maedalab / Mbed 2 deprecated MPU9250_AHRS

Important changes to repositories hosted on mbed.com

Mbed hosted mercurial repositories are deprecated and are due to be permanently deleted in July 2026.

To keep a copy of this software download the repository Zip archive or clone locally using Mercurial.

It is also possible to export all your personal repositories from the account settings page.

Dependencies:   MPU9250_SPI mbed

MadgwickAHRS.h@30:a1bbb934b053, 2016-07-07 (annotated)

Committer:
uribotail
Date:
Thu Jul 07 04:35:04 2016 +0000
Revision:
30:a1bbb934b053
Parent:
29:6075f35f472f
Child:
31:f30e4effec54
without magnetometer

Who changed what in which revision?

UserRevisionLine numberNew contents of line
mfurukawa 17:7a9459ac7469 1 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 2 // Definitions
mfurukawa 17:7a9459ac7469 3
mfurukawa 17:7a9459ac7469 4 #define sampleFreq 500.0f // sample frequency in Hz
uribotail 30:a1bbb934b053 5 #define betaDef 0.02f // 2 * proportional gain
mfurukawa 17:7a9459ac7469 6 #define PI 3.14159265358979f
mfurukawa 17:7a9459ac7469 7 #define DEGREE2RAD PI/180.0f
mfurukawa 17:7a9459ac7469 8 class MadgwickAHRS
mfurukawa 17:7a9459ac7469 9 {
mfurukawa 17:7a9459ac7469 10 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 11 // Variable definitions
mfurukawa 17:7a9459ac7469 12
mfurukawa 17:7a9459ac7469 13 private:
mfurukawa 17:7a9459ac7469 14 volatile float beta; // 2 * proportional gain (Kp)
mfurukawa 17:7a9459ac7469 15
mfurukawa 17:7a9459ac7469 16 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 17 // Function declarations
mfurukawa 17:7a9459ac7469 18 public:
mfurukawa 17:7a9459ac7469 19 volatile float q0,q1,q2,q3; // quaternion of sensor frame relative to auxiliary frame
mfurukawa 17:7a9459ac7469 20
mfurukawa 17:7a9459ac7469 21 MadgwickAHRS();
mfurukawa 17:7a9459ac7469 22 void update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
mfurukawa 17:7a9459ac7469 23 void updateIMU(float gx, float gy, float gz, float ax, float ay, float az);
mfurukawa 17:7a9459ac7469 24 float invSqrt(float x);
mfurukawa 17:7a9459ac7469 25 };
mfurukawa 17:7a9459ac7469 26 //====================================================================================================
mfurukawa 17:7a9459ac7469 27 // Functions
mfurukawa 17:7a9459ac7469 28
mfurukawa 17:7a9459ac7469 29 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 30 // AHRS algorithm update
mfurukawa 17:7a9459ac7469 31 MadgwickAHRS::MadgwickAHRS()
mfurukawa 17:7a9459ac7469 32 {
mfurukawa 17:7a9459ac7469 33 beta = betaDef; // 2 * proportional gain (Kp)
mfurukawa 17:7a9459ac7469 34 q0 = 1.0f;
mfurukawa 17:7a9459ac7469 35 q1 = 0.0f;
mfurukawa 17:7a9459ac7469 36 q2 = 0.0f;
mfurukawa 17:7a9459ac7469 37 q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
mfurukawa 17:7a9459ac7469 38 }
mfurukawa 17:7a9459ac7469 39 void MadgwickAHRS::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz)
mfurukawa 17:7a9459ac7469 40 {
mfurukawa 17:7a9459ac7469 41 float recipNorm;
mfurukawa 17:7a9459ac7469 42 float s0, s1, s2, s3;
mfurukawa 17:7a9459ac7469 43 float qDot1, qDot2, qDot3, qDot4;
mfurukawa 17:7a9459ac7469 44 float hx, hy;
mfurukawa 17:7a9459ac7469 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;
