├── LICENSE ├── README.md ├── examples ├── MPU9250_SPI_SF │ └── MPU9250_SPI_SF.ino └── SensorFusion │ └── SensorFusion.ino ├── extras ├── IMU_tester │ └── IMU_tester.pde └── axis.png ├── keywords.txt ├── library.properties └── src ├── SensorFusion.cpp └── SensorFusion.h /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # SensorFusion 2 | Using IMUs is one of the most struggling part of every Arduino lovers, here there is a simple solution. 3 | 4 | ![Alt text](/extras/axis.png?raw=true "axis") 5 | 6 | This library will work with every IMU, it just need the raw data of gyroscope and accelerometer (the magnetometer isn't mandatory), it is based on these two libraries: 7 | - https://github.com/PaulStoffregen/MahonyAHRS 8 | - https://github.com/PaulStoffregen/MadgwickAHRS 9 | 10 | I just made small modifications in the way the libraries handled the timing between two measurements and melted them together 11 | 12 | 13 | ## Installation 14 | Use the arduino/platformIO library manager or download directly from github 15 | 16 | 17 | ## About 18 | 19 | Click on the video to see it on youtube 20 | 21 | [![Alt text](https://img.youtube.com/vi/uhsOAhe9qgI/0.jpg)](https://www.youtube.com/watch?v=uhsOAhe9qgI) 22 | 23 | please note that the Roll is inverted 24 | 25 | 26 | I am using an STM32F103F103 known as blue pill but also any Arduino board will work 27 | 28 | The IMU is a cheap MPU9250, you could find it everywhere for about 2€ (eBay, Aliexpress, ecc), to use it I strongly suggest you [this library](https://github.com/bolderflight/MPU9250) 29 | 30 | If you wish use `IMU_tester` in the extras folder to see how you IMU works (needs Processing) 31 | Note: I am using also this very useful library: [Streaming](https://github.com/geneReeves/ArduinoStreaming) 32 | 33 | ## Donate 34 | 35 | If you liked the library and wish to donate you can sent to [PayPal](https://paypal.me/aster94) 36 | -------------------------------------------------------------------------------- /examples/MPU9250_SPI_SF/MPU9250_SPI_SF.ino: -------------------------------------------------------------------------------- 1 | #include "MPU9250.h" // https://github.com/bolderflight/MPU9250 2 | #include "Streaming.h" // needed for the Serial output https://github.com/geneReeves/ArduinoStreaming 3 | #include "SensorFusion.h" 4 | SF fusion; 5 | 6 | float gx, gy, gz, ax, ay, az, mx, my, mz, temp; 7 | float pitch, roll, yaw; 8 | float deltat; 9 | 10 | #define SS_PIN PB12 11 | SPIClass mySPI (2); 12 | MPU9250 IMU(mySPI, SS_PIN); 13 | int status; 14 | 15 | #define EULER_DATA 16 | //#define RAW_DATA 17 | //#define PROCESSING 18 | //#define SERIAL_PLOTER 19 | 20 | 21 | void setup() { 22 | // serial to display data 23 | Serial.begin(115200); 24 | while (!Serial) {} 25 | 26 | // start communication with IMU 27 | status = IMU.begin(); 28 | if (status < 0) { 29 | Serial.println("IMU initialization unsuccessful"); 30 | Serial.println("Check IMU wiring or try cycling power"); 31 | Serial.print("Status: "); 32 | Serial.println(status); 33 | while (1) {} 34 | } 35 | } 36 | 37 | void loop() { 38 | 39 | IMU.readSensor(); 40 | 41 | ax = IMU.getAccelX_mss(); 42 | ay = IMU.getAccelY_mss(); 43 | az = IMU.getAccelZ_mss(); 44 | gx = IMU.getGyroX_rads(); 45 | gy = IMU.getGyroY_rads(); 46 | gz = IMU.getGyroZ_rads(); 47 | mx = IMU.getMagX_uT(); 48 | my = IMU.getMagY_uT(); 49 | mz = IMU.getMagZ_uT(); 50 | temp = IMU.getTemperature_C(); 51 | 52 | #ifdef RAW_DATA 53 | Serial << "From last Update:\t"; Serial.println(deltat, 6); 54 | Serial << "GYRO:\tx:" << gx << "\t\ty:" << gy << "\t\tz:" << gz << newl; 55 | Serial << "ACC:\tx:" << ax << "\t\ty:" << ay << "\t\tz:" << az << newl; 56 | Serial << "MAG:\tx:" << mx << "\t\ty:" << my << "\t\tz:" << mz << newl; 57 | Serial << "TEMP:\t" << temp << newl << newl; 58 | #endif 