PQ_Hybrid_Electrical_Equipment_Team / MadgwickFilter

Madgwick Filterをライブラリ化しました．内容はオープンソースになっていたやつのほぼ同じです．

Dependencies:   Quaternion

Dependents:   Hybrid_main_FirstEdtion rocket_logger_sinkan2018_v1 HYBRYD2018_IZU_ROCKET Hybrid_IZU2019 ... more

Fork of MadgwickFilter by Gaku Matsumoto

MadgwickFilter.hpp@2:e1de76e257f6, 2017-01-28 (annotated)

Committer:
Gaku0606
Date:
Sat Jan 28 21:04:15 2017 +0000
Revision:
2:e1de76e257f6
Parent:
1:b6856781fcdd
Child:
3:715924156fcb
Child:
4:85f9e16e445c
Child:
5:1e6fecaea25e
xxx

Who changed what in which revision?

UserRevisionLine numberNew contents of line
Gaku0606 0:c160cac4c370 1 #ifndef _MADGWICK_FILTER_HPP_
Gaku0606 0:c160cac4c370 2 #define _MADGWICK_FILTER_HPP_
Gaku0606 0:c160cac4c370 3
Gaku0606 0:c160cac4c370 4 #include "mbed.h"
Gaku0606 0:c160cac4c370 5 #include "Quaternion.hpp"
Gaku0606 0:c160cac4c370 6
Gaku0606 0:c160cac4c370 7 #define BETA_DEF 0.1
Gaku0606 0:c160cac4c370 8
Gaku0606 0:c160cac4c370 9 /**
Gaku0606 2:e1de76e257f6 10 * @bref Madgwick Filterを用いて，角速度・加速度・地磁気データを統合し，姿勢を推定するライブラリです．
Gaku0606 2:e1de76e257f6 11 * @note Quaternion.hppを利用されることをお勧めいたします．
Gaku0606 0:c160cac4c370 12 */
Gaku0606 0:c160cac4c370 13 class MadgwickFilter{
Gaku0606 0:c160cac4c370 14
Gaku0606 0:c160cac4c370 15 public:
Gaku0606 0:c160cac4c370 16 /**
Gaku0606 2:e1de76e257f6 17 @bref マドグウィックフィルター(マッジュウィックフィルター)クラスのコンストラクタ
Gaku0606 0:c160cac4c370 18 @param B double型, この値を大きくすると重力の影響を大きく取るようになります．
Gaku0606 0:c160cac4c370 19 @note 引数無しの場合，B = 0.1fが代入されます．
Gaku0606 0:c160cac4c370 20 */
Gaku0606 0:c160cac4c370 21 MadgwickFilter(double B = BETA_DEF);
Gaku0606 0:c160cac4c370 22
Gaku0606 0:c160cac4c370 23 public:
Gaku0606 0:c160cac4c370 24 /**
Gaku0606 0:c160cac4c370 25 @bref MadgwickFilterによって角速度・加速度・地磁気データを統合し，姿勢計算します．
Gaku0606 0:c160cac4c370 26 @param gx,gy,gz 角速度データ，[rad]に変換してから入れてください．
Gaku0606 0:c160cac4c370 27 @param ax,ay,az 加速度データ, 特に規格化は必要ありません
Gaku0606 0:c160cac4c370 28 @param mx,my,mz 地磁気データ, キャリブレーションを確実に行って下さい．
Gaku0606 0:c160cac4c370 29 @note 角速度は[rad]にしてください．この関数は出来るだけ高速に呼び出し続けた方が良いと思います．
Gaku0606 0:c160cac4c370 30 @note 外部でローパスフィルタなどをかけることをお勧めします．
Gaku0606 0:c160cac4c370 31 */
Gaku0606 0:c160cac4c370 32 void MadgwickAHRSupdate(double gx, double gy, double gz, double ax, double ay, double az, double mx, double my, double mz);
Gaku0606 0:c160cac4c370 33
Gaku0606 0:c160cac4c370 34 /**
Gaku0606 0:c160cac4c370 35 @bref MadgwickFilterを角速度と加速度のみで動かし，姿勢計算を更新します．
Gaku0606 0:c160cac4c370 36 @param gx,gy,gz 角速度データ，[rad]に変換してから入れてください．
Gaku0606 0:c160cac4c370 37 @param ax,ay,az 加速度データ, 特に規格化は必要ありません
Gaku0606 0:c160cac4c370 38 @note 通常の関数でも，地磁気成分を0.0にすればこの関数が呼ばれます．
Gaku0606 0:c160cac4c370 39 */
Gaku0606 0:c160cac4c370 40 void MadgwickAHRSupdateIMU(double gx, double gy, double gz, double ax, double ay, double az);
