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@5:0f4204941604, 2018-07-13 (annotated)

Committer:
Anaesthetix
Date:
Fri Jul 13 14:27:30 2018 +0000
Revision:
5:0f4204941604
Parent:
0:0929d3d566cf 
Yaw PID added

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 5:0f4204941604 38 Madgwick::Madgwick()
Anaesthetix 5:0f4204941604 39 {
Anaesthetix 0:0929d3d566cf 40 beta = betaDef;
Anaesthetix 0:0929d3d566cf 41 q0 = 1.0f;
Anaesthetix 0:0929d3d566cf 42 q1 = 0.0f;
Anaesthetix 0:0929d3d566cf 43 q2 = 0.0f;
Anaesthetix 0:0929d3d566cf 44 q3 = 0.0f;
Anaesthetix 0:0929d3d566cf 45 invSampleFreq = 1.0f / sampleFreqDef;
Anaesthetix 0:0929d3d566cf 46 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 47 }
Anaesthetix 0:0929d3d566cf 48
Anaesthetix 5:0f4204941604 49 void Madgwick::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz)
Anaesthetix 5:0f4204941604 50 {
Anaesthetix 0:0929d3d566cf 51 float recipNorm;
Anaesthetix 0:0929d3d566cf 52 float s0, s1, s2, s3;
Anaesthetix 0:0929d3d566cf 53 float qDot1, qDot2, qDot3, qDot4;
Anaesthetix 0:0929d3d566cf 54 float hx, hy;
Anaesthetix 0:0929d3d566cf 55 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 56
Anaesthetix 0:0929d3d566cf 57 // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
Anaesthetix 0:0929d3d566cf 58 if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
Anaesthetix 0:0929d3d566cf 59 updateIMU(gx, gy, gz, ax, ay, az);
Anaesthetix 0:0929d3d566cf 60 return;
Anaesthetix 0:0929d3d566cf 61 }
Anaesthetix 0:0929d3d566cf 62
Anaesthetix 0:0929d3d566cf 63 // Convert gyroscope degrees/sec to radians/sec
Anaesthetix 0:0929d3d566cf 64 gx *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 65 gy *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 66 gz *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 67
Anaesthetix 0:0929d3d566cf 68 // Rate of change of quaternion from gyroscope
Anaesthetix 0:0929d3d566cf 69 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Anaesthetix 0:0929d3d566cf 70 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Anaesthetix 0:0929d3d566cf 71 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Anaesthetix 0:0929d3d566cf 72 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Anaesthetix 0:0929d3d566cf 73
Anaesthetix 0:0929d3d566cf 74 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Anaesthetix 0:0929d3d566cf 75 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Anaesthetix 0:0929d3d566cf 76
Anaesthetix 0:0929d3d566cf 77 // Normalise accelerometer measurement
Anaesthetix 0:0929d3d566cf 78 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Anaesthetix 0:0929d3d566cf 79 ax *= recipNorm;
Anaesthetix 0:0929d3d566cf 80 ay *= recipNorm;
Anaesthetix 0:0929d3d566cf 81 az *= recipNorm;
Anaesthetix 0:0929d3d566cf 82
Anaesthetix 0:0929d3d566cf 83 // Normalise magnetometer measurement
Anaesthetix 0:0929d3d566cf 84 recipNorm = invSqrt(mx * mx + my * my + mz * mz);
Anaesthetix 0:0929d3d566cf 85 mx *= recipNorm;
Anaesthetix 0:0929d3d566cf 86 my *= recipNorm;
Anaesthetix 0:0929d3d566cf 87 mz *= recipNorm;
Anaesthetix 0:0929d3d566cf 88
Anaesthetix 0:0929d3d566cf 89 // Auxiliary variables to avoid repeated arithmetic
Anaesthetix 0:0929d3d566cf 90 _2q0mx = 2.0f * q0 * mx;
Anaesthetix 0:0929d3d566cf 91 _2q0my = 2.0f * q0 * my;
Anaesthetix 0:0929d3d566cf 92 _2q0mz = 2.0f * q0 * mz;
Anaesthetix 0:0929d3d566cf 93 _2q1mx = 2.0f * q1 * mx;
Anaesthetix 0:0929d3d566cf 94 _2q0 = 2.0f * q0;
Anaesthetix 0:0929d3d566cf 95 _2q1 = 2.0f * q1;
Anaesthetix 0:0929d3d566cf 96 _2q2 = 2.0f * q2;
Anaesthetix 0:0929d3d566cf 97 _2q3 = 2.0f * q3;
