SensorFusion.cpp

//=============================================================================================
// SensorFusion.cpp
//=============================================================================================
//
// Madgwick's implementation of Mahony's AHRS algorithm.
// 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
// 23/11/2017   Aster94			Simplified time handling and melted in one library
//
// Algorithm paper:
// http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934
//
//=============================================================================================

//-------------------------------------------------------------------------------------------
// Header files

#include "SensorFusion.h" // SF
#include <math.h>
#include "Arduino.h"

//-------------------------------------------------------------------------------------------
// Definitions

#define betaDef     0.1f        	// 2 * proportional gain
#define twoKpDef	(2.0f * 0.5f)	// 2 * proportional gain
#define twoKiDef	(2.0f * 0.0f)	// 2 * integral gain

 
//============================================================================================
// Functions

SF::SF()
{
	beta = betaDef;		
	twoKp = twoKpDef;	
	twoKi = twoKiDef;	
	q0 = 1.0f;
	q1 = 0.0f;
	q2 = 0.0f;
	q3 = 0.0f;
	integralFBx = 0.0f;
	integralFBy = 0.0f;
	integralFBz = 0.0f;
	anglesComputed = 0;
}


// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
float SF::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;
}

//-------------------------------------------------------------------------------------------
void SF::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;
}



//============================================================================================
// Mahony AHRS algorithm update

void SF::MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat)
{
	float recipNorm;
	float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
	float hx, hy, bx, bz;
	float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
	float halfex, halfey, halfez;
	float qa, qb, qc;

	// Use IMU algorithm if magnetometer measurement invalid
	// (avoids NaN in magnetometer normalisation)
	if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
		MahonyUpdate(gx, gy, gz, ax, ay, az, deltat);
		return;
	}

	// 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
		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 = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
		hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
		bx = sqrtf(hx * hx + hy * hy);
		bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));

		// Estimated direction of gravity and magnetic field
		halfvx = q1q3 - q0q2;
		halfvy = q0q1 + q2q3;
		halfvz = q0q0 - 0.5f + q3q3;
		halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
		halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
		halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);

		// Error is sum of cross product between estimated direction
		// and measured direction of field vectors
		halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
		halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
		halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);

		// Compute and apply integral feedback if enabled
		if(twoKi > 0.0f) {
			// integral error scaled by Ki
			integralFBx += twoKi * halfex * deltat;
			integralFBy += twoKi * halfey * deltat;
			integralFBz += twoKi * halfez * deltat;
			gx += integralFBx;	// apply integral feedback
			gy += integralFBy;
			gz += integralFBz;
		} else {
			integralFBx = 0.0f;	// prevent integral windup
			integralFBy = 0.0f;
			integralFBz = 0.0f;
		}

		// Apply proportional feedback
		gx += twoKp * halfex;
		gy += twoKp * halfey;
		gz += twoKp * halfez;
	}

	// Integrate rate of change of quaternion
	gx *= (0.5f * deltat);		// pre-multiply common factors
	gy *= (0.5f * deltat);
	gz *= (0.5f * deltat);
	qa = q0;
	qb = q1;
	qc = q2;
	q0 += (-qb * gx - qc * gy - q3 * gz);
	q1 += (qa * gx + qc * gz - q3 * gy);
	q2 += (qa * gy - qb * gz + q3 * gx);
	q3 += (qa * gz + qb * gy - qc * gx);

	// Normalise quaternion
	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
	q0 *= recipNorm;
	q1 *= recipNorm;
	q2 *= recipNorm;
	q3 *= recipNorm;
	anglesComputed = 0;
}

//-------------------------------------------------------------------------------------------

void SF::MahonyUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat)
{
	float recipNorm;
	float halfvx, halfvy, halfvz;
	float halfex, halfey, halfez;
	float qa, qb, qc;

	// 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;

		// Estimated direction of gravity
		halfvx = q1 * q3 - q0 * q2;
		halfvy = q0 * q1 + q2 * q3;
		halfvz = q0 * q0 - 0.5f + q3 * q3;

		// Error is sum of cross product between estimated
		// and measured direction of gravity
		halfex = (ay * halfvz - az * halfvy);
		halfey = (az * halfvx - ax * halfvz);
		halfez = (ax * halfvy - ay * halfvx);

		// Compute and apply integral feedback if enabled
		if(twoKi > 0.0f) {
			// integral error scaled by Ki
			integralFBx += twoKi * halfex * deltat;
			integralFBy += twoKi * halfey * deltat;
			integralFBz += twoKi * halfez * deltat;
			gx += integralFBx;	// apply integral feedback
			gy += integralFBy;
			gz += integralFBz;
		} else {
			integralFBx = 0.0f;	// prevent integral windup
			integralFBy = 0.0f;
			integralFBz = 0.0f;
		}

		// Apply proportional feedback
		gx += twoKp * halfex;
		gy += twoKp * halfey;
		gz += twoKp * halfez;
	}

