MadgwickAHRS.cpp

00001 //=============================================================================================
00002 // MadgwickAHRS.c
00003 //=============================================================================================
00004 //
00005 // Implementation of Madgwick's IMU and AHRS algorithms.
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 // 19/02/2012   SOH Madgwick    Magnetometer measurement is normalised
00016 //
00017 //=============================================================================================
00018 
00019 //-------------------------------------------------------------------------------------------
00020 // Header files
00021 
00022 #include "MadgwickAHRS.h"
00023 #include <math.h>
00024 #include <stdio.h>
00025 #include "ros.h"
00026 
00027 #if (NO_ROS)
00028 extern Serial pc;
00029 #else
00030 extern ros::NodeHandle nh;
00031 #endif
00032 //-------------------------------------------------------------------------------------------
00033 // Definitions
00034 
00035 #define sampleFreqDef   512.0f          // sample frequency in Hz
00036 #define betaDef         0.1f            // 2 * proportional gain
00037 
00038 
00039 
00040 //============================================================================================
00041 // Functions
00042 
00043 //-------------------------------------------------------------------------------------------
00044 // AHRS algorithm update
00045 
00046 Madgwick::Madgwick() {
00047     beta = betaDef;
00048     q0 = 1.0f;
00049     q1 = 0.0f;
00050     q2 = 0.0f;
00051     q3 = 0.0f;
00052     invSampleFreq = 1.0f / sampleFreqDef;
00053     
00054     anglesComputed = 0;
00055     
00056 }
00057 
00058 void Madgwick::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
00059     float recipNorm;
00060     float s0, s1, s2, s3;
00061     float qDot1, qDot2, qDot3, qDot4;
00062     float hx, hy;
00063     float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
00064     
00065     
00066     // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
00067     if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
00068         updateIMU(gx, gy, gz, ax, ay, az);
00069         return;
00070     }
00071 
00072     // Convert gyroscope degrees/sec to radians/sec
00073     gx *= 0.0174533f;
00074     gy *= 0.0174533f;
00075     gz *= 0.0174533f;
00076 
00077     // Rate of change of quaternion from gyroscope
00078     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00079     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00080     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00081     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00082 
00083     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00084     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00085 
00086         // Normalise accelerometer measurement
00087         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00088         ax *= recipNorm;
00089         ay *= recipNorm;
00090         az *= recipNorm;
00091 
00092         // Normalise magnetometer measurement
00093         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00094         mx *= recipNorm;
00095         my *= recipNorm;
00096         mz *= recipNorm;
00097 
00098         // Auxiliary variables to avoid repeated arithmetic
00099         _2q0mx = 2.0f * q0 * mx;
00100         _2q0my = 2.0f * q0 * my;
00101         _2q0mz = 2.0f * q0 * mz;
00102         _2q1mx = 2.0f * q1 * mx;
00103         _2q0 = 2.0f * q0;
00104         _2q1 = 2.0f * q1;
00105         _2q2 = 2.0f * q2;
00106         _2q3 = 2.0f * q3;
00107         _2q0q2 = 2.0f * q0 * q2;
00108         _2q2q3 = 2.0f * q2 * q3;
00109         q0q0 = q0 * q0;
00110         q0q1 = q0 * q1;
00111         q0q2 = q0 * q2;
00112         q0q3 = q0 * q3;
00113         q1q1 = q1 * q1;
00114         q1q2 = q1 * q2;
00115         q1q3 = q1 * q3;
00116         q2q2 = q2 * q2;
00117         q2q3 = q2 * q3;
00118         q3q3 = q3 * q3;
00119 
00120         // Reference direction of Earth's magnetic field
00121         hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
00122         hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
00123         _2bx = sqrtf(hx * hx + hy * hy);
00124         _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
00125         _4bx = 2.0f * _2bx;
00126         _4bz = 2.0f * _2bz;
00127 
00128         // Gradient decent algorithm corrective step
00129         s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
00130         s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
00131         s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
00132         s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
00133         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00134         s0 *= recipNorm;
00135         s1 *= recipNorm;
00136         s2 *= recipNorm;
00137         s3 *= recipNorm;
00138 
00139         // Apply feedback step
00140         qDot1 -= beta * s0;
00141         qDot2 -= beta * s1;
00142         qDot3 -= beta * s2;
00143         qDot4 -= beta * s3;
00144     }
00145 
00146     // Integrate rate of change of quaternion to yield quaternion
