250 lines
9.2 KiB
C++
250 lines
9.2 KiB
C++
//=============================================================================================
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// Madgwick.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/open-source-imu-and-ahrs-algorithms/
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//
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// From the x-io website "Open-source resources available on this website are
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// provided under the GNU General Public Licence unless an alternative licence
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// is provided in source."
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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 "Madgwick.h"
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#include <math.h>
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#include <stdint.h>
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#include <Arduino.h>
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//-------------------------------------------------------------------------------------------
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// Definitions
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#define sampleFreqDef 512.0f // sample frequency in Hz
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//============================================================================================
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// Functions
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//-------------------------------------------------------------------------------------------
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// AHRS algorithm update
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Madgwick::Madgwick() {
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q0 = 1.0f;
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q1 = 0.0f;
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q2 = 0.0f;
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q3 = 0.0f;
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now = micros();
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}
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void Madgwick::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
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float recipNorm;
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float s0, s1, s2, s3;
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float qDot1, qDot2, qDot3, qDot4;
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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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updateIMU(gx, gy, gz, ax, ay, az);
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return;
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}
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now = micros();
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// Set integration time by time elapsed since last filter update
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delta_t = ((now - last_update) / (float)1000000.0f);
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last_update = now;
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// Convert gyroscope degrees/sec to radians/sec
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gx *= (float)0.0174533f;
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gy *= (float)0.0174533f;
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gz *= (float)0.0174533f;
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// Rate of change of quaternion from gyroscope
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qDot1 = (float)0.5f * (-q1 * gx - q2 * gy - q3 * gz);
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qDot2 = (float)0.5f * (q0 * gx + q2 * gz - q3 * gy);
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qDot3 = (float)0.5f * (q0 * gy - q1 * gz + q3 * gx);
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qDot4 = (float)0.5f * (q0 * gz + q1 * gy - q2 * gx);
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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if(!((ax == (float)0.0f) && (ay == (float)0.0f) && (az == (float)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 = (float)2.0f * q0 * mx;
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_2q0my = (float)2.0f * q0 * my;
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_2q0mz = (float)2.0f * q0 * mz;
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_2q1mx = (float)2.0f * q1 * mx;
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_2q0 = (float)2.0f * q0;
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_2q1 = (float)2.0f * q1;
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_2q2 = (float)2.0f * q2;
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_2q3 = (float)2.0f * q3;
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_2q0q2 = (float)2.0f * q0 * q2;
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_2q2q3 = (float)2.0f * q2 * q3;
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q0q0 = q0 * q0;
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q0q1 = q0 * q1;
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q0q2 = q0 * q2;
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q0q3 = q0 * q3;
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q1q1 = q1 * q1;
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q1q2 = q1 * q2;
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q1q3 = q1 * q3;
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q2q2 = q2 * q2;
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q2q3 = q2 * q3;
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q3q3 = q3 * q3;
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// Reference direction of Earth's magnetic field
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hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
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hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
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_2bx = sqrtf(hx * hx + hy * hy);
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_2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
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_4bx = (float)2.0f * _2bx;
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_4bz = (float)2.0f * _2bz;
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// Gradient decent algorithm corrective step
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s0 = -_2q2 * ((float)2.0f * q1q3 - _2q0q2 - ax) + _2q1 * ((float)2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * ((float)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 * ((float)0.5f - q1q1 - q2q2) - mz);
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s1 = _2q3 * ((float)2.0f * q1q3 - _2q0q2 - ax) + _2q0 * ((float)2.0f * q0q1 + _2q2q3 - ay) - (float)4.0f * q1 * (1 - (float)2.0f * q1q1 - (float)2.0f * q2q2 - az) + _2bz * q3 * (_2bx * ((float)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 * ((float)0.5f - q1q1 - q2q2) - mz);
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s2 = -_2q0 * ((float)2.0f * q1q3 - _2q0q2 - ax) + _2q3 * ((float)2.0f * q0q1 + _2q2q3 - ay) - (float)4.0f * q2 * (1 - (float)2.0f * q1q1 - (float)2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * ((float)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 * ((float)0.5f - q1q1 - q2q2) - mz);
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s3 = _2q1 * ((float)2.0f * q1q3 - _2q0q2 - ax) + _2q2 * ((float)2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * ((float)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 * ((float)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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qDot1 -= beta * s0;
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qDot2 -= beta * s1;
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qDot3 -= beta * s2;
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qDot4 -= beta * s3;
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}
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// Integrate rate of change of quaternion to yield quaternion
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q0 += qDot1 * delta_t;
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q1 += qDot2 * delta_t;
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q2 += qDot3 * delta_t;
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q3 += qDot4 * delta_t;
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// Normalise quaternion
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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q0 *= recipNorm;
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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}
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//-------------------------------------------------------------------------------------------
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// IMU algorithm update
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void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
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float recipNorm;
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float s0, s1, s2, s3;
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float qDot1, qDot2, qDot3, qDot4;
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float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
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// Convert gyroscope degrees/sec to radians/sec
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gx *= (float)0.0174533f;
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gy *= (float)0.0174533f;
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gz *= (float)0.0174533f;
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now = micros();
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// Set integration time by time elapsed since last filter update
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delta_t = ((now - last_update) / (float)1000000.0f);
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last_update = now;
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// Rate of change of quaternion from gyroscope
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qDot1 = (float)0.5f * (-q1 * gx - q2 * gy - q3 * gz);
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qDot2 = (float)0.5f * (q0 * gx + q2 * gz - q3 * gy);
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qDot3 = (float)0.5f * (q0 * gy - q1 * gz + q3 * gx);
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qDot4 = (float)0.5f * (q0 * gz + q1 * gy - q2 * 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 = (float)2.0f * q0;
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_2q1 = (float)2.0f * q1;
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_2q2 = (float)2.0f * q2;
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_2q3 = (float)2.0f * q3;
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_4q0 = (float)4.0f * q0;
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_4q1 = (float)4.0f * q1;
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_4q2 = (float)4.0f * q2;
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_8q1 = (float)8.0f * q1;
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_8q2 = (float)8.0f * q2;
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q0q0 = q0 * q0;
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q1q1 = q1 * q1;
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q2q2 = q2 * q2;
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q3q3 = q3 * q3;
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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 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
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s2 = (float)4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
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s3 = (float)4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _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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qDot1 -= beta * s0;
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qDot2 -= beta * s1;
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qDot3 -= beta * s2;
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qDot4 -= beta * s3;
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}
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// Integrate rate of change of quaternion to yield quaternion
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q0 += qDot1 * delta_t;
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q1 += qDot2 * delta_t;
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q2 += qDot3 * delta_t;
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q3 += qDot4 * delta_t;
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// Normalise quaternion
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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q0 *= recipNorm;
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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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 Madgwick::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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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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