Gaku0606 0:c160cac4c370 41
Gaku0606 0:c160cac4c370 42 /**
Gaku0606 0:c160cac4c370 43 @bref 姿勢を四元数で取得します．
Gaku0606 0:c160cac4c370 44 @param Q クォータニオンクラスのインスタンスアドレス, w・i・j・kを更新します．
Gaku0606 0:c160cac4c370 45 @note unityに入れる際は軸方向を修正してください．
Gaku0606 0:c160cac4c370 46 */
Gaku0606 0:c160cac4c370 47 void getAttitude(Quaternion *Q);
Gaku0606 0:c160cac4c370 48
Gaku0606 0:c160cac4c370 49 /**
Gaku0606 0:c160cac4c370 50 @bref 姿勢を四元数で取得します．
Gaku0606 0:c160cac4c370 51 @param _q0 実部w, double型, アドレス
Gaku0606 0:c160cac4c370 52 @param _q1 虚部i, double型, アドレス
Gaku0606 0:c160cac4c370 53 @param _q2 虚部j, double型, アドレス
Gaku0606 0:c160cac4c370 54 @param _q3 虚部k, double型, アドレス
Gaku0606 0:c160cac4c370 55 @note unityに入れる際は軸方向を修正してください．
Gaku0606 0:c160cac4c370 56 */
Gaku0606 0:c160cac4c370 57 void getAttitude(double *_q0, double *_q1, double *_q2, double *_q3);
Gaku0606 0:c160cac4c370 58
Gaku0606 0:c160cac4c370 59 /**
Gaku0606 0:c160cac4c370 60 @bref オイラー角で姿勢を取得します．
Gaku0606 0:c160cac4c370 61 @param val ロール，ピッチ，ヨーの順に配列に格納します．３つ以上の要素の配列を入れてください．
Gaku0606 0:c160cac4c370 62 @note 値は[rad]です．[degree]に変換が必要な場合は別途計算して下さい．
Gaku0606 0:c160cac4c370 63 */
Gaku0606 0:c160cac4c370 64 void getEulerAngle(double *val);
Gaku0606 0:c160cac4c370 65 public:
Gaku0606 0:c160cac4c370 66 Timer madgwickTimer;
Gaku0606 0:c160cac4c370 67 Quaternion q;
Gaku0606 0:c160cac4c370 68 double q0,q1,q2,q3;
Gaku0606 0:c160cac4c370 69 double beta;
Gaku0606 0:c160cac4c370 70 };
Gaku0606 0:c160cac4c370 71
Gaku0606 0:c160cac4c370 72 MadgwickFilter::MadgwickFilter(double B){
Gaku0606 0:c160cac4c370 73 q.w = 1.0f;
Gaku0606 0:c160cac4c370 74 q.x = 0.0f;
Gaku0606 0:c160cac4c370 75 q.y = 0.0f;
Gaku0606 0:c160cac4c370 76 q.z = 0.0f;
Gaku0606 0:c160cac4c370 77 beta = B;
Gaku0606 0:c160cac4c370 78 q0 = 1.0f;
Gaku0606 0:c160cac4c370 79 q1 = 0.0f;
Gaku0606 0:c160cac4c370 80 q2 = 0.0f;
Gaku0606 0:c160cac4c370 81 q3 = 0.0f;
Gaku0606 0:c160cac4c370 82 madgwickTimer.start();
Gaku0606 0:c160cac4c370 83 }
Gaku0606 0:c160cac4c370 84
Gaku0606 0:c160cac4c370 85 void MadgwickFilter::getAttitude(Quaternion *Q){
Gaku0606 0:c160cac4c370 86 *Q = q;
Gaku0606 0:c160cac4c370 87 return;
Gaku0606 0:c160cac4c370 88 }
Gaku0606 0:c160cac4c370 89
Gaku0606 0:c160cac4c370 90
Gaku0606 0:c160cac4c370 91
Gaku0606 0:c160cac4c370 92 void MadgwickFilter::getAttitude(double *_q0, double *_q1, double *_q2, double *_q3){
Gaku0606 0:c160cac4c370 93 *_q0 = q0;
Gaku0606 0:c160cac4c370 94 *_q1 = q1;
Gaku0606 0:c160cac4c370 95 *_q2 = q2;
Gaku0606 0:c160cac4c370 96 *_q3 = q3;
Gaku0606 0:c160cac4c370 97 return;
Gaku0606 0:c160cac4c370 98 }
Gaku0606 0:c160cac4c370 99
Gaku0606 0:c160cac4c370 100
Gaku0606 0:c160cac4c370 101 void MadgwickFilter::getEulerAngle(double *val){
Gaku0606 0:c160cac4c370 102 double q0q0 = q0 * q0, q1q1q2q2 = q1 * q1 - q2 * q2, q3q3 = q3 * q3;
