imu_filter_madgwick: imu_filter.cpp Source File

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00001 /*
00002  *  Copyright (C) 2010, CCNY Robotics Lab
00003  *  Ivan Dryanovski <ivan.dryanovski@gmail.com>
00004  *
00005  *  http://robotics.ccny.cuny.edu
00006  *
00007  *  Based on implementation of Madgwick's IMU and AHRS algorithms.
00008  *  http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
00009  *
00010  *
00011  *  This program is free software: you can redistribute it and/or modify
00012  *  it under the terms of the GNU General Public License as published by
00013  *  the Free Software Foundation, either version 3 of the License, or
00014  *  (at your option) any later version.
00015  *
00016  *  This program is distributed in the hope that it will be useful,
00017  *  but WITHOUT ANY WARRANTY; without even the implied warranty of
00018  *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00019  *  GNU General Public License for more details.
00020  *
00021  *  You should have received a copy of the GNU General Public License
00022  *  along with this program.  If not, see <http://www.gnu.org/licenses/>.
00023  */
00024 
00025 #include <cmath>
00026 #include "imu_filter_madgwick/imu_filter.h"
00027 
00028 ImuFilter::ImuFilter():
00029   q0(1.0), q1(0.0), q2(0.0), q3(0.0),
00030   w_bx_(0.0), w_by_(0.0), w_bz_(0.0),
00031   zeta_(0.0), gain_(0.0)
00032 {
00033 }
00034 
00035 ImuFilter::~ImuFilter()
00036 {
00037 }
00038 
00039 void ImuFilter::madgwickAHRSupdate(
00040   float gx, float gy, float gz, 
00041   float ax, float ay, float az, 
00042   float mx, float my, float mz, 
00043   float dt)
00044 {
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         float _w_err_x, _w_err_y, _w_err_z;
00051 
00052         // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
00053   if(!std::isfinite(mx) || !std::isfinite(my) || !std::isfinite(mz))
00054   {
00055                 madgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az, dt);
00056                 return;
00057         }
00058 
00059         // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00060         if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) 
00061   {
00062                 // Normalise accelerometer measurement
00063                 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00064                 ax *= recipNorm;
00065                 ay *= recipNorm;
00066                 az *= recipNorm;   
00067 
00068                 // Normalise magnetometer measurement
00069                 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
00070                 mx *= recipNorm;
00071                 my *= recipNorm;
00072                 mz *= recipNorm;
00073 
00074                 // Auxiliary variables to avoid repeated arithmetic
00075                 _2q0mx = 2.0f * q0 * mx;
00076                 _2q0my = 2.0f * q0 * my;
00077                 _2q0mz = 2.0f * q0 * mz;
00078                 _2q1mx = 2.0f * q1 * mx;
00079                 _2q0 = 2.0f * q0;
00080                 _2q1 = 2.0f * q1;
00081                 _2q2 = 2.0f * q2;
00082                 _2q3 = 2.0f * q3;
00083                 _2q0q2 = 2.0f * q0 * q2;
00084                 _2q2q3 = 2.0f * q2 * q3;
00085                 q0q0 = q0 * q0;
00086                 q0q1 = q0 * q1;
00087                 q0q2 = q0 * q2;
00088                 q0q3 = q0 * q3;
00089                 q1q1 = q1 * q1;
00090                 q1q2 = q1 * q2;
00091                 q1q3 = q1 * q3;
00092                 q2q2 = q2 * q2;
00093                 q2q3 = q2 * q3;
00094                 q3q3 = q3 * q3;
00095 
00096                 // Reference direction of Earth's magnetic field
00097                 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
00098                 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
00099                 _2bx = sqrt(hx * hx + hy * hy);
00100                 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
00101                 _4bx = 2.0f * _2bx;
00102                 _4bz = 2.0f * _2bz;
00103 
00104                 // Gradient decent algorithm corrective step
00105                 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);
00106                 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);
00107                 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);
00108                 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);
00109                 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00110                 s0 *= recipNorm;
00111                 s1 *= recipNorm;
00112                 s2 *= recipNorm;
00113                 s3 *= recipNorm;
00114 
00115                 // compute gyro drift bias
00116                 _w_err_x = _2q0 * s1 - _2q1 * s0 - _2q2 * s3 + _2q3 * s2;
