Erik van de Coevering
Latest version of my quadcopter controller with an LPC1768 and MPU9250.
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MahonyAHRS.cpp
00001 //============================================================================================= 00002 // MahonyAHRS.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 "MahonyAHRS.h" 00025 #include <math.h> 00026 00027 //------------------------------------------------------------------------------------------- 00028 // Definitions 00029 00030 #define DEFAULT_SAMPLE_FREQ 1500.0f // sample frequency in Hz 00031 #define twoKpDef (2.0f * 0.5f) // 2 * proportional gain 00032 #define twoKiDef (2.0f * 0.1f) // 2 * integral gain 00033 00034 00035 //============================================================================================ 00036 // Functions 00037 00038 //------------------------------------------------------------------------------------------- 00039 // AHRS algorithm update 00040 00041 Mahony::Mahony() 00042 { 00043 twoKp = twoKpDef; // 2 * proportional gain (Kp) 00044 twoKi = twoKiDef; // 2 * integral gain (Ki) 00045 q0 = 1.0f; 00046 q1 = 0.0f; 00047 q2 = 0.0f; 00048 q3 = 0.0f; 00049 integralFBx = 0.0f; 00050 integralFBy = 0.0f; 00051 integralFBz = 0.0f; 00052 anglesComputed = 0; 00053 invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ; 00054 } 00055 00056 void Mahony::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) 00057 { 00058 float recipNorm; 00059 float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; 00060 float hx, hy, bx, bz; 00061 float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz; 00062 float halfex, halfey, halfez; 00063 float qa, qb, qc; 00064 00065 // Use IMU algorithm if magnetometer measurement invalid 00066 // (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 // Compute feedback only if accelerometer measurement valid 00078 // (avoids NaN in accelerometer normalisation) 00079 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 00080 00081 // Normalise accelerometer measurement 00082 recipNorm = invSqrt(ax * ax + ay * ay + az * az); 00083 ax *= recipNorm; 00084 ay *= recipNorm; 00085 az *= recipNorm; 00086 00087 // Normalise magnetometer measurement 00088 recipNorm = invSqrt(mx * mx + my * my + mz * mz); 00089 mx *= recipNorm; 00090 my *= recipNorm; 00091 mz *= recipNorm; 00092 00093 // Auxiliary variables to avoid repeated arithmetic 00094 q0q0 = q0 * q0; 00095 q0q1 = q0 * q1; 00096 q0q2 = q0 * q2; 00097 q0q3 = q0 * q3; 00098 q1q1 = q1 * q1; 00099 q1q2 = q1 * q2; 00100 q1q3 = q1 * q3; 00101 q2q2 = q2 * q2; 00102 q2q3 = q2 * q3; 00103 q3q3 = q3 * q3; 00104 00105 // Reference direction of Earth's magnetic field 00106 hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2)); 00107 hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1)); 00108 bx = sqrtf(hx * hx + hy * hy); 00109 bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2)); 00110 00111 // Estimated direction of gravity and magnetic field 00112 halfvx = q1q3 - q0q2; 00113 halfvy = q0q1 + q2q3; 00114 halfvz = q0q0 - 0.5f + q3q3; 00115 halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2); 00116 halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3); 00117 halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2); 00118 00119 // Error is sum of cross product between estimated direction 00120 // and measured direction of field vectors 00121 halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy); 00122 halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz); 00123 halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx); 00124 00125 // Compute and apply integral feedback if enabled 00126 if(twoKi > 0.0f) { 00127 // integral error scaled by Ki 00128 integralFBx += twoKi * halfex * invSampleFreq; 00129 integralFBy += twoKi * halfey * invSampleFreq; 00130 integralFBz += twoKi * halfez * invSampleFreq; 00131 gx += integralFBx; // apply integral feedback 00132 gy += integralFBy; 00133 gz += integralFBz; 00134 } else { 00135 integralFBx = 0.0f; // prevent integral windup 00136 integralFBy = 0.0f; 00137 integralFBz = 0.0f; 00138 } 00139 00140 // Apply proportional feedback 00141 gx += twoKp * halfex; 00142 gy += twoKp * halfey; 00143 gz += twoKp * halfez; 00144 } 00145 00146 // Integrate rate of change of quaternion 00147 gx *= (0.5f * invSampleFreq); // pre-multiply common factors 00148 gy *= (0.5f * invSampleFreq); 00149 gz *= (0.5f * invSampleFreq); 