Diff: MahonyAHRS.h

Revision:

27:7dd32c696d17

Child:

28:76e2ba7a1ecd

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/MahonyAHRS.h	Wed Jul 06 09:30:37 2016 +0000
@@ -0,0 +1,247 @@
+//=====================================================================================================
+// MahonyAHRS.h
+//=====================================================================================================
+//
+// Madgwick's implementation of Mayhony's AHRS algorithm.
+// 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
+//
+//=====================================================================================================
+
+//----------------------------------------------------------------------------------------------------
+// Variable declaration
+
+extern volatile float twoKp;			// 2 * proportional gain (Kp)
+extern volatile float twoKi;			// 2 * integral gain (Ki)
+extern volatile float q0, q1, q2, q3;	// quaternion of sensor frame relative to auxiliary frame
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+void MahonyAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
+void MahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az);
+
+
+#include <math.h>
+
+//---------------------------------------------------------------------------------------------------
+// Definitions
+
+#define sampleFreq	512.0f			// sample frequency in Hz
+#define twoKpDef	(2.0f * 0.5f)	// 2 * proportional gain
+#define twoKiDef	(2.0f * 0.0f)	// 2 * integral gain
+
+//---------------------------------------------------------------------------------------------------
+// Variable definitions
+
+volatile float twoKp = twoKpDef;											// 2 * proportional gain (Kp)
+volatile float twoKi = twoKiDef;											// 2 * integral gain (Ki)
+volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f;					// quaternion of sensor frame relative to auxiliary frame
+volatile float integralFBx = 0.0f,  integralFBy = 0.0f, integralFBz = 0.0f;	// integral error terms scaled by Ki
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+float invSqrt(float x);
+
+//====================================================================================================
+// Functions
+
+//---------------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+void MahonyAHRSupdate(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)) {
+		MahonyAHRSupdateIMU(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;   
+
+        // 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 = sqrt(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) {
+			integralFBx += twoKi * halfex * (1.0f / sampleFreq);	// integral error scaled by Ki
+			integralFBy += twoKi * halfey * (1.0f / sampleFreq);
+			integralFBz += twoKi * halfez * (1.0f / sampleFreq);
+			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 * (1.0f / sampleFreq));		// pre-multiply common factors
+	gy *= (0.5f * (1.0f / sampleFreq));
+	gz *= (0.5f * (1.0f / sampleFreq));
+	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 MahonyAHRSupdateIMU(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) {
+			integralFBx += twoKi * halfex * (1.0f / sampleFreq);	// integral error scaled by Ki
+			integralFBy += twoKi * halfey * (1.0f / sampleFreq);
+			integralFBz += twoKi * halfez * (1.0f / sampleFreq);
+			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 * (1.0f / sampleFreq));		// pre-multiply common factors
+	gy *= (0.5f * (1.0f / sampleFreq));
+	gz *= (0.5f * (1.0f / sampleFreq));
+	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
+
+float 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));
+	return y;
+}
+
+//====================================================================================================
+// END OF CODE
+//====================================================================================================
+
+//=====================================================================================================
+// End of file
+//=====================================================================================================
+