Gaku0606 0:c160cac4c370 103 val[0] = (atan2(2.0f * (q0 * q1 + q2 * q3), q0q0 - q1q1q2q2 + q3q3));
Gaku0606 0:c160cac4c370 104 val[1] = (-asin(2.0f * (q1 * q3 - q0 * q2)));
Gaku0606 0:c160cac4c370 105 val[2] = (atan2(2.0f * (q1 * q2 + q0 * q3), q0q0 + q1q1q2q2 - q3q3));
Gaku0606 0:c160cac4c370 106 }
Gaku0606 0:c160cac4c370 107 //---------------------------------------------------------------------------------------------------
Gaku0606 0:c160cac4c370 108 // AHRS algorithm update
Gaku0606 0:c160cac4c370 109
Gaku0606 0:c160cac4c370 110 inline void MadgwickFilter::MadgwickAHRSupdate(double gx, double gy, double gz, double ax, double ay, double az, double mx, double my, double mz) {
Gaku0606 0:c160cac4c370 111 static double deltaT = 0;
Gaku0606 0:c160cac4c370 112 static unsigned int newTime = 0, oldTime = 0;
Gaku0606 0:c160cac4c370 113 double recipNorm;
Gaku0606 0:c160cac4c370 114 double s0, s1, s2, s3;
Gaku0606 0:c160cac4c370 115 double qDot1, qDot2, qDot3, qDot4;
Gaku0606 0:c160cac4c370 116 double hx, hy;
Gaku0606 0:c160cac4c370 117 double _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
Gaku0606 0:c160cac4c370 118
Gaku0606 0:c160cac4c370 119 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
Gaku0606 0:c160cac4c370 120 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
Gaku0606 0:c160cac4c370 121 MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
Gaku0606 0:c160cac4c370 122 return;
Gaku0606 0:c160cac4c370 123 }
Gaku0606 0:c160cac4c370 124
Gaku0606 0:c160cac4c370 125 // Rate of change of quaternion from gyroscope
Gaku0606 0:c160cac4c370 126 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Gaku0606 0:c160cac4c370 127 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Gaku0606 0:c160cac4c370 128 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Gaku0606 0:c160cac4c370 129 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Gaku0606 0:c160cac4c370 130
Gaku0606 0:c160cac4c370 131 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Gaku0606 0:c160cac4c370 132 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Gaku0606 0:c160cac4c370 133
Gaku0606 0:c160cac4c370 134 // Normalise accelerometer measurement
Gaku0606 0:c160cac4c370 135 recipNorm = 1.0 / sqrt(ax * ax + ay * ay + az * az);
Gaku0606 0:c160cac4c370 136 ax *= recipNorm;
Gaku0606 0:c160cac4c370 137 ay *= recipNorm;
Gaku0606 0:c160cac4c370 138 az *= recipNorm;
Gaku0606 0:c160cac4c370 139
Gaku0606 0:c160cac4c370 140 // Normalise magnetometer measurement
Gaku0606 0:c160cac4c370 141 recipNorm = 1.0 / sqrt(mx * mx + my * my + mz * mz);
Gaku0606 0:c160cac4c370 142 mx *= recipNorm;
Gaku0606 0:c160cac4c370 143 my *= recipNorm;
Gaku0606 0:c160cac4c370 144 mz *= recipNorm;
Gaku0606 0:c160cac4c370 145
Gaku0606 0:c160cac4c370 146 // Auxiliary variables to avoid repeated arithmetic
