector a = attitude.toEuler();
+		print("roll: %f pitch: %f yaw: %f\n", degrees(a.x), degrees(a.y), degrees(a.z));
 	} else if (command == "psq") {
-		Serial.printf("qx: %f qy: %f qz: %f qw: %f\n", attitude.x, attitude.y, attitude.z, attitude.w);
+		print("qx: %f qy: %f qz: %f qw: %f\n", attitude.x, attitude.y, attitude.z, attitude.w);
 	} else if (command == "imu") {
 		printIMUInfo();
-		Serial.printf("gyro: %f %f %f\n", rates.x, rates.y, rates.z);
-		Serial.printf("acc: %f %f %f\n", acc.x, acc.y, acc.z);
-		printIMUCal();
-		Serial.printf("rate: %f\n", loopRate);
+		print("gyro: %f %f %f\n", rates.x, rates.y, rates.z);
+		print("acc: %f %f %f\n", acc.x, acc.y, acc.z);
+		printIMUCalibration();
+		print("rate: %.0f\n", loopRate);
+		print("landed: %d\n", landed);
 	} else if (command == "rc") {
-		Serial.printf("Raw: throttle %d yaw %d pitch %d roll %d armed %d mode %d\n",
-			channels[RC_CHANNEL_THROTTLE], channels[RC_CHANNEL_YAW], channels[RC_CHANNEL_PITCH],
-			channels[RC_CHANNEL_ROLL], channels[RC_CHANNEL_ARMED], channels[RC_CHANNEL_MODE]);
-		Serial.printf("Control: throttle %f yaw %f pitch %f roll %f armed %f mode %f\n",
-			controls[RC_CHANNEL_THROTTLE], controls[RC_CHANNEL_YAW], controls[RC_CHANNEL_PITCH],
-			controls[RC_CHANNEL_ROLL], controls[RC_CHANNEL_ARMED], controls[RC_CHANNEL_MODE]);
-		Serial.printf("Mode: %s\n", getModeName());
+		print("channels: ");
+		for (int i = 0; i < 16; i++) {
+			print("%u ", channels[i]);
+		}
+		print("\nroll: %g pitch: %g yaw: %g throttle: %g armed: %g mode: %g\n",
+			controlRoll, controlPitch, controlYaw, controlThrottle, controlArmed, controlMode);
+		print("mode: %s\n", getModeName());
 	} else if (command == "mot") {
-		Serial.printf("MOTOR front-right %f front-left %f rear-right %f rear-left %f\n",
+		print("front-right %g front-left %g rear-right %g rear-left %g\n",
 			motors[MOTOR_FRONT_RIGHT], motors[MOTOR_FRONT_LEFT], motors[MOTOR_REAR_RIGHT], motors[MOTOR_REAR_LEFT]);
 	} else if (command == "log") {
 		dumpLog();
 	} else if (command == "cr") {
 		calibrateRC();
-	} else if (command == "cg") {
-		calibrateGyro();
 	} else if (command == "ca") {
 		calibrateAccel();
 	} else if (command == "mfr") {
-		cliTestMotor(MOTOR_FRONT_RIGHT);
+		testMotor(MOTOR_FRONT_RIGHT);
 	} else if (command == "mfl") {
-		cliTestMotor(MOTOR_FRONT_LEFT);
+		testMotor(MOTOR_FRONT_LEFT);
 	} else if (command == "mrr") {
-		cliTestMotor(MOTOR_REAR_RIGHT);
+		testMotor(MOTOR_REAR_RIGHT);
 	} else if (command == "mrl") {
-		cliTestMotor(MOTOR_REAR_LEFT);
+		testMotor(MOTOR_REAR_LEFT);
+	} else if (command == "sys") {
+#ifdef ESP32
+		print("Chip: %s\n", ESP.getChipModel());
+		print("Temperature: %.1f °C\n", temperatureRead());
+		print("Free heap: %d\n", ESP.getFreeHeap());
+		// Print tasks table
+		print("Num  Task                Stack  Prio  Core  CPU%%\n");
+		int taskCount = uxTaskGetNumberOfTasks();
+		TaskStatus_t *systemState = new TaskStatus_t[taskCount];
+		uint32_t totalRunTime;
+		uxTaskGetSystemState(systemState, taskCount, &totalRunTime);
+		for (int i = 0; i < taskCount; i++) {
+			String core = systemState[i].xCoreID == tskNO_AFFINITY ? "*" : String(systemState[i].xCoreID);
+			int cpuPercentage = systemState[i].ulRunTimeCounter / (totalRunTime / 100);
+			print("%-5d%-20s%-7d%-6d%-6s%d\n",systemState[i].xTaskNumber, systemState[i].pcTaskName,
+				systemState[i].usStackHighWaterMark, systemState[i].uxCurrentPriority, core, cpuPercentage);
+		}
+		delete[] systemState;
+#endif
 	} else if (command == "reset") {
 		attitude = Quaternion();
 	} else if (command == "reboot") {
@@ -97,48 +160,26 @@ void doCommand(String& command, String& arg0, String& arg1) {
 	} else if (command == "") {
 		// do nothing
 	} else {
-		Serial.println("Invalid command: " + command);
+		print("Invalid command: %s\n", command.c_str());
 	}
 }
 
-void cliTestMotor(uint8_t n) {
-	Serial.printf("Testing motor %d\n", n);
-	motors[n] = 1;
-	delay(50); // ESP32 may need to wait until the end of the current cycle to change duty https://github.com/espressif/arduino-esp32/issues/5306
-	sendMotors();
-	delay(3000);
-	motors[n] = 0;
-	sendMotors();
-	Serial.println("Done");
-}
-
-void parseInput() {
+void handleInput() {
 	static bool showMotd = true;
 	static String input;
 
 	if (showMotd) {
-		Serial.println(motd);
+		print("%s\n", motd);
 		showMotd = false;
 	}
 
 	while (Serial.available()) {
 		char c = Serial.read();
 		if (c == '\n') {
-			char chars[input.length() + 1];
-			input.toCharArray(chars, input.length() + 1);
-			String command = stringToken(chars, " ");
-			String arg0 = stringToken(NULL, " ");
-			String arg1 = stringToken(NULL, "");
-			doCommand(command, arg0, arg1);
+			doCommand(input);
 			input.clear();
 		} else {
 			input += c;
 		}
 	}
 }
-
-// Helper function for parsing input
-String stringToken(char* str, const char* delim) {
-	char* token = strtok(str, delim);
-	return token == NULL ? "" : token;
-}

flix/control.ino

@@ -7,6 +7,7 @@
 #include "quaternion.h"
 #include "pid.h"
 #include "lpf.h"
+#include "util.h"
 
 #define PITCHRATE_P 0.05
 #define PITCHRATE_I 0.2
@@ -20,7 +21,7 @@
 #define YAWRATE_I 0.0
 #define YAWRATE_D 0.0
 #define YAWRATE_I_LIM 0.3
-#define ROLL_P 4.5
+#define ROLL_P 6
 #define ROLL_I 0
 #define ROLL_D 0
 #define PITCH_P ROLL_P
@@ -29,9 +30,8 @@
 #define YAW_P 3
 #define PITCHRATE_MAX radians(360)
 #define ROLLRATE_MAX radians(360)
-#define YAWRATE_MAX radians(360)
-#define MAX_TILT radians(30)
-
+#define YAWRATE_MAX radians(300)
+#define TILT_MAX radians(30)
 #define RATES_D_LPF_ALPHA 0.2 // cutoff frequency ~ 40 Hz
 
 enum { MANUAL, ACRO, STAB, USER } mode = STAB;
@@ -44,12 +44,17 @@ PID yawRatePID(YAWRATE_P, YAWRATE_I, YAWRATE_D);
 PID rollPID(ROLL_P, ROLL_I, ROLL_D);
 PID pitchPID(PITCH_P, PITCH_I, PITCH_D);
 PID yawPID(YAW_P, 0, 0);
+Vector maxRate(ROLLRATE_MAX, PITCHRATE_MAX, YAWRATE_MAX);
+float tiltMax = TILT_MAX;
 
