UAVRO / MadgwickAHRS

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Dependents:   Q2_Stabi

MadgwickAHRS.cpp@0:0c61d7209f75, 2016-05-30 (annotated)

Committer:
Decimus
Date:
Mon May 30 08:10:20 2016 +0000
Revision:
0:0c61d7209f75
[+]

Who changed what in which revision?

UserRevisionLine numberNew contents of line
Decimus 0:0c61d7209f75 1
Decimus 0:0c61d7209f75 2 // MadgwickAHRS.c
Decimus 0:0c61d7209f75 3 //=====================================================================================================
Decimus 0:0c61d7209f75 4 //
Decimus 0:0c61d7209f75 5 // Implementation of Madgwick's IMU and AHRS algorithms.
Decimus 0:0c61d7209f75 6 // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
Decimus 0:0c61d7209f75 7 //
Decimus 0:0c61d7209f75 8 // Date Author Notes
Decimus 0:0c61d7209f75 9 // 29/09/2011 SOH Madgwick Initial release
Decimus 0:0c61d7209f75 10 // 02/10/2011 SOH Madgwick Optimised for reduced CPU load
Decimus 0:0c61d7209f75 11 // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
Decimus 0:0c61d7209f75 12 //
Decimus 0:0c61d7209f75 13 //=====================================================================================================
Decimus 0:0c61d7209f75 14
Decimus 0:0c61d7209f75 15 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 16 // Header files
Decimus 0:0c61d7209f75 17
Decimus 0:0c61d7209f75 18 #include "MadgwickAHRS.h"
Decimus 0:0c61d7209f75 19 #include <math.h>
Decimus 0:0c61d7209f75 20
Decimus 0:0c61d7209f75 21 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 22 // Definitions
Decimus 0:0c61d7209f75 23
Decimus 0:0c61d7209f75 24 #define sampleFreq 512.0f // sample frequency in Hz
Decimus 0:0c61d7209f75 25 #define betaDef 0.1f // 2 * proportional gain
Decimus 0:0c61d7209f75 26
Decimus 0:0c61d7209f75 27 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 28 // Variable definitions
Decimus 0:0c61d7209f75 29
Decimus 0:0c61d7209f75 30 volatile float beta = betaDef; // 2 * proportional gain (Kp)
Decimus 0:0c61d7209f75 31 volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
Decimus 0:0c61d7209f75 32 //volatile float quat[4];
Decimus 0:0c61d7209f75 33
Decimus 0:0c61d7209f75 34 //====================================================================================================
Decimus 0:0c61d7209f75 35 // Functions
Decimus 0:0c61d7209f75 36
Decimus 0:0c61d7209f75 37 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 38 // AHRS algorithm update
Decimus 0:0c61d7209f75 39
Decimus 0:0c61d7209f75 40 void MadgwickAHRSupdate(float tdelta, float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
Decimus 0:0c61d7209f75 41 float recipNorm;
Decimus 0:0c61d7209f75 42 float s0, s1, s2, s3;
Decimus 0:0c61d7209f75 43 float qDot1, qDot2, qDot3, qDot4;
Decimus 0:0c61d7209f75 44 float hx, hy;
Decimus 0:0c61d7209f75 45 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;
Decimus 0:0c61d7209f75 46
Decimus 0:0c61d7209f75 47 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
Decimus 0:0c61d7209f75 48 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
Decimus 0:0c61d7209f75 49 MadgwickAHRSupdateIMU( tdelta, gx, gy, gz, ax, ay, az);
Decimus 0:0c61d7209f75 50 return;
Decimus 0:0c61d7209f75 51 }
Decimus 0:0c61d7209f75 52
Decimus 0:0c61d7209f75 53 // Rate of change of quaternion from gyroscope