Gaku0606 0:c160cac4c370 147 _2q0mx = 2.0f * q0 * mx;
Gaku0606 0:c160cac4c370 148 _2q0my = 2.0f * q0 * my;
Gaku0606 0:c160cac4c370 149 _2q0mz = 2.0f * q0 * mz;
Gaku0606 0:c160cac4c370 150 _2q1mx = 2.0f * q1 * mx;
Gaku0606 0:c160cac4c370 151 _2q0 = 2.0f * q0;
Gaku0606 0:c160cac4c370 152 _2q1 = 2.0f * q1;
Gaku0606 0:c160cac4c370 153 _2q2 = 2.0f * q2;
Gaku0606 0:c160cac4c370 154 _2q3 = 2.0f * q3;
Gaku0606 0:c160cac4c370 155 _2q0q2 = 2.0f * q0 * q2;
Gaku0606 0:c160cac4c370 156 _2q2q3 = 2.0f * q2 * q3;
Gaku0606 0:c160cac4c370 157 q0q0 = q0 * q0;
Gaku0606 0:c160cac4c370 158 q0q1 = q0 * q1;
Gaku0606 0:c160cac4c370 159 q0q2 = q0 * q2;
Gaku0606 0:c160cac4c370 160 q0q3 = q0 * q3;
Gaku0606 0:c160cac4c370 161 q1q1 = q1 * q1;
Gaku0606 0:c160cac4c370 162 q1q2 = q1 * q2;
Gaku0606 0:c160cac4c370 163 q1q3 = q1 * q3;
Gaku0606 0:c160cac4c370 164 q2q2 = q2 * q2;
Gaku0606 0:c160cac4c370 165 q2q3 = q2 * q3;
Gaku0606 0:c160cac4c370 166 q3q3 = q3 * q3;
Gaku0606 0:c160cac4c370 167
Gaku0606 0:c160cac4c370 168 // Reference direction of Earth's magnetic field
Gaku0606 0:c160cac4c370 169 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Gaku0606 0:c160cac4c370 170 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Gaku0606 0:c160cac4c370 171 _2bx = sqrt(hx * hx + hy * hy);
Gaku0606 0:c160cac4c370 172 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Gaku0606 0:c160cac4c370 173 _4bx = 2.0f * _2bx;
Gaku0606 0:c160cac4c370 174 _4bz = 2.0f * _2bz;
Gaku0606 0:c160cac4c370 175
Gaku0606 0:c160cac4c370 176 // Gradient decent algorithm corrective step
Gaku0606 0:c160cac4c370 177 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);
Gaku0606 0:c160cac4c370 178 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);
Gaku0606 0:c160cac4c370 179 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);
Gaku0606 0:c160cac4c370 180 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);
Gaku0606 0:c160cac4c370 181 recipNorm = 1.0 / sqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Gaku0606 0:c160cac4c370 182 s0 *= recipNorm;
Gaku0606 0:c160cac4c370 183 s1 *= recipNorm;
Gaku0606 0:c160cac4c370 184 s2 *= recipNorm;
Gaku0606 0:c160cac4c370 185 s3 *= recipNorm;
Gaku0606 0:c160cac4c370 186
Gaku0606 0:c160cac4c370 187 // Apply feedback step
Gaku0606 0:c160cac4c370 188 qDot1 -= beta * s0;
Gaku0606 0:c160cac4c370 189 qDot2 -= beta * s1;
Gaku0606 0:c160cac4c370 190 qDot3 -= beta * s2;
Gaku0606 0:c160cac4c370 191 qDot4 -= beta * s3;
Gaku0606 0:c160cac4c370 192 }
Gaku0606 0:c160cac4c370 193
Gaku0606 0:c160cac4c370 194 // Integrate rate of change of quaternion to yield quaternion
Gaku0606 0:c160cac4c370 195 newTime = (unsigned int)madgwickTimer.read_us();
Gaku0606 0:c160cac4c370 196 deltaT = (newTime - oldTime) / 1000000.0;
Gaku0606 0:c160cac4c370 197 deltaT = fabs(deltaT);
