Library version of MPU9250AHRS code.

Fork of MPU9250AHRS by Janek Mann

Committer:
janekm
Date:
Mon Sep 08 21:50:33 2014 +0000
Revision:
5:ea541d293095
Parent:
4:404c35f32ce3
N/A

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 5:ea541d293095 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 5:ea541d293095 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 5:ea541d293095 14 {
janekm 5:ea541d293095 15 float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability
janekm 5:ea541d293095 16 float norm;
janekm 5:ea541d293095 17 float hx, hy, _2bx, _2bz;
janekm 5:ea541d293095 18 float s1, s2, s3, s4;
janekm 5:ea541d293095 19 float qDot1, qDot2, qDot3, qDot4;
janekm 4:404c35f32ce3 20
janekm 5:ea541d293095 21 // Auxiliary variables to avoid repeated arithmetic
janekm 5:ea541d293095 22 float _2q1mx;
janekm 5:ea541d293095 23 float _2q1my;
janekm 5:ea541d293095 24 float _2q1mz;
janekm 5:ea541d293095 25 float _2q2mx;
janekm 5:ea541d293095 26 float _4bx;
janekm 5:ea541d293095 27 float _4bz;
janekm 5:ea541d293095 28 float _2q1 = 2.0f * q1;
janekm 5:ea541d293095 29 float _2q2 = 2.0f * q2;
janekm 5:ea541d293095 30 float _2q3 = 2.0f * q3;
janekm 5:ea541d293095 31 float _2q4 = 2.0f * q4;
janekm 5:ea541d293095 32 float _2q1q3 = 2.0f * q1 * q3;
janekm 5:ea541d293095 33 float _2q3q4 = 2.0f * q3 * q4;
janekm 5:ea541d293095 34 float q1q1 = q1 * q1;
janekm 5:ea541d293095 35 float q1q2 = q1 * q2;
janekm 5:ea541d293095 36 float q1q3 = q1 * q3;
janekm 5:ea541d293095 37 float q1q4 = q1 * q4;
janekm 5:ea541d293095 38 float q2q2 = q2 * q2;
janekm 5:ea541d293095 39 float q2q3 = q2 * q3;
janekm 5:ea541d293095 40 float q2q4 = q2 * q4;
janekm 5:ea541d293095 41 float q3q3 = q3 * q3;
janekm 5:ea541d293095 42 float q3q4 = q3 * q4;
janekm 5:ea541d293095 43 float q4q4 = q4 * q4;
janekm 4:404c35f32ce3 44
janekm 5:ea541d293095 45 // Normalise accelerometer measurement
janekm 5:ea541d293095 46 norm = sqrt(ax * ax + ay * ay + az * az);
janekm 5:ea541d293095 47 if (norm == 0.0f) return; // handle NaN
janekm 5:ea541d293095 48 norm = 1.0f/norm;
janekm 5:ea541d293095 49 ax *= norm;
janekm 5:ea541d293095 50 ay *= norm;
janekm 5:ea541d293095 51 az *= norm;
janekm 4:404c35f32ce3 52
janekm 5:ea541d293095 53 // Normalise magnetometer measurement
janekm 5:ea541d293095 54 norm = sqrt(mx * mx + my * my + mz * mz);
janekm 5:ea541d293095 55 if (norm == 0.0f) return; // handle NaN
janekm 5:ea541d293095 56 norm = 1.0f/norm;
janekm 5:ea541d293095 57 mx *= norm;
janekm 5:ea541d293095 58 my *= norm;
janekm 5:ea541d293095 59 mz *= norm;
janekm 4:404c35f32ce3 60
janekm 5:ea541d293095 61 // Reference direction of Earth's magnetic field
janekm 5:ea541d293095 62 _2q1mx = 2.0f * q1 * mx;
janekm 5:ea541d293095 63 _2q1my = 2.0f * q1 * my;
janekm 5:ea541d293095 64 _2q1mz = 2.0f * q1 * mz;
janekm 5:ea541d293095 65 _2q2mx = 2.0f * q2 * mx;
janekm 5:ea541d293095 66 hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
janekm 5:ea541d293095 67 hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
janekm 5:ea541d293095 68 _2bx = sqrt(hx * hx + hy * hy);
janekm 5:ea541d293095 69 _2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
janekm 5:ea541d293095 70 _4bx = 2.0f * _2bx;
janekm 5:ea541d293095 71 _4bz = 2.0f * _2bz;
janekm 4:404c35f32ce3 72
janekm 5:ea541d293095 73 // Gradient decent algorithm corrective step