 Quaternion attitudeTarget;
 Vector ratesTarget;
 Vector torqueTarget;
 float thrustTarget;
 
+extern const int MOTOR_REAR_LEFT, MOTOR_REAR_RIGHT, MOTOR_FRONT_RIGHT, MOTOR_FRONT_LEFT;
+extern float controlRoll, controlPitch, controlThrottle, controlYaw, controlArmed, controlMode;
+
 void control() {
 	interpretRC();
 	failsafe();
@@ -66,38 +71,38 @@ void control() {
 }
 
 void interpretRC() {
-	armed = controls[RC_CHANNEL_THROTTLE] >= 0.05 && controls[RC_CHANNEL_ARMED] >= 0.5;
+	armed = controlThrottle >= 0.05 && controlArmed >= 0.5;
 
 	// NOTE: put ACRO or MANUAL modes there if you want to use them
-	if (controls[RC_CHANNEL_MODE] < 0.25) {
+	if (controlMode < 0.25) {
 		mode = STAB;
-	} else if (controls[RC_CHANNEL_MODE] < 0.75) {
+	} else if (controlMode < 0.75) {
 		mode = STAB;
 	} else {
 		mode = STAB;
 	}
 
-	thrustTarget = controls[RC_CHANNEL_THROTTLE];
+	thrustTarget = controlThrottle;
 
 	if (mode == ACRO) {
 		yawMode = YAW_RATE;
-		ratesTarget.x = controls[RC_CHANNEL_ROLL] * ROLLRATE_MAX;
-		ratesTarget.y = controls[RC_CHANNEL_PITCH] * PITCHRATE_MAX;
-		ratesTarget.z = -controls[RC_CHANNEL_YAW] * YAWRATE_MAX; // positive yaw stick means clockwise rotation in FLU
+		ratesTarget.x = controlRoll * maxRate.x;
+		ratesTarget.y = controlPitch* maxRate.y;
+		ratesTarget.z = -controlYaw * maxRate.z; // positive yaw stick means clockwise rotation in FLU
 
 	} else if (mode == STAB) {
-		yawMode = controls[RC_CHANNEL_YAW] == 0 ? YAW : YAW_RATE;
+		yawMode = controlYaw == 0 ? YAW : YAW_RATE;
 
-		attitudeTarget = Quaternion::fromEulerZYX(Vector(
-			controls[RC_CHANNEL_ROLL] * MAX_TILT,
-			controls[RC_CHANNEL_PITCH] * MAX_TILT,
+		attitudeTarget = Quaternion::fromEuler(Vector(
+			controlRoll * tiltMax,
+			controlPitch * tiltMax,
 			attitudeTarget.getYaw()));
-		ratesTarget.z = -controls[RC_CHANNEL_YAW] * YAWRATE_MAX; // positive yaw stick means clockwise rotation in FLU
+		ratesTarget.z = -controlYaw * maxRate.z; // positive yaw stick means clockwise rotation in FLU
 
 	} else if (mode == MANUAL) {
 		// passthrough mode
 		yawMode = YAW_RATE;
-		torqueTarget = Vector(controls[RC_CHANNEL_ROLL], controls[RC_CHANNEL_PITCH], -controls[RC_CHANNEL_YAW]) * 0.01;
+		torqueTarget = Vector(controlRoll, controlPitch, -controlYaw) * 0.01;
 	}
 
 	if (yawMode == YAW_RATE || !motorsActive()) {
@@ -115,10 +120,10 @@ void controlAttitude() {
 	}
 
 	const Vector up(0, 0, 1);
-	Vector upActual = attitude.rotate(up);
-	Vector upTarget = attitudeTarget.rotate(up);
+	Vector upActual = Quaternion::rotateVector(up, attitude);
+	Vector upTarget = Quaternion::rotateVector(up, attitudeTarget);
 
-	Vector error = Vector::angularRatesBetweenVectors(upTarget, upActual);
+	Vector error = Vector::rotationVectorBetween(upTarget, upActual);
 
 	ratesTarget.x = rollPID.update(error.x, dt);
 	ratesTarget.y = pitchPID.update(error.y, dt);
@@ -162,10 +167,6 @@ void controlTorque() {
 	motors[3] = constrain(motors[3], 0, 1);
 }
 
-bool motorsActive() {
-	return motors[0] > 0 || motors[1] > 0 || motors[2] > 0 || motors[3] > 0;
-}
-
 const char* getModeName() {
 	switch (mode) {
 		case MANUAL: return "MANUAL";

flix/estimate.ino

@@ -6,12 +6,11 @@
 #include "quaternion.h"
 #include "vector.h"
 #include "lpf.h"
+#include "util.h"
 
-#define WEIGHT_ACC 0.5f
+#define WEIGHT_ACC 0.003
 #define RATES_LFP_ALPHA 0.2 // cutoff frequency ~ 40 Hz
 
-LowPassFilter<Vector> ratesFilter(RATES_LFP_ALPHA);
-
 void estimate() {
 	applyGyro();
 	applyAcc();
@@ -19,26 +18,24 @@ void estimate() {
 
 void applyGyro() {
 	// filter gyro to get angular rates
+	static LowPassFilter<Vector> ratesFilter(RATES_LFP_ALPHA);
 	rates = ratesFilter.update(gyro);
 
 	// apply rates to attitude
-	attitude *= Quaternion::fromAngularRates(rates * dt);
-	attitude.normalize();
+	attitude = Quaternion::rotate(attitude, Quaternion::fromRotationVector(rates * dt));
 }
 
 void applyAcc() {
 	// test should we apply accelerometer gravity correction
 	float accNorm = acc.norm();
-	bool landed = !motorsActive() && abs(accNorm - ONE_G) < ONE_G * 0.1f;
+	landed = !motorsActive() && abs(accNorm - ONE_G) < ONE_G * 0.1f;
 
-	setLED(landed);
 	if (!landed) return;
 
 	// calculate accelerometer correction
-	Vector up = attitude.rotate(Vector(0, 0, 1));
-	Vector correction = Vector::angularRatesBetweenVectors(acc, up) * dt * WEIGHT_ACC;
+	Vector up = Quaternion::rotateVector(Vector(0, 0, 1), attitude);
+	Vector correction = Vector::rotationVectorBetween(acc, up) * WEIGHT_ACC;
 
 	// apply correction
-	attitude *= Quaternion::fromAngularRates(correction);
-	attitude.normalize();
+	attitude = Quaternion::rotate(attitude, Quaternion::fromRotationVector(correction));
 }

flix/failsafe.ino

@@ -1,23 +1,41 @@
 // Copyright (c) 2024 Oleg Kalachev <okalachev@gmail.com>
 // Repository: https://github.com/okalachev/flix
 
-// Fail-safe for RC loss
+// Fail-safe functions
 
-#define RC_LOSS_TIMEOUT 0.2
+#define RC_LOSS_TIMEOUT 0.5
 #define DESCEND_TIME 3.0 // time to descend from full throttle to zero
 
