Diff: Quaternion/Quaternion.cpp

Revision:

0:ebbc3cd3a61e

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Quaternion/Quaternion.cpp	Sat Dec 05 18:39:33 2015 +0000
@@ -0,0 +1,302 @@
+
+#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;
+}