	// Integrate rate of change of quaternion
	gx *= (0.5f * deltat);		// pre-multiply common factors
	gy *= (0.5f * deltat);
	gz *= (0.5f * deltat);
	qa = q0;
	qb = q1;
	qc = q2;
	q0 += (-qb * gx - qc * gy - q3 * gz);
	q1 += (qa * gx + qc * gz - q3 * gy);
	q2 += (qa * gy - qb * gz + q3 * gx);
	q3 += (qa * gz + qb * gy - qc * gx);

	// Normalise quaternion
	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
	q0 *= recipNorm;
	q1 *= recipNorm;
	q2 *= recipNorm;
	q3 *= recipNorm;
	anglesComputed = 0;
}



//============================================================================================
// Madgwick AHRS algorithm update

void SF::MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz, float deltat) {
	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)) {
		MadgwickUpdate(gx, gy, gz, ax, ay, az, deltat);
		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 = 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 * deltat;
	q1 += qDot2 * deltat;
	q2 += qDot3 * deltat;
	q3 += qDot4 * deltat;

	// Normalise quaternion
	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
	q0 *= recipNorm;
	q1 *= recipNorm;
	q2 *= recipNorm;
	q3 *= recipNorm;
	anglesComputed = 0;
}

//-------------------------------------------------------------------------------------------

void SF::MadgwickUpdate(float gx, float gy, float gz, float ax, float ay, float az, float deltat) {
	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 * deltat;
	q1 += qDot2 * deltat;
	q2 += qDot3 * deltat;
	q3 += qDot4 * deltat;

	// Normalise quaternion
	recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
	q0 *= recipNorm;
	q1 *= recipNorm;
	q2 *= recipNorm;
	q3 *= recipNorm;
	anglesComputed = 0;
}


bool SF::initQuat(float ax, float ay, float az, float mx, float my, float mz){
    // Compute feedback only if accelerometer measurement valid
	// (avoids NaN in accelerometer normalisation)
	if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
		float recipNorm;
		float N[3], D[3], E[3]; //Global vectors North, Down, East relative to sensor
		
		// Down is negative accelerometer measurement
		recipNorm = invSqrt(ax * ax + ay * ay + az * az);
		D[0] = - ax * recipNorm;
		D[1] = - ay * recipNorm;
		D[2] = - az * recipNorm;
		
		// Magnetometer is not exatly perpendicular to Down, therefor not exatly North
		// we will calculate North later
		float m[3];
		recipNorm = invSqrt(mx * mx + my * my + mz * mz);
		m[0] = mx * recipNorm;
		m[1] = mx * recipNorm;
		m[2] = mx * recipNorm;
        
		// Calculate East
		vectorCross(m, D, E);
		recipNorm = invSqrt(E[0] * E[0] + E[1] * E[1] + E[2] * E[2]);
		E[0] *= recipNorm;
		E[1] *= recipNorm;
		E[2] *= recipNorm;
		
		// Calculate North
		vectorCross(D, E, N);
		
		// Calculate Euler Parameter (quaternion) from the rotation matrix A=(N|D|E).
		// Using Shepperd algorithm (Woernle 2011)
		float Trace = N[0] + D[1] + E[2];
		float a[4] = {Trace, N[0], D[1], E[2]};
		float e[4];
		
		//find index of Largest Euler parameter
		int k=0;
		for (int i=1; i<4; i++){
			if (a[i] > a[k])
				k = i;
		}
		//calculate that parameter
		e[k] = sqrt(1 + 2 * a[k] - Trace)/2;
		
		switch (k){
			case 0:
				e[1] = (D[2] - E[1]) / (4 * e[0]);
				e[2] = (E[0] - N[2]) / (4 * e[0]);
				e[3] = (N[1] - D[0]) / (4 * e[0]);
				break;
			case 1:
				e[0] = (D[2] - E[1]) / (4 * e[1]);
				e[2] = (D[0] + N[1]) / (4 * e[1]);
				e[3] = (E[0] + N[2]) / (4 * e[1]);
				break;
			case 2:
				e[0] = (E[0] - N[2]) / (4 * e[2]);
				e[1] = (D[0] + N[1]) / (4 * e[2]);
				e[3] = (E[1] + D[2]) / (4 * e[2]);
				break;
			case 3:
				e[0] = (N[1] - D[0]) / (4 * e[3]);
				e[1] = (E[0] + N[2]) / (4 * e[3]);
				e[2] = (E[1] + D[2]) / (4 * e[3]);
		}
		
		// invert the quaternion rotation
		// we calculated the rotation of Global NDE relative to the sensor 
		// but we need the rotation of the Sensor relative to NDE
		q0 = e[0];
		q1 = -e[1];
		q2 = -e[2];
		q3 = -e[3];
		
		return true;
	} else return false;
}

void SF::vectorCross(float A[3], float B[3], float cross[3])
{
	cross[0] = A[1] * B[2] - A[2] * B[1];
	cross[1] = A[2] * B[0] - A[0] * B[2];
	cross[2] = A[0] * B[1] - A[1] * B[0];
}


//============================================================================================
// END OF CODE
//============================================================================================