Gaku0606 0:c160cac4c370 198 oldTime = newTime;
Gaku0606 0:c160cac4c370 199
Gaku0606 0:c160cac4c370 200 q0 += qDot1 * deltaT;//(1.0f / sampleFreq);
Gaku0606 0:c160cac4c370 201 q1 += qDot2 * deltaT;//(1.0f / sampleFreq);
Gaku0606 0:c160cac4c370 202 q2 += qDot3 * deltaT;//(1.0f / sampleFreq);
Gaku0606 0:c160cac4c370 203 q3 += qDot4 * deltaT;//(1.0f / sampleFreq);
Gaku0606 0:c160cac4c370 204
Gaku0606 0:c160cac4c370 205 // Normalise quaternion
Gaku0606 0:c160cac4c370 206 recipNorm = 1.0 / sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Gaku0606 0:c160cac4c370 207 q0 *= recipNorm;
Gaku0606 0:c160cac4c370 208 q1 *= recipNorm;
Gaku0606 0:c160cac4c370 209 q2 *= recipNorm;
Gaku0606 0:c160cac4c370 210 q3 *= recipNorm;
Gaku0606 0:c160cac4c370 211
Gaku0606 0:c160cac4c370 212 q.w = q0;
Gaku0606 0:c160cac4c370 213 q.x = q1;
Gaku0606 0:c160cac4c370 214 q.y = q2;
Gaku0606 0:c160cac4c370 215 q.z = q3;
Gaku0606 0:c160cac4c370 216 }
Gaku0606 0:c160cac4c370 217
Gaku0606 0:c160cac4c370 218 //---------------------------------------------------------------------------------------------------
Gaku0606 0:c160cac4c370 219 // IMU algorithm update
Gaku0606 0:c160cac4c370 220
Gaku0606 0:c160cac4c370 221 inline void MadgwickFilter::MadgwickAHRSupdateIMU(double gx, double gy, double gz, double ax, double ay, double az) {
Gaku0606 0:c160cac4c370 222 static double deltaT = 0;
Gaku0606 0:c160cac4c370 223 static unsigned int newTime = 0, oldTime = 0;
Gaku0606 0:c160cac4c370 224 double recipNorm;
Gaku0606 0:c160cac4c370 225 double s0, s1, s2, s3;
Gaku0606 0:c160cac4c370 226 double qDot1, qDot2, qDot3, qDot4;
Gaku0606 0:c160cac4c370 227 double _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
Gaku0606 0:c160cac4c370 228
Gaku0606 0:c160cac4c370 229 // Rate of change of quaternion from gyroscope
Gaku0606 0:c160cac4c370 230 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Gaku0606 0:c160cac4c370 231 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Gaku0606 0:c160cac4c370 232 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Gaku0606 0:c160cac4c370 233 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Gaku0606 0:c160cac4c370 234
Gaku0606 0:c160cac4c370 235 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Gaku0606 0:c160cac4c370 236 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Gaku0606 0:c160cac4c370 237
Gaku0606 0:c160cac4c370 238 // Normalise accelerometer measurement
Gaku0606 0:c160cac4c370 239 recipNorm = 1.0 / sqrt(ax * ax + ay * ay + az * az);
Gaku0606 0:c160cac4c370 240 ax *= recipNorm;
Gaku0606 0:c160cac4c370 241 ay *= recipNorm;
Gaku0606 0:c160cac4c370 242 az *= recipNorm;
Gaku0606 0:c160cac4c370 243
Gaku0606 0:c160cac4c370 244 // Auxiliary variables to avoid repeated arithmetic
Gaku0606 0:c160cac4c370 245 _2q0 = 2.0f * q0;