+extern double controlTime;
+extern float controlRoll, controlPitch, controlThrottle, controlYaw;
+
 void failsafe() {
-	if (t - controlsTime > RC_LOSS_TIMEOUT) {
+	armingFailsafe();
+	rcLossFailsafe();
+}
+
+// Prevent arming without zero throttle input
+void armingFailsafe() {
+	static double zeroThrottleTime;
+	static double armingTime;
+	if (!armed) armingTime = t; // stores the last time when the drone was disarmed, therefore contains arming time
+	if (controlTime > 0 && controlThrottle < 0.05) zeroThrottleTime = controlTime;
+	if (armingTime - zeroThrottleTime > 0.1) armed = false; // prevent arming if there was no zero throttle for 0.1 sec
+}
+
+// RC loss failsafe
+void rcLossFailsafe() {
+	if (t - controlTime > RC_LOSS_TIMEOUT) {
 		descend();
 	}
 }
 
+// Smooth descend on RC lost
 void descend() {
-	// Smooth descend on RC lost
 	mode = STAB;
-	controls[RC_CHANNEL_ROLL] = 0;
-	controls[RC_CHANNEL_PITCH] = 0;
-	controls[RC_CHANNEL_YAW] = 0;
-	controls[RC_CHANNEL_THROTTLE] -= dt / DESCEND_TIME;
-	if (controls[RC_CHANNEL_THROTTLE] < 0) controls[RC_CHANNEL_THROTTLE] = 0;
+	controlRoll = 0;
+	controlPitch = 0;
+	controlYaw = 0;
+	controlThrottle -= dt / DESCEND_TIME;
+	if (controlThrottle < 0) controlThrottle = 0;
 }

flix/flix.ino

@@ -5,55 +5,36 @@
 
 #include "vector.h"
 #include "quaternion.h"
+#include "util.h"
 
 #define SERIAL_BAUDRATE 115200
-
 #define WIFI_ENABLED 1
 
-#define RC_CHANNELS 16
-#define RC_CHANNEL_ROLL 0
-#define RC_CHANNEL_PITCH 1
-#define RC_CHANNEL_THROTTLE 2
-#define RC_CHANNEL_YAW 3
-#define RC_CHANNEL_ARMED 4
-#define RC_CHANNEL_MODE 5
-
-#define MOTOR_REAR_LEFT 0
-#define MOTOR_REAR_RIGHT 1
-#define MOTOR_FRONT_RIGHT 2
-#define MOTOR_FRONT_LEFT 3
-
-#define ONE_G 9.80665
-
-float t = NAN; // current step time, s
+double t = NAN; // current step time, s
 float dt; // time delta from previous step, s
-float loopRate; // loop rate, Hz
-int16_t channels[RC_CHANNELS]; // raw rc channels
-float controls[RC_CHANNELS]; // normalized controls in range [-1..1] ([0..1] for throttle)
-float controlsTime; // time of the last controls update
+float controlRoll, controlPitch, controlYaw, controlThrottle, controlArmed, controlMode; // pilot's inputs, range [-1, 1]
 Vector gyro; // gyroscope data
 Vector acc; // accelerometer data, m/s/s
 Vector rates; // filtered angular rates, rad/s
 Quaternion attitude; // estimated attitude
 bool landed; // are we landed and stationary
-float motors[4]; // normalized motors thrust in range [-1..1]
+float motors[4]; // normalized motors thrust in range [0..1]
 
 void setup() {
 	Serial.begin(SERIAL_BAUDRATE);
-	Serial.println("Initializing flix");
+	print("Initializing flix\n");
 	disableBrownOut();
 	setupParameters();
 	setupLED();
 	setupMotors();
 	setLED(true);
-#if WIFI_ENABLED == 1
+#if WIFI_ENABLED
 	setupWiFi();
 #endif
 	setupIMU();
 	setupRC();
-
 	setLED(false);
-	Serial.println("Initializing complete");
+	print("Initializing complete\n");
 }
 
 void loop() {
@@ -63,10 +44,10 @@ void loop() {
 	estimate();
 	control();
 	sendMotors();
-	parseInput();
-#if WIFI_ENABLED == 1
+	handleInput();
+#if WIFI_ENABLED
 	processMavlink();
 #endif
 	logData();
-	flushParameters();
+	syncParameters();
 }

flix/imu.ino

@@ -5,24 +5,19 @@
 
 #include <SPI.h>
 #include <MPU9250.h>
+#include "lpf.h"
+#include "util.h"
 
 MPU9250 IMU(SPI);
 
 Vector accBias;
-Vector gyroBias;
 Vector accScale(1, 1, 1);
+Vector gyroBias;
 
 void setupIMU() {
-	Serial.println("Setup IMU");
-	bool status = IMU.begin();
-	if (!status) {
-		while (true) {
-			Serial.println("IMU begin error");
-			delay(1000);
-		}
-	}
+	print("Setup IMU\n");
+	IMU.begin();
 	configureIMU();
-	// calibrateGyro();
 }
 
 void configureIMU() {
@@ -30,6 +25,7 @@ void configureIMU() {
 	IMU.setGyroRange(IMU.GYRO_RANGE_2000DPS);
 	IMU.setDLPF(IMU.DLPF_MAX);
 	IMU.setRate(IMU.RATE_1KHZ_APPROX);
+	IMU.setupInterrupt();
 }
 
 void readIMU() {
@@ -53,48 +49,39 @@ void rotateIMU(Vector& data) {
 }
 
 void calibrateGyroOnce() {
-	if (!landed) return;
-	static float samples = 0; // overflows after 49 days at 1000 Hz
-	samples++;
-	gyroBias = gyroBias + (gyro - gyroBias) / samples; // running average
-}
+	static float landedTime = 0;
+	landedTime = landed ? landedTime + dt : 0;
+	if (landedTime < 2) return; // calibrate only if definitely stationary
 
-void calibrateGyro() {
-	const int samples = 1000;
-	Serial.println("Calibrating gyro, stand still");
-	IMU.setGyroRange(IMU.GYRO_RANGE_250DPS); // the most sensitive mode
-
-	gyroBias = Vector(0, 0, 0);
-	for (int i = 0; i < samples; i++) {
-		IMU.waitForData();
-		IMU.getGyro(gyro.x, gyro.y, gyro.z);
-		gyroBias = gyroBias + gyro;
-	}
-	gyroBias = gyroBias / samples;
-
-	printIMUCal();
-	configureIMU();
+	static LowPassFilter<Vector> gyroCalibrationFilter(0.001);
+	gyroBias = gyroCalibrationFilter.update(gyro);
 }
 
 void calibrateAccel() {
-	Serial.println("Calibrating accelerometer");
+	print("Calibrating accelerometer\n");
 	IMU.setAccelRange(IMU.ACCEL_RANGE_2G); // the most sensitive mode
 
-	Serial.setTimeout(60000);
-	Serial.print("Place level [enter] "); Serial.readStringUntil('\n');
+	print("1/6 Place level [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
-	Serial.print("Place nose up [enter] "); Serial.readStringUntil('\n');
+	print("2/6 Place nose up [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
-	Serial.print("Place nose down [enter] "); Serial.readStringUntil('\n');
+	print("3/6 Place nose down [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
-	Serial.print("Place on right side [enter] "); Serial.readStringUntil('\n');
+	print("4/6 Place on right side [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
-	Serial.print("Place on left side [enter] "); Serial.readStringUntil('\n');
+	print("5/6 Place on left side [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
-	Serial.print("Place upside down [enter] "); Serial.readStringUntil('\n');
+	print("6/6 Place upside down [8 sec]\n");
+	pause(8);
 	calibrateAccelOnce();
 
