Janek Mann / MPU9250AHRS-cleaned

Library version of MPU9250AHRS code.

Fork of MPU9250AHRS by Janek Mann

AHRS.c@4:404c35f32ce3, 2014-09-04 (annotated)

Committer:
janekm
Date:
Thu Sep 04 21:19:05 2014 +0000
Revision:
4:404c35f32ce3
Child:
5:ea541d293095
turning it into more of a library...

Who changed what in which revision?

UserRevisionLine numberNew contents of line
janekm 4:404c35f32ce3 1 #include "AHRS.h"
janekm 4:404c35f32ce3 2 #include "math.h"
janekm 4:404c35f32ce3 3
janekm 4:404c35f32ce3 4 static float eInt[3] = {0.0f, 0.0f, 0.0f};
janekm 4:404c35f32ce3 5
janekm 4:404c35f32ce3 6 // Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
janekm 4:404c35f32ce3 7 // (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
janekm 4:404c35f32ce3 8 // which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
janekm 4:404c35f32ce3 9 // device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
janekm 4:404c35f32ce3 10 // The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
janekm 4:404c35f32ce3 11 // but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
janekm 4:404c35f32ce3 12
janekm 4:404c35f32ce3 13 void MadgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat, float *q, float beta) {
janekm 4:404c35f32ce3 14 float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability
janekm 4:404c35f32ce3 15 float norm;
janekm 4:404c35f32ce3 16 float hx, hy, _2bx, _2bz;
janekm 4:404c35f32ce3 17 float s1, s2, s3, s4;
janekm 4:404c35f32ce3 18 float qDot1, qDot2, qDot3, qDot4;
janekm 4:404c35f32ce3 19
janekm 4:404c35f32ce3 20 // Auxiliary variables to avoid repeated arithmetic
janekm 4:404c35f32ce3 21 float _2q1mx;
janekm 4:404c35f32ce3 22 float _2q1my;
janekm 4:404c35f32ce3 23 float _2q1mz;
janekm 4:404c35f32ce3 24 float _2q2mx;
janekm 4:404c35f32ce3 25 float _4bx;
janekm 4:404c35f32ce3 26 float _4bz;
janekm 4:404c35f32ce3 27 float _2q1 = 2.0f * q1;
janekm 4:404c35f32ce3 28 float _2q2 = 2.0f * q2;
janekm 4:404c35f32ce3 29 float _2q3 = 2.0f * q3;
janekm 4:404c35f32ce3 30 float _2q4 = 2.0f * q4;
janekm 4:404c35f32ce3 31 float _2q1q3 = 2.0f * q1 * q3;
janekm 4:404c35f32ce3 32 float _2q3q4 = 2.0f * q3 * q4;
janekm 4:404c35f32ce3 33 float q1q1 = q1 * q1;
janekm 4:404c35f32ce3 34 float q1q2 = q1 * q2;
janekm 4:404c35f32ce3 35 float q1q3 = q1 * q3;
janekm 4:404c35f32ce3 36 float q1q4 = q1 * q4;
janekm 4:404c35f32ce3 37 float q2q2 = q2 * q2;
janekm 4:404c35f32ce3 38 float q2q3 = q2 * q3;
janekm 4:404c35f32ce3 39 float q2q4 = q2 * q4;
janekm 4:404c35f32ce3 40 float q3q3 = q3 * q3;
janekm 4:404c35f32ce3 41 float q3q4 = q3 * q4;
janekm 4:404c35f32ce3 42 float q4q4 = q4 * q4;
janekm 4:404c35f32ce3 43
janekm 4:404c35f32ce3 44 // Normalise accelerometer measurement
janekm 4:404c35f32ce3 45 norm = sqrt(ax * ax + ay * ay + az * az);
janekm 4:404c35f32ce3 46 if (norm == 0.0f) return; // handle NaN
janekm 4:404c35f32ce3 47 norm = 1.0f/norm;
janekm 4:404c35f32ce3 48 ax *= norm;
janekm 4:404c35f32ce3 49 ay *= norm;
janekm 4:404c35f32ce3 50 az *= norm;
janekm 4:404c35f32ce3 51
janekm 4:404c35f32ce3 52 // Normalise magnetometer measurement
janekm 4:404c35f32ce3 53 norm = sqrt(mx * mx + my * my + mz * mz);
janekm 4:404c35f32ce3 54 if (norm == 0.0f) return; // handle NaN
janekm 4:404c35f32ce3 55 norm = 1.0f/norm;
janekm 4:404c35f32ce3 56 mx *= norm;
janekm 4:404c35f32ce3 57 my *= norm;
janekm 4:404c35f32ce3 58 mz *= norm;
janekm 4:404c35f32ce3 59
janekm 4:404c35f32ce3 60 // Reference direction of Earth's magnetic field
janekm 4:404c35f32ce3 61 _2q1mx = 2.0f * q1 * mx;
janekm 4:404c35f32ce3 62 _2q1my = 2.0f * q1 * my;
janekm 4:404c35f32ce3 63 _2q1mz = 2.0f * q1 * mz;
