maedalab / Mbed 2 deprecated MPU9250_AHRS

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Dependencies:   MPU9250_SPI mbed

MadgwickAHRS.h@17:7a9459ac7469, 2016-06-22 (annotated)

Committer:
mfurukawa
Date:
Wed Jun 22 13:06:36 2016 +0000
Revision:
17:7a9459ac7469
Child:
24:50b3c20b1abe
- remove offset function; - optimized eventFunc loop; - change scale setting;

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
mfurukawa 17:7a9459ac7469 5 #define betaDef 1.0f // 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;
mfurukawa 17:7a9459ac7469 46
mfurukawa 17:7a9459ac7469 47 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
mfurukawa 17:7a9459ac7469 48 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
mfurukawa 17:7a9459ac7469 49 updateIMU(gx, gy, gz, ax, ay, az);
mfurukawa 17:7a9459ac7469 50 return;
mfurukawa 17:7a9459ac7469 51 }
mfurukawa 17:7a9459ac7469 52
mfurukawa 17:7a9459ac7469 53 // Rate of change of quaternion from gyroscope
mfurukawa 17:7a9459ac7469 54 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 17:7a9459ac7469 55 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 17:7a9459ac7469 56 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 17:7a9459ac7469 57 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 17:7a9459ac7469 58
mfurukawa 17:7a9459ac7469 59 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 17:7a9459ac7469 60 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 17:7a9459ac7469 61
mfurukawa 17:7a9459ac7469 62 // Normalise accelerometer measurement
mfurukawa 17:7a9459ac7469 63 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 17:7a9459ac7469 64 ax *= recipNorm;
mfurukawa 17:7a9459ac7469 65 ay *= recipNorm;
mfurukawa 17:7a9459ac7469 66 az *= recipNorm;
mfurukawa 17:7a9459ac7469 67
mfurukawa 17:7a9459ac7469 68 // Normalise magnetometer measurement
mfurukawa 17:7a9459ac7469 69 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
mfurukawa 17:7a9459ac7469 70 mx *= recipNorm;
mfurukawa 17:7a9459ac7469 71 my *= recipNorm;
mfurukawa 17:7a9459ac7469 72 mz *= recipNorm;
mfurukawa 17:7a9459ac7469 73
mfurukawa 17:7a9459ac7469 74 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 17:7a9459ac7469 75 _2q0mx = 2.0f * q0 * mx;
mfurukawa 17:7a9459ac7469 76 _2q0my = 2.0f * q0 * my;
mfurukawa 17:7a9459ac7469 77 _2q0mz = 2.0f * q0 * mz;
mfurukawa 17:7a9459ac7469 78 _2q1mx = 2.0f * q1 * mx;
mfurukawa 17:7a9459ac7469 79 _2q0 = 2.0f * q0;
mfurukawa 17:7a9459ac7469 80 _2q1 = 2.0f * q1;
mfurukawa 17:7a9459ac7469 81 _2q2 = 2.0f * q2;
mfurukawa 17:7a9459ac7469 82 _2q3 = 2.0f * q3;
mfurukawa 17:7a9459ac7469 83 _2q0q2 = 2.0f * q0 * q2;
mfurukawa 17:7a9459ac7469 84 _2q2q3 = 2.0f * q2 * q3;
mfurukawa 17:7a9459ac7469 85 q0q0 = q0 * q0;
mfurukawa 17:7a9459ac7469 86 q0q1 = q0 * q1;
mfurukawa 17:7a9459ac7469 87 q0q2 = q0 * q2;
mfurukawa 17:7a9459ac7469 88 q0q3 = q0 * q3;
mfurukawa 17:7a9459ac7469 89 q1q1 = q1 * q1;
mfurukawa 17:7a9459ac7469 90 q1q2 = q1 * q2;
mfurukawa 17:7a9459ac7469 91 q1q3 = q1 * q3;
mfurukawa 17:7a9459ac7469 92 q2q2 = q2 * q2;
mfurukawa 17:7a9459ac7469 93 q2q3 = q2 * q3;
mfurukawa 17:7a9459ac7469 94 q3q3 = q3 * q3;
mfurukawa 17:7a9459ac7469 95
mfurukawa 17:7a9459ac7469 96 // Reference direction of Earth's magnetic field
mfurukawa 17:7a9459ac7469 97 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
mfurukawa 17:7a9459ac7469 98 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
