Erik van de Coevering
Library implementing Madgwick's IMU and AHRS algorithms
Dependents: Hexi_GPSIMU_Hotshoe
Diff: MadgwickAHRS.cpp
- Revision:
- 0:9b434b5e28d4
- Child:
- 1:d7c70d593694
diff -r 000000000000 -r 9b434b5e28d4 MadgwickAHRS.cpp
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/MadgwickAHRS.cpp Sun Dec 18 21:50:15 2016 +0000
@@ -0,0 +1,257 @@
+//=============================================================================================
+// MadgwickAHRS.c
+//=============================================================================================
+//
+// Implementation of Madgwick's IMU and AHRS algorithms.
+// See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
+//
+// From the x-io website "Open-source resources available on this website are
+// provided under the GNU General Public Licence unless an alternative licence
+// is provided in source."
+//
+// Date Author Notes
+// 29/09/2011 SOH Madgwick Initial release
+// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
+// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
+// 18/12/2016 Added better fast inverse square root
+//
+//=============================================================================================
+
+//-------------------------------------------------------------------------------------------
+// Header files
+
+#include "MadgwickAHRS.h"
+#include <math.h>
+
+//-------------------------------------------------------------------------------------------
+// Definitions
+
+#define sampleFreqDef 500.0f // sample frequency in Hz
+#define betaDef 0.75f // 2 * proportional gain 0.1 - 0.5 - 5
+
+
+//============================================================================================
+// Functions
+
+//-------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+Madgwick::Madgwick() {
+ beta = betaDef;
+ q0 = 1.0f;
+ q1 = 0.0f;
+ q2 = 0.0f;
+ q3 = 0.0f;
+ invSampleFreq = 1.0f / sampleFreqDef;
+ anglesComputed = 0;
+}
+
+void Madgwick::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
+ float recipNorm;
+ float s0, s1, s2, s3;
+ float qDot1, qDot2, qDot3, qDot4;
+ float hx, hy;
+ 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;
+
+ // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
+ if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
+ updateIMU(gx, gy, gz, ax, ay, az);
+ return;
+ }
+
+ // Convert gyroscope degrees/sec to radians/sec
+ gx *= 0.0174533f;
+ gy *= 0.0174533f;
+ gz *= 0.0174533f;
+
+ // Rate of change of quaternion from gyroscope
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
+
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+ // Normalise accelerometer measurement
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+ ax *= recipNorm;
+ ay *= recipNorm;
+ az *= recipNorm;
+
+ // Normalise magnetometer measurement
+ recipNorm = invSqrt(mx * mx + my * my + mz * mz);
+ mx *= recipNorm;
+ my *= recipNorm;
+ mz *= recipNorm;
+
+ // Auxiliary variables to avoid repeated arithmetic
+ _2q0mx = 2.0f * q0 * mx;
+ _2q0my = 2.0f * q0 * my;
+ _2q0mz = 2.0f * q0 * mz;
+ _2q1mx = 2.0f * q1 * mx;
+ _2q0 = 2.0f * q0;
+ _2q1 = 2.0f * q1;
+ _2q2 = 2.0f * q2;
+ _2q3 = 2.0f * q3;
+ _2q0q2 = 2.0f * q0 * q2;
+ _2q2q3 = 2.0f * q2 * q3;
+ q0q0 = q0 * q0;
+ q0q1 = q0 * q1;
+ q0q2 = q0 * q2;
+ q0q3 = q0 * q3;
+ q1q1 = q1 * q1;
+ q1q2 = q1 * q2;
+ q1q3 = q1 * q3;
+ q2q2 = q2 * q2;
+ q2q3 = q2 * q3;
+ q3q3 = q3 * q3;
+
+ // Reference direction of Earth's magnetic field
+ hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
+ hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
+ _2bx = sqrtf(hx * hx + hy * hy);
+ _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
+ _4bx = 2.0f * _2bx;
+ _4bz = 2.0f * _2bz;
+
+ // Gradient decent algorithm corrective step
+ 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);
+ 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);
+ 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);
+ 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);
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
+ s0 *= recipNorm;
+ s1 *= recipNorm;
+ s2 *= recipNorm;
+ s3 *= recipNorm;
+
+ // Apply feedback step
+ qDot1 -= beta * s0;
+ qDot2 -= beta * s1;
+ qDot3 -= beta * s2;
+ qDot4 -= beta * s3;
+ }
+
+ // Integrate rate of change of quaternion to yield quaternion
+ q0 += qDot1 * invSampleFreq;
+ q1 += qDot2 * invSampleFreq;
+ q2 += qDot3 * invSampleFreq;
+ q3 += qDot4 * invSampleFreq;
+
+ // Normalise quaternion
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+ anglesComputed = 0;
+}
+
+//-------------------------------------------------------------------------------------------
+// IMU algorithm update
+
+void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
+ float recipNorm;
+ float s0, s1, s2, s3;
+ float qDot1, qDot2, qDot3, qDot4;
+ float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
+
+ // Convert gyroscope degrees/sec to radians/sec
+ gx *= 0.0174533f;
+ gy *= 0.0174533f;
+ gz *= 0.0174533f;
+
+ // Rate of change of quaternion from gyroscope
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
+
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+ // Normalise accelerometer measurement
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+ ax *= recipNorm;
+ ay *= recipNorm;
+ az *= recipNorm;
+
+ // Auxiliary variables to avoid repeated arithmetic
+ _2q0 = 2.0f * q0;
+ _2q1 = 2.0f * q1;
+ _2q2 = 2.0f * q2;
+ _2q3 = 2.0f * q3;
+ _4q0 = 4.0f * q0;
+ _4q1 = 4.0f * q1;
+ _4q2 = 4.0f * q2;
+ _8q1 = 8.0f * q1;
+ _8q2 = 8.0f * q2;
+ q0q0 = q0 * q0;
+ q1q1 = q1 * q1;
+ q2q2 = q2 * q2;
+ q3q3 = q3 * q3;
+
+ // Gradient decent algorithm corrective step
+ s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
+ s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
+ s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
+ s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
+ s0 *= recipNorm;
+ s1 *= recipNorm;
+ s2 *= recipNorm;
+ s3 *= recipNorm;
+
+ // Apply feedback step
+ qDot1 -= beta * s0;
+ qDot2 -= beta * s1;
+ qDot3 -= beta * s2;
+ qDot4 -= beta * s3;
+ }
+
+ // Integrate rate of change of quaternion to yield quaternion
+ q0 += qDot1 * invSampleFreq;
+ q1 += qDot2 * invSampleFreq;
+ q2 += qDot3 * invSampleFreq;
+ q3 += qDot4 * invSampleFreq;
+
+ // Normalise quaternion
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+ anglesComputed = 0;
+}
+
+//-------------------------------------------------------------------------------------------
+// Fast inverse square-root
+// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
+
+/*float Madgwick::invSqrt(float x) {
+ float halfx = 0.5f * x;
+ float y = x;
+ long i = *(long*)&y;
+ i = 0x5f3759df - (i>>1);
+ y = *(float*)&i;
+ y = y * (1.5f - (halfx * y * y));
+ y = y * (1.5f - (halfx * y * y));
+ return y;
+} */
+
+float Madgwick::invSqrt(float x){
+ unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
+ float tmp = *(float*)&i;
+ return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
+}
+
+//-------------------------------------------------------------------------------------------
+
+void Madgwick::computeAngles()
+{
+ roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
+ pitch = asinf(-2.0f * (q1*q3 - q0*q2));
+ yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
+ anglesComputed = 1;
+}
\ No newline at end of file