File content as of revision 8:981f7e2365b6:

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

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

#include "MahonyAHRS.h"
#include <math.h>

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

#define DEFAULT_SAMPLE_FREQ 1500.0f  // sample frequency in Hz
#define twoKpDef    (2.0f * 0.5f)   // 2 * proportional gain
#define twoKiDef    (2.0f * 0.1f)   // 2 * integral gain


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

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

Mahony::Mahony()
{
    twoKp = twoKpDef;   // 2 * proportional gain (Kp)
    twoKi = twoKiDef;   // 2 * integral gain (Ki)
    q0 = 1.0f;
    q1 = 0.0f;
    q2 = 0.0f;
    q3 = 0.0f;
    integralFBx = 0.0f;
    integralFBy = 0.0f;
    integralFBz = 0.0f;
    anglesComputed = 0;
    invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ;
}

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)) {
        updateIMU(gx, gy, gz, ax, ay, az);
        return;
    }

    // Convert gyroscope degrees/sec to radians/sec
    gx *= 0.0174533f;
    gy *= 0.0174533f;
    gz *= 0.0174533f;

    // 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 * invSampleFreq;
            integralFBy += twoKi * halfey * invSampleFreq;
            integralFBz += twoKi * halfez * invSampleFreq;
            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 * invSampleFreq);       // pre-multiply common factors
    gy *= (0.5f * invSampleFreq);
    gz *= (0.5f * invSampleFreq);
    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;
}

//-------------------------------------------------------------------------------------------
// 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;

    // Convert gyroscope degrees/sec to radians/sec
    gx *= 0.0174533f;
    gy *= 0.0174533f;
    gz *= 0.0174533f;

    // 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 * invSampleFreq;
            integralFBy += twoKi * halfey * invSampleFreq;
            integralFBz += twoKi * halfez * invSampleFreq;
            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 * invSampleFreq);       // pre-multiply common factors
    gy *= (0.5f * invSampleFreq);
    gz *= (0.5f * invSampleFreq);
    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;
}

//-------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
/*
float Mahony::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;
}
*/
/*
float Mahony::invSqrt(float x){
   unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
   float tmp = *(float*)&i;
   return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
}
*/

float Mahony::invSqrt(float x)
{
    float temp = 1/(sqrt(x));
    return temp;
}

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

void Mahony::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;
}


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