uribotail 29:6075f35f472f 46 /*
uribotail 29:6075f35f472f 47 printf("%+4.3f %+4.3f %+4.3f ",gx,gy,gz);
uribotail 29:6075f35f472f 48 printf("%+4.3f %+4.3f %+4.3f ",ax,ay,az);
uribotail 29:6075f35f472f 49 printf("%.3f %.3f %.3f ",mx,my,mz);
uribotail 29:6075f35f472f 50 printf("\n");*/
mfurukawa 17:7a9459ac7469 51 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
mfurukawa 17:7a9459ac7469 52 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
mfurukawa 17:7a9459ac7469 53 updateIMU(gx, gy, gz, ax, ay, az);
mfurukawa 17:7a9459ac7469 54 return;
mfurukawa 17:7a9459ac7469 55 }
uribotail 30:a1bbb934b053 56
uribotail 30:a1bbb934b053 57 //printf("test\n");
mfurukawa 17:7a9459ac7469 58 // Rate of change of quaternion from gyroscope
mfurukawa 17:7a9459ac7469 59 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 17:7a9459ac7469 60 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 17:7a9459ac7469 61 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 17:7a9459ac7469 62 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 17:7a9459ac7469 63
mfurukawa 17:7a9459ac7469 64 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 17:7a9459ac7469 65 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 17:7a9459ac7469 66
mfurukawa 17:7a9459ac7469 67 // Normalise accelerometer measurement
mfurukawa 17:7a9459ac7469 68 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 17:7a9459ac7469 69 ax *= recipNorm;
mfurukawa 17:7a9459ac7469 70 ay *= recipNorm;
mfurukawa 17:7a9459ac7469 71 az *= recipNorm;
mfurukawa 17:7a9459ac7469 72
mfurukawa 17:7a9459ac7469 73 // Normalise magnetometer measurement
mfurukawa 17:7a9459ac7469 74 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
mfurukawa 17:7a9459ac7469 75 mx *= recipNorm;
mfurukawa 17:7a9459ac7469 76 my *= recipNorm;
mfurukawa 17:7a9459ac7469 77 mz *= recipNorm;
mfurukawa 17:7a9459ac7469 78
mfurukawa 17:7a9459ac7469 79 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 17:7a9459ac7469 80 _2q0mx = 2.0f * q0 * mx;
mfurukawa 17:7a9459ac7469 81 _2q0my = 2.0f * q0 * my;
mfurukawa 17:7a9459ac7469 82 _2q0mz = 2.0f * q0 * mz;
mfurukawa 17:7a9459ac7469 83 _2q1mx = 2.0f * q1 * mx;
mfurukawa 17:7a9459ac7469 84 _2q0 = 2.0f * q0;
mfurukawa 17:7a9459ac7469 85 _2q1 = 2.0f * q1;
mfurukawa 17:7a9459ac7469 86 _2q2 = 2.0f * q2;
mfurukawa 17:7a9459ac7469 87 _2q3 = 2.0f * q3;
mfurukawa 17:7a9459ac7469 88 _2q0q2 = 2.0f * q0 * q2;
mfurukawa 17:7a9459ac7469 89 _2q2q3 = 2.0f * q2 * q3;
mfurukawa 17:7a9459ac7469 90 q0q0 = q0 * q0;
mfurukawa 17:7a9459ac7469 91 q0q1 = q0 * q1;
mfurukawa 17:7a9459ac7469 92 q0q2 = q0 * q2;
mfurukawa 17:7a9459ac7469 93 q0q3 = q0 * q3;
mfurukawa 17:7a9459ac7469 94 q1q1 = q1 * q1;
mfurukawa 17:7a9459ac7469 95 q1q2 = q1 * q2;
mfurukawa 17:7a9459ac7469 96 q1q3 = q1 * q3;
mfurukawa 17:7a9459ac7469 97 q2q2 = q2 * q2;
mfurukawa 17:7a9459ac7469 98 q2q3 = q2 * q3;
mfurukawa 17:7a9459ac7469 99 q3q3 = q3 * q3;
mfurukawa 17:7a9459ac7469 100
mfurukawa 17:7a9459ac7469 101 // Reference direction of Earth's magnetic field
mfurukawa 17:7a9459ac7469 102 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
mfurukawa 17:7a9459ac7469 103 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
mfurukawa 17:7a9459ac7469 104 _2bx = sqrt(hx * hx + hy * hy);