00117                 _w_err_y = _2q0 * s2 + _2q1 * s3 - _2q2 * s0 - _2q3 * s1;
00118                 _w_err_z = _2q0 * s3 - _2q1 * s2 + _2q2 * s1 - _2q3 * s0;
00119                 
00120                 w_bx_ += _w_err_x * dt * zeta_;
00121                 w_by_ += _w_err_y * dt * zeta_;
00122                 w_bz_ += _w_err_z * dt * zeta_;
00123                 
00124                 gx -= w_bx_;
00125                 gy -= w_by_;
00126                 gz -= w_bz_;
00127                 
00128                 // Rate of change of quaternion from gyroscope
00129                 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00130                 qDot2 = 0.5f * ( q0 * gx + q2 * gz - q3 * gy);
00131                 qDot3 = 0.5f * ( q0 * gy - q1 * gz + q3 * gx);
00132                 qDot4 = 0.5f * ( q0 * gz + q1 * gy - q2 * gx);
00133 
00134                 // Apply feedback step
00135                 qDot1 -= gain_ * s0;
00136                 qDot2 -= gain_ * s1;
00137                 qDot3 -= gain_ * s2;
00138                 qDot4 -= gain_ * s3;
00139         } else{
00140                 // Rate of change of quaternion from gyroscope
00141                 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00142                 qDot2 = 0.5f * ( q0 * gx + q2 * gz - q3 * gy);
00143                 qDot3 = 0.5f * ( q0 * gy - q1 * gz + q3 * gx);
00144                 qDot4 = 0.5f * ( q0 * gz + q1 * gy - q2 * gx);
00145         }
00146 
00147         // Integrate rate of change of quaternion to yield quaternion
00148         q0 += qDot1 * dt;
00149         q1 += qDot2 * dt;
00150         q2 += qDot3 * dt;
00151         q3 += qDot4 * dt;
00152 
00153         // Normalise quaternion
00154         recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00155         q0 *= recipNorm;
00156         q1 *= recipNorm;
00157         q2 *= recipNorm;
00158         q3 *= recipNorm;
00159 }
00160 
00161 void ImuFilter::madgwickAHRSupdateIMU(
00162   float gx, float gy, float gz, 
00163   float ax, float ay, float az,
00164   float dt) 
00165 {
00166         float recipNorm;
00167         float s0, s1, s2, s3;
00168         float qDot1, qDot2, qDot3, qDot4;
00169         float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
00170 
00171         // Rate of change of quaternion from gyroscope
00172         qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
00173         qDot2 = 0.5f * ( q0 * gx + q2 * gz - q3 * gy);
00174         qDot3 = 0.5f * ( q0 * gy - q1 * gz + q3 * gx);
00175         qDot4 = 0.5f * ( q0 * gz + q1 * gy - q2 * gx);
00176 
00177         // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
00178         if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) 
00179   {
00180                 // Normalise accelerometer measurement
00181                 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
00182                 ax *= recipNorm;
00183                 ay *= recipNorm;
00184                 az *= recipNorm;   
00185 
00186                 // Auxiliary variables to avoid repeated arithmetic
00187                 _2q0 = 2.0f * q0;
00188                 _2q1 = 2.0f * q1;
00189                 _2q2 = 2.0f * q2;
00190                 _2q3 = 2.0f * q3;
00191                 _4q0 = 4.0f * q0;
00192                 _4q1 = 4.0f * q1;
00193                 _4q2 = 4.0f * q2;
00194                 _8q1 = 8.0f * q1;
00195                 _8q2 = 8.0f * q2;
00196                 q0q0 = q0 * q0;
00197                 q1q1 = q1 * q1;
00198                 q2q2 = q2 * q2;
00199                 q3q3 = q3 * q3;
00200 
00201                 // Gradient decent algorithm corrective step
00202                 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
00203                 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
00204                 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
00205                 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
00206                 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
00207                 s0 *= recipNorm;
00208                 s1 *= recipNorm;
00209                 s2 *= recipNorm;
00210                 s3 *= recipNorm;
00211 
00212                 // Apply feedback step
00213                 qDot1 -= gain_ * s0;
00214                 qDot2 -= gain_ * s1;
00215                 qDot3 -= gain_ * s2;
00216                 qDot4 -= gain_ * s3;
00217         }
00218 
00219         // Integrate rate of change of quaternion to yield quaternion
00220         q0 += qDot1 * dt;
00221         q1 += qDot2 * dt;
00222         q2 += qDot3 * dt;
00223         q3 += qDot4 * dt;
00224 
00225         // Normalise quaternion
00226         recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
00227         q0 *= recipNorm;
00228         q1 *= recipNorm;
00229         q2 *= recipNorm;
00230         q3 *= recipNorm;
00231 }