Fabio Bobrow
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Cubli
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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 "MadgwickAHRS.h" 00019 #include <math.h> 00020 00021 //--------------------------------------------------------------------------------------------------- 00022 // Definitions 00023 00024 #define sampleFreq 512.0f // sample frequency in Hz 00025 #define betaDef 0.1f // 2 * proportional gain 00026 00027 //--------------------------------------------------------------------------------------------------- 00028 // Variable definitions 00029 00030 volatile float beta = betaDef; // 2 * proportional gain (Kp) 00031 volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame 00032 00033 //--------------------------------------------------------------------------------------------------- 00034 // Function declarations 00035 00036 float invSqrt(float x); 00037 00038 //==================================================================================================== 00039 // Functions 00040 00041 //--------------------------------------------------------------------------------------------------- 00042 // AHRS algorithm update 00043 00044 void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) { 00045 float recipNorm; 00046 float s0, s1, s2, s3; 00047 float qDot1, qDot2, qDot3, qDot4; 00048 float hx, hy; 00049 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; 00050 00051 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation) 00052 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { 00053 MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az); 00054 return; 00055 } 00056 00057 // Rate of change of quaternion from gyroscope 00058 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); 00059 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); 00060 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); 00061 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); 00062 00063 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) 00064 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 00065 00066 // Normalise accelerometer measurement 00067 recipNorm = invSqrt(ax * ax + ay * ay + az * az); 00068 ax *= recipNorm; 00069 ay *= recipNorm; 00070 az *= recipNorm; 00071 00072 // Normalise magnetometer measurement 00073 recipNorm = invSqrt(mx * mx + my * my + mz * mz); 00074 mx *= recipNorm; 00075 my *= recipNorm; 00076 mz *= recipNorm; 00077 00078 // Auxiliary variables to avoid repeated arithmetic 00079 _2q0mx = 2.0f * q0 * mx; 00080 _2q0my = 2.0f * q0 * my; 00081 _2q0mz = 2.0f * q0 * mz; 00082 _2q1mx = 2.0f * q1 * mx; 00083 _2q0 = 2.0f * q0; 00084 _2q1 = 2.0f * q1; 00085 _2q2 = 2.0f * q2; 00086 _2q3 = 2.0f * q3; 00087 _2q0q2 = 2.0f * q0 * q2; 00088 _2q2q3 = 2.0f * q2 * q3; 00089 q0q0 = q0 * q0; 00090 q0q1 = q0 * q1; 00091 q0q2 = q0 * q2; 00092 q0q3 = q0 * q3; 00093 q1q1 = q1 * q1; 00094 q1q2 = q1 * q2; 00095 q1q3 = q1 * q3; 00096 q2q2 = q2 * q2; 00097 q2q3 = q2 * q3; 00098 q3q3 = q3 * q3; 00099 00100 // Reference direction of Earth's magnetic field 00101 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3; 00102 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3; 00103 _2bx = sqrt(hx * hx + hy * hy); 00104 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3; 00105 _4bx = 2.0f * _2bx; 00106 _4bz = 2.0f * _2bz; 00107 00108 // Gradient decent algorithm corrective step 00109 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); 00110 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); 00111 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); 00112 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); 00113 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude 00114 s0 *= recipNorm; 00115 s1 *= recipNorm; 00116 s2 *= recipNorm; 00117 s3 *= recipNorm; 00118 00119 // Apply feedback step 00120 qDot1 -= beta * s0; 00121 qDot2 -= beta * s1; 00122 qDot3 -= beta * s2; 00123 qDot4 -= beta * s3; 00124 } 00125 00126 // Integrate rate of change of quaternion to yield quaternion 00127 q0 += qDot1 * (1.0f / sampleFreq); 00128 q1 += qDot2 * (1.0f / sampleFreq); 00129 q2 += qDot3 * (1.0f / sampleFreq); 00130 q3 += qDot4 * (1.0f / sampleFreq); 00131 00132 // Normalise quaternion 00133 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 00134 q0 *= recipNorm; 00135 q1 *= recipNorm; 00136 q2 *= recipNorm; 00137 q3 *= recipNorm; 00138 } 00139 00140 //--------------------------------------------------------------------------------------------------- 00141 // IMU algorithm update 00142 00143 void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) { 00144 float recipNorm; 00145 float s0, s1, s2, s3; 00146 float qDot1, qDot2, qDot3, qDot4; 00147 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3; 00148 00149 // Rate of change of quaternion from gyroscope 00150 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); 00151 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); 00152 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); 00153 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); 00154 00155 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) 00156 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 00157 00158 // Normalise accelerometer measurement 00159 recipNorm = invSqrt(ax * ax + ay * ay + az * az); 00160 ax *= recipNorm; 00161 ay *= recipNorm; 00162 az *= recipNorm; 00163 00164 // Auxiliary variables to avoid repeated arithmetic 00165 _2q0 = 2.0f * q0; 00166 _2q1 = 2.0f * q1; 00167 _2q2 = 2.0f * q2; 00168 _2q3 = 2.0f * q3; 00169 _4q0 = 4.0f * q0; 00170 _4q1 = 4.0f * q1; 00171 _4q2 = 4.0f * q2; 00172 _8q1 = 8.0f * q1; 00173 _8q2 = 8.0f * q2; 00174 q0q0 = q0 * q0; 00175 q1q1 = q1 * q1; 00176 q2q2 = q2 * q2; 00177 q3q3 = q3 * q3; 00178 00179 // Gradient decent algorithm corrective step 00180 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay; 00181 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az; 00182 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az; 00183 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay; 00184 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude 00185 s0 *= recipNorm; 00186 s1 *= recipNorm; 00187 s2 *= recipNorm; 00188 s3 *= recipNorm; 00189 00190 // Apply feedback step 00191 qDot1 -= beta * s0; 00192 qDot2 -= beta * s1; 00193 qDot3 -= beta * s2; 00194 qDot4 -= beta * s3; 00195 } 00196 00197 // Integrate rate of change of quaternion to yield quaternion 00198 q0 += qDot1 * (1.0f / sampleFreq); 00199 q1 += qDot2 * (1.0f / sampleFreq); 00200 q2 += qDot3 * (1.0f / sampleFreq); 00201 q3 += qDot4 * (1.0f / sampleFreq); 00202 00203 // Normalise quaternion 00204 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 00205 q0 *= recipNorm; 00206 q1 *= recipNorm; 00207 q2 *= recipNorm; 00208 q3 *= recipNorm; 00209 } 00210 00211 //--------------------------------------------------------------------------------------------------- 00212 // Fast inverse square-root 00213 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root 00214 00215 float invSqrt(float x) { 00216 float halfx = 0.5f * x; 00217 float y = x; 00218 long i = *(long*)&y; 00219 i = 0x5f3759df - (i>>1); 00220 y = *(float*)&i; 00221 y = y * (1.5f - (halfx * y * y)); 00222 return y; 00223 } 00224 00225 //==================================================================================================== 00226 // END OF CODE 00227 //====================================================================================================
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