AHRS Library
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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
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