janekm 4:404c35f32ce3 64 _2q2mx = 2.0f * q2 * mx;
janekm 4:404c35f32ce3 65 hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
janekm 4:404c35f32ce3 66 hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
janekm 4:404c35f32ce3 67 _2bx = sqrt(hx * hx + hy * hy);
janekm 4:404c35f32ce3 68 _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
janekm 4:404c35f32ce3 69 _4bx = 2.0f * _2bx;
janekm 4:404c35f32ce3 70 _4bz = 2.0f * _2bz;
janekm 4:404c35f32ce3 71
janekm 4:404c35f32ce3 72 // Gradient decent algorithm corrective step
janekm 4:404c35f32ce3 73 s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
janekm 4:404c35f32ce3 74 s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
janekm 4:404c35f32ce3 75 s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
janekm 4:404c35f32ce3 76 s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
janekm 4:404c35f32ce3 77 norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4); // normalise step magnitude
janekm 4:404c35f32ce3 78 norm = 1.0f/norm;
janekm 4:404c35f32ce3 79 s1 *= norm;
janekm 4:404c35f32ce3 80 s2 *= norm;
janekm 4:404c35f32ce3 81 s3 *= norm;
janekm 4:404c35f32ce3 82 s4 *= norm;
janekm 4:404c35f32ce3 83
janekm 4:404c35f32ce3 84 // Compute rate of change of quaternion
janekm 4:404c35f32ce3 85 qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
janekm 4:404c35f32ce3 86 qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
janekm 4:404c35f32ce3 87 qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
janekm 4:404c35f32ce3 88 qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
janekm 4:404c35f32ce3 89
janekm 4:404c35f32ce3 90 // Integrate to yield quaternion
janekm 4:404c35f32ce3 91 q1 += qDot1 * deltat;
janekm 4:404c35f32ce3 92 q2 += qDot2 * deltat;
janekm 4:404c35f32ce3 93 q3 += qDot3 * deltat;
janekm 4:404c35f32ce3 94 q4 += qDot4 * deltat;
janekm 4:404c35f32ce3 95 norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion
janekm 4:404c35f32ce3 96 norm = 1.0f/norm;
janekm 4:404c35f32ce3 97 q[0] = q1 * norm;
janekm 4:404c35f32ce3 98 q[1] = q2 * norm;
janekm 4:404c35f32ce3 99 q[2] = q3 * norm;
janekm 4:404c35f32ce3 100 q[3] = q4 * norm;
janekm 4:404c35f32ce3 101
janekm 4:404c35f32ce3 102 }
janekm 4:404c35f32ce3 103
janekm 4:404c35f32ce3 104
janekm 4:404c35f32ce3 105
janekm 4:404c35f32ce3 106 // Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
janekm 4:404c35f32ce3 107 // measured ones.
janekm 4:404c35f32ce3 108 void MahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz, float deltat, float *q) {
janekm 4:404c35f32ce3 109 float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability
janekm 4:404c35f32ce3 110 float norm;
janekm 4:404c35f32ce3 111 float hx, hy, bx, bz;
janekm 4:404c35f32ce3 112 float vx, vy, vz, wx, wy, wz;
janekm 4:404c35f32ce3 113 float ex, ey, ez;
janekm 4:404c35f32ce3 114 float pa, pb, pc;
janekm 4:404c35f32ce3 115
janekm 4:404c35f32ce3 116 // Auxiliary variables to avoid repeated arithmetic
janekm 4:404c35f32ce3 117 float q1q1 = q1 * q1;
janekm 4:404c35f32ce3 118 float q1q2 = q1 * q2;
janekm 4:404c35f32ce3 119 float q1q3 = q1 * q3;
janekm 4:404c35f32ce3 120 float q1q4 = q1 * q4;
janekm 4:404c35f32ce3 121 float q2q2 = q2 * q2;
janekm 4:404c35f32ce3 122 float q2q3 = q2 * q3;
janekm 4:404c35f32ce3 123 float q2q4 = q2 * q4;
janekm 4:404c35f32ce3 124 float q3q3 = q3 * q3;
janekm 4:404c35f32ce3 125 float q3q4 = q3 * q4;
janekm 4:404c35f32ce3 126 float q4q4 = q4 * q4;
janekm 4:404c35f32ce3 127
janekm 4:404c35f32ce3 128 // Normalise accelerometer measurement
janekm 4:404c35f32ce3 129 norm = sqrt(ax * ax + ay * ay + az * az);
