Masahiro Furukawa / Mbed 2 deprecated MPU-9250-Ch2

MPU-9250 with Kalman Filter

Dependencies:   ADXL362-helloworld MPU9250_SPI mbed

Fork of ADXL362-helloworld by Analog Devices

AHRS/MadgwickAHRS.c@10:f2ef74678956, 2017-04-26 (annotated)

Committer:
mfurukawa
Date:
Wed Apr 26 07:52:10 2017 +0000
Revision:
10:f2ef74678956
public revision

Who changed what in which revision?

UserRevisionLine numberNew contents of line
mfurukawa 10:f2ef74678956 1 //=====================================================================================================
mfurukawa 10:f2ef74678956 2 // MadgwickAHRS.c
mfurukawa 10:f2ef74678956 3 //=====================================================================================================
mfurukawa 10:f2ef74678956 4 //
mfurukawa 10:f2ef74678956 5 // Implementation of Madgwick's IMU and AHRS algorithms.
mfurukawa 10:f2ef74678956 6 // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
mfurukawa 10:f2ef74678956 7 //
mfurukawa 10:f2ef74678956 8 // Date Author Notes
mfurukawa 10:f2ef74678956 9 // 29/09/2011 SOH Madgwick Initial release
mfurukawa 10:f2ef74678956 10 // 02/10/2011 SOH Madgwick Optimised for reduced CPU load
mfurukawa 10:f2ef74678956 11 // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
mfurukawa 10:f2ef74678956 12 //
mfurukawa 10:f2ef74678956 13 //=====================================================================================================
mfurukawa 10:f2ef74678956 14
mfurukawa 10:f2ef74678956 15 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 16 // Header files
mfurukawa 10:f2ef74678956 17
mfurukawa 10:f2ef74678956 18 #include "MadgwickAHRS.h"
mfurukawa 10:f2ef74678956 19 #include <math.h>
mfurukawa 10:f2ef74678956 20
mfurukawa 10:f2ef74678956 21 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 22 // Definitions
mfurukawa 10:f2ef74678956 23
mfurukawa 10:f2ef74678956 24 #define sampleFreq 512.0f // sample frequency in Hz
mfurukawa 10:f2ef74678956 25 #define betaDef 0.1f // 2 * proportional gain
mfurukawa 10:f2ef74678956 26
mfurukawa 10:f2ef74678956 27 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 28 // Variable definitions
mfurukawa 10:f2ef74678956 29
mfurukawa 10:f2ef74678956 30 volatile float beta = betaDef; // 2 * proportional gain (Kp)
mfurukawa 10:f2ef74678956 31 volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
mfurukawa 10:f2ef74678956 32
mfurukawa 10:f2ef74678956 33 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 34 // Function declarations
mfurukawa 10:f2ef74678956 35
mfurukawa 10:f2ef74678956 36 float invSqrt(float x);
mfurukawa 10:f2ef74678956 37
mfurukawa 10:f2ef74678956 38 //====================================================================================================
mfurukawa 10:f2ef74678956 39 // Functions
mfurukawa 10:f2ef74678956 40
mfurukawa 10:f2ef74678956 41 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 42 // AHRS algorithm update
mfurukawa 10:f2ef74678956 43
mfurukawa 10:f2ef74678956 44 void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
mfurukawa 10:f2ef74678956 45 float recipNorm;
mfurukawa 10:f2ef74678956 46 float s0, s1, s2, s3;
mfurukawa 10:f2ef74678956 47 float qDot1, qDot2, qDot3, qDot4;
mfurukawa 10:f2ef74678956 48 float hx, hy;
mfurukawa 10:f2ef74678956 49 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;
mfurukawa 10:f2ef74678956 50
mfurukawa 10:f2ef74678956 51 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
mfurukawa 10:f2ef74678956 52 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
mfurukawa 10:f2ef74678956 53 MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
mfurukawa 10:f2ef74678956 54 return;
mfurukawa 10:f2ef74678956 55 }
mfurukawa 10:f2ef74678956 56
mfurukawa 10:f2ef74678956 57 // Rate of change of quaternion from gyroscope
mfurukawa 10:f2ef74678956 58 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 10:f2ef74678956 59 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 10:f2ef74678956 60 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 10:f2ef74678956 61 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 10:f2ef74678956 62
mfurukawa 10:f2ef74678956 63 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 10:f2ef74678956 64 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 10:f2ef74678956 65
mfurukawa 10:f2ef74678956 66 // Normalise accelerometer measurement
mfurukawa 10:f2ef74678956 67 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 10:f2ef74678956 68 ax *= recipNorm;