Anaesthetix 0:0929d3d566cf 98 _2q0q2 = 2.0f * q0 * q2;
Anaesthetix 0:0929d3d566cf 99 _2q2q3 = 2.0f * q2 * q3;
Anaesthetix 0:0929d3d566cf 100 q0q0 = q0 * q0;
Anaesthetix 0:0929d3d566cf 101 q0q1 = q0 * q1;
Anaesthetix 0:0929d3d566cf 102 q0q2 = q0 * q2;
Anaesthetix 0:0929d3d566cf 103 q0q3 = q0 * q3;
Anaesthetix 0:0929d3d566cf 104 q1q1 = q1 * q1;
Anaesthetix 0:0929d3d566cf 105 q1q2 = q1 * q2;
Anaesthetix 0:0929d3d566cf 106 q1q3 = q1 * q3;
Anaesthetix 0:0929d3d566cf 107 q2q2 = q2 * q2;
Anaesthetix 0:0929d3d566cf 108 q2q3 = q2 * q3;
Anaesthetix 0:0929d3d566cf 109 q3q3 = q3 * q3;
Anaesthetix 5:0f4204941604 110 /*
Anaesthetix 5:0f4204941604 111 // Reference direction of Earth's magnetic field
Anaesthetix 5:0f4204941604 112 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Anaesthetix 5:0f4204941604 113 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Anaesthetix 5:0f4204941604 114 _2bx = sqrtf(hx * hx + hy * hy);
Anaesthetix 5:0f4204941604 115 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Anaesthetix 5:0f4204941604 116 _4bx = 2.0f * _2bx;
Anaesthetix 5:0f4204941604 117 _4bz = 2.0f * _2bz;
Anaesthetix 5:0f4204941604 118
Anaesthetix 5:0f4204941604 119 // Gradient decent algorithm corrective step
Anaesthetix 5:0f4204941604 120 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 5:0f4204941604 121 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 5:0f4204941604 122 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 5:0f4204941604 123 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 5:0f4204941604 124 */
Anaesthetix 0:0929d3d566cf 125 // Reference direction of Earth's magnetic field
Anaesthetix 0:0929d3d566cf 126 hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
Anaesthetix 0:0929d3d566cf 127 hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
Anaesthetix 5:0f4204941604 128 _2bx = sqrt(hx * hx + hy * hy);
Anaesthetix 0:0929d3d566cf 129 _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
Anaesthetix 0:0929d3d566cf 130 _4bx = 2.0f * _2bx;
Anaesthetix 0:0929d3d566cf 131 _4bz = 2.0f * _2bz;
Anaesthetix 5:0f4204941604 132 _8bx = 2.0f * _4bx;
Anaesthetix 5:0f4204941604 133 _8bz = 2.0f * _4bz;
Anaesthetix 0:0929d3d566cf 134
Anaesthetix 0:0929d3d566cf 135 // Gradient decent algorithm corrective step
Anaesthetix 5:0f4204941604 136 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 5:0f4204941604 137 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 5:0f4204941604 138 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 5:0f4204941604 139 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 5:0f4204941604 140 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Anaesthetix 0:0929d3d566cf 141 s0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 142 s1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 143 s2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 144 s3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 145
Anaesthetix 0:0929d3d566cf 146 // Apply feedback step
Anaesthetix 0:0929d3d566cf 147 qDot1 -= beta * s0;
Anaesthetix 0:0929d3d566cf 148 qDot2 -= beta * s1;
Anaesthetix 0:0929d3d566cf 149 qDot3 -= beta * s2;
Anaesthetix 0:0929d3d566cf 150 qDot4 -= beta * s3;
Anaesthetix 0:0929d3d566cf 151 }
Anaesthetix 0:0929d3d566cf 152
Anaesthetix 0:0929d3d566cf 153 // Integrate rate of change of quaternion to yield quaternion
Anaesthetix 0:0929d3d566cf 154 q0 += qDot1 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 155 q1 += qDot2 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 156 q2 += qDot3 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 157 q3 += qDot4 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 158