59 | 60 | deltat = fusion.deltatUpdate(); 61 | //fusion.MahonyUpdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltat); //mahony is suggested if there isn't the mag 62 | fusion.MadgwickUpdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltat); //else use the magwick 63 | 64 | roll = fusion.getRoll(); 65 | pitch = fusion.getPitch(); 66 | yaw = fusion.getYaw(); 67 | 68 | #ifdef EULER_DATA 69 | Serial << "Pitch:\t" << pitch << "\t\tRoll:\t" << roll << "\t\tYaw:\t" << yaw << newl << newl; 70 | #endif 71 | 72 | #ifdef PROCESSING 73 | roll = fusion.getRollRadians(); 74 | pitch = fusion.getPitchRadians(); 75 | yaw = fusion.getYawRadians(); 76 | Serial << pitch << ":" << roll << ":" << yaw << newl; 77 | #endif 78 | 79 | #ifdef SERIAL_PLOTER 80 | Serial << pitch << " " << roll << " " << yaw << endl; 81 | #endif 82 | 83 | //delay(200); //for readability 84 | 85 | } 86 | -------------------------------------------------------------------------------- /examples/SensorFusion/SensorFusion.ino: -------------------------------------------------------------------------------- 1 | // IMPORTANT 2 | // this is not a working example, this is just to show how to set the library 3 | // if you need a working example please see the other example 4 | 5 | 6 | #include "SensorFusion.h" //SF 7 | SF fusion; 8 | 9 | float gx, gy, gz, ax, ay, az, mx, my, mz; 10 | float pitch, roll, yaw; 11 | float deltat; 12 | 13 | 14 | void setup() { 15 | 16 | Serial.begin(115200); //serial to display data 17 | // your IMU begin code goes here 18 | } 19 | 20 | void loop() { 21 | 22 | // now you should read the gyroscope, accelerometer (and magnetometer if you have it also) 23 | // NOTE: the gyroscope data have to be in radians 24 | // if you have them in degree convert them with: DEG_TO_RAD example: gx * DEG_TO_RAD 25 | 26 | deltat = fusion.deltatUpdate(); //this have to be done before calling the fusion update 27 | //choose only one of these two: 28 | fusion.MahonyUpdate(gx, gy, gz, ax, ay, az, deltat); //mahony is suggested if there isn't the mag and the mcu is slow 29 | //fusion.MadgwickUpdate(gx, gy, gz, ax, ay, az, mx, my, mz, deltat); //else use the magwick, it is slower but more accurate 30 | 31 | pitch = fusion.getPitch(); 32 | roll = fusion.getRoll(); //you could also use getRollRadians() ecc 33 | yaw = fusion.getYaw(); 34 | 35 | Serial.print("Pitch:\t"); Serial.println(pitch); 36 | Serial.print("Roll:\t"); Serial.println(roll); 37 | Serial.print("Yaw:\t"); Serial.println(yaw); 38 | Serial.println(); 39 | } 40 | -------------------------------------------------------------------------------- /extras/IMU_tester/IMU_tester.pde: -------------------------------------------------------------------------------- 1 | /* 2 | This code is made for processing https://processing.org/ 3 | */ 4 | 5 | import processing.serial.*; // import the Processing serial library 6 | Serial myPort; // The serial port 7 | String my_port = "COM11"; // choose your port 8 | float xx, yy, zz; 9 | 10 | void setup() { 11 | size(1024, 800, P3D); 12 | 13 | myPort = new Serial(this, my_port, 115200); 14 | myPort.bufferUntil('\n'); 15 | 16 | smooth(); 17 | } 18 | 19 | void draw() { 20 | background(0); 21 | noStroke(); 22 | translate(width/2, height/2); 23 | pushMatrix(); 24 | rotateX(xx);//pitch 25 | rotateY(zz);//yaw 26 | rotateZ(yy);//roll 27 | box(100, 50, 600); 28 | popMatrix(); 29 | } 30 | 31 | 32 | void serialEvent(Serial myPort) { 33 | 34 | String myString = myPort.readStringUntil('\n'); 35 | myString = trim(myString); 36 | float sensors[] = float(split(myString, ':')); 37 | 38 | xx = sensors[0]; 39 | yy = sensors[1]; 40 | zz = sensors[2]; 41 | 42 | //println("roll: " + xx + " pitch: " + yy + " yaw: " + zz + "\n"); //debug 43 | 44 | } -------------------------------------------------------------------------------- /extras/axis.