mfurukawa 10:f2ef74678956 69 ay *= recipNorm;
mfurukawa 10:f2ef74678956 70 az *= recipNorm;
mfurukawa 10:f2ef74678956 71
mfurukawa 10:f2ef74678956 72 // Normalise magnetometer measurement
mfurukawa 10:f2ef74678956 73 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
mfurukawa 10:f2ef74678956 74 mx *= recipNorm;
mfurukawa 10:f2ef74678956 75 my *= recipNorm;
mfurukawa 10:f2ef74678956 76 mz *= recipNorm;
mfurukawa 10:f2ef74678956 77
mfurukawa 10:f2ef74678956 78 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 10:f2ef74678956 79 _2q0mx = 2.0f * q0 * mx;
mfurukawa 10:f2ef74678956 80 _2q0my = 2.0f * q0 * my;
mfurukawa 10:f2ef74678956 81 _2q0mz = 2.0f * q0 * mz;
mfurukawa 10:f2ef74678956 82 _2q1mx = 2.0f * q1 * mx;
mfurukawa 10:f2ef74678956 83 _2q0 = 2.0f * q0;
mfurukawa 10:f2ef74678956 84 _2q1 = 2.0f * q1;
mfurukawa 10:f2ef74678956 85 _2q2 = 2.0f * q2;
mfurukawa 10:f2ef74678956 86 _2q3 = 2.0f * q3;
mfurukawa 10:f2ef74678956 87 _2q0q2 = 2.0f * q0 * q2;
mfurukawa 10:f2ef74678956 88 _2q2q3 = 2.0f * q2 * q3;
mfurukawa 10:f2ef74678956 89 q0q0 = q0 * q0;
mfurukawa 10:f2ef74678956 90 q0q1 = q0 * q1;
mfurukawa 10:f2ef74678956 91 q0q2 = q0 * q2;
mfurukawa 10:f2ef74678956 92 q0q3 = q0 * q3;
mfurukawa 10:f2ef74678956 93 q1q1 = q1 * q1;
mfurukawa 10:f2ef74678956 94 q1q2 = q1 * q2;
mfurukawa 10:f2ef74678956 95 q1q3 = q1 * q3;
mfurukawa 10:f2ef74678956 96 q2q2 = q2 * q2;
mfurukawa 10:f2ef74678956 97 q2q3 = q2 * q3;
mfurukawa 10:f2ef74678956 98 q3q3 = q3 * q3;
mfurukawa 10:f2ef74678956 99
mfurukawa 10:f2ef74678956 100 // Reference direction of Earth's magnetic field
mfurukawa 10:f2ef74678956 101 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
mfurukawa 10:f2ef74678956 102 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
mfurukawa 10:f2ef74678956 103 _2bx = sqrt(hx * hx + hy * hy);
mfurukawa 10:f2ef74678956 104 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
mfurukawa 10:f2ef74678956 105 _4bx = 2.0f * _2bx;
mfurukawa 10:f2ef74678956 106 _4bz = 2.0f * _2bz;
mfurukawa 10:f2ef74678956 107
mfurukawa 10:f2ef74678956 108 // Gradient decent algorithm corrective step
mfurukawa 10:f2ef74678956 109 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);
mfurukawa 10:f2ef74678956 110 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);
mfurukawa 10:f2ef74678956 111 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);
mfurukawa 10:f2ef74678956 112 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);
mfurukawa 10:f2ef74678956 113 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 10:f2ef74678956 114 s0 *= recipNorm;
mfurukawa 10:f2ef74678956 115 s1 *= recipNorm;
mfurukawa 10:f2ef74678956 116 s2 *= recipNorm;
mfurukawa 10:f2ef74678956 117 s3 *= recipNorm;
mfurukawa 10:f2ef74678956 118
mfurukawa 10:f2ef74678956 119 // Apply feedback step
mfurukawa 10:f2ef74678956 120 qDot1 -= beta * s0;
mfurukawa 10:f2ef74678956 121 qDot2 -= beta * s1;
mfurukawa 10:f2ef74678956 122 qDot3 -= beta * s2;
mfurukawa 10:f2ef74678956 123 qDot4 -= beta * s3;
mfurukawa 10:f2ef74678956 124 }
mfurukawa 10:f2ef74678956 125
mfurukawa 10:f2ef74678956 126 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 10:f2ef74678956 127 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 128 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 129 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 130 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 131
mfurukawa 10:f2ef74678956 132 // Normalise quaternion
mfurukawa 10:f2ef74678956 133 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 10:f2ef74678956 134 q0 *= recipNorm;
mfurukawa 10:f2ef74678956 135 q1 *= recipNorm;
mfurukawa 10:f2ef74678956 136 q2 *= recipNorm;
mfurukawa 10:f2ef74678956 137 q3 *= recipNorm;
mfurukawa 10:f2ef74678956 138 }
mfurukawa 10:f2ef74678956 139
mfurukawa 10:f2ef74678956 140 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 141 // IMU algorithm update
mfurukawa 10:f2ef74678956 142
mfurukawa 10:f2ef74678956 143 void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
mfurukawa 10:f2ef74678956 144 float recipNorm;
mfurukawa 10:f2ef74678956 145 float s0, s1, s2, s3;
mfurukawa 10:f2ef74678956 146 float qDot1, qDot2, qDot3, qDot4;
mfurukawa 10:f2ef74678956 147 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
mfurukawa 10:f2ef74678956 148
mfurukawa 10:f2ef74678956 149 // Rate of change of quaternion from gyroscope