-	printIMUCal();
+	printIMUCalibration();
+	print("✓ Calibration done!\n");
 	configureIMU();
 }
 
@@ -120,21 +107,19 @@ void calibrateAccelOnce() {
 	if (acc.x < accMin.x) accMin.x = acc.x;
 	if (acc.y < accMin.y) accMin.y = acc.y;
 	if (acc.z < accMin.z) accMin.z = acc.z;
-	Serial.printf("acc %f %f %f\n", acc.x, acc.y, acc.z);
-	Serial.printf("max %f %f %f\n", accMax.x, accMax.y, accMax.z);
-	Serial.printf("min %f %f %f\n", accMin.x, accMin.y, accMin.z);
 	// Compute scale and bias
 	accScale = (accMax - accMin) / 2 / ONE_G;
 	accBias = (accMax + accMin) / 2;
 }
 
-void printIMUCal() {
-	Serial.printf("gyro bias: %f, %f, %f\n", gyroBias.x, gyroBias.y, gyroBias.z);
-	Serial.printf("accel bias: %f, %f, %f\n", accBias.x, accBias.y, accBias.z);
-	Serial.printf("accel scale: %f, %f, %f\n", accScale.x, accScale.y, accScale.z);
+void printIMUCalibration() {
+	print("gyro bias: %f %f %f\n", gyroBias.x, gyroBias.y, gyroBias.z);
+	print("accel bias: %f %f %f\n", accBias.x, accBias.y, accBias.z);
+	print("accel scale: %f %f %f\n", accScale.x, accScale.y, accScale.z);
 }
 
 void printIMUInfo() {
-	Serial.printf("model: %s\n", IMU.getModel());
-	Serial.printf("who am I: 0x%02X\n", IMU.whoAmI());
+	IMU.status() ? print("status: ERROR %d\n", IMU.status()) : print("status: OK\n");
+	print("model: %s\n", IMU.getModel());
+	print("who am I: 0x%02X\n", IMU.whoAmI());
 }

flix/log.ino

@@ -3,36 +3,60 @@
 
 // In-RAM logging
 
+#include "vector.h"
+
 #define LOG_RATE 100
 #define LOG_DURATION 10
 #define LOG_PERIOD 1.0 / LOG_RATE
 #define LOG_SIZE LOG_DURATION * LOG_RATE
-#define LOG_COLUMNS 14
 
-float logBuffer[LOG_SIZE][LOG_COLUMNS]; // * 4 (float)
-int logPointer = 0;
+float tFloat;
+Vector attitudeEuler;
+Vector attitudeTargetEuler;
+
+struct LogEntry {
+	const char *name;
+	float *value;
+};
+
+LogEntry logEntries[] = {
+	{"t", &tFloat},
+	{"rates.x", &rates.x},
+	{"rates.y", &rates.y},
+	{"rates.z", &rates.z},
+	{"ratesTarget.x", &ratesTarget.x},
+	{"ratesTarget.y", &ratesTarget.y},
+	{"ratesTarget.z", &ratesTarget.z},
+	{"attitude.x", &attitudeEuler.x},
+	{"attitude.y", &attitudeEuler.y},
+	{"attitude.z", &attitudeEuler.z},
+	{"attitudeTarget.x", &attitudeTargetEuler.x},
+	{"attitudeTarget.y", &attitudeTargetEuler.y},
+	{"attitudeTarget.z", &attitudeTargetEuler.z},
+	{"thrustTarget", &thrustTarget}
+};
+
+const int logColumns = sizeof(logEntries) / sizeof(logEntries[0]);
+float logBuffer[LOG_SIZE][logColumns];
+
+void prepareLogData() {
+	tFloat = t;
+	attitudeEuler = attitude.toEuler();
+	attitudeTargetEuler = attitudeTarget.toEuler();
+}
 
 void logData() {
 	if (!armed) return;
-
-	static float logTime = 0;
+	static int logPointer = 0;
+	static double logTime = 0;
 	if (t - logTime < LOG_PERIOD) return;
 	logTime = t;
 
-	logBuffer[logPointer][0] = t;
-	logBuffer[logPointer][1] = rates.x;
-	logBuffer[logPointer][2] = rates.y;
-	logBuffer[logPointer][3] = rates.z;
-	logBuffer[logPointer][4] = ratesTarget.x;
-	logBuffer[logPointer][5] = ratesTarget.y;
-	logBuffer[logPointer][6] = ratesTarget.z;
-	logBuffer[logPointer][7] = attitude.toEulerZYX().x;
-	logBuffer[logPointer][8] = attitude.toEulerZYX().y;
-	logBuffer[logPointer][9] = attitude.toEulerZYX().z;
-	logBuffer[logPointer][10] = attitudeTarget.toEulerZYX().x;
-	logBuffer[logPointer][11] = attitudeTarget.toEulerZYX().y;
-	logBuffer[logPointer][12] = attitudeTarget.toEulerZYX().z;
-	logBuffer[logPointer][13] = thrustTarget;
+	prepareLogData();
+
+	for (int i = 0; i < logColumns; i++) {
+		logBuffer[logPointer][i] = *logEntries[i].value;
+	}
 
 	logPointer++;
 	if (logPointer >= LOG_SIZE) {
@@ -41,13 +65,15 @@ void logData() {
 }
 
 void dumpLog() {
-	Serial.printf("t,rates.x,rates.y,rates.z,ratesTarget.x,ratesTarget.y,ratesTarget.z,"
-		"attitude.x,attitude.y,attitude.z,attitudeTarget.x,attitudeTarget.y,attitudeTarget.z,thrustTarget\n");
+	// Print header
+	for (int i = 0; i < logColumns; i++) {
+		print("%s%s", logEntries[i].name, i < logColumns - 1 ? "," : "\n");
+	}
+	// Print data
 	for (int i = 0; i < LOG_SIZE; i++) {
 		if (logBuffer[i][0] == 0) continue; // skip empty records
-		for (int j = 0; j < LOG_COLUMNS - 1; j++) {
-			Serial.printf("%f,", logBuffer[i][j]);
+		for (int j = 0; j < logColumns; j++) {
+			print("%g%s", logBuffer[i][j], j < logColumns - 1 ? "," : "\n");
 		}
-		Serial.printf("%f\n", logBuffer[i][LOG_COLUMNS - 1]);
 	}
 }

flix/lpf.h

@@ -22,7 +22,8 @@ public:
 			output = input;
 			initialized = true;
 		}
-		return output = output * (1 - alpha) + input * alpha;
+
+		return output += alpha * (input - output);
 	}
 
 	void setCutOffFrequency(float cutOffFreq, float dt) {

flix/mavlink.ino

@@ -3,24 +3,31 @@
 
 // MAVLink communication
 
-#if WIFI_ENABLED == 1
+#if WIFI_ENABLED
 
 #include <MAVLink.h>
 
 #define SYSTEM_ID 1
 #define PERIOD_SLOW 1.0
 #define PERIOD_FAST 0.1
-#define MAVLINK_CONTROL_SCALE 0.7f
 #define MAVLINK_CONTROL_YAW_DEAD_ZONE 0.1f
 
+float mavlinkControlScale = 0.7;
+String mavlinkPrintBuffer;
+
+extern double controlTime;
+extern float controlRoll, controlPitch, controlThrottle, controlYaw, controlArmed, controlMode;
+
 void processMavlink() {
 	sendMavlink();
 	receiveMavlink();
 }
 
 void sendMavlink() {
-	static float lastSlow = 0;
-	static float lastFast = 0;
+	sendMavlinkPrint();
+
+	static double lastSlow = 0;
+	static double lastFast = 0;
 
 	mavlink_message_t msg;
 	uint32_t time = t * 1000;
@@ -28,9 +35,13 @@ void sendMavlink() {
 	if (t - lastSlow >= PERIOD_SLOW) {
 		lastSlow = t;
 