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/aster94/SensorFusion/babe6684c68d379d14d755311a38f2de4104d2ce/extras/axis.png -------------------------------------------------------------------------------- /keywords.txt: -------------------------------------------------------------------------------- 1 | ####################################### 2 | # Datatypes (KEYWORD1) 3 | ####################################### 4 | SF KEYWORD1 5 | 6 | ####################################### 7 | # Methods and Functions (KEYWORD2) 8 | ####################################### 9 | MadgwickUpdate KEYWORD2 10 | MahonyUpdate KEYWORD2 11 | deltatUpdate KEYWORD2 12 | getPitch KEYWORD2 13 | getYaw KEYWORD2 14 | getRoll KEYWORD2 15 | getRollRadians KEYWORD2 16 | getPitchRadians KEYWORD2 17 | getYawRadians KEYWORD2 18 | getQuat KEYWORD2 19 | 20 | ####################################### 21 | # Constants (LITERAL1) 22 | ####################################### 23 | DEG_TO_RAD LITERAL1 24 | RAD_TO_DEG LITERAL1 25 | -------------------------------------------------------------------------------- /library.properties: -------------------------------------------------------------------------------- 1 | name=SensorFusion 2 | version=1.0.6 3 | author=aster94 4 | maintainer=aster94 5 | sentence=A library that makes using a IMU a breeze. 6 | paragraph=Mahony and Madgwick algorithms. 7 | category=Sensors 8 | url=https://github.com/aster94/SensorFusion 9 | architectures=* 10 | -------------------------------------------------------------------------------- /src/SensorFusion.cpp: -------------------------------------------------------------------------------- 1 | //============================================================================================= 2 | // SensorFusion.cpp 3 | //============================================================================================= 4 | // 5 | // Madgwick's implementation of Mahony's AHRS algorithm. 6 | // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/ 7 | // 8 | // From the x-io website "Open-source resources available on this website are 9 | // provided under the GNU General Public Licence unless an alternative licence 10 | // is provided in source." 11 | // 12 | // Date Author Notes 13 | // 29/09/2011 SOH Madgwick Initial release 14 | // 02/10/2011 SOH Madgwick Optimised for reduced CPU load 15 | // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised 16 | // 23/11/2017 Aster94 Simplified time handling and melted in one library 17 | // 18 | // Algorithm paper: 19 | // http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934 20 | // 21 | //============================================================================================= 22 | 23 | //------------------------------------------------------------------------------------------- 24 | // Header files 25 | 26 | #include "SensorFusion.h" // SF 27 | #include 28 | #include "Arduino.h" 29 | 30 | //------------------------------------------------------------------------------------------- 31 | // Definitions 32 | 33 | #define betaDef 0.1f // 2 * proportional gain 34 | #define twoKpDef (2.0f * 0.5f) // 2 * proportional gain 35 | #define twoKiDef (2.0f * 0.0f) // 2 * integral gain 36 | 37 | 38 | //============================================================================================ 39 | // Functions 40 | 41 | SF::SF() 42 | { 43 | beta = betaDef; 44 | twoKp = twoKpDef; 45 | twoKi = twoKiDef; 46 | q0 = 1.0f; 47 | q1 = 0.0f; 48 | q2 = 0.0f; 49 | q3 = 0.0f; 50 | integralFBx = 0.0f; 51 | integralFBy = 0.0f; 52 | integralFBz = 0.0f; 53 | anglesComputed = 0; 54 | } 55 | 56 | // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root 57 | float SF::invSqrt(float x) 58 | { 59 | float halfx = 0.5f * x; 60 | union { 61 | float f; 