mahony.c

//==============================================================================================
// MahonyAHRS.c
//==============================================================================================
//
// Madgwick's implementation of Mayhony'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
//
// 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
//
//==============================================================================================

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

#include "imuread.h"

#ifdef USE_MAHONY_FUSION

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

#define twoKpDef	(2.0f * 0.02f)	// 2 * proportional gain
#define twoKiDef	(2.0f * 0.0f)	// 2 * integral gain

#define INV_SAMPLE_RATE  (1.0f / SENSORFS)

//----------------------------------------------------------------------------------------------
// Variable definitions

static float twoKp = twoKpDef;		// 2 * proportional gain (Kp)
static float twoKi = twoKiDef;		// 2 * integral gain (Ki)
static float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
static float integralFBx = 0.0f,  integralFBy = 0.0f, integralFBz = 0.0f; // integral error terms scaled by Ki


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

static float invSqrt(float x);
static void mahony_init();
static void mahony_update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
void mahony_updateIMU(float gx, float gy, float gz, float ax, float ay, float az);

static int reset_next_update=0;


void fusion_init(void)
{
	mahony_init();
}

void fusion_update(const AccelSensor_t *Accel, const MagSensor_t *Mag, const GyroSensor_t *Gyro,
    const MagCalibration_t *MagCal)
{
	int i;
	float ax, ay, az, gx, gy, gz, mx, my, mz;
	float factor = M_PI / 180.0;

	ax = Accel->Gp[0];
	ay = Accel->Gp[1];
	az = Accel->Gp[2];
	mx = Mag->Bc[0];
	my = Mag->Bc[1];
	mz = Mag->Bc[2];
	for (i=0; i < OVERSAMPLE_RATIO; i++) {
		gx = Gyro->YpFast[i][0];
		gy = Gyro->YpFast[i][1];
		gz = Gyro->YpFast[i][2];
		gx *= factor;
		gy *= factor;
		gz *= factor;
		mahony_update(gx, gy, gz, ax, ay, az, mx, my, mz);
	}
}

void fusion_read(Quaternion_t *q)
{
	q->q0 = q0;
	q->q1 = q1;
	q->q2 = q2;
	q->q3 = q3;
}


//----------------------------------------------------------------------------------------------
// AHRS algorithm update

static void mahony_init()
{
	static int first=1;

	twoKp = twoKpDef;	// 2 * proportional gain (Kp)
	twoKi = twoKiDef;	// 2 * integral gain (Ki)
	if (first) {
		q0 = 1.0f;
		q1 = 0.0f;	// TODO: set a flag to immediately capture
		q2 = 0.0f;	// magnetic orientation on next update
		q3 = 0.0f;
		first = 0;
	}
	reset_next_update = 1;
	integralFBx = 0.0f;
	integralFBy = 0.0f;
	integralFBz = 0.0f;
}

static void mahony_update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz)
{
	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)) {
		mahony_updateIMU(gx, gy, gz, ax, ay, az);
		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;
#if 0
		// crazy experiement - no filter, just use magnetometer...
		q0 = 0;
		q1 = mx;
		q2 = my;
		q3 = mz;
		return;
#endif
		// 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 * INV_SAMPLE_RATE;
			integralFBy += twoKi * halfey * INV_SAMPLE_RATE;
			integralFBz += twoKi * halfez * INV_SAMPLE_RATE;
			gx += integralFBx;	// apply integral feedback
			gy += integralFBy;
			gz += integralFBz;
		} else {
			integralFBx = 0.0f;	// prevent integral windup
			integralFBy = 0.0f;
			integralFBz = 0.0f;
		}

		//printf("err =  %.3f, %.3f, %.3f\n", halfex, halfey, halfez);

		// Apply proportional feedback
		if (reset_next_update) {
			gx += 2.0f * halfex;
			gy += 2.0f * halfey;
			gz += 2.0f * halfez;
			reset_next_update = 0;
		} else {
			gx += twoKp * halfex;
			gy += twoKp * halfey;
			gz += twoKp * halfez;
		}
	}

	// Integrate rate of change of quaternion
	gx *= (0.5f * INV_SAMPLE_RATE);		// pre-multiply common factors
	gy *= (0.5f * INV_SAMPLE_RATE);
	gz *= (0.5f * INV_SAMPLE_RATE);
	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;
}

//---------------------------------------------------------------------------------------------
// IMU algorithm update

void mahony_updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
{
	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 and vector perpendicular to magnetic flux
		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 * INV_SAMPLE_RATE;
			integralFBy += twoKi * halfey * INV_SAMPLE_RATE;
			integralFBz += twoKi * halfez * INV_SAMPLE_RATE;
			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 * INV_SAMPLE_RATE);		// pre-multiply common factors
	gy *= (0.5f * INV_SAMPLE_RATE);
	gz *= (0.5f * INV_SAMPLE_RATE);
	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;
}

//---------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root

static float invSqrt(float x) {
	union {
		float f;
		int32_t i;
	} y;
	float halfx = 0.5f * x;

	y.f = x;
	y.i = 0x5f375a86 - (y.i >> 1);
	y.f = y.f * (1.5f - (halfx * y.f * y.f));
	y.f = y.f * (1.5f - (halfx * y.f * y.f));
	y.f = y.f * (1.5f - (halfx * y.f * y.f));
	return y.f;
}

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

#endif // USE_MAHONY_FUSION