Patrick Ciccone / MadgwickAHRS

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Show/hide line numbers MadgwickAHRS.cpp Source File

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  28.0f      // sample frequency in Hz
00025 #define betaDef     0.9f        // 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, float &q0, float &q1, float &q2, float &q3)
00045 {
00046     float recipNorm;
00047     float s0, s1, s2, s3;
00048     float qDot1, qDot2, qDot3, qDot4;
00049     float hx, hy;
00050     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;
00051 
00052     // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
00053     if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
00054         MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az, q0, q1, q2, q3);
00055         return;
00056     }
00057 
00058     // Rate of change of quaternion from gyroscope
00059     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00060     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00061     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00062     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00063 
00064     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00065     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00066 
00067         // Normalise accelerometer measurement
00068         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00069         ax *= recipNorm;
00070         ay *= recipNorm;
00071         az *= recipNorm;
00072 
00073         // Normalise magnetometer measurement
00074         recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00075         mx *= recipNorm;
00076         my *= recipNorm;
00077         mz *= recipNorm;
00078 
00079         // Auxiliary variables to avoid repeated arithmetic
00080         _2q0mx = 2.0f * q0 * mx;
00081         _2q0my = 2.0f * q0 * my;
00082         _2q0mz = 2.0f * q0 * mz;
00083         _2q1mx = 2.0f * q1 * mx;
00084         _2q0 = 2.0f * q0;
00085         _2q1 = 2.0f * q1;
00086         _2q2 = 2.0f * q2;
00087         _2q3 = 2.0f * q3;
00088         _2q0q2 = 2.0f * q0 * q2;
00089         _2q2q3 = 2.0f * q2 * q3;
00090         q0q0 = q0 * q0;
00091         q0q1 = q0 * q1;
00092         q0q2 = q0 * q2;
00093         q0q3 = q0 * q3;
00094         q1q1 = q1 * q1;
00095         q1q2 = q1 * q2;
00096         q1q3 = q1 * q3;
00097         q2q2 = q2 * q2;
00098         q2q3 = q2 * q3;
00099         q3q3 = q3 * q3;
00100 
00101         // Reference direction of Earth's magnetic field
00102         hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
00103         hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
00104         _2bx = sqrt(hx * hx + hy * hy);
00105         _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
00106         _4bx = 2.0f * _2bx;
00107         _4bz = 2.0f * _2bz;
00108 
00109         // Gradient decent algorithm corrective step
00110         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);
00111         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);
00112         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);
00113         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);
00114         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00115         s0 *= recipNorm;
00116         s1 *= recipNorm;
00117         s2 *= recipNorm;
00118         s3 *= recipNorm;
00119 
00120         // Apply feedback step
00121         qDot1 -= beta * s0;
00122         qDot2 -= beta * s1;
00123         qDot3 -= beta * s2;
00124         qDot4 -= beta * s3;
00125     }
00126 
00127     // Integrate rate of change of quaternion to yield quaternion
00128     q0 += qDot1 * (1.0f / sampleFreq);
00129     q1 += qDot2 * (1.0f / sampleFreq);
00130     q2 += qDot3 * (1.0f / sampleFreq);
00131     q3 += qDot4 * (1.0f / sampleFreq);
00132 
00133     // Normalise quaternion
00134     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00135     q0 *= recipNorm;
00136     q1 *= recipNorm;
00137     q2 *= recipNorm;
00138     q3 *= recipNorm;
00139 }
00140 
00141 //---------------------------------------------------------------------------------------------------
00142 // IMU algorithm update
00143 
00144 void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az, float &q0, float &q1, float &q2, float &q3)
00145 {
00146     float recipNorm;
00147     float s0, s1, s2, s3;
00148     float qDot1, qDot2, qDot3, qDot4;
00149     float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
00150 
00151     // Rate of change of quaternion from gyroscope
00152     qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00153     qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
00154     qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
00155     qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
00156 
00157     // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00158     if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
00159 
00160         // Normalise accelerometer measurement
00161         recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00162         ax *= recipNorm;
00163         ay *= recipNorm;
00164         az *= recipNorm;
00165 
00166         // Auxiliary variables to avoid repeated arithmetic
00167         _2q0 = 2.0f * q0;
00168         _2q1 = 2.0f * q1;
00169         _2q2 = 2.0f * q2;
00170         _2q3 = 2.0f * q3;
00171         _4q0 = 4.0f * q0;
00172         _4q1 = 4.0f * q1;
00173         _4q2 = 4.0f * q2;
00174         _8q1 = 8.0f * q1;
00175         _8q2 = 8.0f * q2;
00176         q0q0 = q0 * q0;
00177         q1q1 = q1 * q1;
00178         q2q2 = q2 * q2;
00179         q3q3 = q3 * q3;
00180 
00181         // Gradient decent algorithm corrective step
00182         s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
00183         s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
00184         s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
00185         s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
00186         recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00187         s0 *= recipNorm;
00188         s1 *= recipNorm;
00189         s2 *= recipNorm;
00190         s3 *= recipNorm;
00191 
00192         // Apply feedback step
00193         qDot1 -= beta * s0;
00194         qDot2 -= beta * s1;
00195         qDot3 -= beta * s2;
00196         qDot4 -= beta * s3;
00197     }
00198 
00199     // Integrate rate of change of quaternion to yield quaternion
00200     q0 += qDot1 * (1.0f / sampleFreq);
00201     q1 += qDot2 * (1.0f / sampleFreq);
00202     q2 += qDot3 * (1.0f / sampleFreq);
00203     q3 += qDot4 * (1.0f / sampleFreq);
00204 
00205     // Normalise quaternion
00206     recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00207     q0 *= recipNorm;
00208     q1 *= recipNorm;
00209     q2 *= recipNorm;
00210     q3 *= recipNorm;
00211 }
00212 
00213 //---------------------------------------------------------------------------------------------------
00214 // Fast inverse square-root
00215 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
00216 
00217 float invSqrt(float x)
00218 {
00219     float halfx = 0.5f * x;
00220     float y = x;
00221     long i = *(long*)&y;
00222     i = 0x5f3759df - (i>>1);
00223     y = *(float*)&i;
00224     y = y * (1.5f - (halfx * y * y));
00225     return y;
00226 }
00227 
00228 //====================================================================================================
00229 // END OF CODE
00230 //====================================================================================================
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