253 lines
10 KiB
C
253 lines
10 KiB
C
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//=====================================================================================================
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// MadgwickAHRS.c
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//=====================================================================================================
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//
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// Implementation of Madgwick's IMU and AHRS algorithms.
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// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
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//
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// Date Author Notes
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// 29/09/2011 SOH Madgwick Initial release
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// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
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// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
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//
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//=====================================================================================================
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//---------------------------------------------------------------------------------------------------
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// Header files
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#include "MadgwickAHRS.h"
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#include <math.h>
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#include <stdio.h>
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//---------------------------------------------------------------------------------------------------
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// Definitions
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//#define sampleFreq 512.0f // sample frequency in Hz
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//#define betaDef 0.1f // 2 * proportional gain
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//---------------------------------------------------------------------------------------------------
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// Variable definitions
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//volatile float beta = betaDef; // 2 * proportional gain (Kp)
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//volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
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//---------------------------------------------------------------------------------------------------
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// Function declarations
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float invSqrt(float x);
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//====================================================================================================
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// Functions
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void MadgwickAHRS_init (MadgwickAHRS_Filter* filter, float beta, float sample_freq) {
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filter->q[0] = 1.0f; // qw
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filter->q[1] = 0.0f; // qx
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filter->q[2] = 0.0f; // qy
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filter->q[3] = 0.0f; // qz
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filter->beta = beta;
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filter->sample_freq = sample_freq;
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}
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//---------------------------------------------------------------------------------------------------
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// AHRS algorithm update
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void MadgwickAHRS_update(MadgwickAHRS_Filter* filter, float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
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float q[4] = {filter->q[0], filter->q[1], filter->q[2], filter->q[3]};
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float recipNorm;
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float s0, s1, s2, s3;
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float qDot[4];
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float hx, hy;
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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;
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// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
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if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
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MadgwickAHRS_update_IMU(filter, gx, gy, gz, ax, ay, az);
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return;
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}
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// Rate of change of quaternion from gyroscope
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qDot[0] = 0.5f * (-q[1] * gx - q[2] * gy - q[3] * gz);
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qDot[1] = 0.5f * (q[0] * gx + q[2] * gz - q[3] * gy);
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qDot[2] = 0.5f * (q[0] * gy - q[1] * gz + q[3] * gx);
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qDot[3] = 0.5f * (q[0] * gz + q[1] * gy - q[2] * gx);
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
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// Normalise accelerometer measurement
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recipNorm = invSqrt(ax * ax + ay * ay + az * az);
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ax *= recipNorm;
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ay *= recipNorm;
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az *= recipNorm;
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// Normalise magnetometer measurement
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recipNorm = invSqrt(mx * mx + my * my + mz * mz);
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mx *= recipNorm;
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my *= recipNorm;
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mz *= recipNorm;
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// Auxiliary variables to avoid repeated arithmetic
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_2q0mx = 2.0f * q[0] * mx;
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_2q0my = 2.0f * q[0] * my;
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_2q0mz = 2.0f * q[0] * mz;
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_2q1mx = 2.0f * q[1] * mx;
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_2q0 = 2.0f * q[0];
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_2q1 = 2.0f * q[1];
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_2q2 = 2.0f * q[2];
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_2q3 = 2.0f * q[3];
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_2q0q2 = 2.0f * q[0] * q[2];
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_2q2q3 = 2.0f * q[2] * q[3];
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q0q0 = q[0] * q[0];
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q0q1 = q[0] * q[1];
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q0q2 = q[0] * q[2];
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q0q3 = q[0] * q[3];
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q1q1 = q[1] * q[1];
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q1q2 = q[1] * q[2];
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q1q3 = q[1] * q[3];
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q2q2 = q[2] * q[2];
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q2q3 = q[2] * q[3];
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q3q3 = q[3] * q[3];
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// Reference direction of Earth's magnetic field
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hx = mx * q0q0 - _2q0my * q[3] + _2q0mz * q[2] + mx * q1q1 + _2q1 * my * q[2] + _2q1 * mz * q[3] - mx * q2q2 - mx * q3q3;
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hy = _2q0mx * q[3] + my * q0q0 - _2q0mz * q[1] + _2q1mx * q[2] - my * q1q1 + my * q2q2 + _2q2 * mz * q[3] - my * q3q3;
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_2bx = sqrt(hx * hx + hy * hy);
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_2bz = -_2q0mx * q[2] + _2q0my * q[1] + mz * q0q0 + _2q1mx * q[3] - mz * q1q1 + _2q2 * my * q[3] - mz * q2q2 + mz * q3q3;
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_4bx = 2.0f * _2bx;
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_4bz = 2.0f * _2bz;
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// Gradient decent algorithm corrective step
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s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q[2] * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q[3] + _2bz * q[1]) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q[2] * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q[1] * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q[3] * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q[2] + _2bz * q[0]) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q[3] - _4bz * q[1]) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q[2] * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q[2] - _2bz * q[0]) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q[1] + _2bz * q[3]) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q[0] - _4bz * q[2]) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q[3] + _2bz * q[1]) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q[0] + _2bz * q[2]) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q[1] * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