62 | uint32_t i; 63 | } conv = { .f = x }; 64 | conv.i = 0x5f3759df - (conv.i >> 1); 65 | conv.f *= 1.5f - (halfx * conv.f * conv.f); 66 | conv.f *= 1.5f - (halfx * conv.f * conv.f); 67 | return conv.f; 68 | } 69 | 70 | //------------------------------------------------------------------------------------------- 71 | void SF::computeAngles() 72 | { 73 | roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2); 74 | pitch = asinf(-2.0f * (q1*q3 - q0*q2)); 75 | yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3); 76 | anglesComputed = 1; 77 | } 78 | 79 | 80 | 81 | //============================================================================================ 82 | // Mahony AHRS algorithm update 83 | 84 | void SF::MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat) 85 | { 86 | float recipNorm; 87 | float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; 88 | float hx, hy, bx, bz; 89 | float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz; 90 | float halfex, halfey, halfez; 91 | float qa, qb, qc; 92 | 93 | // Use IMU algorithm if magnetometer measurement invalid 94 | // (avoids NaN in magnetometer normalisation) 95 | if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { 96 | MahonyUpdate(gx, gy, gz, ax, ay, az, deltat); 97 | return; 98 | } 99 | 100 | // Compute feedback only if accelerometer measurement valid 101 | // (avoids NaN in accelerometer normalisation) 102 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 103 | 104 | // Normalise accelerometer measurement 105 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); 106 | ax *= recipNorm; 107 | ay *= recipNorm; 108 | az *= recipNorm; 109 | 110 | // Normalise magnetometer measurement 111 | recipNorm = invSqrt(mx * mx + my * my + mz * mz); 112 | mx *= recipNorm; 113 | my *= recipNorm; 114 | mz *= recipNorm; 115 | 116 | // Auxiliary variables to avoid repeated arithmetic 117 | q0q0 = q0 * q0; 118 | q0q1 = q0 * q1; 119 | q0q2 = q0 * q2; 120 | q0q3 = q0 * q3; 121 | q1q1 = q1 * q1; 122 | q1q2 = q1 * q2; 123 | q1q3 = q1 * q3; 124 | q2q2 = q2 * q2; 125 | q2q3 = q2 * q3; 126 | q3q3 = q3 * q3; 127 | 128 | // Reference direction of Earth's magnetic field 129 | hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2)); 130 | hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1)); 131 | bx = sqrtf(hx * hx + hy * hy); 132 | bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2)); 133 | 134 | // Estimated direction of gravity and magnetic field 135 | halfvx = q1q3 - q0q2; 136 | halfvy = q0q1 + q2q3; 137 | halfvz = q0q0 - 0.5f + q3q3; 138 | halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2); 139 | halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3); 140 | halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2); 141 | 142 | // Error is sum of cross product between estimated direction 143 | // and measured direction of field vectors 144 | halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy); 145 | halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz); 146 | halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx); 147 | 148 | // Compute and apply integral feedback if enabled 149 | if(twoKi > 0.0f) { 150 | // integral error scaled by Ki 151 | integralFBx += twoKi * halfex * deltat; 152 | integralFBy += twoKi * halfey * deltat; 153 | integralFBz += twoKi * halfez * deltat; 154 | gx += integralFBx; // apply integral feedback 155 | gy += integralFBy; 156 | gz += integralFBz; 157 | } else { 158 | integralFBx = 0.0f; // prevent integral windup 159 | integralFBy = 0.0f; 160 | integralFBz = 0.0f; 161 | } 162 | 163 | // Apply proportional feedback 164 | gx += twoKp * halfex; 165 | gy += twoKp * halfey; 166 | gz += twoKp * halfez; 167 | } 168 | 169 | // Integrate rate of change of quaternion 170 | gx *= (0.5f * deltat); // pre-multiply common factors 