janekm 5:ea541d293095 74 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 5:ea541d293095 75 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 5:ea541d293095 76 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 5:ea541d293095 77 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 5:ea541d293095 78 norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4); // normalise step magnitude
janekm 5:ea541d293095 79 norm = 1.0f/norm;
janekm 5:ea541d293095 80 s1 *= norm;
janekm 5:ea541d293095 81 s2 *= norm;
janekm 5:ea541d293095 82 s3 *= norm;
janekm 5:ea541d293095 83 s4 *= norm;
janekm 4:404c35f32ce3 84
janekm 5:ea541d293095 85 // Compute rate of change of quaternion
janekm 5:ea541d293095 86 qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
janekm 5:ea541d293095 87 qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
janekm 5:ea541d293095 88 qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
janekm 5:ea541d293095 89 qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;
janekm 4:404c35f32ce3 90
janekm 5:ea541d293095 91 // Integrate to yield quaternion
janekm 5:ea541d293095 92 q1 += qDot1 * deltat;
janekm 5:ea541d293095 93 q2 += qDot2 * deltat;
janekm 5:ea541d293095 94 q3 += qDot3 * deltat;
janekm 5:ea541d293095 95 q4 += qDot4 * deltat;
janekm 5:ea541d293095 96 norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4); // normalise quaternion
janekm 5:ea541d293095 97 norm = 1.0f/norm;
janekm 5:ea541d293095 98 q[0] = q1 * norm;
janekm 5:ea541d293095 99 q[1] = q2 * norm;
janekm 5:ea541d293095 100 q[2] = q3 * norm;
janekm 5:ea541d293095 101 q[3] = q4 * norm;
janekm 4:404c35f32ce3 102
janekm 4:404c35f32ce3 103 }
janekm 4:404c35f32ce3 104
janekm 4:404c35f32ce3 105
janekm 4:404c35f32ce3 106
janekm 4:404c35f32ce3 107 // Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
janekm 4:404c35f32ce3 108 // measured ones.
janekm 5:ea541d293095 109 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 5:ea541d293095 110 {
janekm 5:ea541d293095 111 float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3]; // short name local variable for readability
janekm 5:ea541d293095 112 float norm;
janekm 5:ea541d293095 113 float hx, hy, bx, bz;
janekm 5:ea541d293095 114 float vx, vy, vz, wx, wy, wz;
janekm 5:ea541d293095 115 float ex, ey, ez;
janekm 5:ea541d293095 116 float pa, pb, pc;
janekm 4:404c35f32ce3 117
janekm 5:ea541d293095 118 // Auxiliary variables to avoid repeated arithmetic
janekm 5:ea541d293095 119 float q1q1 = q1 * q1;
janekm 5:ea541d293095 120 float q1q2 = q1 * q2;
janekm 5:ea541d293095 121 float q1q3 = q1 * q3;
janekm 5:ea541d293095 122 float q1q4 = q1 * q4;
janekm 5:ea541d293095 123 float q2q2 = q2 * q2;
janekm 5:ea541d293095 124 float q2q3 = q2 * q3;
janekm 5:ea541d293095 125 float q2q4 = q2 * q4;
janekm 5:ea541d293095 126 float q3q3 = q3 * q3;
janekm 5:ea541d293095 127 float q3q4 = q3 * q4;
janekm 5:ea541d293095 128 float q4q4 = q4 * q4;
janekm 4:404c35f32ce3 129
janekm 5:ea541d293095 130 // Normalise accelerometer measurement
janekm 5:ea541d293095 131 norm = sqrt(ax * ax + ay * ay + az * az);
janekm 5:ea541d293095 132 if (norm == 0.0f) return; // handle NaN
janekm 5:ea541d293095 133 norm = 1.0f / norm; // use reciprocal for division
janekm 5:ea541d293095 134 ax *= norm;
janekm 5:ea541d293095 135 ay *= norm;
janekm 5:ea541d293095 136 az *= norm;
janekm 4:404c35f32ce3 137
