MahonyAHRS陀螺仪、加速度计、地磁计的融合代码

//===================================================================================================== // MahonyAHRS.c

//===================================================================================================== //

// 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 //

//=====================================================================================================

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

#include \#include

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

floatinvSqrt(float x);

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

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

voidMahonyAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) { floatrecipNorm;

float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; floathx, hy, bx, bz; floathalfvx, halfvy, halfvz, halfwx, halfwy, halfwz; floathalfex, halfey, halfez; floatqa, 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

voidMahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) { floatrecipNorm; floathalfvx, halfvy, halfvz; floathalfex, halfey, halfez; floatqa, 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); 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; }

// integral error scaled by Ki

// 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

floatinvSqrt(float x) { floathalfx = 0.5f * x; float y = x; longi = *(long*)&y; i = 0x5f3759df - (i>>1); y = *(float*)&i; y = y * (1.5f - (halfx * y * y)); return y; }

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

//====================================================================================================

// 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

floatinvSqrt(float x) { floathalfx = 0.5f * x; float y = x; longi = *(long*)&y; i = 0x5f3759df - (i>>1); y = *(float*)&i; y = y * (1.5f - (halfx * y * y)); return y; }

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

//====================================================================================================

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