Decimus 0:0c61d7209f75 54 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Decimus 0:0c61d7209f75 55 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Decimus 0:0c61d7209f75 56 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Decimus 0:0c61d7209f75 57 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Decimus 0:0c61d7209f75 58
Decimus 0:0c61d7209f75 59 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Decimus 0:0c61d7209f75 60 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Decimus 0:0c61d7209f75 61
Decimus 0:0c61d7209f75 62 // Normalise accelerometer measurement
Decimus 0:0c61d7209f75 63 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Decimus 0:0c61d7209f75 64 ax *= recipNorm;
Decimus 0:0c61d7209f75 65 ay *= recipNorm;
Decimus 0:0c61d7209f75 66 az *= recipNorm;
Decimus 0:0c61d7209f75 67
Decimus 0:0c61d7209f75 68 // Normalise magnetometer measurement
Decimus 0:0c61d7209f75 69 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
Decimus 0:0c61d7209f75 70 mx *= recipNorm;
Decimus 0:0c61d7209f75 71 my *= recipNorm;
Decimus 0:0c61d7209f75 72 mz *= recipNorm;
Decimus 0:0c61d7209f75 73
Decimus 0:0c61d7209f75 74 // Auxiliary variables to avoid repeated arithmetic
Decimus 0:0c61d7209f75 75 _2q0mx = 2.0f * q0 * mx;
Decimus 0:0c61d7209f75 76 _2q0my = 2.0f * q0 * my;
Decimus 0:0c61d7209f75 77 _2q0mz = 2.0f * q0 * mz;
Decimus 0:0c61d7209f75 78 _2q1mx = 2.0f * q1 * mx;
Decimus 0:0c61d7209f75 79 _2q0 = 2.0f * q0;
Decimus 0:0c61d7209f75 80 _2q1 = 2.0f * q1;
Decimus 0:0c61d7209f75 81 _2q2 = 2.0f * q2;
Decimus 0:0c61d7209f75 82 _2q3 = 2.0f * q3;
Decimus 0:0c61d7209f75 83 _2q0q2 = 2.0f * q0 * q2;
Decimus 0:0c61d7209f75 84 _2q2q3 = 2.0f * q2 * q3;
Decimus 0:0c61d7209f75 85 q0q0 = q0 * q0;
Decimus 0:0c61d7209f75 86 q0q1 = q0 * q1;
Decimus 0:0c61d7209f75 87 q0q2 = q0 * q2;
Decimus 0:0c61d7209f75 88 q0q3 = q0 * q3;
Decimus 0:0c61d7209f75 89 q1q1 = q1 * q1;
Decimus 0:0c61d7209f75 90 q1q2 = q1 * q2;
Decimus 0:0c61d7209f75 91 q1q3 = q1 * q3;
Decimus 0:0c61d7209f75 92 q2q2 = q2 * q2;
Decimus 0:0c61d7209f75 93 q2q3 = q2 * q3;
Decimus 0:0c61d7209f75 94 q3q3 = q3 * q3;
Decimus 0:0c61d7209f75 95
Decimus 0:0c61d7209f75 96 // Reference direction of Earth's magnetic field
Decimus 0:0c61d7209f75 97 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Decimus 0:0c61d7209f75 98 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Decimus 0:0c61d7209f75 99 _2bx = sqrt(hx * hx + hy * hy);
Decimus 0:0c61d7209f75 100 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Decimus 0:0c61d7209f75 101 _4bx = 2.0f * _2bx;
Decimus 0:0c61d7209f75 102 _4bz = 2.0f * _2bz;
Decimus 0:0c61d7209f75 103
Decimus 0:0c61d7209f75 104 // Gradient decent algorithm corrective step
Decimus 0:0c61d7209f75 105 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);
Decimus 0:0c61d7209f75 106 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);
Decimus 0:0c61d7209f75 107 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);
Decimus 0:0c61d7209f75 108 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);
Decimus 0:0c61d7209f75 109 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Decimus 0:0c61d7209f75 110 s0 *= recipNorm;
Decimus 0:0c61d7209f75 111 s1 *= recipNorm;
Decimus 0:0c61d7209f75 112 s2 *= recipNorm;
Decimus 0:0c61d7209f75 113 s3 *= recipNorm;
Decimus 0:0c61d7209f75 114
Decimus 0:0c61d7209f75 115 // Apply feedback step
Decimus 0:0c61d7209f75 116 qDot1 -= beta * s0;
Decimus 0:0c61d7209f75 117 qDot2 -= beta * s1;