Anaesthetix 0:0929d3d566cf 159 // Normalise quaternion
Anaesthetix 0:0929d3d566cf 160 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Anaesthetix 0:0929d3d566cf 161 q0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 162 q1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 163 q2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 164 q3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 165 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 166 }
Anaesthetix 0:0929d3d566cf 167
Anaesthetix 0:0929d3d566cf 168 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 169 // IMU algorithm update
Anaesthetix 0:0929d3d566cf 170
Anaesthetix 5:0f4204941604 171 void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
Anaesthetix 5:0f4204941604 172 {
Anaesthetix 0:0929d3d566cf 173 float recipNorm;
Anaesthetix 0:0929d3d566cf 174 float s0, s1, s2, s3;
Anaesthetix 0:0929d3d566cf 175 float qDot1, qDot2, qDot3, qDot4;
Anaesthetix 0:0929d3d566cf 176 float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
Anaesthetix 0:0929d3d566cf 177
Anaesthetix 0:0929d3d566cf 178 // Convert gyroscope degrees/sec to radians/sec
Anaesthetix 0:0929d3d566cf 179 gx *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 180 gy *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 181 gz *= 0.0174533f;
Anaesthetix 0:0929d3d566cf 182
Anaesthetix 0:0929d3d566cf 183 // Rate of change of quaternion from gyroscope
Anaesthetix 0:0929d3d566cf 184 qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
Anaesthetix 0:0929d3d566cf 185 qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
Anaesthetix 0:0929d3d566cf 186 qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
Anaesthetix 0:0929d3d566cf 187 qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
Anaesthetix 0:0929d3d566cf 188
Anaesthetix 0:0929d3d566cf 189 // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
Anaesthetix 0:0929d3d566cf 190 if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
Anaesthetix 0:0929d3d566cf 191
Anaesthetix 0:0929d3d566cf 192 // Normalise accelerometer measurement
Anaesthetix 0:0929d3d566cf 193 recipNorm = invSqrt(ax * ax + ay * ay + az * az);
Anaesthetix 0:0929d3d566cf 194 ax *= recipNorm;
Anaesthetix 0:0929d3d566cf 195 ay *= recipNorm;
Anaesthetix 0:0929d3d566cf 196 az *= recipNorm;
Anaesthetix 0:0929d3d566cf 197
Anaesthetix 0:0929d3d566cf 198 // Auxiliary variables to avoid repeated arithmetic
Anaesthetix 0:0929d3d566cf 199 _2q0 = 2.0f * q0;
Anaesthetix 0:0929d3d566cf 200 _2q1 = 2.0f * q1;
Anaesthetix 0:0929d3d566cf 201 _2q2 = 2.0f * q2;
Anaesthetix 0:0929d3d566cf 202 _2q3 = 2.0f * q3;
Anaesthetix 0:0929d3d566cf 203 _4q0 = 4.0f * q0;
Anaesthetix 0:0929d3d566cf 204 _4q1 = 4.0f * q1;
Anaesthetix 0:0929d3d566cf 205 _4q2 = 4.0f * q2;
Anaesthetix 0:0929d3d566cf 206 _8q1 = 8.0f * q1;
Anaesthetix 0:0929d3d566cf 207 _8q2 = 8.0f * q2;
Anaesthetix 0:0929d3d566cf 208 q0q0 = q0 * q0;
Anaesthetix 0:0929d3d566cf 209 q1q1 = q1 * q1;
Anaesthetix 0:0929d3d566cf 210 q2q2 = q2 * q2;
Anaesthetix 0:0929d3d566cf 211 q3q3 = q3 * q3;
Anaesthetix 0:0929d3d566cf 212
Anaesthetix 0:0929d3d566cf 213 // Gradient decent algorithm corrective step
Anaesthetix 0:0929d3d566cf 214 s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
Anaesthetix 0:0929d3d566cf 215 s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
Anaesthetix 0:0929d3d566cf 216 s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
Anaesthetix 0:0929d3d566cf 217 s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
