2 * Copyright (c) 2014, Olivier MATZ <zer0@droids-corp.org>
3 * Copyright (c) 2011-2012, SOH Madgwick
5 * This program is free software: you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation, either version 3 of the License, or
8 * (at your option) any later version.
10 * This program is distributed in the hope that it will be useful,
11 * but WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 * GNU General Public License for more details.
15 * You should have received a copy of the GNU General Public License
16 * along with this program. If not, see <http://www.gnu.org/licenses/>.
20 //============================================================================
22 //============================================================================
24 // Implementation of Madgwick's IMU and AHRS algorithms.
25 // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
28 // 29/09/2011 SOH Madgwick Initial release
29 // 02/10/2011 SOH Madgwick Optimised for reduced CPU load
30 // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
32 //============================================================================
34 #include "MadgwickAHRS.h"
37 /* in Hz, must be synchronized with imu.c callback */
38 #define sampleFreq 50.0f
39 #define betaDef 0.1f // 2 * proportional gain
41 static float invSqrt(float x)
43 return 1.0f / sqrtf(x);
46 /* AHRS algorithm update */
47 void MadgwickAHRSupdate(const struct imu_info *imu, struct quaternion *quat)
51 float qDot1, qDot2, qDot3, qDot4;
53 float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz;
54 float _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3;
55 float q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
56 float mx, my, mz, ax, ay, az, gx, gy, gz;
59 /* Use IMU algorithm if magnetometer measurement invalid (avoids NaN in
60 * magnetometer normalisation) */
61 //if ((imu->mx == 0.0f) && (imu->my == 0.0f) && (imu->mz == 0.0f)) {
63 MadgwickAHRSupdateIMU(imu, quat);
67 /* use local variables, it's more readable */
68 q0 = quat->q0; q1 = quat->q1; q2 = quat->q2; q3 = quat->q3;
69 gx = imu->gx; gy = imu->gy; gz = imu->gz;
70 ax = imu->ax; ay = imu->ay; az = imu->az;
71 mx = imu->mx; my = imu->my; mz = imu->mz;
73 /* Rate of change of quaternion from gyroscope */
74 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
75 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
76 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
77 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
79 /* Compute feedback only if accelerometer measurement valid (avoids NaN
80 * in accelerometer normalisation) */
81 if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
83 /* Normalise accelerometer measurement */
84 recipNorm = invSqrt(ax * ax + ay * ay +
90 /* Normalise magnetometer measurement */
91 recipNorm = invSqrt(mx * mx + my * my +
97 /* Auxiliary variables to avoid repeated arithmetic */
98 _2q0mx = 2.0f * q0 * mx;
99 _2q0my = 2.0f * q0 * my;
100 _2q0mz = 2.0f * q0 * mz;
101 _2q1mx = 2.0f * q1 * mx;
106 _2q0q2 = 2.0f * q0 * q2;
107 _2q2q3 = 2.0f * q2 * q3;
119 /* Reference direction of Earth's magnetic field */
120 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
121 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
122 _2bx = sqrt(hx * hx + hy * hy);
123 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
127 /* Gradient decent algorithm corrective step */
128 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);
129 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);
130 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);
131 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);
133 /* normalize step magnitude */
134 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3);
140 /* Apply feedback step */
141 qDot1 -= betaDef * s0;
142 qDot2 -= betaDef * s1;
143 qDot3 -= betaDef * s2;
144 qDot4 -= betaDef * s3;
147 /* Integrate rate of change of quaternion to yield quaternion */
148 q0 += qDot1 * (1.0f / sampleFreq);
149 q1 += qDot2 * (1.0f / sampleFreq);
150 q2 += qDot3 * (1.0f / sampleFreq);
151 q3 += qDot4 * (1.0f / sampleFreq);
153 /* Normalise quaternion */
154 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
160 /* update quaternion in structure */
167 /* IMU algorithm update (does not take magneto in account) */
168 void MadgwickAHRSupdateIMU(const struct imu_info *imu, struct quaternion *quat)
171 float s0, s1, s2, s3;
172 float qDot1, qDot2, qDot3, qDot4;
173 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
174 float ax, ay, az, gx, gy, gz;
175 float q0, q1, q2, q3;
177 /* use local variables, it's more readable */
178 q0 = quat->q0; q1 = quat->q1; q2 = quat->q2; q3 = quat->q3;
179 gx = imu->gx; gy = imu->gy; gz = imu->gz;
180 ax = imu->ax; ay = imu->ay; az = imu->az;
182 /* Rate of change of quaternion from gyroscope */
183 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
184 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
185 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
186 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
189 /* Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) */
190 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
192 /* Normalise accelerometer measurement */
193 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
198 /* Auxiliary variables to avoid repeated arithmetic */
213 /* Gradient decent algorithm corrective step */
214 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
215 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
216 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
217 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
218 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); /* normalise step magnitude */
225 /* Apply feedback step */
226 qDot1 -= betaDef * s0;
227 qDot2 -= betaDef * s1;
228 qDot3 -= betaDef * s2;
229 qDot4 -= betaDef * s3;
232 /* Integrate rate of change of quaternion to yield quaternion */
233 q0 += qDot1 * (1.0f / sampleFreq);
234 q1 += qDot2 * (1.0f / sampleFreq);
235 q2 += qDot3 * (1.0f / sampleFreq);
236 q3 += qDot4 * (1.0f / sampleFreq);
238 /* Normalise quaternion */
239 recipNorm = invSqrt(q0 * q0 + q1 * q1 +
246 /* update quaternion in structure */