-		mavlink_msg_heartbeat_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, MAV_TYPE_QUADROTOR,
-			MAV_AUTOPILOT_GENERIC, MAV_MODE_FLAG_MANUAL_INPUT_ENABLED | (armed ? MAV_MODE_FLAG_SAFETY_ARMED : 0),
-			0, MAV_STATE_STANDBY);
+		mavlink_msg_heartbeat_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, MAV_TYPE_QUADROTOR, MAV_AUTOPILOT_GENERIC,
+			MAV_MODE_FLAG_MANUAL_INPUT_ENABLED | (armed * MAV_MODE_FLAG_SAFETY_ARMED) | ((mode == STAB) * MAV_MODE_FLAG_STABILIZE_ENABLED),
+			mode, MAV_STATE_STANDBY);
+		sendMessage(&msg);
+
+		mavlink_msg_extended_sys_state_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
+			MAV_VTOL_STATE_UNDEFINED, landed ? MAV_LANDED_STATE_ON_GROUND : MAV_LANDED_STATE_IN_AIR);
 		sendMessage(&msg);
 	}
 
@@ -38,16 +49,13 @@ void sendMavlink() {
 		lastFast = t;
 
 		const float zeroQuat[] = {0, 0, 0, 0};
-		Quaternion attitudeFRD = FLU2FRD(attitude); // MAVLink uses FRD coordinate system
 		mavlink_msg_attitude_quaternion_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
-			time, attitudeFRD.w, attitudeFRD.x, attitudeFRD.y, attitudeFRD.z, rates.x, rates.y, rates.z, zeroQuat);
+			time, attitude.w, attitude.x, -attitude.y, -attitude.z, rates.x, -rates.y, -rates.z, zeroQuat); // convert to frd
 		sendMessage(&msg);
 
-		mavlink_msg_rc_channels_scaled_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, time, 0,
-			controls[0] * 10000, controls[1] * 10000, controls[2] * 10000,
-			controls[3] * 10000, controls[4] * 10000, controls[5] * 10000,
-			INT16_MAX, INT16_MAX, UINT8_MAX);
-		sendMessage(&msg);
+		mavlink_msg_rc_channels_raw_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, controlTime * 1000, 0,
+			channels[0], channels[1], channels[2], channels[3], channels[4], channels[5], channels[6], channels[7], UINT8_MAX);
+		if (channels[0] != 0) sendMessage(&msg); // 0 means no RC input
 
 		float actuator[32];
 		memcpy(actuator, motors, sizeof(motors));
@@ -55,8 +63,8 @@ void sendMavlink() {
 		sendMessage(&msg);
 
 		mavlink_msg_scaled_imu_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, time,
-			acc.x * 1000, acc.y * 1000, acc.z * 1000,
-			gyro.x * 1000, gyro.y * 1000, gyro.z * 1000,
+			acc.x * 1000, -acc.y * 1000, -acc.z * 1000, // convert to frd
+			gyro.x * 1000, -gyro.y * 1000, -gyro.z * 1000,
 			0, 0, 0, 0);
 		sendMessage(&msg);
 	}
@@ -83,23 +91,29 @@ void receiveMavlink() {
 }
 
 void handleMavlink(const void *_msg) {
-	mavlink_message_t *msg = (mavlink_message_t *)_msg;
+	const mavlink_message_t& msg = *(mavlink_message_t *)_msg;
 
-	if (msg->msgid == MAVLINK_MSG_ID_MANUAL_CONTROL) {
-		mavlink_manual_control_t manualControl;
-		mavlink_msg_manual_control_decode(msg, &manualControl);
-		controls[RC_CHANNEL_THROTTLE] = manualControl.z / 1000.0f;
-		controls[RC_CHANNEL_PITCH] = manualControl.x / 1000.0f * MAVLINK_CONTROL_SCALE;
-		controls[RC_CHANNEL_ROLL] = manualControl.y / 1000.0f * MAVLINK_CONTROL_SCALE;
-		controls[RC_CHANNEL_YAW] = manualControl.r / 1000.0f * MAVLINK_CONTROL_SCALE;
-		controls[RC_CHANNEL_MODE] = 1; // STAB mode
-		controls[RC_CHANNEL_ARMED] = 1; // armed
-		controlsTime = t;
+	if (msg.msgid == MAVLINK_MSG_ID_MANUAL_CONTROL) {
+		mavlink_manual_control_t m;
+		mavlink_msg_manual_control_decode(&msg, &m);
+		if (m.target && m.target != SYSTEM_ID) return; // 0 is broadcast
 
-		if (abs(controls[RC_CHANNEL_YAW]) < MAVLINK_CONTROL_YAW_DEAD_ZONE) controls[RC_CHANNEL_YAW] = 0;
+		controlThrottle = m.z / 1000.0f;
+		controlPitch = m.x / 1000.0f * mavlinkControlScale;
+		controlRoll = m.y / 1000.0f * mavlinkControlScale;
+		controlYaw = m.r / 1000.0f * mavlinkControlScale;
+		controlMode = 1; // STAB mode
+		controlArmed = 1; // armed
+		controlTime = t;
+
+		if (abs(controlYaw) < MAVLINK_CONTROL_YAW_DEAD_ZONE) controlYaw = 0;
 	}
 
-	if (msg->msgid == MAVLINK_MSG_ID_PARAM_REQUEST_LIST) {
+	if (msg.msgid == MAVLINK_MSG_ID_PARAM_REQUEST_LIST) {
+		mavlink_param_request_list_t m;
+		mavlink_msg_param_request_list_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
+
 		mavlink_message_t msg;
 		for (int i = 0; i < parametersCount(); i++) {
 			mavlink_msg_param_value_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
@@ -108,63 +122,98 @@ void handleMavlink(const void *_msg) {
 		}
 	}
 
-	if (msg->msgid == MAVLINK_MSG_ID_PARAM_REQUEST_READ) {
-		mavlink_param_request_read_t paramRequestRead;
-		mavlink_msg_param_request_read_decode(msg, &paramRequestRead);
-		char name[16 + 1];
-		strlcpy(name, paramRequestRead.param_id, sizeof(name)); // param_id might be not null-terminated
-		float value = strlen(name) == 0 ? getParameter(paramRequestRead.param_index) : getParameter(name);
-		if (paramRequestRead.param_index != -1) {
-			memcpy(name, getParameterName(paramRequestRead.param_index), 16);
+	if (msg.msgid == MAVLINK_MSG_ID_PARAM_REQUEST_READ) {
+		mavlink_param_request_read_t m;
+		mavlink_msg_param_request_read_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
+
+		char name[MAVLINK_MSG_PARAM_REQUEST_READ_FIELD_PARAM_ID_LEN + 1];
+		strlcpy(name, m.param_id, sizeof(name)); // param_id might be not null-terminated
+		float value = strlen(name) == 0 ? getParameter(m.param_index) : getParameter(name);
+		if (m.param_index != -1) {
+			memcpy(name, getParameterName(m.param_index), 16);
 		}
 		mavlink_message_t msg;
 		mavlink_msg_param_value_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
-			name, value, MAV_PARAM_TYPE_REAL32, parametersCount(), paramRequestRead.param_index);
+			name, value, MAV_PARAM_TYPE_REAL32, parametersCount(), m.param_index);
 		sendMessage(&msg);
 	}
 