Decimus 0:0c61d7209f75 118 qDot3 -= beta * s2;
Decimus 0:0c61d7209f75 119 qDot4 -= beta * s3;
Decimus 0:0c61d7209f75 120 }
Decimus 0:0c61d7209f75 121
Decimus 0:0c61d7209f75 122 // Integrate rate of change of quaternion to yield quaternion
Decimus 0:0c61d7209f75 123 q0 += qDot1 * tdelta;
Decimus 0:0c61d7209f75 124 q1 += qDot2 * tdelta;
Decimus 0:0c61d7209f75 125 q2 += qDot3 * tdelta;
Decimus 0:0c61d7209f75 126 q3 += qDot4 * tdelta;
Decimus 0:0c61d7209f75 127
Decimus 0:0c61d7209f75 128 // Normalise quaternion
Decimus 0:0c61d7209f75 129 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Decimus 0:0c61d7209f75 130 q0 *= recipNorm;
Decimus 0:0c61d7209f75 131 q1 *= recipNorm;
Decimus 0:0c61d7209f75 132 q2 *= recipNorm;
Decimus 0:0c61d7209f75 133 q3 *= recipNorm;
Decimus 0:0c61d7209f75 134 }
Decimus 0:0c61d7209f75 135
Decimus 0:0c61d7209f75 136 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 137 // IMU algorithm update
Decimus 0:0c61d7209f75 138
Decimus 0:0c61d7209f75 139 void MadgwickAHRSupdateIMU(float tdelta, float gx, float gy, float gz, float ax, float ay, float az) {
Decimus 0:0c61d7209f75 140 float recipNorm;
Decimus 0:0c61d7209f75 141 float s0, s1, s2, s3;
Decimus 0:0c61d7209f75 142 float qDot1, qDot2, qDot3, qDot4;
Decimus 0:0c61d7209f75 143 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
Decimus 0:0c61d7209f75 144
Decimus 0:0c61d7209f75 145 // Rate of change of quaternion from gyroscope
Decimus 0:0c61d7209f75 146 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Decimus 0:0c61d7209f75 147 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Decimus 0:0c61d7209f75 148 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Decimus 0:0c61d7209f75 149 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Decimus 0:0c61d7209f75 150
Decimus 0:0c61d7209f75 151 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Decimus 0:0c61d7209f75 152 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Decimus 0:0c61d7209f75 153 // Normalise accelerometer measurement
Decimus 0:0c61d7209f75 154 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Decimus 0:0c61d7209f75 155 ax *= recipNorm;
Decimus 0:0c61d7209f75 156 ay *= recipNorm;
Decimus 0:0c61d7209f75 157 az *= recipNorm;
Decimus 0:0c61d7209f75 158
Decimus 0:0c61d7209f75 159 // Auxiliary variables to avoid repeated arithmetic
Decimus 0:0c61d7209f75 160 _2q0 = 2.0f * q0;
Decimus 0:0c61d7209f75 161 _2q1 = 2.0f * q1;
Decimus 0:0c61d7209f75 162 _2q2 = 2.0f * q2;
Decimus 0:0c61d7209f75 163 _2q3 = 2.0f * q3;
Decimus 0:0c61d7209f75 164 _4q0 = 4.0f * q0;
Decimus 0:0c61d7209f75 165 _4q1 = 4.0f * q1;
Decimus 0:0c61d7209f75 166 _4q2 = 4.0f * q2;
Decimus 0:0c61d7209f75 167 _8q1 = 8.0f * q1;
Decimus 0:0c61d7209f75 168 _8q2 = 8.0f * q2;
Decimus 0:0c61d7209f75 169 q0q0 = q0 * q0;
Decimus 0:0c61d7209f75 170 q1q1 = q1 * q1;
Decimus 0:0c61d7209f75 171 q2q2 = q2 * q2;
Decimus 0:0c61d7209f75 172 q3q3 = q3 * q3;
Decimus 0:0c61d7209f75 173
Decimus 0:0c61d7209f75 174 // Gradient decent algorithm corrective step
Decimus 0:0c61d7209f75 175 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
Decimus 0:0c61d7209f75 176 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
Decimus 0:0c61d7209f75 177 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
Decimus 0:0c61d7209f75 178 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