mfurukawa 17:7a9459ac7469 105 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
mfurukawa 17:7a9459ac7469 106 _4bx = 2.0f * _2bx;
mfurukawa 17:7a9459ac7469 107 _4bz = 2.0f * _2bz;
mfurukawa 17:7a9459ac7469 108
mfurukawa 17:7a9459ac7469 109 // Gradient decent algorithm corrective step
mfurukawa 17:7a9459ac7469 110 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 17:7a9459ac7469 111 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 17:7a9459ac7469 112 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 17:7a9459ac7469 113 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 17:7a9459ac7469 114 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 17:7a9459ac7469 115 s0 *= recipNorm;
mfurukawa 17:7a9459ac7469 116 s1 *= recipNorm;
mfurukawa 17:7a9459ac7469 117 s2 *= recipNorm;
mfurukawa 17:7a9459ac7469 118 s3 *= recipNorm;
mfurukawa 17:7a9459ac7469 119
mfurukawa 17:7a9459ac7469 120 // Apply feedback step
mfurukawa 17:7a9459ac7469 121 qDot1 -= beta * s0;
mfurukawa 17:7a9459ac7469 122 qDot2 -= beta * s1;
mfurukawa 17:7a9459ac7469 123 qDot3 -= beta * s2;
mfurukawa 17:7a9459ac7469 124 qDot4 -= beta * s3;
mfurukawa 17:7a9459ac7469 125 }
mfurukawa 17:7a9459ac7469 126
mfurukawa 17:7a9459ac7469 127 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 17:7a9459ac7469 128 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 129 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 130 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 131 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 132
mfurukawa 17:7a9459ac7469 133 // Normalise quaternion
mfurukawa 17:7a9459ac7469 134 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 17:7a9459ac7469 135 q0 *= recipNorm;
mfurukawa 17:7a9459ac7469 136 q1 *= recipNorm;
mfurukawa 17:7a9459ac7469 137 q2 *= recipNorm;
mfurukawa 17:7a9459ac7469 138 q3 *= recipNorm;
mfurukawa 17:7a9459ac7469 139 }
mfurukawa 17:7a9459ac7469 140
mfurukawa 17:7a9459ac7469 141 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 142 // IMU algorithm update
mfurukawa 17:7a9459ac7469 143
mfurukawa 17:7a9459ac7469 144 void MadgwickAHRS::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
mfurukawa 17:7a9459ac7469 145 {
mfurukawa 17:7a9459ac7469 146 float recipNorm;
mfurukawa 17:7a9459ac7469 147 float s0, s1, s2, s3;
mfurukawa 17:7a9459ac7469 148 float qDot1, qDot2, qDot3, qDot4;
mfurukawa 17:7a9459ac7469 149 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
mfurukawa 17:7a9459ac7469 150
mfurukawa 17:7a9459ac7469 151 // Rate of change of quaternion from gyroscope
mfurukawa 17:7a9459ac7469 152 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 17:7a9459ac7469 153 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 17:7a9459ac7469 154 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 17:7a9459ac7469 155 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 17:7a9459ac7469 156
mfurukawa 17:7a9459ac7469 157 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 17:7a9459ac7469 158 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 17:7a9459ac7469 159
mfurukawa 17:7a9459ac7469 160 // Normalise accelerometer measurement
mfurukawa 17:7a9459ac7469 161 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 17:7a9459ac7469 162 ax *= recipNorm;
mfurukawa 17:7a9459ac7469 163 ay *= recipNorm;
