Mahony.cpp

00001 //=============================================================================================
00002 // Mahony.c
00003 //=============================================================================================
00004 //
00005 // Madgwick's implementation of Mayhony's AHRS algorithm.
00006 // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
00007 //
00008 // From the x-io website "Open-source resources available on this website are
00009 // provided under the GNU General Public Licence unless an alternative licence
00010 // is provided in source."
00011 //
00012 // Date         Author          Notes
00013 // 29/09/2011   SOH Madgwick    Initial release
00014 // 02/10/2011   SOH Madgwick    Optimised for reduced CPU load
00015 //
00016 // Algorithm paper:
00017 // http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934
00018 //
00019 //=============================================================================================
00020 
00021 //-------------------------------------------------------------------------------------------
00022 // Header files
00023 
00024 #include "Mahony.h"
00025 #include <math.h>
00026 
00027 //-------------------------------------------------------------------------------------------
00028 // Definitions
00029 
00030 #define twoKpDef    (2.0f * 0.5f)   // 2 * proportional gain
00031 #define twoKiDef    (2.0f * 0.0f)   // 2 * integral gain
00032 
00033 
00034 //============================================================================================
00035 // Functions
00036 
00037 //-------------------------------------------------------------------------------------------
00038 // AHRS algorithm update
00039 
00040 Mahony::Mahony(float Ts)
00041 {
00042     twoKp = twoKpDef;   // 2 * proportional gain (Kp)
00043     twoKi = twoKiDef;   // 2 * integral gain (Ki)
00044     q0 = 1.0f;
00045     q1 = 0.0f;
00046     q2 = 0.0f;
00047     q3 = 0.0f;
00048     integralFBx = 0.0f;
00049     integralFBy = 0.0f;
00050     integralFBz = 0.0f;
00051     anglesComputed = 0;
00052     invSampleFreq = Ts;
00053 }
00054 
00055 void Mahony::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz)
00056 {
00057     float recipNorm;
00058     float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
00059     float hx, hy, bx, bz;
00060     float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
00061     float halfex, halfey, halfez;
00062     float qa, qb, qc;
00063 
00064     // Use IMU algorithm if magnetometer measurement invalid
00065     // (avoids NaN in magnetometer normalisation)
00066     if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
00067         updateIMU(gx, gy, gz, ax, ay, az);
00068         return;
00069     }
00070 
00071     // Convert gyroscope degrees/sec to radians/sec
00072 //    gx *= 0.0174533f;
00073 //    gy *= 0.0174533f;
00074 //    gz *= 0.0174533f;
00075 
00076     // Compute feedback only if accelerometer measurement valid
00077     // (avoids NaN in accelerometer normalisation)
00078     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00079 
00080         // Normalise accelerometer measurement
00081         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00082         ax *= recipNorm;
00083         ay *= recipNorm;
00084         az *= recipNorm;
00085 
00086         // Normalise magnetometer measurement
00087         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00088         mx *= recipNorm;
00089         my *= recipNorm;
00090         mz *= recipNorm;
00091 
00092         // Auxiliary variables to avoid repeated arithmetic
00093         q0q0 = q0 * q0;
00094         q0q1 = q0 * q1;
00095         q0q2 = q0 * q2;
00096         q0q3 = q0 * q3;
00097         q1q1 = q1 * q1;
00098         q1q2 = q1 * q2;
00099         q1q3 = q1 * q3;
00100         q2q2 = q2 * q2;
00101         q2q3 = q2 * q3;
00102         q3q3 = q3 * q3;
00103 
00104         // Reference direction of Earth's magnetic field
00105         hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
00106         hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
00107         bx = sqrtf(hx * hx + hy * hy);
00108         bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
00109 
00110         // Estimated direction of gravity and magnetic field
00111         halfvx = q1q3 - q0q2;
00112         halfvy = q0q1 + q2q3;
00113         halfvz = q0q0 - 0.5f + q3q3;
00114         halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
00115         halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
00116         halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);
00117 
00118         // Error is sum of cross product between estimated direction
00119         // and measured direction of field vectors
00120         halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
00121         halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
00122         halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);
00123 
00124         // Compute and apply integral feedback if enabled
00125         if(twoKi > 0.0f) {
00126             // integral error scaled by Ki
00127             integralFBx += twoKi * halfex * invSampleFreq;
00128             integralFBy += twoKi * halfey * invSampleFreq;
00129             integralFBz += twoKi * halfez * invSampleFreq;