171 | gy *= (0.5f * deltat); 172 | gz *= (0.5f * deltat); 173 | qa = q0; 174 | qb = q1; 175 | qc = q2; 176 | q0 += (-qb * gx - qc * gy - q3 * gz); 177 | q1 += (qa * gx + qc * gz - q3 * gy); 178 | q2 += (qa * gy - qb * gz + q3 * gx); 179 | q3 += (qa * gz + qb * gy - qc * gx); 180 | 181 | // Normalise quaternion 182 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 183 | q0 *= recipNorm; 184 | q1 *= recipNorm; 185 | q2 *= recipNorm; 186 | q3 *= recipNorm; 187 | anglesComputed = 0; 188 | } 189 | 190 | //------------------------------------------------------------------------------------------- 191 | 192 | void SF::MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat) 193 | { 194 | float recipNorm; 195 | float halfvx, halfvy, halfvz; 196 | float halfex, halfey, halfez; 197 | float qa, qb, qc; 198 | 199 | // Compute feedback only if accelerometer measurement valid 200 | // (avoids NaN in accelerometer normalisation) 201 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 202 | 203 | // Normalise accelerometer measurement 204 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); 205 | ax *= recipNorm; 206 | ay *= recipNorm; 207 | az *= recipNorm; 208 | 209 | // Estimated direction of gravity 210 | halfvx = q1 * q3 - q0 * q2; 211 | halfvy = q0 * q1 + q2 * q3; 212 | halfvz = q0 * q0 - 0.5f + q3 * q3; 213 | 214 | // Error is sum of cross product between estimated 215 | // and measured direction of gravity 216 | halfex = (ay * halfvz - az * halfvy); 217 | halfey = (az * halfvx - ax * halfvz); 218 | halfez = (ax * halfvy - ay * halfvx); 219 | 220 | // Compute and apply integral feedback if enabled 221 | if(twoKi > 0.0f) { 222 | // integral error scaled by Ki 223 | integralFBx += twoKi * halfex * deltat; 224 | integralFBy += twoKi * halfey * deltat; 225 | integralFBz += twoKi * halfez * deltat; 226 | gx += integralFBx; // apply integral feedback 227 | gy += integralFBy; 228 | gz += integralFBz; 229 | } else { 230 | integralFBx = 0.0f; // prevent integral windup 231 | integralFBy = 0.0f; 232 | integralFBz = 0.0f; 233 | } 234 | 235 | // Apply proportional feedback 236 | gx += twoKp * halfex; 237 | gy += twoKp * halfey; 238 | gz += twoKp * halfez; 239 | } 240 | 241 | // Integrate rate of change of quaternion 242 | gx *= (0.5f * deltat); // pre-multiply common factors 243 | gy *= (0.5f * deltat); 244 | gz *= (0.5f * deltat); 245 | qa = q0; 246 | qb = q1; 247 | qc = q2; 248 | q0 += (-qb * gx - qc * gy - q3 * gz); 249 | q1 += (qa * gx + qc * gz - q3 * gy); 250 | q2 += (qa * gy - qb * gz + q3 * gx); 251 | q3 += (qa * gz + qb * gy - qc * gx); 252 | 253 | // Normalise quaternion 254 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 255 | q0 *= recipNorm; 256 | q1 *= recipNorm; 257 | q2 *= recipNorm; 258 | q3 *= recipNorm; 259 | anglesComputed = 0; 260 | } 261 | 262 | 263 | 264 | //============================================================================================ 265 | // Madgwick AHRS algorithm update 266 | 267 | void SF::MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat) { 268 | float recipNorm; 269 | float s0, s1, s2, s3; 270 | float qDot1, qDot2, qDot3, qDot4; 271 | float hx, hy; 272 | float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; 273 | 274 | // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation) 275 | if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { 276 | MadgwickUpdate(gx, gy, gz, ax, ay, az, deltat); 277 | return; 278 | } 279 | 280 | // Rate of change of quaternion from gyroscope 281 | qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); 282 | qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); 283 | qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); 284 | qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); 285 | 286 | // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) 