janekm 4:404c35f32ce3 130 if (norm == 0.0f) return; // handle NaN
janekm 4:404c35f32ce3 131 norm = 1.0f / norm; // use reciprocal for division
janekm 4:404c35f32ce3 132 ax *= norm;
janekm 4:404c35f32ce3 133 ay *= norm;
janekm 4:404c35f32ce3 134 az *= norm;
janekm 4:404c35f32ce3 135
janekm 4:404c35f32ce3 136 // Normalise magnetometer measurement
janekm 4:404c35f32ce3 137 norm = sqrt(mx * mx + my * my + mz * mz);
janekm 4:404c35f32ce3 138 if (norm == 0.0f) return; // handle NaN
janekm 4:404c35f32ce3 139 norm = 1.0f / norm; // use reciprocal for division
janekm 4:404c35f32ce3 140 mx *= norm;
janekm 4:404c35f32ce3 141 my *= norm;
janekm 4:404c35f32ce3 142 mz *= norm;
janekm 4:404c35f32ce3 143
janekm 4:404c35f32ce3 144 // Reference direction of Earth's magnetic field
janekm 4:404c35f32ce3 145 hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
janekm 4:404c35f32ce3 146 hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
janekm 4:404c35f32ce3 147 bx = sqrt((hx * hx) + (hy * hy));
janekm 4:404c35f32ce3 148 bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
janekm 4:404c35f32ce3 149
janekm 4:404c35f32ce3 150 // Estimated direction of gravity and magnetic field
janekm 4:404c35f32ce3 151 vx = 2.0f * (q2q4 - q1q3);
janekm 4:404c35f32ce3 152 vy = 2.0f * (q1q2 + q3q4);
janekm 4:404c35f32ce3 153 vz = q1q1 - q2q2 - q3q3 + q4q4;
janekm 4:404c35f32ce3 154 wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
janekm 4:404c35f32ce3 155 wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
janekm 4:404c35f32ce3 156 wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);
janekm 4:404c35f32ce3 157
janekm 4:404c35f32ce3 158 // Error is cross product between estimated direction and measured direction of gravity
janekm 4:404c35f32ce3 159 ex = (ay * vz - az * vy) + (my * wz - mz * wy);
janekm 4:404c35f32ce3 160 ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
janekm 4:404c35f32ce3 161 ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
janekm 4:404c35f32ce3 162 if (Ki > 0.0f) {
janekm 4:404c35f32ce3 163 eInt[0] += ex; // accumulate integral error
janekm 4:404c35f32ce3 164 eInt[1] += ey;
janekm 4:404c35f32ce3 165 eInt[2] += ez;
janekm 4:404c35f32ce3 166 } else {
janekm 4:404c35f32ce3 167 eInt[0] = 0.0f; // prevent integral wind up
janekm 4:404c35f32ce3 168 eInt[1] = 0.0f;
janekm 4:404c35f32ce3 169 eInt[2] = 0.0f;
janekm 4:404c35f32ce3 170 }
janekm 4:404c35f32ce3 171
janekm 4:404c35f32ce3 172 // Apply feedback terms
janekm 4:404c35f32ce3 173 gx = gx + Kp * ex + Ki * eInt[0];
janekm 4:404c35f32ce3 174 gy = gy + Kp * ey + Ki * eInt[1];
janekm 4:404c35f32ce3 175 gz = gz + Kp * ez + Ki * eInt[2];
janekm 4:404c35f32ce3 176
janekm 4:404c35f32ce3 177 // Integrate rate of change of quaternion
janekm 4:404c35f32ce3 178 pa = q2;
janekm 4:404c35f32ce3 179 pb = q3;
janekm 4:404c35f32ce3 180 pc = q4;
janekm 4:404c35f32ce3 181 q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
janekm 4:404c35f32ce3 182 q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
janekm 4:404c35f32ce3 183 q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
janekm 4:404c35f32ce3 184 q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
janekm 4:404c35f32ce3 185
janekm 4:404c35f32ce3 186 // Normalise quaternion
janekm 4:404c35f32ce3 187 norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
janekm 4:404c35f32ce3 188 norm = 1.0f / norm;
janekm 4:404c35f32ce3 189 q[0] = q1 * norm;
janekm 4:404c35f32ce3 190 q[1] = q2 * norm;
janekm 4:404c35f32ce3 191 q[2] = q3 * norm;
janekm 4:404c35f32ce3 192 q[3] = q4 * norm;
janekm 4:404c35f32ce3 193
janekm 4:404c35f32ce3 194 }