-	if (msg->msgid == MAVLINK_MSG_ID_PARAM_SET) {
-		mavlink_param_set_t paramSet;
-		mavlink_msg_param_set_decode(msg, &paramSet);
-		char name[16 + 1];
-		strlcpy(name, paramSet.param_id, sizeof(name)); // param_id might be not null-terminated
-		setParameter(name, paramSet.param_value);
+	if (msg.msgid == MAVLINK_MSG_ID_PARAM_SET) {
+		mavlink_param_set_t m;
+		mavlink_msg_param_set_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
+
+		char name[MAVLINK_MSG_PARAM_SET_FIELD_PARAM_ID_LEN + 1];
+		strlcpy(name, m.param_id, sizeof(name)); // param_id might be not null-terminated
+		setParameter(name, m.param_value);
 		// send ack
 		mavlink_message_t msg;
 		mavlink_msg_param_value_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
-			paramSet.param_id, paramSet.param_value, MAV_PARAM_TYPE_REAL32, parametersCount(), 0); // index is unknown
+			m.param_id, m.param_value, MAV_PARAM_TYPE_REAL32, parametersCount(), 0); // index is unknown
 		sendMessage(&msg);
 	}
 
-	if (msg->msgid == MAVLINK_MSG_ID_MISSION_REQUEST_LIST) { // handle to make qgc happy
+	if (msg.msgid == MAVLINK_MSG_ID_MISSION_REQUEST_LIST) { // handle to make qgc happy
+		mavlink_mission_request_list_t m;
+		mavlink_msg_mission_request_list_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
+
 		mavlink_message_t msg;
 		mavlink_msg_mission_count_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg, 0, 0, 0, MAV_MISSION_TYPE_MISSION, 0);
 		sendMessage(&msg);
 	}
 
+	if (msg.msgid == MAVLINK_MSG_ID_SERIAL_CONTROL) {
+		mavlink_serial_control_t m;
+		mavlink_msg_serial_control_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
+
+		char data[MAVLINK_MSG_SERIAL_CONTROL_FIELD_DATA_LEN + 1];
+		strlcpy(data, (const char *)m.data, m.count); // data might be not null-terminated
+		doCommand(data, true);
+	}
+
 	// Handle commands
-	if (msg->msgid == MAVLINK_MSG_ID_COMMAND_LONG) {
-		mavlink_command_long_t commandLong;
-		mavlink_msg_command_long_decode(msg, &commandLong);
+	if (msg.msgid == MAVLINK_MSG_ID_COMMAND_LONG) {
+		mavlink_command_long_t m;
+		mavlink_msg_command_long_decode(&msg, &m);
+		if (m.target_system && m.target_system != SYSTEM_ID) return;
 		mavlink_message_t ack;
 		mavlink_message_t response;
 
-		if (commandLong.command == MAV_CMD_REQUEST_MESSAGE && commandLong.param1 == MAVLINK_MSG_ID_AUTOPILOT_VERSION) {
-			mavlink_msg_command_ack_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &ack, commandLong.command, MAV_RESULT_ACCEPTED, UINT8_MAX, 0, msg->sysid, msg->compid);
+		if (m.command == MAV_CMD_REQUEST_MESSAGE && m.param1 == MAVLINK_MSG_ID_AUTOPILOT_VERSION) {
+			mavlink_msg_command_ack_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &ack, m.command, MAV_RESULT_ACCEPTED, UINT8_MAX, 0, msg.sysid, msg.compid);
 			sendMessage(&ack);
 			mavlink_msg_autopilot_version_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &response,
 				MAV_PROTOCOL_CAPABILITY_PARAM_FLOAT | MAV_PROTOCOL_CAPABILITY_MAVLINK2, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0);
 			sendMessage(&response);
 		} else {
-			mavlink_msg_command_ack_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &ack, commandLong.command, MAV_RESULT_UNSUPPORTED, UINT8_MAX, 0, msg->sysid, msg->compid);
+			mavlink_msg_command_ack_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &ack, m.command, MAV_RESULT_UNSUPPORTED, UINT8_MAX, 0, msg.sysid, msg.compid);
 			sendMessage(&ack);
 		}
 	}
 }
 
-// Convert Forward-Left-Up to Forward-Right-Down quaternion
-inline Quaternion FLU2FRD(const Quaternion &q) {
-	return Quaternion(q.w, q.x, -q.y, -q.z);
+// Send shell output to GCS
+void mavlinkPrint(const char* str) {
+	mavlinkPrintBuffer += str;
+}
+
+void sendMavlinkPrint() {
+	// Send mavlink print data in chunks
+	const char *str = mavlinkPrintBuffer.c_str();
+	for (int i = 0; i < strlen(str); i += MAVLINK_MSG_SERIAL_CONTROL_FIELD_DATA_LEN) {
+		char data[MAVLINK_MSG_SERIAL_CONTROL_FIELD_DATA_LEN + 1];
+		strlcpy(data, str + i, sizeof(data));
+		mavlink_message_t msg;
+		mavlink_msg_serial_control_pack(SYSTEM_ID, MAV_COMP_ID_AUTOPILOT1, &msg,
+			SERIAL_CONTROL_DEV_SHELL,
+			i + MAVLINK_MSG_SERIAL_CONTROL_FIELD_DATA_LEN < strlen(str) ? SERIAL_CONTROL_FLAG_MULTI : 0, // more chunks to go
+			0, 0, strlen(data), (uint8_t *)data, 0, 0);
+		sendMessage(&msg);
+	}
+	mavlinkPrintBuffer.clear();
 }
 
 #endif

flix/motors.ino

@@ -2,19 +2,29 @@
 // Repository: https://github.com/okalachev/flix
 
 // Motors output control using MOSFETs
-// In case of using ESC, use this version of the code: https://gist.github.com/okalachev/8871d3a94b6b6c0a298f41a4edd34c61.
-// Motor: 8520 3.7V
+// In case of using ESCs, change PWM_STOP, PWM_MIN and PWM_MAX to appropriate values in μs, decrease PWM_FREQUENCY (to 400)
+
+#include "util.h"
 
 #define MOTOR_0_PIN 12 // rear left
 #define MOTOR_1_PIN 13 // rear right
 #define MOTOR_2_PIN 14 // front right
 #define MOTOR_3_PIN 15 // front left
 
-#define PWM_FREQUENCY 200
-#define PWM_RESOLUTION 8
+#define PWM_FREQUENCY 78000
+#define PWM_RESOLUTION 10
+#define PWM_STOP 0
+#define PWM_MIN 0
+#define PWM_MAX 1000000 / PWM_FREQUENCY
+
+// Motors array indexes:
+const int MOTOR_REAR_LEFT = 0;
+const int MOTOR_REAR_RIGHT = 1;
+const int MOTOR_FRONT_RIGHT = 2;
+const int MOTOR_FRONT_LEFT = 3;
 
 void setupMotors() {
-	Serial.println("Setup Motors");
+	print("Setup Motors\n");
 
 	// configure pins
 	ledcAttach(MOTOR_0_PIN, PWM_FREQUENCY, PWM_RESOLUTION);
@@ -23,17 +33,35 @@ void setupMotors() {
 	ledcAttach(MOTOR_3_PIN, PWM_FREQUENCY, PWM_RESOLUTION);
 
 	sendMotors();
-	Serial.println("Motors initialized");
+	print("Motors initialized\n");
 }
 