mfurukawa 17:7a9459ac7469 99 _2bx = sqrt(hx * hx + hy * hy);
mfurukawa 17:7a9459ac7469 100 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
mfurukawa 17:7a9459ac7469 101 _4bx = 2.0f * _2bx;
mfurukawa 17:7a9459ac7469 102 _4bz = 2.0f * _2bz;
mfurukawa 17:7a9459ac7469 103
mfurukawa 17:7a9459ac7469 104 // Gradient decent algorithm corrective step
mfurukawa 17:7a9459ac7469 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);
mfurukawa 17:7a9459ac7469 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);
mfurukawa 17:7a9459ac7469 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);
mfurukawa 17:7a9459ac7469 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);
mfurukawa 17:7a9459ac7469 109 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 17:7a9459ac7469 110 s0 *= recipNorm;
mfurukawa 17:7a9459ac7469 111 s1 *= recipNorm;
mfurukawa 17:7a9459ac7469 112 s2 *= recipNorm;
mfurukawa 17:7a9459ac7469 113 s3 *= recipNorm;
mfurukawa 17:7a9459ac7469 114
mfurukawa 17:7a9459ac7469 115 // Apply feedback step
mfurukawa 17:7a9459ac7469 116 qDot1 -= beta * s0;
mfurukawa 17:7a9459ac7469 117 qDot2 -= beta * s1;
mfurukawa 17:7a9459ac7469 118 qDot3 -= beta * s2;
mfurukawa 17:7a9459ac7469 119 qDot4 -= beta * s3;
mfurukawa 17:7a9459ac7469 120 }
mfurukawa 17:7a9459ac7469 121
mfurukawa 17:7a9459ac7469 122 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 17:7a9459ac7469 123 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 124 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 125 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 126 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 127
mfurukawa 17:7a9459ac7469 128 // Normalise quaternion
mfurukawa 17:7a9459ac7469 129 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 17:7a9459ac7469 130 q0 *= recipNorm;
mfurukawa 17:7a9459ac7469 131 q1 *= recipNorm;
mfurukawa 17:7a9459ac7469 132 q2 *= recipNorm;
mfurukawa 17:7a9459ac7469 133 q3 *= recipNorm;
mfurukawa 17:7a9459ac7469 134 }
mfurukawa 17:7a9459ac7469 135
mfurukawa 17:7a9459ac7469 136 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 137 // IMU algorithm update
mfurukawa 17:7a9459ac7469 138
mfurukawa 17:7a9459ac7469 139 void MadgwickAHRS::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
mfurukawa 17:7a9459ac7469 140 {
mfurukawa 17:7a9459ac7469 141 float recipNorm;
mfurukawa 17:7a9459ac7469 142 float s0, s1, s2, s3;
mfurukawa 17:7a9459ac7469 143 float qDot1, qDot2, qDot3, qDot4;
mfurukawa 17:7a9459ac7469 144 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
mfurukawa 17:7a9459ac7469 145
mfurukawa 17:7a9459ac7469 146 // Rate of change of quaternion from gyroscope
mfurukawa 17:7a9459ac7469 147 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
mfurukawa 17:7a9459ac7469 148 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
mfurukawa 17:7a9459ac7469 149 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
mfurukawa 17:7a9459ac7469 150 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
mfurukawa 17:7a9459ac7469 151
mfurukawa 17:7a9459ac7469 152 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
mfurukawa 17:7a9459ac7469 153 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
mfurukawa 17:7a9459ac7469 154
mfurukawa 17:7a9459ac7469 155 // Normalise accelerometer measurement
mfurukawa 17:7a9459ac7469 156 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
mfurukawa 17:7a9459ac7469 157 ax *= recipNorm;
mfurukawa 17:7a9459ac7469 158 ay *= recipNorm;