Anaesthetix 0:0929d3d566cf 218 recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
Anaesthetix 0:0929d3d566cf 219 s0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 220 s1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 221 s2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 222 s3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 223
Anaesthetix 0:0929d3d566cf 224 // Apply feedback step
Anaesthetix 0:0929d3d566cf 225 qDot1 -= beta * s0;
Anaesthetix 0:0929d3d566cf 226 qDot2 -= beta * s1;
Anaesthetix 0:0929d3d566cf 227 qDot3 -= beta * s2;
Anaesthetix 0:0929d3d566cf 228 qDot4 -= beta * s3;
Anaesthetix 0:0929d3d566cf 229 }
Anaesthetix 0:0929d3d566cf 230
Anaesthetix 0:0929d3d566cf 231 // Integrate rate of change of quaternion to yield quaternion
Anaesthetix 0:0929d3d566cf 232 q0 += qDot1 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 233 q1 += qDot2 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 234 q2 += qDot3 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 235 q3 += qDot4 * invSampleFreq;
Anaesthetix 0:0929d3d566cf 236
Anaesthetix 0:0929d3d566cf 237 // Normalise quaternion
Anaesthetix 0:0929d3d566cf 238 recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
Anaesthetix 0:0929d3d566cf 239 q0 *= recipNorm;
Anaesthetix 0:0929d3d566cf 240 q1 *= recipNorm;
Anaesthetix 0:0929d3d566cf 241 q2 *= recipNorm;
Anaesthetix 0:0929d3d566cf 242 q3 *= recipNorm;
Anaesthetix 0:0929d3d566cf 243 anglesComputed = 0;
Anaesthetix 0:0929d3d566cf 244 }
Anaesthetix 0:0929d3d566cf 245
Anaesthetix 0:0929d3d566cf 246 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 247 // Fast inverse square-root
Anaesthetix 0:0929d3d566cf 248 // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
Anaesthetix 0:0929d3d566cf 249
Anaesthetix 0:0929d3d566cf 250 /*float Madgwick::invSqrt(float x) {
Anaesthetix 0:0929d3d566cf 251 float halfx = 0.5f * x;
Anaesthetix 0:0929d3d566cf 252 float y = x;
Anaesthetix 0:0929d3d566cf 253 long i = *(long*)&y;
Anaesthetix 0:0929d3d566cf 254 i = 0x5f3759df - (i>>1);
Anaesthetix 0:0929d3d566cf 255 y = *(float*)&i;
Anaesthetix 0:0929d3d566cf 256 y = y * (1.5f - (halfx * y * y));
Anaesthetix 0:0929d3d566cf 257 y = y * (1.5f - (halfx * y * y));
Anaesthetix 0:0929d3d566cf 258 return y;
Anaesthetix 5:0f4204941604 259 }
Anaesthetix 0:0929d3d566cf 260
Anaesthetix 0:0929d3d566cf 261 float Madgwick::invSqrt(float x){
Anaesthetix 0:0929d3d566cf 262 unsigned int i = 0x5F1F1412 - (*(unsigned int*)&x >> 1);
Anaesthetix 0:0929d3d566cf 263 float tmp = *(float*)&i;
Anaesthetix 0:0929d3d566cf 264 return tmp * (1.69000231f - 0.714158168f * x * tmp * tmp);
Anaesthetix 0:0929d3d566cf 265 }
Anaesthetix 0:0929d3d566cf 266 */
Anaesthetix 5:0f4204941604 267 float Madgwick::invSqrt(float x)
Anaesthetix 5:0f4204941604 268 {
Anaesthetix 5:0f4204941604 269 float tmp = 1/(sqrt(x));
Anaesthetix 5:0f4204941604 270 return tmp;
Anaesthetix 0:0929d3d566cf 271 }
Anaesthetix 0:0929d3d566cf 272
Anaesthetix 0:0929d3d566cf 273 //-------------------------------------------------------------------------------------------
Anaesthetix 0:0929d3d566cf 274
Anaesthetix 0:0929d3d566cf 275 void Madgwick::computeAngles()
Anaesthetix 0:0929d3d566cf 276 {
Anaesthetix 0:0929d3d566cf 277 roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
Anaesthetix 0:0929d3d566cf 278 pitch = asinf(-2.0f * (q1*q3 - q0*q2));
Anaesthetix 0:0929d3d566cf 279 yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
Anaesthetix 0:0929d3d566cf 280 anglesComputed = 1;
Anaesthetix 0:0929d3d566cf 281 }
Anaesthetix 0:0929d3d566cf 282