Gaku0606 0:c160cac4c370 246 _2q1 = 2.0f * q1;
Gaku0606 0:c160cac4c370 247 _2q2 = 2.0f * q2;
Gaku0606 0:c160cac4c370 248 _2q3 = 2.0f * q3;
Gaku0606 0:c160cac4c370 249 _4q0 = 4.0f * q0;
Gaku0606 0:c160cac4c370 250 _4q1 = 4.0f * q1;
Gaku0606 0:c160cac4c370 251 _4q2 = 4.0f * q2;
Gaku0606 0:c160cac4c370 252 _8q1 = 8.0f * q1;
Gaku0606 0:c160cac4c370 253 _8q2 = 8.0f * q2;
Gaku0606 0:c160cac4c370 254 q0q0 = q0 * q0;
Gaku0606 0:c160cac4c370 255 q1q1 = q1 * q1;
Gaku0606 0:c160cac4c370 256 q2q2 = q2 * q2;
Gaku0606 0:c160cac4c370 257 q3q3 = q3 * q3;
Gaku0606 0:c160cac4c370 258
Gaku0606 0:c160cac4c370 259 // Gradient decent algorithm corrective step
Gaku0606 0:c160cac4c370 260 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
Gaku0606 0:c160cac4c370 261 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
Gaku0606 0:c160cac4c370 262 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
Gaku0606 0:c160cac4c370 263 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
Gaku0606 0:c160cac4c370 264 recipNorm = 1.0 / sqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Gaku0606 0:c160cac4c370 265 s0 *= recipNorm;
Gaku0606 0:c160cac4c370 266 s1 *= recipNorm;
Gaku0606 0:c160cac4c370 267 s2 *= recipNorm;
Gaku0606 0:c160cac4c370 268 s3 *= recipNorm;
Gaku0606 0:c160cac4c370 269
Gaku0606 0:c160cac4c370 270 // Apply feedback step
Gaku0606 0:c160cac4c370 271 qDot1 -= beta * s0;
Gaku0606 0:c160cac4c370 272 qDot2 -= beta * s1;
Gaku0606 0:c160cac4c370 273 qDot3 -= beta * s2;
Gaku0606 0:c160cac4c370 274 qDot4 -= beta * s3;
Gaku0606 0:c160cac4c370 275 }
Gaku0606 0:c160cac4c370 276
Gaku0606 0:c160cac4c370 277 // Integrate rate of change of quaternion to yield quaternion
Gaku0606 0:c160cac4c370 278 newTime = (unsigned int)madgwickTimer.read_us();
Gaku0606 0:c160cac4c370 279 deltaT = (newTime - oldTime) / 1000000.0;
Gaku0606 0:c160cac4c370 280 deltaT = fabs(deltaT);
Gaku0606 0:c160cac4c370 281 oldTime = newTime;
Gaku0606 0:c160cac4c370 282 q0 += qDot1 * deltaT;;
Gaku0606 0:c160cac4c370 283 q1 += qDot2 * deltaT;;
Gaku0606 0:c160cac4c370 284 q2 += qDot3 * deltaT;;
Gaku0606 0:c160cac4c370 285 q3 += qDot4 * deltaT;;
Gaku0606 0:c160cac4c370 286
Gaku0606 0:c160cac4c370 287 // Normalise quaternion
Gaku0606 0:c160cac4c370 288 recipNorm = 1.0 / sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Gaku0606 0:c160cac4c370 289 q0 *= recipNorm;
Gaku0606 0:c160cac4c370 290 q1 *= recipNorm;
Gaku0606 0:c160cac4c370 291 q2 *= recipNorm;
Gaku0606 0:c160cac4c370 292 q3 *= recipNorm;
Gaku0606 0:c160cac4c370 293
Gaku0606 0:c160cac4c370 294 q.w = q0;
Gaku0606 0:c160cac4c370 295 q.x = q1;
Gaku0606 0:c160cac4c370 296 q.y = q2;
Gaku0606 0:c160cac4c370 297 q.z = q3;
Gaku0606 0:c160cac4c370 298 }
Gaku0606 0:c160cac4c370 299
Gaku0606 0:c160cac4c370 300
Gaku0606 0:c160cac4c370 301 #endif