janekm 5:ea541d293095 138 // Normalise magnetometer measurement
janekm 5:ea541d293095 139 norm = sqrt(mx * mx + my * my + mz * mz);
janekm 5:ea541d293095 140 if (norm == 0.0f) return; // handle NaN
janekm 5:ea541d293095 141 norm = 1.0f / norm; // use reciprocal for division
janekm 5:ea541d293095 142 mx *= norm;
janekm 5:ea541d293095 143 my *= norm;
janekm 5:ea541d293095 144 mz *= norm;
janekm 4:404c35f32ce3 145
janekm 5:ea541d293095 146 // Reference direction of Earth's magnetic field
janekm 5:ea541d293095 147 hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
janekm 5:ea541d293095 148 hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
janekm 5:ea541d293095 149 bx = sqrt((hx * hx) + (hy * hy));
janekm 5:ea541d293095 150 bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);
janekm 4:404c35f32ce3 151
janekm 5:ea541d293095 152 // Estimated direction of gravity and magnetic field
janekm 5:ea541d293095 153 vx = 2.0f * (q2q4 - q1q3);
janekm 5:ea541d293095 154 vy = 2.0f * (q1q2 + q3q4);
janekm 5:ea541d293095 155 vz = q1q1 - q2q2 - q3q3 + q4q4;
janekm 5:ea541d293095 156 wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
janekm 5:ea541d293095 157 wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
janekm 5:ea541d293095 158 wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);
janekm 4:404c35f32ce3 159
janekm 5:ea541d293095 160 // Error is cross product between estimated direction and measured direction of gravity
janekm 5:ea541d293095 161 ex = (ay * vz - az * vy) + (my * wz - mz * wy);
janekm 5:ea541d293095 162 ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
janekm 5:ea541d293095 163 ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
janekm 5:ea541d293095 164 if (Ki > 0.0f) {
janekm 5:ea541d293095 165 eInt[0] += ex; // accumulate integral error
janekm 5:ea541d293095 166 eInt[1] += ey;
janekm 5:ea541d293095 167 eInt[2] += ez;
janekm 5:ea541d293095 168 } else {
janekm 5:ea541d293095 169 eInt[0] = 0.0f; // prevent integral wind up
janekm 5:ea541d293095 170 eInt[1] = 0.0f;
janekm 5:ea541d293095 171 eInt[2] = 0.0f;
janekm 5:ea541d293095 172 }
janekm 4:404c35f32ce3 173
janekm 5:ea541d293095 174 // Apply feedback terms
janekm 5:ea541d293095 175 gx = gx + Kp * ex + Ki * eInt[0];
janekm 5:ea541d293095 176 gy = gy + Kp * ey + Ki * eInt[1];
janekm 5:ea541d293095 177 gz = gz + Kp * ez + Ki * eInt[2];
janekm 4:404c35f32ce3 178
janekm 5:ea541d293095 179 // Integrate rate of change of quaternion
janekm 5:ea541d293095 180 pa = q2;
janekm 5:ea541d293095 181 pb = q3;
janekm 5:ea541d293095 182 pc = q4;
janekm 5:ea541d293095 183 q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * deltat);
janekm 5:ea541d293095 184 q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * deltat);
janekm 5:ea541d293095 185 q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * deltat);
janekm 5:ea541d293095 186 q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * deltat);
janekm 4:404c35f32ce3 187
janekm 5:ea541d293095 188 // Normalise quaternion
janekm 5:ea541d293095 189 norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
janekm 5:ea541d293095 190 norm = 1.0f / norm;
janekm 5:ea541d293095 191 q[0] = q1 * norm;
janekm 5:ea541d293095 192 q[1] = q2 * norm;
janekm 5:ea541d293095 193 q[2] = q3 * norm;
janekm 5:ea541d293095 194 q[3] = q4 * norm;
janekm 5:ea541d293095 195 }