Quaternion.cpp

00001 
00002 #include "Quaternion.h"
00003 #include "mbed.h"
00004 #define M_PI 3.14159265
00005 
00006 Timer t;
00007 /**
00008 * Default constructor. 
00009 **/
00010 Quaternion::Quaternion() {
00011     q0 = 1.0f;
00012     q1 = 0.0f;
00013     q2 = 0.0f;
00014     q3 = 0.0f;
00015     twoKp = twoKpDef;
00016     twoKi = twoKiDef;
00017     sampleFreq = 0.0f;
00018     lastUpdate = 0L;
00019     now = 0L;
00020     integralFBx = 0.0f;
00021     integralFBy = 0.0f;
00022     integralFBz = 0.0f;
00023     t.start();
00024 }
00025 
00026 /**
00027 * Updates the sample frequency based on the elapsed time. 
00028 **/
00029 void Quaternion::updateSampleFrequency() {
00030     now = t.read();
00031     sampleFreq = 1.0 / ((now - lastUpdate));
00032     lastUpdate = now;
00033 }
00034 /**
00035 * Returns the quaternion representation of the orientation. 
00036 **/
00037 void Quaternion::getQ(float * q) {
00038     q[0] = q0;
00039     q[1] = q1;
00040     q[2] = q2;
00041     q[3] = q3;
00042 }
00043 
00044 /**
00045 * Gets the linear acceleration by estimating gravity and then subtracting it. All accelerations
00046 * need to be scaled to 1 g. So if at 1 g your accelerometer reads 245, divide it by 245 before passing it 
00047 * to this function. 
00048 * @param *linearAccel, pointer to float array for linear accelerations,
00049 * @param ax, the scaled acceleration in the x direction. 
00050 * @param ay, the scaled acceleration in the y direction.
00051 * @param az, the scaled acceleration in the z direction.
00052 **/
00053 void Quaternion::getLinearAcceleration(float * linearAccel, float ax, float ay, float az) {
00054     
00055     float gravity[3];
00056     getGravity(gravity);
00057     
00058 
00059     
00060     float xwog = ax - gravity[0];
00061     float ywog = ay - gravity[1];
00062     float zwog = az - gravity[2];
00063 
00064     linearAccel[0] = xwog * 9.8;
00065     linearAccel[1] =  ywog * 9.8;
00066     linearAccel[2] = zwog * 9.8;
00067 }
00068 
00069 /**
00070 * Returns the euler angles psi, theta and phi. 
00071 **/
00072 void Quaternion::getEulerAngles(float * angles) {
00073     angles[0] = atan2(2 * q1 * q2- 2 * q0 * q3, 2 * q0*q0 + 2 * q1 * q1 - 1) * 180/M_PI; // psi
00074     angles[1] = -asin(2 * q1 * q3 + 2 * q0 * q2) * 180/M_PI; // theta
00075     angles[2] = atan2(2 * q2 * q3 - 2 * q0 * q1, 2 * q0 * q0 + 2 * q3 * q3 - 1) * 180/M_PI; // phi
00076 }
00077 
00078 /**
00079 * Returns the yaw pitch and roll of the device. 
00080 **/
00081 void Quaternion::getYawPitchRoll(double * ypr) {
00082 
00083     ypr[0] =  atan2(double(2*q1*q2 + 2*q0*q3), double(q0*q0 + q1*q1 - q2*q2 - q3*q3)) * 180/M_PI; //yaw
00084     ypr[1] = -asin(2*q0*q2 - 2*q1*q3)  * 180/M_PI; // pitch
00085     ypr[2]  = -atan2(2*q2*q3 + 2*q0*q1, -q0*q0 + q1*q1 + q2*q2 - q3*q3)  * 180/M_PI; //roll
00086 
00087 }
00088 /**
00089 * Gets an estimation of gravity based on quaternion orientation representation. 