mfurukawa 10:f2ef74678956 150 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 10:f2ef74678956 151 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 10:f2ef74678956 152 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 10:f2ef74678956 153 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 10:f2ef74678956 154
mfurukawa 10:f2ef74678956 155 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 10:f2ef74678956 156 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 10:f2ef74678956 157
mfurukawa 10:f2ef74678956 158 // Normalise accelerometer measurement
mfurukawa 10:f2ef74678956 159 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 10:f2ef74678956 160 ax *= recipNorm;
mfurukawa 10:f2ef74678956 161 ay *= recipNorm;
mfurukawa 10:f2ef74678956 162 az *= recipNorm;
mfurukawa 10:f2ef74678956 163
mfurukawa 10:f2ef74678956 164 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 10:f2ef74678956 165 _2q0 = 2.0f * q0;
mfurukawa 10:f2ef74678956 166 _2q1 = 2.0f * q1;
mfurukawa 10:f2ef74678956 167 _2q2 = 2.0f * q2;
mfurukawa 10:f2ef74678956 168 _2q3 = 2.0f * q3;
mfurukawa 10:f2ef74678956 169 _4q0 = 4.0f * q0;
mfurukawa 10:f2ef74678956 170 _4q1 = 4.0f * q1;
mfurukawa 10:f2ef74678956 171 _4q2 = 4.0f * q2;
mfurukawa 10:f2ef74678956 172 _8q1 = 8.0f * q1;
mfurukawa 10:f2ef74678956 173 _8q2 = 8.0f * q2;
mfurukawa 10:f2ef74678956 174 q0q0 = q0 * q0;
mfurukawa 10:f2ef74678956 175 q1q1 = q1 * q1;
mfurukawa 10:f2ef74678956 176 q2q2 = q2 * q2;
mfurukawa 10:f2ef74678956 177 q3q3 = q3 * q3;
mfurukawa 10:f2ef74678956 178
mfurukawa 10:f2ef74678956 179 // Gradient decent algorithm corrective step
mfurukawa 10:f2ef74678956 180 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
mfurukawa 10:f2ef74678956 181 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
mfurukawa 10:f2ef74678956 182 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
mfurukawa 10:f2ef74678956 183 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
mfurukawa 10:f2ef74678956 184 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 10:f2ef74678956 185 s0 *= recipNorm;
mfurukawa 10:f2ef74678956 186 s1 *= recipNorm;
mfurukawa 10:f2ef74678956 187 s2 *= recipNorm;
mfurukawa 10:f2ef74678956 188 s3 *= recipNorm;
mfurukawa 10:f2ef74678956 189
mfurukawa 10:f2ef74678956 190 // Apply feedback step
mfurukawa 10:f2ef74678956 191 qDot1 -= beta * s0;
mfurukawa 10:f2ef74678956 192 qDot2 -= beta * s1;
mfurukawa 10:f2ef74678956 193 qDot3 -= beta * s2;
mfurukawa 10:f2ef74678956 194 qDot4 -= beta * s3;
mfurukawa 10:f2ef74678956 195 }
mfurukawa 10:f2ef74678956 196
mfurukawa 10:f2ef74678956 197 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 10:f2ef74678956 198 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 199 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 200 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 201 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 10:f2ef74678956 202
mfurukawa 10:f2ef74678956 203 // Normalise quaternion
mfurukawa 10:f2ef74678956 204 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 10:f2ef74678956 205 q0 *= recipNorm;
mfurukawa 10:f2ef74678956 206 q1 *= recipNorm;
mfurukawa 10:f2ef74678956 207 q2 *= recipNorm;
mfurukawa 10:f2ef74678956 208 q3 *= recipNorm;
mfurukawa 10:f2ef74678956 209 }
mfurukawa 10:f2ef74678956 210
mfurukawa 10:f2ef74678956 211 //---------------------------------------------------------------------------------------------------
mfurukawa 10:f2ef74678956 212 // Fast inverse square-root
mfurukawa 10:f2ef74678956 213 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
mfurukawa 10:f2ef74678956 214
mfurukawa 10:f2ef74678956 215 float invSqrt(float x) {
mfurukawa 10:f2ef74678956 216 float halfx = 0.5f * x;
mfurukawa 10:f2ef74678956 217 float y = x;
mfurukawa 10:f2ef74678956 218 long i = *(long*)&y;
mfurukawa 10:f2ef74678956 219 i = 0x5f3759df - (i>>1);
mfurukawa 10:f2ef74678956 220 y = *(float*)&i;
mfurukawa 10:f2ef74678956 221 y = y * (1.5f - (halfx * y * y));
mfurukawa 10:f2ef74678956 222 return y;
mfurukawa 10:f2ef74678956 223 }
mfurukawa 10:f2ef74678956 224
mfurukawa 10:f2ef74678956 225 //====================================================================================================
mfurukawa 10:f2ef74678956 226 // END OF CODE
mfurukawa 10:f2ef74678956 227 //====================================================================================================