-uint8_t signalToDutyCycle(float control) {
-	float duty = mapff(control, 0, 1, 0, (1 << PWM_RESOLUTION) - 1);
-	return round(constrain(duty, 0, (1 << PWM_RESOLUTION) - 1));
+int getDutyCycle(float value) {
+	value = constrain(value, 0, 1);
+	float pwm = mapff(value, 0, 1, PWM_MIN, PWM_MAX);
+	if (value == 0) pwm = PWM_STOP;
+	float duty = mapff(pwm, 0, 1000000 / PWM_FREQUENCY, 0, (1 << PWM_RESOLUTION) - 1);
+	return round(duty);
 }
 
 void sendMotors() {
-	ledcWrite(MOTOR_0_PIN, signalToDutyCycle(motors[0]));
-	ledcWrite(MOTOR_1_PIN, signalToDutyCycle(motors[1]));
-	ledcWrite(MOTOR_2_PIN, signalToDutyCycle(motors[2]));
-	ledcWrite(MOTOR_3_PIN, signalToDutyCycle(motors[3]));
+	ledcWrite(MOTOR_0_PIN, getDutyCycle(motors[0]));
+	ledcWrite(MOTOR_1_PIN, getDutyCycle(motors[1]));
+	ledcWrite(MOTOR_2_PIN, getDutyCycle(motors[2]));
+	ledcWrite(MOTOR_3_PIN, getDutyCycle(motors[3]));
+}
+
+bool motorsActive() {
+	return motors[0] != 0 || motors[1] != 0 || motors[2] != 0 || motors[3] != 0;
+}
+
+void testMotor(int n) {
+	print("Testing motor %d\n", n);
+	motors[n] = 1;
+	delay(50); // ESP32 may need to wait until the end of the current cycle to change duty https://github.com/espressif/arduino-esp32/issues/5306
+	sendMotors();
+	pause(3);
+	motors[n] = 0;
+	sendMotors();
+	print("Done\n");
 }

flix/parameters.ino

@@ -1,15 +1,19 @@
-#pragma once
+// Copyright (c) 2024 Oleg Kalachev <okalachev@gmail.com>
+// Repository: https://github.com/okalachev/flix
+
+// Parameters storage in flash memory
 
 #include <Preferences.h>
-#include <vector>
 
-extern float channelNeutral[RC_CHANNELS];
-extern float channelMax[RC_CHANNELS];
+extern float channelZero[16];
+extern float channelMax[16];
+extern float rollChannel, pitchChannel, throttleChannel, yawChannel, armedChannel, modeChannel;
+extern float mavlinkControlScale;
 
 Preferences storage;
 
 struct Parameter {
-	const char *name;
+	const char *name; // max length is 16
 	float *variable;
 	float value; // cache
 };
@@ -34,6 +38,10 @@ Parameter parameters[] = {
 	{"PITCH_I", &pitchPID.i},
 	{"PITCH_D", &pitchPID.d},
 	{"YAW_P", &yawPID.p},
+	{"PITCHRATE_MAX", &maxRate.y},
+	{"ROLLRATE_MAX", &maxRate.x},
+	{"YAWRATE_MAX", &maxRate.z},
+	{"TILT_MAX", &tiltMax},
 	// imu
 	{"ACC_BIAS_X", &accBias.x},
 	{"ACC_BIAS_Y", &accBias.y},
@@ -41,18 +49,15 @@ Parameter parameters[] = {
 	{"ACC_SCALE_X", &accScale.x},
 	{"ACC_SCALE_Y", &accScale.y},
 	{"ACC_SCALE_Z", &accScale.z},
-	// {"GYRO_BIAS_X", &gyroBias.x},
-	// {"GYRO_BIAS_Y", &gyroBias.y},
-	// {"GYRO_BIAS_Z", &gyroBias.z},
 	// rc
-	{"RC_NEUTRAL_0", &channelNeutral[0]},
-	{"RC_NEUTRAL_1", &channelNeutral[1]},
-	{"RC_NEUTRAL_2", &channelNeutral[2]},
-	{"RC_NEUTRAL_3", &channelNeutral[3]},
-	{"RC_NEUTRAL_4", &channelNeutral[4]},
-	{"RC_NEUTRAL_5", &channelNeutral[5]},
-	{"RC_NEUTRAL_6", &channelNeutral[6]},
-	{"RC_NEUTRAL_7", &channelNeutral[7]},
+	{"RC_ZERO_0", &channelZero[0]},
+	{"RC_ZERO_1", &channelZero[1]},
+	{"RC_ZERO_2", &channelZero[2]},
+	{"RC_ZERO_3", &channelZero[3]},
+	{"RC_ZERO_4", &channelZero[4]},
+	{"RC_ZERO_5", &channelZero[5]},
+	{"RC_ZERO_6", &channelZero[6]},
+	{"RC_ZERO_7", &channelZero[7]},
 	{"RC_MAX_0", &channelMax[0]},
 	{"RC_MAX_1", &channelMax[1]},
 	{"RC_MAX_2", &channelMax[2]},
@@ -60,7 +65,17 @@ Parameter parameters[] = {
 	{"RC_MAX_4", &channelMax[4]},
 	{"RC_MAX_5", &channelMax[5]},
 	{"RC_MAX_6", &channelMax[6]},
-	{"RC_MAX_7", &channelMax[7]}
+	{"RC_MAX_7", &channelMax[7]},
+	{"RC_ROLL", &rollChannel},
+	{"RC_PITCH", &pitchChannel},
+	{"RC_THROTTLE", &throttleChannel},
+	{"RC_YAW", &yawChannel},
+	{"RC_ARMED", &armedChannel},
+	{"RC_MODE", &modeChannel},
+#if WIFI_ENABLED
+	// MAVLink
+	{"MAV_CTRL_SCALE", &mavlinkControlScale},
+#endif
 };
 
 void setupParameters() {
@@ -68,7 +83,6 @@ void setupParameters() {
 	// Read parameters from storage
 	for (auto &parameter : parameters) {
 		if (!storage.isKey(parameter.name)) {
-			Serial.printf("Define new parameter %s = %f\n", parameter.name, *parameter.variable);
 			storage.putFloat(parameter.name, *parameter.variable);
 		}
 		*parameter.variable = storage.getFloat(parameter.name, *parameter.variable);
@@ -81,10 +95,12 @@ int parametersCount() {
 }
 
 const char *getParameterName(int index) {
+	if (index < 0 || index >= parametersCount()) return "";
 	return parameters[index].name;
 }
 
 float getParameter(int index) {
+	if (index < 0 || index >= parametersCount()) return NAN;
 	return *parameters[index].variable;
 }
 
@@ -107,11 +123,11 @@ bool setParameter(const char *name, const float value) {
 	return false;
 }
 
-void flushParameters() {
-	static float lastFlush = 0;
-	if (t - lastFlush < 1) return; // flush once per second
+void syncParameters() {
+	static double lastSync = 0;
+	if (t - lastSync < 1) return; // sync once per second
 	if (motorsActive()) return; // don't use flash while flying, it may cause a delay
-	lastFlush = t;
+	lastSync = t;
 
 	for (auto &parameter : parameters) {
 		if (parameter.value == *parameter.variable) continue;
@@ -123,7 +139,7 @@ void flushParameters() {
 
 void printParameters() {
 	for (auto &parameter : parameters) {
-		Serial.printf("%s = %g\n", parameter.name, *parameter.variable);
+		print("%s = %g\n", parameter.name, *parameter.variable);
 	}
 }
 

flix/quaternion.h

@@ -15,22 +15,22 @@ public:
 
 	Quaternion(float w, float x, float y, float z): w(w), x(x), y(y), z(z) {};
 
