Revision 0:0c61d7209f75, committed 2016-05-30

Comitter:

Decimus

Date:

Mon May 30 08:10:20 2016 +0000

Commit message:

[+]

Changed in this revision

diff -r 000000000000 -r 0c61d7209f75 MadgwickAHRS.cpp
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MadgwickAHRS.cpp	Mon May 30 08:10:20 2016 +0000
@@ -0,0 +1,244 @@
+
+// MadgwickAHRS.c
+//=====================================================================================================
+//
+// Implementation of Madgwick's IMU and AHRS algorithms.
+// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
+//
+// 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
+//
+//=====================================================================================================
+
+//---------------------------------------------------------------------------------------------------
+// Header files
+
+#include "MadgwickAHRS.h"
+#include <math.h>
+
+//---------------------------------------------------------------------------------------------------
+// Definitions
+
+#define sampleFreq	512.0f		// sample frequency in Hz
+#define betaDef		0.1f		// 2 * proportional gain
+
+//---------------------------------------------------------------------------------------------------
+// Variable definitions
+
+volatile float beta = betaDef;								// 2 * proportional gain (Kp)
+volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f;	// quaternion of sensor frame relative to auxiliary frame
+//volatile float quat[4];
+
+//====================================================================================================
+// Functions
+
+//---------------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+void MadgwickAHRSupdate(float tdelta, 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)) {
+		MadgwickAHRSupdateIMU( tdelta, gx, gy, gz, ax, ay, az);
+		return;
+	}
+
+	// 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 = sqrt(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 * tdelta;
+	q1 += qDot2 * tdelta;
+	q2 += qDot3 * tdelta;
+	q3 += qDot4 * tdelta;
+
+	// Normalise quaternion
+	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+	q0 *= recipNorm;
+	q1 *= recipNorm;
+	q2 *= recipNorm;
+	q3 *= recipNorm;
+}
+
+//---------------------------------------------------------------------------------------------------
+// IMU algorithm update
+
+void MadgwickAHRSupdateIMU(float tdelta, 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;
+
+	// 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 * tdelta;
+	q1 += qDot2 * tdelta;
+	q2 += qDot3 * tdelta;
+	q3 += qDot4 * tdelta;
+
+	// Normalise quaternion
+	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+	q0 *= recipNorm;
+	q1 *= recipNorm;
+	q2 *= recipNorm;
+	q3 *= recipNorm;
+    //quat[0] = q0;
+    //quat[1] = q1;
+    //quat[2] = q2;
+    //quat[3] = q3;
+}
+
+
+int instability_fix = 1;
+
+//---------------------------------------------------------------------------------------------------
+// Fast inverse square-root
+// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
+
+float invSqrt(float x) {
+	if (instability_fix == 0)
+	{
+		/* original code */
+		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));
+		return y;
+	}
+	else if (instability_fix == 1)
+	{
+		/* close-to-optimal  method with low cost from http://pizer.wordpress.com/2008/10/12/fast-inverse-square-root */
+		unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
+		float tmp = *(float*)&i;
+		return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
+	}
+	else
+	{
+		/* optimal but expensive method: */
+		return 1.0f / sqrtf(x);
+	}
+}
+
+//====================================================================================================
+// END OF CODE
+//====================================================================================================
\ No newline at end of file

diff -r 000000000000 -r 0c61d7209f75 MadgwickAHRS.h
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MadgwickAHRS.h	Mon May 30 08:10:20 2016 +0000
@@ -0,0 +1,33 @@
+// MadgwickAHRS.h
+//=====================================================================================================
+//
+// Implementation of Madgwick's IMU and AHRS algorithms.
+// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
+//
+// Date			Author          Notes
+// 29/09/2011	SOH Madgwick    Initial release
+// 02/10/2011	SOH Madgwick	Optimised for reduced CPU load
+//
+//=====================================================================================================
+#ifndef MadgwickAHRS_h
+#define MadgwickAHRS_h
+
+//----------------------------------------------------------------------------------------------------
+// Variable declaration
+extern int instability_fix;
+extern volatile float beta;				// algorithm gain
+extern volatile float q0, q1, q2, q3;	// quaternion of sensor frame relative to auxiliary frame
+
+//extern volatile float quat[4];
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+void MadgwickAHRSupdate(float tdelta, float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
+void MadgwickAHRSupdateIMU(float tdelta, float gx, float gy, float gz, float ax, float ay, float az);
+float invSqrt(float x);
+
+#endif
+//=====================================================================================================
+// End of file
+//=====================================================================================================