00130             gx += integralFBx;  // apply integral feedback
00131             gy += integralFBy;
00132             gz += integralFBz;
00133         } else {
00134             integralFBx = 0.0f; // prevent integral windup
00135             integralFBy = 0.0f;
00136             integralFBz = 0.0f;
00137         }
00138 
00139         // Apply proportional feedback
00140         gx += twoKp * halfex;
00141         gy += twoKp * halfey;
00142         gz += twoKp * halfez;
00143     }
00144 
00145     // Integrate rate of change of quaternion
00146     gx *= (0.5f * invSampleFreq);       // pre-multiply common factors
00147     gy *= (0.5f * invSampleFreq);
00148     gz *= (0.5f * invSampleFreq);
00149     qa = q0;
00150     qb = q1;
00151     qc = q2;
00152     q0 += (-qb * gx - qc * gy - q3 * gz);
00153     q1 += (qa * gx + qc * gz - q3 * gy);
00154     q2 += (qa * gy - qb * gz + q3 * gx);
00155     q3 += (qa * gz + qb * gy - qc * gx);
00156 
00157     // Normalise quaternion
00158     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00159     q0 *= recipNorm;
00160     q1 *= recipNorm;
00161     q2 *= recipNorm;
00162     q3 *= recipNorm;
00163     anglesComputed = 0;
00164 }
00165 
00166 //-------------------------------------------------------------------------------------------
00167 // IMU algorithm update
00168 
00169 void Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
00170 {
00171     float recipNorm;
00172     float halfvx, halfvy, halfvz;
00173     float halfex, halfey, halfez;
00174     float qa, qb, qc;
00175 
00176     // Convert gyroscope degrees/sec to radians/sec
00177   //  gx *= 0.0174533f;
00178   //  gy *= 0.0174533f;
00179   //  gz *= 0.0174533f;
00180 
00181     // Compute feedback only if accelerometer measurement valid
00182     // (avoids NaN in accelerometer normalisation)
00183     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00184 
00185         // Normalise accelerometer measurement
00186         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00187         ax *= recipNorm;
00188         ay *= recipNorm;
00189         az *= recipNorm;
00190 
00191         // Estimated direction of gravity
00192         halfvx = q1 * q3 - q0 * q2;
00193         halfvy = q0 * q1 + q2 * q3;
00194         halfvz = q0 * q0 - 0.5f + q3 * q3;
00195 
00196         // Error is sum of cross product between estimated
00197         // and measured direction of gravity
00198         halfex = (ay * halfvz - az * halfvy);
00199         halfey = (az * halfvx - ax * halfvz);
00200         halfez = (ax * halfvy - ay * halfvx);
00201 
00202         // Compute and apply integral feedback if enabled
00203         if(twoKi > 0.0f) {
00204             // integral error scaled by Ki
00205             integralFBx += twoKi * halfex * invSampleFreq;
00206             integralFBy += twoKi * halfey * invSampleFreq;
00207             integralFBz += twoKi * halfez * invSampleFreq;
00208             gx += integralFBx;  // apply integral feedback
00209             gy += integralFBy;
00210             gz += integralFBz;
00211         } else {
00212             integralFBx = 0.0f; // prevent integral windup
00213             integralFBy = 0.0f;
00214             integralFBz = 0.0f;
00215         }
00216 
00217         // Apply proportional feedback
00218         gx += twoKp * halfex;
00219         gy += twoKp * halfey;
00220         gz += twoKp * halfez;
00221     }
00222 
00223     // Integrate rate of change of quaternion
00224     gx *= (0.5f * invSampleFreq);       // pre-multiply common factors
00225     gy *= (0.5f * invSampleFreq);
00226     gz *= (0.5f * invSampleFreq);
00227     qa = q0;
00228     qb = q1;
00229     qc = q2;
00230     q0 += (-qb * gx - qc * gy - q3 * gz);
00231     q1 += (qa * gx + qc * gz - q3 * gy);
00232     q2 += (qa * gy - qb * gz + q3 * gx);
00233     q3 += (qa * gz + qb * gy - qc * gx);
00234 
00235     // Normalise quaternion
00236     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00237     q0 *= recipNorm;
00238     q1 *= recipNorm;
00239     q2 *= recipNorm;
00240     q3 *= recipNorm;
00241     anglesComputed = 0;
00242 }
00243 
00244 //-------------------------------------------------------------------------------------------
00245 // Fast inverse square-root
00246 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
00247 
00248 float Mahony::invSqrt(float x)
00249 {
00250     float halfx = 0.5f * x;
00251     float y = x;
00252     long i = *(long*)&y;
00253     i = 0x5f3759df - (i>>1);
00254     y = *(float*)&i;
00255     y = y * (1.5f - (halfx * y * y));
00256     y = y * (1.5f - (halfx * y * y));
00257     return y;
00258 }
00259 
00260 //-------------------------------------------------------------------------------------------
00261 
00262 void Mahony::computeAngles()
00263 {
00264     roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
00265     pitch = asinf(-2.0f * (q1*q3 - q0*q2));
00266     yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
00267     anglesComputed = 1;
00268 }
00269 
00270 
00271 //============================================================================================
00272 // END OF CODE
00273 //============================================================================================
00274