mfurukawa 17:7a9459ac7469 164 az *= recipNorm;
mfurukawa 17:7a9459ac7469 165
mfurukawa 17:7a9459ac7469 166 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 17:7a9459ac7469 167 _2q0 = 2.0f * q0;
mfurukawa 17:7a9459ac7469 168 _2q1 = 2.0f * q1;
mfurukawa 17:7a9459ac7469 169 _2q2 = 2.0f * q2;
mfurukawa 17:7a9459ac7469 170 _2q3 = 2.0f * q3;
mfurukawa 17:7a9459ac7469 171 _4q0 = 4.0f * q0;
mfurukawa 17:7a9459ac7469 172 _4q1 = 4.0f * q1;
mfurukawa 17:7a9459ac7469 173 _4q2 = 4.0f * q2;
mfurukawa 17:7a9459ac7469 174 _8q1 = 8.0f * q1;
mfurukawa 17:7a9459ac7469 175 _8q2 = 8.0f * q2;
mfurukawa 17:7a9459ac7469 176 q0q0 = q0 * q0;
mfurukawa 17:7a9459ac7469 177 q1q1 = q1 * q1;
mfurukawa 17:7a9459ac7469 178 q2q2 = q2 * q2;
mfurukawa 17:7a9459ac7469 179 q3q3 = q3 * q3;
mfurukawa 17:7a9459ac7469 180
mfurukawa 17:7a9459ac7469 181 // Gradient decent algorithm corrective step
mfurukawa 17:7a9459ac7469 182 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
mfurukawa 17:7a9459ac7469 183 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
mfurukawa 17:7a9459ac7469 184 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
mfurukawa 17:7a9459ac7469 185 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
mfurukawa 17:7a9459ac7469 186 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 17:7a9459ac7469 187 s0 *= recipNorm;
mfurukawa 17:7a9459ac7469 188 s1 *= recipNorm;
mfurukawa 17:7a9459ac7469 189 s2 *= recipNorm;
mfurukawa 17:7a9459ac7469 190 s3 *= recipNorm;
mfurukawa 17:7a9459ac7469 191
mfurukawa 17:7a9459ac7469 192 // Apply feedback step
mfurukawa 17:7a9459ac7469 193 qDot1 -= beta * s0;
mfurukawa 17:7a9459ac7469 194 qDot2 -= beta * s1;
mfurukawa 17:7a9459ac7469 195 qDot3 -= beta * s2;
mfurukawa 17:7a9459ac7469 196 qDot4 -= beta * s3;
mfurukawa 17:7a9459ac7469 197 }
mfurukawa 17:7a9459ac7469 198
mfurukawa 17:7a9459ac7469 199 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 17:7a9459ac7469 200 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 201 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 202 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 203 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 204
mfurukawa 17:7a9459ac7469 205 // Normalise quaternion
mfurukawa 17:7a9459ac7469 206 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 17:7a9459ac7469 207 q0 *= recipNorm;
mfurukawa 17:7a9459ac7469 208 q1 *= recipNorm;
mfurukawa 17:7a9459ac7469 209 q2 *= recipNorm;
mfurukawa 17:7a9459ac7469 210 q3 *= recipNorm;
mfurukawa 17:7a9459ac7469 211 }
mfurukawa 17:7a9459ac7469 212
mfurukawa 17:7a9459ac7469 213 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 214 // Fast inverse square-root
mfurukawa 17:7a9459ac7469 215 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
mfurukawa 17:7a9459ac7469 216
mfurukawa 17:7a9459ac7469 217 float MadgwickAHRS::invSqrt(float x)
mfurukawa 17:7a9459ac7469 218 {
mfurukawa 17:7a9459ac7469 219 float halfx = 0.5f * x;
mfurukawa 17:7a9459ac7469 220 float y = x;
mfurukawa 17:7a9459ac7469 221 long i = *(long*)&y;
mfurukawa 17:7a9459ac7469 222 i = 0x5f3759df - (i>>1);
mfurukawa 17:7a9459ac7469 223 y = *(float*)&i;
mfurukawa 17:7a9459ac7469 224 y = y * (1.5f - (halfx * y * y));
mfurukawa 17:7a9459ac7469 225 return y;
mfurukawa 17:7a9459ac7469 226 }