00150 qa = q0; 00151 qb = q1; 00152 qc = q2; 00153 q0 += (-qb * gx - qc * gy - q3 * gz); 00154 q1 += (qa * gx + qc * gz - q3 * gy); 00155 q2 += (qa * gy - qb * gz + q3 * gx); 00156 q3 += (qa * gz + qb * gy - qc * gx); 00157 00158 // Normalise quaternion 00159 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 00160 q0 *= recipNorm; 00161 q1 *= recipNorm; 00162 q2 *= recipNorm; 00163 q3 *= recipNorm; 00164 anglesComputed = 0; 00165 } 00166 00167 //------------------------------------------------------------------------------------------- 00168 // IMU algorithm update 00169 00170 void Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) 00171 { 00172 float recipNorm; 00173 float halfvx, halfvy, halfvz; 00174 float halfex, halfey, halfez; 00175 float qa, qb, qc; 00176 00177 // Convert gyroscope degrees/sec to radians/sec 00178 gx *= 0.0174533f; 00179 gy *= 0.0174533f; 00180 gz *= 0.0174533f; 00181 00182 // Compute feedback only if accelerometer measurement valid 00183 // (avoids NaN in accelerometer normalisation) 00184 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { 00185 00186 // Normalise accelerometer measurement 00187 recipNorm = invSqrt(ax * ax + ay * ay + az * az); 00188 ax *= recipNorm; 00189 ay *= recipNorm; 00190 az *= recipNorm; 00191 00192 // Estimated direction of gravity 00193 halfvx = q1 * q3 - q0 * q2; 00194 halfvy = q0 * q1 + q2 * q3; 00195 halfvz = q0 * q0 - 0.5f + q3 * q3; 00196 00197 // Error is sum of cross product between estimated 00198 // and measured direction of gravity 00199 halfex = (ay * halfvz - az * halfvy); 00200 halfey = (az * halfvx - ax * halfvz); 00201 halfez = (ax * halfvy - ay * halfvx); 00202 00203 // Compute and apply integral feedback if enabled 00204 if(twoKi > 0.0f) { 00205 // integral error scaled by Ki 00206 integralFBx += twoKi * halfex * invSampleFreq; 00207 integralFBy += twoKi * halfey * invSampleFreq; 00208 integralFBz += twoKi * halfez * invSampleFreq; 00209 gx += integralFBx; // apply integral feedback 00210 gy += integralFBy; 00211 gz += integralFBz; 00212 } else { 00213 integralFBx = 0.0f; // prevent integral windup 00214 integralFBy = 0.0f; 00215 integralFBz = 0.0f; 00216 } 00217 00218 // Apply proportional feedback 00219 gx += twoKp * halfex; 00220 gy += twoKp * halfey; 00221 gz += twoKp * halfez; 00222 } 00223 00224 // Integrate rate of change of quaternion 00225 gx *= (0.5f * invSampleFreq); // pre-multiply common factors 00226 gy *= (0.5f * invSampleFreq); 00227 gz *= (0.5f * invSampleFreq); 00228 qa = q0; 00229 qb = q1; 00230 qc = q2; 00231 q0 += (-qb * gx - qc * gy - q3 * gz); 00232 q1 += (qa * gx + qc * gz - q3 * gy); 00233 q2 += (qa * gy - qb * gz + q3 * gx); 00234 q3 += (qa * gz + qb * gy - qc * gx); 00235 00236 // Normalise quaternion 00237 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); 00238 q0 *= recipNorm; 00239 q1 *= recipNorm; 00240 q2 *= recipNorm; 00241 q3 *= recipNorm; 00242 anglesComputed = 0; 00243 } 00244 00245 //------------------------------------------------------------------------------------------- 00246 // Fast inverse square-root 00247 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root 00248 /* 00249 float Mahony::invSqrt(float x) 00250 { 00251 float halfx = 0.5f * x; 00252 float y = x; 00253 long i = *(long*)&y; 00254 i = 0x5f3759df - (i>>1); 00255 y = *(float*)&i; 00256 y = y * (1.5f - (halfx * y * y)); 00257 y = y * (1.5f - (halfx * y * y)); 00258 return y; 00259 } 00260 */ 00261 /* 00262 float Mahony::invSqrt(float x){ 00263 unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1); 00264 float tmp = *(float*)&i; 00265 return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp); 00266 } 00267 */ 00268 00269 float Mahony::invSqrt(float x) 00270 { 00271 float temp = 1/(sqrt(x)); 00272 return temp; 00273 } 00274 00275 //------------------------------------------------------------------------------------------- 00276 00277 void Mahony::computeAngles() 00278 { 00279 roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2); 00280 pitch = asinf(-2.0f * (q1*q3 - q0*q2)); 00281 yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3); 00282 anglesComputed = 1; 00283 } 00284 00285 00286 //============================================================================================ 00287 // END OF CODE 00288 //============================================================================================
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