Erik van de Coevering / Mbed 2 deprecated Multicopter_2018

Latest version of my quadcopter controller with an LPC1768 and MPU9250.

Dependencies:   mbed

Currently running on a custom PCB with 30.5 x 30.5mm mounts. There are also 2 PC apps that go with the software; one to set up the PID controller and one to balance the motors and props. If anyone is interested, send me a message and I'll upload them.

Madgwick/MadgwickAHRS.cpp@0:0929d3d566cf, 2018-07-09 (annotated)

Committer:
Anaesthetix
Date:
Mon Jul 09 16:31:40 2018 +0000
Revision:
0:0929d3d566cf
Child:
5:0f4204941604
Latest version of my multicopter controller

Who changed what in which revision?

UserRevisionLine numberNew contents of line
Anaesthetix 0:0929d3d566cf 1 //=============================================================================================
Anaesthetix 0:0929d3d566cf 2 // MadgwickAHRS.c
Anaesthetix 0:0929d3d566cf 3 //=============================================================================================
Anaesthetix 0:0929d3d566cf 4 //
Anaesthetix 0:0929d3d566cf 5 // Implementation of Madgwick's IMU and AHRS algorithms.
Anaesthetix 0:0929d3d566cf 6 // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
Anaesthetix 0:0929d3d566cf 7 //
Anaesthetix 0:0929d3d566cf 8 // From the x-io website "Open-source resources available on this website are
Anaesthetix 0:0929d3d566cf 9 // provided under the GNU General Public Licence unless an alternative licence
Anaesthetix 0:0929d3d566cf 10 // is provided in source."
Anaesthetix 0:0929d3d566cf 11 //
Anaesthetix 0:0929d3d566cf 12 // Date Author Notes
Anaesthetix 0:0929d3d566cf 13 // 29/09/2011 SOH Madgwick Initial release
Anaesthetix 0:0929d3d566cf 14 // 02/10/2011 SOH Madgwick Optimised for reduced CPU load
Anaesthetix 0:0929d3d566cf 15 // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
Anaesthetix 0:0929d3d566cf 16 //
Anaesthetix 0:0929d3d566cf 17 //=============================================================================================
Anaesthetix 0:0929d3d566cf 18
Anaesthetix 0:0929d3d566cf 19 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 20 // Header files
Anaesthetix 0:0929d3d566cf 21
Anaesthetix 0:0929d3d566cf 22 #include "MadgwickAHRS.h"
Anaesthetix 0:0929d3d566cf 23 #include <math.h>
Anaesthetix 0:0929d3d566cf 24
Anaesthetix 0:0929d3d566cf 25 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 26 // Definitions
Anaesthetix 0:0929d3d566cf 27
Anaesthetix 0:0929d3d566cf 28 #define sampleFreqDef 1500.0f // sample frequency in Hz
Anaesthetix 0:0929d3d566cf 29 #define betaDef 0.1f // 2 * proportional gain 0.1 - 0.5 - 5 was 2.5
Anaesthetix 0:0929d3d566cf 30
Anaesthetix 0:0929d3d566cf 31
Anaesthetix 0:0929d3d566cf 32 //============================================================================================
Anaesthetix 0:0929d3d566cf 33 // Functions
Anaesthetix 0:0929d3d566cf 34
Anaesthetix 0:0929d3d566cf 35 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 36 // AHRS algorithm update
Anaesthetix 0:0929d3d566cf 37
Anaesthetix 0:0929d3d566cf 38 Madgwick::Madgwick() {
Anaesthetix 0:0929d3d566cf 39 beta = betaDef;
Anaesthetix 0:0929d3d566cf 40 q0 = 1.0f;
Anaesthetix 0:0929d3d566cf 41 q1 = 0.0f;
Anaesthetix 0:0929d3d566cf 42 q2 = 0.0f;
Anaesthetix 0:0929d3d566cf 43 q3 = 0.0f;
Anaesthetix 0:0929d3d566cf 44 invSampleFreq = 1.0f / sampleFreqDef;
Anaesthetix 0:0929d3d566cf 45 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 46 }
Anaesthetix 0:0929d3d566cf 47
Anaesthetix 0:0929d3d566cf 48 void Madgwick::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
Anaesthetix 0:0929d3d566cf 49 float recipNorm;
