File content as of revision 0:ebbc3cd3a61e:

#include "Quaternion.h"
#include "mbed.h"
#define M_PI 3.14159265

Timer t;
/**
* Default constructor. 
**/
Quaternion::Quaternion() {
    q0 = 1.0f;
    q1 = 0.0f;
    q2 = 0.0f;
    q3 = 0.0f;
    twoKp = twoKpDef;
    twoKi = twoKiDef;
    sampleFreq = 0.0f;
    lastUpdate = 0L;
    now = 0L;
    integralFBx = 0.0f;
    integralFBy = 0.0f;
    integralFBz = 0.0f;
    t.start();
}

/**
* Updates the sample frequency based on the elapsed time. 
**/
void Quaternion::updateSampleFrequency() {
    now = t.read();
    sampleFreq = 1.0 / ((now - lastUpdate));
    lastUpdate = now;
}
/**
* Returns the quaternion representation of the orientation. 
**/
void Quaternion::getQ(float * q) {
    q[0] = q0;
    q[1] = q1;
    q[2] = q2;
    q[3] = q3;
}

/**
* Gets the linear acceleration by estimating gravity and then subtracting it. All accelerations
* need to be scaled to 1 g. So if at 1 g your accelerometer reads 245, divide it by 245 before passing it 
* to this function. 
* @param *linearAccel, pointer to float array for linear accelerations,
* @param ax, the scaled acceleration in the x direction. 
* @param ay, the scaled acceleration in the y direction.
* @param az, the scaled acceleration in the z direction.
**/
void Quaternion::getLinearAcceleration(float * linearAccel, float ax, float ay, float az) {
    
    float gravity[3];
    getGravity(gravity);
    

    
    float xwog = ax - gravity[0];
    float ywog = ay - gravity[1];
    float zwog = az - gravity[2];

    linearAccel[0] = xwog * 9.8;
    linearAccel[1] =  ywog * 9.8;
    linearAccel[2] = zwog * 9.8;
}

/**
* Returns the euler angles psi, theta and phi. 
**/
void Quaternion::getEulerAngles(float * angles) {
    angles[0] = atan2(2 * q1 * q2- 2 * q0 * q3, 2 * q0*q0 + 2 * q1 * q1 - 1) * 180/M_PI; // psi
    angles[1] = -asin(2 * q1 * q3 + 2 * q0 * q2) * 180/M_PI; // theta
    angles[2] = atan2(2 * q2 * q3 - 2 * q0 * q1, 2 * q0 * q0 + 2 * q3 * q3 - 1) * 180/M_PI; // phi
}

/**
* Returns the yaw pitch and roll of the device. 
**/
void Quaternion::getYawPitchRoll(double * ypr) {

    ypr[0] =  atan2(double(2*q1*q2 + 2*q0*q3), double(q0*q0 + q1*q1 - q2*q2 - q3*q3)) * 180/M_PI; //yaw
    ypr[1] = -asin(2*q0*q2 - 2*q1*q3)  * 180/M_PI; // pitch
    ypr[2]  = -atan2(2*q2*q3 + 2*q0*q1, -q0*q0 + q1*q1 + q2*q2 - q3*q3)  * 180/M_PI; //roll

}
/**
* Gets an estimation of gravity based on quaternion orientation representation. 
**/
void Quaternion::getGravity(float * gravity) {
    float q[4];
    getQ(q);
    gravity[0] = 2 * (q[1] * q[3] - q[0] *q[2]);
    gravity[1] = 2 * (q[0] * q[1] + q[2] * q[3]);
    gravity[2] = q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3];
}

/**
* Calculates the quaternion representation based on a 6DOF sensor. 
* @param gx, the rotation about the x axis in rad/sec
* @param gy, the rotation about the y axis in rad/sec 
* @param gz, the rotation about the z axis in rad/sec
* @param ax, the raw acceleration in the x direction.
* @param ay, the raw acceleration in the y direction.
* @param az, the raw acceleration in the z direction. 
**/
void Quaternion::update6DOF(float gx, float gy, float gz, float ax, float ay, float az) {
    updateSampleFrequency();
    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;
    
}

/**
* Calculates the quaternion representation based on a 9DOF sensor. 
* @param gx, the rotation about the x axis in rad/sec
* @param gy, the rotation about the y axis in rad/sec 
* @param gz, the rotation about the z axis in rad/sec
* @param ax, the raw acceleration in the x direction.
* @param ay, the raw acceleration in the y direction.
* @param az, the raw acceleration in the z direction. 
* @param mx, the raw magnometer heading in the x direction. 
* @param my, the raw magnometer heading in the y direction. 
* @param mz, the raw magnometer heading in the z direction. 
**/
void Quaternion::update9DOF(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
    //update the frequency first. 
    updateSampleFrequency();
    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)) {
        update6DOF(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;
}

/**
* Super fast inverted square root. 
**/ 
float Quaternion::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;
}