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recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
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s0 *= recipNorm;
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s1 *= recipNorm;
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s2 *= recipNorm;
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s3 *= recipNorm;
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// Apply feedback step
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qDot[0] -= filter->beta * s0;
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qDot[1] -= filter->beta * s1;
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qDot[2] -= filter->beta * s2;
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qDot[3] -= filter->beta * s3;
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}
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// Integrate rate of change of quaternion to yield quaternion
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q[0] += qDot[0] * (1.0f / filter->sample_freq);
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q[1] += qDot[1] * (1.0f / filter->sample_freq);
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q[2] += qDot[2] * (1.0f / filter->sample_freq);
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q[3] += qDot[3] * (1.0f / filter->sample_freq);
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// Normalise quaternion
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recipNorm = invSqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
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q[0] *= recipNorm;
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q[1] *= recipNorm;
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q[2] *= recipNorm;
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q[3] *= recipNorm;
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// Update filter state
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filter->q[0] = q[0];
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filter->q[1] = q[1];
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filter->q[2] = q[2];
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filter->q[3] = q[3];
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}
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//---------------------------------------------------------------------------------------------------
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// IMU algorithm update
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void MadgwickAHRS_update_IMU(MadgwickAHRS_Filter* filter, float gx, float gy, float gz, float ax, float ay, float az) {
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float q[4] = {filter->q[0], filter->q[1], filter->q[2], filter->q[3]};
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float recipNorm;
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float s0, s1, s2, s3;
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float qDot[4];
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float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
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// Rate of change of quaternion from gyroscope
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qDot[0] = 0.5f * (-q[1] * gx - q[2] * gy - q[3] * gz);
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qDot[1] = 0.5f * (q[0] * gx + q[2] * gz - q[3] * gy);
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qDot[2] = 0.5f * (q[0] * gy - q[1] * gz + q[3] * gx);
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qDot[3] = 0.5f * (q[0] * gz + q[1] * gy - q[2] * gx);
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
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// Normalise accelerometer measurement
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recipNorm = invSqrt(ax * ax + ay * ay + az * az);
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ax *= recipNorm;
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ay *= recipNorm;
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az *= recipNorm;
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// Auxiliary variables to avoid repeated arithmetic
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_2q0 = 2.0f * q[0];
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_2q1 = 2.0f * q[1];
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_2q2 = 2.0f * q[2];
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_2q3 = 2.0f * q[3];
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_4q0 = 4.0f * q[0];
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_4q1 = 4.0f * q[1];
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_4q2 = 4.0f * q[2];
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_8q1 = 8.0f * q[1];
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_8q2 = 8.0f * q[2];
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q0q0 = q[0] * q[0];
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q1q1 = q[1] * q[1];
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q2q2 = q[2] * q[2];
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q3q3 = q[3] * q[3];
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// Gradient decent algorithm corrective step
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s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
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s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q[1] - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
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s2 = 4.0f * q0q0 * q[2] + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
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s3 = 4.0f * q1q1 * q[3] - _2q1 * ax + 4.0f * q2q2 * q[3] - _2q2 * ay;
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recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
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s0 *= recipNorm;
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s1 *= recipNorm;
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s2 *= recipNorm;
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s3 *= recipNorm;
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// Apply feedback step
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qDot[0] -= filter->beta * s0;
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qDot[1] -= filter->beta * s1;
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qDot[2] -= filter->beta * s2;
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qDot[3] -= filter->beta * s3;
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}
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// Integrate rate of change of quaternion to yield quaternion
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q[0] += qDot[0] * (1.0f / filter->sample_freq);
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q[1] += qDot[1] * (1.0f / filter->sample_freq);
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q[2] += qDot[2] * (1.0f / filter->sample_freq);
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q[3] += qDot[3] * (1.0f / filter->sample_freq);
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// Normalise quaternion
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recipNorm = invSqrt(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]);
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q[0] *= recipNorm;
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q[1] *= recipNorm;
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q[2] *= recipNorm;
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q[3] *= recipNorm;
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// Update filter state
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filter->q[0] = q[0];
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filter->q[1] = q[1];
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filter->q[2] = q[2];
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filter->q[3] = q[3];
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}
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//---------------------------------------------------------------------------------------------------
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// Fast inverse square-root
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// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
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float invSqrt(float x) {
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float halfx = 0.5f * x;
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float y = x;
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long i = *(long*)&y;
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i = 0x5f3759df - (i>>1);
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y = *(float*)&i;
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y = y * (1.5f - (halfx * y * y));
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return y;
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}
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//====================================================================================================
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// END OF CODE
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//====================================================================================================
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