Anaesthetix 0:0929d3d566cf 50 float s0, s1, s2, s3;
Anaesthetix 0:0929d3d566cf 51 float qDot1, qDot2, qDot3, qDot4;
Anaesthetix 0:0929d3d566cf 52 float hx, hy;
Anaesthetix 0:0929d3d566cf 53 float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _8bx, _8bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
Anaesthetix 0:0929d3d566cf 54
Anaesthetix 0:0929d3d566cf 55 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
Anaesthetix 0:0929d3d566cf 56 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
Anaesthetix 0:0929d3d566cf 57 updateIMU(gx, gy, gz, ax, ay, az);
Anaesthetix 0:0929d3d566cf 58 return;
Anaesthetix 0:0929d3d566cf 59 }
Anaesthetix 0:0929d3d566cf 60
Anaesthetix 0:0929d3d566cf 61 // Convert gyroscope degrees/sec to radians/sec
Anaesthetix 0:0929d3d566cf 62 gx *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 63 gy *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 64 gz *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 65
Anaesthetix 0:0929d3d566cf 66 // Rate of change of quaternion from gyroscope
Anaesthetix 0:0929d3d566cf 67 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Anaesthetix 0:0929d3d566cf 68 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Anaesthetix 0:0929d3d566cf 69 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Anaesthetix 0:0929d3d566cf 70 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Anaesthetix 0:0929d3d566cf 71
Anaesthetix 0:0929d3d566cf 72 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Anaesthetix 0:0929d3d566cf 73 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Anaesthetix 0:0929d3d566cf 74
Anaesthetix 0:0929d3d566cf 75 // Normalise accelerometer measurement
Anaesthetix 0:0929d3d566cf 76 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Anaesthetix 0:0929d3d566cf 77 ax *= recipNorm;
Anaesthetix 0:0929d3d566cf 78 ay *= recipNorm;
Anaesthetix 0:0929d3d566cf 79 az *= recipNorm;
Anaesthetix 0:0929d3d566cf 80
Anaesthetix 0:0929d3d566cf 81 // Normalise magnetometer measurement
Anaesthetix 0:0929d3d566cf 82 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
Anaesthetix 0:0929d3d566cf 83 mx *= recipNorm;
Anaesthetix 0:0929d3d566cf 84 my *= recipNorm;
Anaesthetix 0:0929d3d566cf 85 mz *= recipNorm;
Anaesthetix 0:0929d3d566cf 86
Anaesthetix 0:0929d3d566cf 87 // Auxiliary variables to avoid repeated arithmetic
Anaesthetix 0:0929d3d566cf 88 _2q0mx = 2.0f * q0 * mx;
Anaesthetix 0:0929d3d566cf 89 _2q0my = 2.0f * q0 * my;
Anaesthetix 0:0929d3d566cf 90 _2q0mz = 2.0f * q0 * mz;
Anaesthetix 0:0929d3d566cf 91 _2q1mx = 2.0f * q1 * mx;
Anaesthetix 0:0929d3d566cf 92 _2q0 = 2.0f * q0;
Anaesthetix 0:0929d3d566cf 93 _2q1 = 2.0f * q1;
Anaesthetix 0:0929d3d566cf 94 _2q2 = 2.0f * q2;
Anaesthetix 0:0929d3d566cf 95 _2q3 = 2.0f * q3;
Anaesthetix 0:0929d3d566cf 96 _2q0q2 = 2.0f * q0 * q2;
Anaesthetix 0:0929d3d566cf 97 _2q2q3 = 2.0f * q2 * q3;
Anaesthetix 0:0929d3d566cf 98 q0q0 = q0 * q0;
Anaesthetix 0:0929d3d566cf 99 q0q1 = q0 * q1;
Anaesthetix 0:0929d3d566cf 100 q0q2 = q0 * q2;
Anaesthetix 0:0929d3d566cf 101 q0q3 = q0 * q3;
Anaesthetix 0:0929d3d566cf 102 q1q1 = q1 * q1;
Anaesthetix 0:0929d3d566cf 103 q1q2 = q1 * q2;
Anaesthetix 0:0929d3d566cf 104 q1q3 = q1 * q3;
Anaesthetix 0:0929d3d566cf 105 q2q2 = q2 * q2;
Anaesthetix 0:0929d3d566cf 106 q2q3 = q2 * q3;
Anaesthetix 0:0929d3d566cf 107 q3q3 = q3 * q3;
Anaesthetix 0:0929d3d566cf 108 /*
Anaesthetix 0:0929d3d566cf 109 // Reference direction of Earth's magnetic field
Anaesthetix 0:0929d3d566cf 110 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Anaesthetix 0:0929d3d566cf 111 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Anaesthetix 0:0929d3d566cf 112 _2bx = sqrtf(hx * hx + hy * hy);