Decimus 0:0c61d7209f75 179 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Decimus 0:0c61d7209f75 180 s0 *= recipNorm;
Decimus 0:0c61d7209f75 181 s1 *= recipNorm;
Decimus 0:0c61d7209f75 182 s2 *= recipNorm;
Decimus 0:0c61d7209f75 183 s3 *= recipNorm;
Decimus 0:0c61d7209f75 184 // Apply feedback step
Decimus 0:0c61d7209f75 185 qDot1 -= beta * s0;
Decimus 0:0c61d7209f75 186 qDot2 -= beta * s1;
Decimus 0:0c61d7209f75 187 qDot3 -= beta * s2;
Decimus 0:0c61d7209f75 188 qDot4 -= beta * s3;
Decimus 0:0c61d7209f75 189 }
Decimus 0:0c61d7209f75 190
Decimus 0:0c61d7209f75 191 // Integrate rate of change of quaternion to yield quaternion
Decimus 0:0c61d7209f75 192 q0 += qDot1 * tdelta;
Decimus 0:0c61d7209f75 193 q1 += qDot2 * tdelta;
Decimus 0:0c61d7209f75 194 q2 += qDot3 * tdelta;
Decimus 0:0c61d7209f75 195 q3 += qDot4 * tdelta;
Decimus 0:0c61d7209f75 196
Decimus 0:0c61d7209f75 197 // Normalise quaternion
Decimus 0:0c61d7209f75 198 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Decimus 0:0c61d7209f75 199 q0 *= recipNorm;
Decimus 0:0c61d7209f75 200 q1 *= recipNorm;
Decimus 0:0c61d7209f75 201 q2 *= recipNorm;
Decimus 0:0c61d7209f75 202 q3 *= recipNorm;
Decimus 0:0c61d7209f75 203 //quat[0] = q0;
Decimus 0:0c61d7209f75 204 //quat[1] = q1;
Decimus 0:0c61d7209f75 205 //quat[2] = q2;
Decimus 0:0c61d7209f75 206 //quat[3] = q3;
Decimus 0:0c61d7209f75 207 }
Decimus 0:0c61d7209f75 208
Decimus 0:0c61d7209f75 209
Decimus 0:0c61d7209f75 210 int instability_fix = 1;
Decimus 0:0c61d7209f75 211
Decimus 0:0c61d7209f75 212 //---------------------------------------------------------------------------------------------------
Decimus 0:0c61d7209f75 213 // Fast inverse square-root
Decimus 0:0c61d7209f75 214 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
Decimus 0:0c61d7209f75 215
Decimus 0:0c61d7209f75 216 float invSqrt(float x) {
Decimus 0:0c61d7209f75 217 if (instability_fix == 0)
Decimus 0:0c61d7209f75 218 {
Decimus 0:0c61d7209f75 219 /* original code */
Decimus 0:0c61d7209f75 220 float halfx = 0.5f * x;
Decimus 0:0c61d7209f75 221 float y = x;
Decimus 0:0c61d7209f75 222 long i = *(long*)&y;
Decimus 0:0c61d7209f75 223 i = 0x5f3759df - (i>>1);
Decimus 0:0c61d7209f75 224 y = *(float*)&i;
Decimus 0:0c61d7209f75 225 y = y * (1.5f - (halfx * y * y));
Decimus 0:0c61d7209f75 226 return y;
Decimus 0:0c61d7209f75 227 }
Decimus 0:0c61d7209f75 228 else if (instability_fix == 1)
Decimus 0:0c61d7209f75 229 {
Decimus 0:0c61d7209f75 230 /* close-to-optimal method with low cost from http://pizer.wordpress.com/2008/10/12/fast-inverse-square-root */
Decimus 0:0c61d7209f75 231 unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
Decimus 0:0c61d7209f75 232 float tmp = *(float*)&i;
Decimus 0:0c61d7209f75 233 return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
Decimus 0:0c61d7209f75 234 }
Decimus 0:0c61d7209f75 235 else
Decimus 0:0c61d7209f75 236 {
Decimus 0:0c61d7209f75 237 /* optimal but expensive method: */
Decimus 0:0c61d7209f75 238 return 1.0f / sqrtf(x);
Decimus 0:0c61d7209f75 239 }
Decimus 0:0c61d7209f75 240 }
Decimus 0:0c61d7209f75 241
Decimus 0:0c61d7209f75 242 //====================================================================================================
Decimus 0:0c61d7209f75 243 // END OF CODE
Decimus 0:0c61d7209f75 244 //====================================================================================================