00147     q0 += qDot1 * invSampleFreq;
00148     q1 += qDot2 * invSampleFreq;
00149     q2 += qDot3 * invSampleFreq;
00150     q3 += qDot4 * invSampleFreq;
00151 
00152     // Normalise quaternion
00153     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00154     q0 *= recipNorm;
00155     q1 *= recipNorm;
00156     q2 *= recipNorm;
00157     q3 *= recipNorm;
00158     anglesComputed = 0;
00159 }
00160 
00161 //-------------------------------------------------------------------------------------------
00162 // IMU algorithm update
00163 
00164 void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
00165     float recipNorm;
00166     float s0, s1, s2, s3;
00167     float qDot1, qDot2, qDot3, qDot4;
00168     float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
00169     char tempstr[64] = {};
00170     //pc.printf("q_pre: %.3f  %.3f  %.3f  %.3f\n\r",q0,q1,q2,q3);
00171     /*
00172     sprintf(tempstr,"%f  %f  %f  %f  %f  %f",gx,gy,gz,ax,ay,az);
00173     nh.loginfo("gx  gy  gz  ax  ay  az");
00174     nh.loginfo(tempstr);
00175     */
00176     
00177     // Convert gyroscope degrees/sec to radians/sec
00178     
00179     gx *= 0.0174533f;
00180     gy *= 0.0174533f;
00181     gz *= 0.0174533f;
00182     //pc.printf("%f  %f  %f  %f  %f  %f  \n\r",gx,gy,gz,ax,ay,az);
00183     // Rate of change of quaternion from gyroscope
00184     
00185     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00186     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00187     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00188     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00189     //pc.printf("%.5f  %.5f  %.5f  %.5f  ",qDot1,qDot2,qDot3,qDot4);
00190     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00191     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00192 
00193         // Normalise accelerometer measurement
00194         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00195         //pc.printf("nomalized acc: %.5f\n\r",recipNorm);
00196         ax *= recipNorm;
00197         ay *= recipNorm;
00198         az *= recipNorm;
00199 
00200         // Auxiliary variables to avoid repeated arithmetic
00201         _2q0 = 2.0f * q0;
00202         _2q1 = 2.0f * q1;
00203         _2q2 = 2.0f * q2;
00204         _2q3 = 2.0f * q3;
00205         _4q0 = 4.0f * q0;
00206         _4q1 = 4.0f * q1;
00207         _4q2 = 4.0f * q2;
00208         _8q1 = 8.0f * q1;
00209         _8q2 = 8.0f * q2;
00210         q0q0 = q0 * q0;
00211         q1q1 = q1 * q1;
00212         q2q2 = q2 * q2;
00213         q3q3 = q3 * q3;
00214         
00215         // Gradient decent algorithm corrective step
00216         s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
00217         s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
00218         s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
00219         s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
00220         
00221         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00222         //pc.printf("nomalized step: %.5f\n\r",recipNorm);
00223         s0 *= recipNorm;
00224         s1 *= recipNorm;
00225         s2 *= recipNorm;
00226         s3 *= recipNorm;
00227         //pc.printf("%.5f  %.5f  %.5f  %.5f  ",s0,s1,s2,s3);
00228         // Apply feedback step
00229         qDot1 -= beta * s0;
00230         qDot2 -= beta * s1;
00231         qDot3 -= beta * s2;
00232         qDot4 -= beta * s3;
00233         //pc.printf("%.5f  %.5f  %.5f  %.5f  ",qDot1,qDot2,qDot3,qDot4);
00234         //pc.printf("\n\r---------------------------------------------------------------------------\n\r");
00235     }
00236 
00237     // Integrate rate of change of quaternion to yield quaternion
00238     q0 += qDot1 * invSampleFreq;
00239     q1 += qDot2 * invSampleFreq;
00240     q2 += qDot3 * invSampleFreq;
00241     q3 += qDot4 * invSampleFreq;
00242     //pc.printf("\n\rinvSampleFreq: %.5f\n\r",invSampleFreq);
00243     // Normalise quaternion
00244     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00245     q0 *= recipNorm;
00246     q1 *= recipNorm;
00247     q2 *= recipNorm;
00248     q3 *= recipNorm;
00249     //pc.printf("nomalized quaternion: %.5f\n\r",recipNorm);
00250     anglesComputed = 0;
00251 }
00252 
00253 //-------------------------------------------------------------------------------------------
00254 // Fast inverse square-root
00255 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
00256 
00257 float Madgwick::invSqrt(float x) {
00258     float halfx = 0.5f * x;
00259     float y = x;
00260     long i = *(long*)&y;
00261     i = 0x5f3759df - (i>>1);
00262     y = *(float*)&i;
00263     y = y * (1.5f - (halfx * y * y));
00264     y = y * (1.5f - (halfx * y * y));
00265     return y;
00266 }
00267 
00268 //-------------------------------------------------------------------------------------------
00269 
00270 void Madgwick::computeAngles()
00271 {
00272     roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
00273     pitch = asinf(-2.0f * (q1*q3 - q0*q2));
00274     yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
00275     anglesComputed = 1;
00276 }
00277 
00278