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/node/8#open_source_ahrs_and_imu_algorithms
00007 //
00008 // Date         Author          Notes
00009 // 29/09/2011   SOH Madgwick    Initial release
00010 // 02/10/2011   SOH Madgwick    Optimised for reduced CPU load
00011 // 19/02/2012   SOH Madgwick    Magnetometer measurement is normalised
00012 //
00013 //=====================================================================================================
00014 
00015 //---------------------------------------------------------------------------------------------------
00016 // Header files
00017 
00018 #include "mbed.h"
00019 #include "MadgwickAHRS.h"
00020 #include <math.h>
00021 
00022 //---------------------------------------------------------------------------------------------------
00023 // Definitions
00024 
00025 //#define sampleFreq  512.0f      // sample frequency in Hz
00026 #define betaDef     0.2f          //2* proportional gain
00027 #define PI     3.14159265359f
00028 
00029 //---------------------------------------------------------------------------------------------------
00030 
00031 MadgwickAHRS::MadgwickAHRS(float Freq){
00032 
00033 sampleFreq = Freq;
00034 
00035 }
00036 
00037 float beta = betaDef;                              // 2 * proportional gain (Kp)
00038 float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f;  // quaternion of sensor frame relative to auxiliary frame
00039 
00040 float invSqrt(float x);
00041 
00042 //====================================================================================================
00043 // Functions
00044 
00045 //---------------------------------------------------------------------------------------------------
00046 // AHRS algorithm update
00047 
00048 void MadgwickAHRS::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
00049     float recipNorm;
00050     float s0, s1, s2, s3;
00051     float qDot1, qDot2, qDot3, qDot4;
00052     float hx, hy;
00053     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;
00054 
00055     // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
00056     if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
00057         MadgwickAHRS::updateIMU(gx, gy, gz, ax, ay, az);
00058         return;
00059     }
00060 
00061     // Rate of change of quaternion from gyroscope
00062     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00063     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00064     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00065     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00066 
00067     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00068     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00069 
00070         // Normalise accelerometer measurement
00071         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00072         ax *= recipNorm;
00073         ay *= recipNorm;
00074         az *= recipNorm;   
00075 
00076         // Normalise magnetometer measurement
00077         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00078         mx *= recipNorm;
00079         my *= recipNorm;
00080         mz *= recipNorm;
00081 
00082         // Auxiliary variables to avoid repeated arithmetic
00083         _2q0mx = 2.0f * q0 * mx;
00084         _2q0my = 2.0f * q0 * my;
00085         _2q0mz = 2.0f * q0 * mz;
00086         _2q1mx = 2.0f * q1 * mx;
00087         _2q0 = 2.0f * q0;
00088         _2q1 = 2.0f * q1;
00089         _2q2 = 2.0f * q2;
00090         _2q3 = 2.0f * q3;
00091         _2q0q2 = 2.0f * q0 * q2;
00092         _2q2q3 = 2.0f * q2 * q3;
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 = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
00106         hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
00107         _2bx = sqrt(hx * hx + hy * hy);
00108         _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
00109         _4bx = 2.0f * _2bx;
00110         _4bz = 2.0f * _2bz;
00111 
00112         // Gradient decent algorithm corrective step
00113         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);
00114         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);
00115         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);
00116         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);
00117         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00118         s0 *= recipNorm;
00119         s1 *= recipNorm;
00120         s2 *= recipNorm;
00121         s3 *= recipNorm;
00122 
00123         // Apply feedback step
00124         qDot1 -= beta * s0;
00125         qDot2 -= beta * s1;
00126         qDot3 -= beta * s2;
00127         qDot4 -= beta * s3;
00128     }
00129 
00130     // Integrate rate of change of quaternion to yield quaternion
00131     q0 += qDot1 * (1.0f / sampleFreq);
00132     q1 += qDot2 * (1.0f / sampleFreq);
00133     q2 += qDot3 * (1.0f / sampleFreq);
00134     q3 += qDot4 * (1.0f / sampleFreq);
00135 
00136     // Normalise quaternion
00137     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00138     q0 *= recipNorm;
00139     q1 *= recipNorm;
00140     q2 *= recipNorm;
00141     q3 *= recipNorm;
00142 }
00143 