Anaesthetix 0:0929d3d566cf 113 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Anaesthetix 0:0929d3d566cf 114 _4bx = 2.0f * _2bx;
Anaesthetix 0:0929d3d566cf 115 _4bz = 2.0f * _2bz;
Anaesthetix 0:0929d3d566cf 116
Anaesthetix 0:0929d3d566cf 117 // Gradient decent algorithm corrective step
Anaesthetix 0:0929d3d566cf 118 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);
Anaesthetix 0:0929d3d566cf 119 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);
Anaesthetix 0:0929d3d566cf 120 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);
Anaesthetix 0:0929d3d566cf 121 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);
Anaesthetix 0:0929d3d566cf 122 */
Anaesthetix 0:0929d3d566cf 123 // Reference direction of Earth's magnetic field
Anaesthetix 0:0929d3d566cf 124 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Anaesthetix 0:0929d3d566cf 125 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Anaesthetix 0:0929d3d566cf 126 _2bx = sqrt(hx * hx + hy * hy);
Anaesthetix 0:0929d3d566cf 127 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Anaesthetix 0:0929d3d566cf 128 _4bx = 2.0f * _2bx;
Anaesthetix 0:0929d3d566cf 129 _4bz = 2.0f * _2bz;
Anaesthetix 0:0929d3d566cf 130 _8bx = 2.0f * _4bx;
Anaesthetix 0:0929d3d566cf 131 _8bz = 2.0f * _4bz;
Anaesthetix 0:0929d3d566cf 132
Anaesthetix 0:0929d3d566cf 133 // Gradient decent algorithm corrective step
Anaesthetix 0:0929d3d566cf 134 s0= -_2q2*(2.0f*(q1q3 - q0q2) - ax) + _2q1*(2.0f*(q0q1 + q2q3) - ay) + -_4bz*q2*(_4bx*(0.5 - q2q2 - q3q3) + _4bz*(q1q3 - q0q2) - mx) + (-_4bx*q3+_4bz*q1)*(_4bx*(q1q2 - q0q3) + _4bz*(q0q1 + q2q3) - my) + _4bx*q2*(_4bx*(q0q2 + q1q3) + _4bz*(0.5 - q1q1 - q2q2) - mz);
Anaesthetix 0:0929d3d566cf 135 s1= _2q3*(2.0f*(q1q3 - q0q2) - ax) + _2q0*(2.0f*(q0q1 + q2q3) - ay) + -4.0f*q1*(2.0f*(0.5 - q1q1 - q2q2) - az) + _4bz*q3*(_4bx*(0.5 - q2q2 - q3q3) + _4bz*(q1q3 - q0q2) - mx) + (_4bx*q2+_4bz*q0)*(_4bx*(q1q2 - q0q3) + _4bz*(q0q1 + q2q3) - my) + (_4bx*q3-_8bz*q1)*(_4bx*(q0q2 + q1q3) + _4bz*(0.5 - q1q1 - q2q2) - mz);
Anaesthetix 0:0929d3d566cf 136 s2= -_2q0*(2.0f*(q1q3 - q0q2) - ax) + _2q3*(2.0f*(q0q1 + q2q3) - ay) + (-4.0f*q2)*(2.0f*(0.5 - q1q1 - q2q2) - az) + (-_8bx*q2-_4bz*q0)*(_4bx*(0.5 - q2q2 - q3q3) + _4bz*(q1q3 - q0q2) - mx)+(_4bx*q1+_4bz*q3)*(_4bx*(q1q2 - q0q3) + _4bz*(q0q1 + q2q3) - my)+(_4bx*q0-_8bz*q2)*(_4bx*(q0q2 + q1q3) + _4bz*(0.5 - q1q1 - q2q2) - mz);
Anaesthetix 0:0929d3d566cf 137 s3= _2q1*(2.0f*(q1q3 - q0q2) - ax) + _2q2*(2.0f*(q0q1 + q2q3) - ay)+(-_8bx*q3+_4bz*q1)*(_4bx*(0.5 - q2q2 - q3q3) + _4bz*(q1q3 - q0q2) - mx)+(-_4bx*q0+_4bz*q2)*(_4bx*(q1q2 - q0q3) + _4bz*(q0q1 + q2q3) - my)+(_4bx*q1)*(_4bx*(q0q2 + q1q3) + _4bz*(0.5 - q1q1 - q2q2) - mz);
Anaesthetix 0:0929d3d566cf 138 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Anaesthetix 0:0929d3d566cf 139 s0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 140 s1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 141 s2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 142 s3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 143
Anaesthetix 0:0929d3d566cf 144 // Apply feedback step
Anaesthetix 0:0929d3d566cf 145 qDot1 -= beta * s0;
Anaesthetix 0:0929d3d566cf 146 qDot2 -= beta * s1;
Anaesthetix 0:0929d3d566cf 147 qDot3 -= beta * s2;
Anaesthetix 0:0929d3d566cf 148 qDot4 -= beta * s3;
Anaesthetix 0:0929d3d566cf 149 }
Anaesthetix 0:0929d3d566cf 150
Anaesthetix 0:0929d3d566cf 151 // Integrate rate of change of quaternion to yield quaternion