00090 **/
00091 void Quaternion::getGravity(float * gravity) {
00092     float q[4];
00093     getQ(q);
00094     gravity[0] = 2 * (q[1] * q[3] - q[0] *q[2]);
00095     gravity[1] = 2 * (q[0] * q[1] + q[2] * q[3]);
00096     gravity[2] = q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3];
00097 }
00098 
00099 /**
00100 * Calculates the quaternion representation based on a 6DOF sensor. 
00101 * @param gx, the rotation about the x axis in rad/sec
00102 * @param gy, the rotation about the y axis in rad/sec 
00103 * @param gz, the rotation about the z axis in rad/sec
00104 * @param ax, the raw acceleration in the x direction.
00105 * @param ay, the raw acceleration in the y direction.
00106 * @param az, the raw acceleration in the z direction. 
00107 **/
00108 void Quaternion::update6DOF(float gx, float gy, float gz, float ax, float ay, float az) {
00109     updateSampleFrequency();
00110     float recipNorm;
00111     float halfvx, halfvy, halfvz;
00112     float halfex, halfey, halfez;
00113     float qa, qb, qc;
00114 
00115     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00116     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00117 
00118         // Normalise accelerometer measurement
00119         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00120         ax *= recipNorm;
00121         ay *= recipNorm;
00122         az *= recipNorm;        
00123 
00124         // Estimated direction of gravity and vector perpendicular to magnetic flux
00125         halfvx = q1 * q3 - q0 * q2;
00126         halfvy = q0 * q1 + q2 * q3;
00127         halfvz = q0 * q0 - 0.5f + q3 * q3;
00128     
00129         // Error is sum of cross product between estimated and measured direction of gravity
00130         halfex = (ay * halfvz - az * halfvy);
00131         halfey = (az * halfvx - ax * halfvz);
00132         halfez = (ax * halfvy - ay * halfvx);
00133 
00134         // Compute and apply integral feedback if enabled
00135         if(twoKi > 0.0f) {
00136             integralFBx += twoKi * halfex * (1.0f / sampleFreq);    // integral error scaled by Ki
00137             integralFBy += twoKi * halfey * (1.0f / sampleFreq);
00138             integralFBz += twoKi * halfez * (1.0f / sampleFreq);
00139             gx += integralFBx;  // apply integral feedback
00140             gy += integralFBy;
00141             gz += integralFBz;
00142         }
00143         else {
00144             integralFBx = 0.0f; // prevent integral windup
00145             integralFBy = 0.0f;
00146             integralFBz = 0.0f;
00147         }
00148 
00149         // Apply proportional feedback
00150         gx += twoKp * halfex;
00151         gy += twoKp * halfey;
00152         gz += twoKp * halfez;
00153     }
00154     
00155     // Integrate rate of change of quaternion
00156     gx *= (0.5f * (1.0f / sampleFreq));     // pre-multiply common factors
00157     gy *= (0.5f * (1.0f / sampleFreq));
00158     gz *= (0.5f * (1.0f / sampleFreq));
00159     qa = q0;
00160     qb = q1;
00161     qc = q2;
00162     q0 += (-qb * gx - qc * gy - q3 * gz);
00163     q1 += (qa * gx + qc * gz - q3 * gy);
00164     q2 += (qa * gy - qb * gz + q3 * gx);
00165     q3 += (qa * gz + qb * gy - qc * gx); 
00166     
00167     // Normalise quaternion
00168     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00169     q0 *= recipNorm;
00170     q1 *= recipNorm;
00171     q2 *= recipNorm;
00172     q3 *= recipNorm;
00173     
00174 }
00175 
00176 /**
00177 * Calculates the quaternion representation based on a 9DOF sensor. 
00178 * @param gx, the rotation about the x axis in rad/sec
00179 * @param gy, the rotation about the y axis in rad/sec 
00180 * @param gz, the rotation about the z axis in rad/sec
00181 * @param ax, the raw acceleration in the x direction.
00182 * @param ay, the raw acceleration in the y direction.
00183 * @param az, the raw acceleration in the z direction. 
00184 * @param mx, the raw magnometer heading in the x direction. 
00185 * @param my, the raw magnometer heading in the y direction. 
00186 * @param mz, the raw magnometer heading in the z direction. 