287 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 288 | 289 | // Normalise accelerometer measurement 290 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); 291 | ax *= recipNorm; 292 | ay *= recipNorm; 293 | az *= recipNorm; 294 | 295 | // Normalise magnetometer measurement 296 | recipNorm = invSqrt(mx * mx + my * my + mz * mz); 297 | mx *= recipNorm; 298 | my *= recipNorm; 299 | mz *= recipNorm; 300 | 301 | // Auxiliary variables to avoid repeated arithmetic 302 | _2q0mx = 2.0f * q0 * mx; 303 | _2q0my = 2.0f * q0 * my; 304 | _2q0mz = 2.0f * q0 * mz; 305 | _2q1mx = 2.0f * q1 * mx; 306 | _2q0 = 2.0f * q0; 307 | _2q1 = 2.0f * q1; 308 | _2q2 = 2.0f * q2; 309 | _2q3 = 2.0f * q3; 310 | _2q0q2 = 2.0f * q0 * q2; 311 | _2q2q3 = 2.0f * q2 * q3; 312 | q0q0 = q0 * q0; 313 | q0q1 = q0 * q1; 314 | q0q2 = q0 * q2; 315 | q0q3 = q0 * q3; 316 | q1q1 = q1 * q1; 317 | q1q2 = q1 * q2; 318 | q1q3 = q1 * q3; 319 | q2q2 = q2 * q2; 320 | q2q3 = q2 * q3; 321 | q3q3 = q3 * q3; 322 | 323 | // Reference direction of Earth's magnetic field 324 | hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3; 325 | hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3; 326 | _2bx = sqrtf(hx * hx + hy * hy); 327 | _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3; 328 | _4bx = 2.0f * _2bx; 329 | _4bz = 2.0f * _2bz; 330 | 331 | // Gradient decent algorithm corrective step 332 | s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); 333 | s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); 334 | s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); 335 | s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); 336 | recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude 337 | s0 *= recipNorm; 338 | s1 *= recipNorm; 339 | s2 *= recipNorm; 340 | s3 *= recipNorm; 341 | 342 | // Apply feedback step 343 | qDot1 -= beta * s0; 344 | qDot2 -= beta * s1; 345 | qDot3 -= beta * s2; 346 | qDot4 -= beta * s3; 347 | } 348 | 349 | // Integrate rate of change of quaternion to yield quaternion 350 | q0 += qDot1 * deltat; 351 | q1 += qDot2 * deltat; 352 | q2 += qDot3 * deltat; 353 | q3 += qDot4 * deltat; 354 | 355 | // Normalise quaternion 356 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 357 | q0 *= recipNorm; 358 | q1 *= recipNorm; 359 | q2 *= recipNorm; 360 | q3 *= recipNorm; 361 | anglesComputed = 0; 362 | } 363 | 364 | //------------------------------------------------------------------------------------------- 365 | 366 | void SF::MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat) { 367 | float recipNorm; 368 | float s0, s1, s2, s3; 369 | float qDot1, qDot2, qDot3, qDot4; 370 | float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3; 371 | 372 | // Rate of change of quaternion from gyroscope 373 | qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); 374 | qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); 375 | qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); 376 | qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); 377 | 378 | // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) 379 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 380 | 381 | // Normalise accelerometer measurement 382 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); 383 | ax *= recipNorm; 384 | ay *= recipNorm; 385 | az *= recipNorm; 386 | 387 | // Auxiliary variables to avoid repeated arithmetic 388 | _2q0 = 2.0f * q0; 389 | _2q1 = 2.0f * q1; 390 | _2q2 = 2.0f * q2; 391 | _2q3 = 2.0f * q3; 392 | _4q0 = 4.0f * q0; 393 | _4q1 = 4.0f * q1; 394 | _4q2 = 4.0f * q2; 395 | _8q1 = 8.0f * q1; 396 | _8q2 = 8.0f * q2; 397 | q0q0 = q0 * q0; 398 | q1q1 = q1 * q1; 399 | q2q2 = q2 * q2; 400 | q3q3 = q3 * q3; 401 | 402 | // Gradient decent algorithm corrective step 403 | s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay; 404 | s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az; 405 | s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az; 406 | s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay; 407 | recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude 408 | s0 *= recipNorm; 409 | s1 *= recipNorm; 410 | s2 *= recipNorm; 411 | s3 *= recipNorm; 412 | 413 | // Apply feedback step 414 | qDot1 -= beta * s0; 415 | qDot2 -= beta * s1; 416 | qDot3 -= beta * s2; 417 | qDot4 -= beta * s3; 418 | } 419 | 420 | // Integrate rate of change of quaternion to yield quaternion 421 | q0 += qDot1 * deltat; 422 | q1 += qDot2 * deltat; 423 | q2 += qDot3 * deltat; 424 | q3 += qDot4 * deltat; 425 | 426 | // Normalise quaternion 427 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 428 | q0 *= recipNorm; 429 | q1 *= recipNorm; 430 | q2 *= recipNorm; 431 | q3 *= recipNorm; 432 | anglesComputed = 0; 433 | } 434 | 435 | 436 | bool SF::initQuat(float ax, float ay, float az, float mx, float my, float mz){ 437 | // Compute feedback only if accelerometer measurement valid 438 | // (avoids NaN in accelerometer normalisation) 439 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 440 | float recipNorm; 441 | float N[3], D[3], E[3]; //Global vectors North, Down, East relative to sensor 442 | 443 | // Down is negative accelerometer measurement 444 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); 445 | D[0] = - ax * recipNorm; 446 | D[1] = - ay * recipNorm; 447 | D[2] = - az * recipNorm; 448 | 449 | // Magnetometer is not exatly perpendicular to Down, therefor not exatly North 450 | // we will calculate North later 451 | float m[3]; 452 | recipNorm = invSqrt(mx * mx + my * my + mz * mz); 453 | m[0] = mx * recipNorm; 454 | m[1] = mx * recipNorm; 455 | m[2] = mx * recipNorm; 456 | 457 | // Calculate East 458 | vectorCross(m, D, E); 459 | recipNorm = invSqrt(E[0] * E[0] + E[1] * E[1] + E[2] * E[2]); 460 | E[0] *= recipNorm; 461 | E[1] *= recipNorm; 462 | E[2] *= recipNorm; 463 | 464 | // Calculate North 465 | vectorCross(D, E, N); 466 | 467 | // Calculate Euler Parameter (quaternion) from the rotation matrix A=(N|D|E). 468 | // Using Shepperd algorithm (Woernle 2011) 469 | float Trace = N[0] + D[1] + E[2]; 470 | float a[4] = {Trace, N[0], D[1], E[2]}; 471 | float e[4]; 472 | 473 | //find index of Largest Euler parameter 474 | int k=0; 475 | for (int i=1; i<4; i++){ 476 | if (a[i] > a[k]) 477 | k = i; 478 | } 479 | //calculate that parameter 480 | e[k] = sqrt(1 + 2 * a[k] - Trace)/2; 481 | 482 | switch (k){ 483 | case 0: 484 | e[1] = (D[2] - E[1]) / (4 * e[0]); 485 | e[2] = (E[0] - N[2]) / (4 * e[0]); 486 | e[3] = (N[1] - D[0]) / (4 * e[0]); 487 | break; 488 | case 1: 489 | e[0] = (D[2] - E[1]) / (4 * e[1]); 490 | e[2] = (D[0] + N[1]) / (4 * e[1]); 491 | e[3] = (E[0] + N[2]) / (4 * e[1]); 492 | break; 493 | case 2: 494 | e[0] = (E[0] - N[2]) / (4 * e[2]); 495 | e[1] = (D[0] + N[1]) / (4 * e[2]); 496 | e[3] = (E[1] + D[2]) / (4 * e[2]); 497 | break; 498 | case 3: 499 | e[0] = (N[1] - D[0]) / (4 * e[3]); 500 | e[1] = (E[0] + N[2]) / (4 * e[3]); 501 | e[2] = (E[1] + D[2]) / (4 * e[3]); 502 | } 503 | 504 | // invert the quaternion rotation 505 | // we calculated the rotation of Global NDE relative to the sensor 506 | // but we need the rotation of the Sensor relative to NDE 507 | q0 = e[0]; 508 | q1 = -e[1]; 509 | q2 = -e[2]; 510 | q3 = -e[3]; 511 | 512 | return true; 513 | } else return false; 514 | } 515 | 516 | void SF::vectorCross(float A[3], float B[3], float cross[3]) 517 | { 518 | cross[0] = A[1] * B[2] - A[2] * B[1]; 519 | cross[1] = A[2] * B[0] - A[0] * B[2]; 520 | cross[2] = A[0] * B[1] - A[1] * B[0]; 521 | } 522 | 523 | 524 | //============================================================================================ 525 | // END OF CODE 526 | //============================================================================================ 527 | -------------------------------------------------------------------------------- /src/SensorFusion.h: -------------------------------------------------------------------------------- 1 | //============================================================================================= 2 | // SensorFusion.h 3 | //============================================================================================= 4 | // 5 | // Madgwick's implementation of Mahony's AHRS algorithm. 