Anaesthetix 0:0929d3d566cf 152 q0 += qDot1 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 153 q1 += qDot2 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 154 q2 += qDot3 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 155 q3 += qDot4 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 156
Anaesthetix 0:0929d3d566cf 157 // Normalise quaternion
Anaesthetix 0:0929d3d566cf 158 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Anaesthetix 0:0929d3d566cf 159 q0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 160 q1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 161 q2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 162 q3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 163 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 164 }
Anaesthetix 0:0929d3d566cf 165
Anaesthetix 0:0929d3d566cf 166 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 167 // IMU algorithm update
Anaesthetix 0:0929d3d566cf 168
Anaesthetix 0:0929d3d566cf 169 void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
Anaesthetix 0:0929d3d566cf 170 float recipNorm;
Anaesthetix 0:0929d3d566cf 171 float s0, s1, s2, s3;
Anaesthetix 0:0929d3d566cf 172 float qDot1, qDot2, qDot3, qDot4;
Anaesthetix 0:0929d3d566cf 173 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
Anaesthetix 0:0929d3d566cf 174
Anaesthetix 0:0929d3d566cf 175 // Convert gyroscope degrees/sec to radians/sec
Anaesthetix 0:0929d3d566cf 176 gx *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 177 gy *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 178 gz *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 179
Anaesthetix 0:0929d3d566cf 180 // Rate of change of quaternion from gyroscope
Anaesthetix 0:0929d3d566cf 181 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Anaesthetix 0:0929d3d566cf 182 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Anaesthetix 0:0929d3d566cf 183 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Anaesthetix 0:0929d3d566cf 184 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Anaesthetix 0:0929d3d566cf 185
Anaesthetix 0:0929d3d566cf 186 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Anaesthetix 0:0929d3d566cf 187 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Anaesthetix 0:0929d3d566cf 188
Anaesthetix 0:0929d3d566cf 189 // Normalise accelerometer measurement
Anaesthetix 0:0929d3d566cf 190 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Anaesthetix 0:0929d3d566cf 191 ax *= recipNorm;
Anaesthetix 0:0929d3d566cf 192 ay *= recipNorm;
Anaesthetix 0:0929d3d566cf 193 az *= recipNorm;
Anaesthetix 0:0929d3d566cf 194
Anaesthetix 0:0929d3d566cf 195 // Auxiliary variables to avoid repeated arithmetic
Anaesthetix 0:0929d3d566cf 196 _2q0 = 2.0f * q0;
Anaesthetix 0:0929d3d566cf 197 _2q1 = 2.0f * q1;
Anaesthetix 0:0929d3d566cf 198 _2q2 = 2.0f * q2;
Anaesthetix 0:0929d3d566cf 199 _2q3 = 2.0f * q3;
Anaesthetix 0:0929d3d566cf 200 _4q0 = 4.0f * q0;
Anaesthetix 0:0929d3d566cf 201 _4q1 = 4.0f * q1;
Anaesthetix 0:0929d3d566cf 202 _4q2 = 4.0f * q2;
Anaesthetix 0:0929d3d566cf 203 _8q1 = 8.0f * q1;
Anaesthetix 0:0929d3d566cf 204 _8q2 = 8.0f * q2;
Anaesthetix 0:0929d3d566cf 205 q0q0 = q0 * q0;
Anaesthetix 0:0929d3d566cf 206 q1q1 = q1 * q1;
Anaesthetix 0:0929d3d566cf 207 q2q2 = q2 * q2;
Anaesthetix 0:0929d3d566cf 208 q3q3 = q3 * q3;
Anaesthetix 0:0929d3d566cf 209
Anaesthetix 0:0929d3d566cf 210 // Gradient decent algorithm corrective step
Anaesthetix 0:0929d3d566cf 211 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
Anaesthetix 0:0929d3d566cf 212 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
Anaesthetix 0:0929d3d566cf 213 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