-	static Quaternion fromAxisAngle(float a, float b, float c, float angle) {
+	static Quaternion fromAxisAngle(const Vector& axis, float angle) {
 		float halfAngle = angle * 0.5;
 		float sin2 = sin(halfAngle);
 		float cos2 = cos(halfAngle);
-		float sinNorm = sin2 / sqrt(a * a + b * b + c * c);
-		return Quaternion(cos2, a * sinNorm, b * sinNorm, c * sinNorm);
+		float sinNorm = sin2 / axis.norm();
+		return Quaternion(cos2, axis.x * sinNorm, axis.y * sinNorm, axis.z * sinNorm);
 	}
 
-	static Quaternion fromAngularRates(const Vector& rates) {
-		if (rates.zero()) {
+	static Quaternion fromRotationVector(const Vector& rotation) {
+		if (rotation.zero()) {
 			return Quaternion();
 		}
-		return Quaternion::fromAxisAngle(rates.x, rates.y, rates.z, rates.norm());
+		return Quaternion::fromAxisAngle(rotation, rotation.norm());
 	}
 
-	static Quaternion fromEulerZYX(const Vector& euler) {
+	static Quaternion fromEuler(const Vector& euler) {
 		float cx = cos(euler.x / 2);
 		float cy = cos(euler.y / 2);
 		float cz = cos(euler.z / 2);
@@ -60,14 +60,38 @@ public:
 		return ret;
 	}
 
-	void toAxisAngle(float& a, float& b, float& c, float& angle) {
-		angle = acos(w) * 2;
-		a = x / sin(angle / 2);
-		b = y / sin(angle / 2);
-		c = z / sin(angle / 2);
+	bool finite() const {
+		return isfinite(w) && isfinite(x) && isfinite(y) && isfinite(z);
 	}
 
-	Vector toEulerZYX() const {
+	float norm() const {
+		return sqrt(w * w + x * x + y * y + z * z);
+	}
+
+	void normalize() {
+		float n = norm();
+		w /= n;
+		x /= n;
+		y /= n;
+		z /= n;
+	}
+
+	void toAxisAngle(Vector& axis, float& angle) const {
+		angle = acos(w) * 2;
+		axis.x = x / sin(angle / 2);
+		axis.y = y / sin(angle / 2);
+		axis.z = z / sin(angle / 2);
+	}
+
+	Vector toRotationVector() const {
+		if (w == 1 && x == 0 && y == 0 && z == 0) return Vector(0, 0, 0); // neutral quaternion
+		float angle;
+		Vector axis;
+		toAxisAngle(axis, angle);
+		return angle * axis;
+	}
+
+	Vector toEuler() const {
 		// https://github.com/ros/geometry2/blob/589caf083cae9d8fae7effdb910454b4681b9ec1/tf2/include/tf2/impl/utils.h#L87
 		Vector euler;
 		float sqx = x * x;
@@ -92,41 +116,34 @@ public:
 		return euler;
 	}
 
+	float getRoll() const {
+		return toEuler().x;
+	}
+
+	float getPitch() const {
+		return toEuler().y;
+	}
+
 	float getYaw() const {
-		// https://github.com/ros/geometry2/blob/589caf083cae9d8fae7effdb910454b4681b9ec1/tf2/include/tf2/impl/utils.h#L122
-		float yaw;
-		float sqx = x * x;
-		float sqy = y * y;
-		float sqz = z * z;
-		float sqw = w * w;
-		double sarg = -2 * (x * z - w * y) / (sqx + sqy + sqz + sqw);
-		if (sarg <= -0.99999) {
-			yaw = -2 * atan2(y, x);
-		} else if (sarg >= 0.99999) {
-			yaw = 2 * atan2(y, x);
-		} else {
-			yaw = atan2(2 * (x * y + w * z), sqw + sqx - sqy - sqz);
-		}
-		return yaw;
+		return toEuler().z;
+	}
+
+	void setRoll(float roll) {
+		Vector euler = toEuler();
+		*this = Quaternion::fromEuler(Vector(roll, euler.y, euler.z));
+	}
+
+	void setPitch(float pitch) {
+		Vector euler = toEuler();
+		*this = Quaternion::fromEuler(Vector(euler.x, pitch, euler.z));
 	}
 
 	void setYaw(float yaw) {
-		// TODO: optimize?
-		Vector euler = toEulerZYX();
-		euler.z = yaw;
-		(*this) = Quaternion::fromEulerZYX(euler);
+		Vector euler = toEuler();
+		*this = Quaternion::fromEuler(Vector(euler.x, euler.y, yaw));
 	}
 
-	Quaternion& operator *= (const Quaternion& q) {
-		Quaternion ret(
-			w * q.w - x * q.x - y * q.y - z * q.z,
-			w * q.x + x * q.w + y * q.z - z * q.y,
-			w * q.y + y * q.w + z * q.x - x * q.z,
-			w * q.z + z * q.w + x * q.y - y * q.x);
-		return (*this = ret);
-	}
-
-	Quaternion operator * (const Quaternion& q) {
+	Quaternion operator * (const Quaternion& q) const {
 		return Quaternion(
 			w * q.w - x * q.x - y * q.y - z * q.z,
 			w * q.x + x * q.w + y * q.z - z * q.y,
@@ -134,6 +151,14 @@ public:
 			w * q.z + z * q.w + x * q.y - y * q.x);
 	}
 
+	bool operator == (const Quaternion& q) const {
+		return w == q.w && x == q.x && y == q.y && z == q.z;
+	}
+
+	bool operator != (const Quaternion& q) const {
+		return !(*this == q);
+	}
+
 	Quaternion inversed() const {
 		float normSqInv = 1 / (w * w + x * x + y * y + z * z);
 		return Quaternion(
@@ -143,37 +168,39 @@ public:
 			-z * normSqInv);
 	}
 
-	float norm() const {
-		return sqrt(w * w + x * x + y * y + z * z);
-	}
-
-	void normalize() {
-		float n = norm();
-		w /= n;
-		x /= n;
-		y /= n;
-		z /= n;
-	}
-
-	Vector conjugate(const Vector& v) {
+	Vector conjugate(const Vector& v) const {
 		Quaternion qv(0, v.x, v.y, v.z);
 		Quaternion res = (*this) * qv * inversed();
 		return Vector(res.x, res.y, res.z);
 	}
 
-	Vector conjugateInversed(const Vector& v) {
+	Vector conjugateInversed(const Vector& v) const {
 		Quaternion qv(0, v.x, v.y, v.z);
 		Quaternion res = inversed() * qv * (*this);
 		return Vector(res.x, res.y, res.z);
 	}
 
-	// Rotate vector by quaternion
-	inline Vector rotate(const Vector& v) {
-		return conjugateInversed(v);
+	// Rotate quaternion by quaternion
+	static Quaternion rotate(const Quaternion& a, const Quaternion& b, const bool normalize = true) {
+		Quaternion rotated = a * b;
+		if (normalize) {
+			rotated.normalize();
+		}
+		return rotated;
 	}
 
-	inline bool finite() const {
-		return isfinite(w) && isfinite(x) && isfinite(y) && isfinite(z);
+	// Rotate vector by quaternion
+	static Vector rotateVector(const Vector& v, const Quaternion& q) {
+		return q.conjugateInversed(v);
+	}
+
+	// Quaternion between two quaternions a and b
+	static Quaternion between(const Quaternion& a, const Quaternion& b, const bool normalize = true) {
+		Quaternion q = a * b.inversed();
+		if (normalize) {
+			q.normalize();
+		}
+		return q;
 	}
 
 	size_t printTo(Print& p) const {