00144 //---------------------------------------------------------------------------------------------------
00145 // IMU algorithm update
00146 
00147 void MadgwickAHRS::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
00148     float recipNorm;
00149     float s0, s1, s2, s3;
00150     float qDot1, qDot2, qDot3, qDot4;
00151     float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
00152 
00153     // Rate of change of quaternion from gyroscope
00154     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00155     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00156     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00157     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00158 
00159     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00160     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00161 
00162         // Normalise accelerometer measurement
00163         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00164         ax *= recipNorm;
00165         ay *= recipNorm;
00166         az *= recipNorm;   
00167 
00168         // Auxiliary variables to avoid repeated arithmetic
00169         _2q0 = 2.0f * q0;
00170         _2q1 = 2.0f * q1;
00171         _2q2 = 2.0f * q2;
00172         _2q3 = 2.0f * q3;
00173         _4q0 = 4.0f * q0;
00174         _4q1 = 4.0f * q1;
00175         _4q2 = 4.0f * q2;
00176         _8q1 = 8.0f * q1;
00177         _8q2 = 8.0f * q2;
00178         q0q0 = q0 * q0;
00179         q1q1 = q1 * q1;
00180         q2q2 = q2 * q2;
00181         q3q3 = q3 * q3;
00182 
00183         // Gradient decent algorithm corrective step
00184         s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
00185         s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
00186         s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
00187         s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
00188         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00189         s0 *= recipNorm;
00190         s1 *= recipNorm;
00191         s2 *= recipNorm;
00192         s3 *= recipNorm;
00193 
00194         // Apply feedback step
00195         qDot1 -= beta * s0;
00196         qDot2 -= beta * s1;
00197         qDot3 -= beta * s2;
00198         qDot4 -= beta * s3;
00199     }
00200 
00201     // Integrate rate of change of quaternion to yield quaternion
00202     q0 += qDot1 * (1.0f / sampleFreq);
00203     q1 += qDot2 * (1.0f / sampleFreq);
00204     q2 += qDot3 * (1.0f / sampleFreq);
00205     q3 += qDot4 * (1.0f / sampleFreq);
00206 
00207     // Normalise quaternion
00208     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00209     q0 *= recipNorm;
00210     q1 *= recipNorm;
00211     q2 *= recipNorm;
00212     q3 *= recipNorm;
00213 }
00214 
00215 //---------------------------------------------------------------------------------------------------
00216 // Fast inverse square-root
00217 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
00218 
00219 float invSqrt(float x) {
00220     float halfx = 0.5f * x;
00221     float y = x;
00222     long i = *(long*)&y;
00223     i = 0x5f3759df - (i>>1);
00224     y = *(float*)&i;
00225     y = y * (1.5f - (halfx * y * y));
00226     return y;
00227     //return 1.0/sqrt(x);
00228     }
00229 
00230 
00231 void MadgwickAHRS::getEuler(){
00232     
00233     float gx = 2*(q1*q3 - q0*q2);
00234     float gy = 2 * (q0*q1 + q2*q3);
00235     float gz = q0*q0 - q1*q1 - q2*q2 + q3*q3;
00236     
00237     //roll = atan2(2*(q0*q1 + q2*q3), 1 - 2*(q1*q1 + q2*q2));
00238     //pitch = asin(2*(q0*q2 - q3*q1));
00239     //yaw = atan2(2*(q0*q3 + q1*q2), 1 - 2*(q2*q2 + q3*q3));;
00240     
00241     roll = atan(gy / sqrt(gx*gx + gz*gz));
00242     pitch = atan(gx / sqrt(gy*gy + gz*gz));
00243     yaw = atan2(2 * q1 * q2 - 2 * q0 * q3, 2 * q0*q0 + 2 * q1 * q1 - 1);
00244     
00245     roll = roll*180/PI;
00246     pitch = pitch*180/PI;
00247     yaw = yaw*180/PI;
00248     
00249     /*roll = roll*1000;
00250     pitch = pitch*1000;
00251     yaw = yaw*1000;*/
00252     
00253     if (ceil(roll) - roll <= .5){
00254         roll = ceil(roll);
00255         }
00256     else{
00257          roll = floor(roll);
00258         }
00259         
00260     if (ceil(pitch) - pitch <= .5){
00261         pitch = ceil(pitch);
00262         }
00263     else{
00264          pitch = floor(pitch);
00265         }
00266     
00267     if (ceil(yaw) - yaw <= .5){
00268         yaw = ceil(yaw);
00269         }
00270     else{
00271          yaw = floor(yaw);
00272         }
00273         
00274     //printf("Roll: %6.2f, Pitch: %6.2f, Yaw: %6.2f\r\n", roll, pitch, yaw);
00275     }
00276     
00277 int16_t MadgwickAHRS::getRoll(){
00278     return (int16_t)roll;
00279     }
00280     
00281 int16_t MadgwickAHRS::getPitch(){
00282     return (int16_t)pitch;
00283     }
00284     
00285 int16_t MadgwickAHRS::getYaw(){
00286     return (int16_t)yaw;
00287     }
00288 
00289 //====================================================================================================
00290 // END OF CODE
00291 //====================================================================================================