mfurukawa 17:7a9459ac7469 159 az *= recipNorm;
mfurukawa 17:7a9459ac7469 160
mfurukawa 17:7a9459ac7469 161 // Auxiliary variables to avoid repeated arithmetic
mfurukawa 17:7a9459ac7469 162 _2q0 = 2.0f * q0;
mfurukawa 17:7a9459ac7469 163 _2q1 = 2.0f * q1;
mfurukawa 17:7a9459ac7469 164 _2q2 = 2.0f * q2;
mfurukawa 17:7a9459ac7469 165 _2q3 = 2.0f * q3;
mfurukawa 17:7a9459ac7469 166 _4q0 = 4.0f * q0;
mfurukawa 17:7a9459ac7469 167 _4q1 = 4.0f * q1;
mfurukawa 17:7a9459ac7469 168 _4q2 = 4.0f * q2;
mfurukawa 17:7a9459ac7469 169 _8q1 = 8.0f * q1;
mfurukawa 17:7a9459ac7469 170 _8q2 = 8.0f * q2;
mfurukawa 17:7a9459ac7469 171 q0q0 = q0 * q0;
mfurukawa 17:7a9459ac7469 172 q1q1 = q1 * q1;
mfurukawa 17:7a9459ac7469 173 q2q2 = q2 * q2;
mfurukawa 17:7a9459ac7469 174 q3q3 = q3 * q3;
mfurukawa 17:7a9459ac7469 175
mfurukawa 17:7a9459ac7469 176 // Gradient decent algorithm corrective step
mfurukawa 17:7a9459ac7469 177 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
mfurukawa 17:7a9459ac7469 178 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
mfurukawa 17:7a9459ac7469 179 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
mfurukawa 17:7a9459ac7469 180 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
mfurukawa 17:7a9459ac7469 181 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
mfurukawa 17:7a9459ac7469 182 s0 *= recipNorm;
mfurukawa 17:7a9459ac7469 183 s1 *= recipNorm;
mfurukawa 17:7a9459ac7469 184 s2 *= recipNorm;
mfurukawa 17:7a9459ac7469 185 s3 *= recipNorm;
mfurukawa 17:7a9459ac7469 186
mfurukawa 17:7a9459ac7469 187 // Apply feedback step
mfurukawa 17:7a9459ac7469 188 qDot1 -= beta * s0;
mfurukawa 17:7a9459ac7469 189 qDot2 -= beta * s1;
mfurukawa 17:7a9459ac7469 190 qDot3 -= beta * s2;
mfurukawa 17:7a9459ac7469 191 qDot4 -= beta * s3;
mfurukawa 17:7a9459ac7469 192 }
mfurukawa 17:7a9459ac7469 193
mfurukawa 17:7a9459ac7469 194 // Integrate rate of change of quaternion to yield quaternion
mfurukawa 17:7a9459ac7469 195 q0 += qDot1 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 196 q1 += qDot2 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 197 q2 += qDot3 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 198 q3 += qDot4 * (1.0f / sampleFreq);
mfurukawa 17:7a9459ac7469 199
mfurukawa 17:7a9459ac7469 200 // Normalise quaternion
mfurukawa 17:7a9459ac7469 201 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
mfurukawa 17:7a9459ac7469 202 q0 *= recipNorm;
mfurukawa 17:7a9459ac7469 203 q1 *= recipNorm;
mfurukawa 17:7a9459ac7469 204 q2 *= recipNorm;
mfurukawa 17:7a9459ac7469 205 q3 *= recipNorm;
mfurukawa 17:7a9459ac7469 206 }
mfurukawa 17:7a9459ac7469 207
mfurukawa 17:7a9459ac7469 208 //---------------------------------------------------------------------------------------------------
mfurukawa 17:7a9459ac7469 209 // Fast inverse square-root
mfurukawa 17:7a9459ac7469 210 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
mfurukawa 17:7a9459ac7469 211
mfurukawa 17:7a9459ac7469 212 float MadgwickAHRS::invSqrt(float x)
mfurukawa 17:7a9459ac7469 213 {
mfurukawa 17:7a9459ac7469 214 float halfx = 0.5f * x;
mfurukawa 17:7a9459ac7469 215 float y = x;
mfurukawa 17:7a9459ac7469 216 long i = *(long*)&y;
mfurukawa 17:7a9459ac7469 217 i = 0x5f3759df - (i>>1);
mfurukawa 17:7a9459ac7469 218 y = *(float*)&i;
mfurukawa 17:7a9459ac7469 219 y = y * (1.5f - (halfx * y * y));
mfurukawa 17:7a9459ac7469 220 return y;
mfurukawa 17:7a9459ac7469 221 }