Anaesthetix 0:0929d3d566cf 214 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
Anaesthetix 0:0929d3d566cf 215 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Anaesthetix 0:0929d3d566cf 216 s0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 217 s1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 218 s2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 219 s3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 220
Anaesthetix 0:0929d3d566cf 221 // Apply feedback step
Anaesthetix 0:0929d3d566cf 222 qDot1 -= beta * s0;
Anaesthetix 0:0929d3d566cf 223 qDot2 -= beta * s1;
Anaesthetix 0:0929d3d566cf 224 qDot3 -= beta * s2;
Anaesthetix 0:0929d3d566cf 225 qDot4 -= beta * s3;
Anaesthetix 0:0929d3d566cf 226 }
Anaesthetix 0:0929d3d566cf 227
Anaesthetix 0:0929d3d566cf 228 // Integrate rate of change of quaternion to yield quaternion
Anaesthetix 0:0929d3d566cf 229 q0 += qDot1 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 230 q1 += qDot2 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 231 q2 += qDot3 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 232 q3 += qDot4 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 233
Anaesthetix 0:0929d3d566cf 234 // Normalise quaternion
Anaesthetix 0:0929d3d566cf 235 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Anaesthetix 0:0929d3d566cf 236 q0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 237 q1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 238 q2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 239 q3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 240 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 241 }
Anaesthetix 0:0929d3d566cf 242
Anaesthetix 0:0929d3d566cf 243 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 244 // Fast inverse square-root
Anaesthetix 0:0929d3d566cf 245 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
Anaesthetix 0:0929d3d566cf 246
Anaesthetix 0:0929d3d566cf 247 /*float Madgwick::invSqrt(float x) {
Anaesthetix 0:0929d3d566cf 248 float halfx = 0.5f * x;
Anaesthetix 0:0929d3d566cf 249 float y = x;
Anaesthetix 0:0929d3d566cf 250 long i = *(long*)&y;
Anaesthetix 0:0929d3d566cf 251 i = 0x5f3759df - (i>>1);
Anaesthetix 0:0929d3d566cf 252 y = *(float*)&i;
Anaesthetix 0:0929d3d566cf 253 y = y * (1.5f - (halfx * y * y));
Anaesthetix 0:0929d3d566cf 254 y = y * (1.5f - (halfx * y * y));
Anaesthetix 0:0929d3d566cf 255 return y;
Anaesthetix 0:0929d3d566cf 256 }
Anaesthetix 0:0929d3d566cf 257
Anaesthetix 0:0929d3d566cf 258 float Madgwick::invSqrt(float x){
Anaesthetix 0:0929d3d566cf 259 unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
Anaesthetix 0:0929d3d566cf 260 float tmp = *(float*)&i;
Anaesthetix 0:0929d3d566cf 261 return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
Anaesthetix 0:0929d3d566cf 262 }
Anaesthetix 0:0929d3d566cf 263 */
Anaesthetix 0:0929d3d566cf 264 float Madgwick::invSqrt(float x) {
Anaesthetix 0:0929d3d566cf 265 float tmp = 1/(sqrt(x));
Anaesthetix 0:0929d3d566cf 266 return tmp;
Anaesthetix 0:0929d3d566cf 267 }
Anaesthetix 0:0929d3d566cf 268
Anaesthetix 0:0929d3d566cf 269 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 270
Anaesthetix 0:0929d3d566cf 271 void Madgwick::computeAngles()
Anaesthetix 0:0929d3d566cf 272 {
Anaesthetix 0:0929d3d566cf 273 roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
Anaesthetix 0:0929d3d566cf 274 pitch = asinf(-2.0f * (q1*q3 - q0*q2));
Anaesthetix 0:0929d3d566cf 275 yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
Anaesthetix 0:0929d3d566cf 276 anglesComputed = 1;
Anaesthetix 0:0929d3d566cf 277 }
Anaesthetix 0:0929d3d566cf 278