00187 **/
00188 void Quaternion::update9DOF(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
00189     //update the frequency first. 
00190     updateSampleFrequency();
00191     float recipNorm;
00192     float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;  
00193     float hx, hy, bx, bz;
00194     float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
00195     float halfex, halfey, halfez;
00196     float qa, qb, qc;
00197 
00198     // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
00199     if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
00200         update6DOF(gx, gy, gz, ax, ay, az);
00201         return;
00202     }
00203 
00204     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00205     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00206 
00207         // Normalise accelerometer measurement
00208         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00209         ax *= recipNorm;
00210         ay *= recipNorm;
00211         az *= recipNorm;     
00212 
00213         // Normalise magnetometer measurement
00214         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00215         mx *= recipNorm;
00216         my *= recipNorm;
00217         mz *= recipNorm;   
00218 
00219         // Auxiliary variables to avoid repeated arithmetic
00220         q0q0 = q0 * q0;
00221         q0q1 = q0 * q1;
00222         q0q2 = q0 * q2;
00223         q0q3 = q0 * q3;
00224         q1q1 = q1 * q1;
00225         q1q2 = q1 * q2;
00226         q1q3 = q1 * q3;
00227         q2q2 = q2 * q2;
00228         q2q3 = q2 * q3;
00229         q3q3 = q3 * q3;   
00230 
00231         // Reference direction of Earth's magnetic field
00232         hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
00233         hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
00234         bx = sqrt(hx * hx + hy * hy);
00235         bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
00236 
00237         // Estimated direction of gravity and magnetic field
00238         halfvx = q1q3 - q0q2;
00239         halfvy = q0q1 + q2q3;
00240         halfvz = q0q0 - 0.5f + q3q3;
00241         halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
00242         halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
00243         halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);  
00244     
00245         // Error is sum of cross product between estimated direction and measured direction of field vectors
00246         halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
00247         halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
00248         halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);
00249 
00250         // Compute and apply integral feedback if enabled
00251         if(twoKi > 0.0f) {
00252             integralFBx += twoKi * halfex * (1.0f / sampleFreq);    // integral error scaled by Ki
00253             integralFBy += twoKi * halfey * (1.0f / sampleFreq);
00254             integralFBz += twoKi * halfez * (1.0f / sampleFreq);
00255             gx += integralFBx;  // apply integral feedback
00256             gy += integralFBy;
00257             gz += integralFBz;
00258         }
00259         else {
00260             integralFBx = 0.0f; // prevent integral windup
00261             integralFBy = 0.0f;
00262             integralFBz = 0.0f;
00263         }
00264 
00265         // Apply proportional feedback
00266         gx += twoKp * halfex;
00267         gy += twoKp * halfey;
00268         gz += twoKp * halfez;
00269     }
00270     
00271     // Integrate rate of change of quaternion
00272     gx *= (0.5f * (1.0f / sampleFreq));     // pre-multiply common factors
00273     gy *= (0.5f * (1.0f / sampleFreq));
00274     gz *= (0.5f * (1.0f / sampleFreq));
00275     qa = q0;
00276     qb = q1;
00277     qc = q2;
00278     q0 += (-qb * gx - qc * gy - q3 * gz);
00279     q1 += (qa * gx + qc * gz - q3 * gy);
00280     q2 += (qa * gy - qb * gz + q3 * gx);
00281     q3 += (qa * gz + qb * gy - qc * gx); 
00282     
00283     // Normalise quaternion
00284     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00285     q0 *= recipNorm;
00286     q1 *= recipNorm;
00287     q2 *= recipNorm;
00288     q3 *= recipNorm;
00289 }
00290 
00291 /**
00292 * Super fast inverted square root. 
00293 **/ 
00294 float Quaternion::invSqrt(float x) {
00295     float halfx = 0.5f * x;
00296     float y = x;
00297     long i = *(long*)&y;
00298     i = 0x5f3759df - (i>>1);
00299     y = *(float*)&i;
00300     y = y * (1.5f - (halfx * y * y));
00301     return y;
00302 }