6 | // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/ 7 | // 8 | // Date Author Notes 9 | // 29/09/2011 SOH Madgwick Initial release 10 | // 02/10/2011 SOH Madgwick Optimised for reduced CPU load 11 | // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised 12 | // 23/11/2017 Aster Optimised time handling and melted in one library 13 | // 14 | //============================================================================================= 15 | #ifndef SensorFusion_h 16 | #define SensorFusion_h 17 | 18 | #include 19 | #include "Arduino.h" 20 | 21 | //-------------------------------------------------------------------------------------------- 22 | // Variable declaration 23 | 24 | class SF { 25 | //------------------------------------------------------------------------------------------- 26 | // Function declarations 27 | 28 | public: 29 | 30 | SF(); 31 | 32 | void MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat); 33 | void MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat); 34 | 35 | void MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat); 36 | void MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat); 37 | 38 | // find initial Quaternios 39 | // it is good practice to provide mean values from multiple measurements 40 | bool initQuat(float ax, float ay, float az, float mx, float my, float mz); 41 | //these values are already defined by arduino 42 | //const float DEG_TO_RAD = 0.0174532925199433f; //PI/180.0f; 43 | //const float RAD_TO_DEG = 57.29577951308233f; //180.0f/PI 44 | 45 | float deltatUpdate (){ 46 | Now = micros(); 47 | deltat = ((Now - lastUpdate) / 1000000.0f); // set integration time by time elapsed since last filter update 48 | lastUpdate = Now; 49 | return deltat; 50 | } 51 | 52 | float getRoll() { 53 | if (!anglesComputed) computeAngles(); 54 | return roll * RAD_TO_DEG; 55 | } 56 | float getPitch() { 57 | if (!anglesComputed) computeAngles(); 58 | return pitch * RAD_TO_DEG; 59 | } 60 | float getYaw() { 61 | if (!anglesComputed) computeAngles(); 62 | return yaw * RAD_TO_DEG + 180.0f; 63 | } 64 | float getRollRadians() { 65 | if (!anglesComputed) computeAngles(); 66 | return roll; 67 | } 68 | float getPitchRadians() { 69 | if (!anglesComputed) computeAngles(); 70 | return pitch; 71 | } 72 | float getYawRadians() { 73 | if (!anglesComputed) computeAngles(); 74 | return yaw; 75 | } 76 | float* getQuat() { 77 | memcpy(_copyQuat, &q0, sizeof(float)*4); 78 | return _copyQuat; 79 | } 80 | 81 | private: 82 | float beta; //Madgwick: 2 * proportional gain 83 | float twoKp; //Mahony: 2 * proportional gain (Kp) 84 | float twoKi; //Mahony: 2 * integral gain (Ki) 85 | float q0, q1, q2, q3; // quaternion of sensor frame relative to auxiliary frame 86 | float integralFBx, integralFBy, integralFBz; // integral error terms scaled by Ki 87 | bool anglesComputed; 88 | static float invSqrt(float x); 89 | void vectorCross(float A[3], float B[3], float cross[3]); 90 | void computeAngles(); 91 | float roll, pitch, yaw; 92 | float Now,lastUpdate,deltat; 93 | float _copyQuat[4]; // copy buffer to protect the quaternion values since getters!=setters 94 | 95 | }; 96 | 97 | #endif 98 | --------------------------------------------------------------------------------