New Madgwick filter library
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//=====================================================================================================
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//=============================================================================================
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// MadgwickAHRS.c
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//=====================================================================================================
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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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// 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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//---------------------------------------------------------------------------------------------------
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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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//---------------------------------------------------------------------------------------------------
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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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#define sampleFreqDef 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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//============================================================================================
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// Functions
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//---------------------------------------------------------------------------------------------------
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//-------------------------------------------------------------------------------------------
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// AHRS algorithm update
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void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
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Madgwick::Madgwick() {
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beta = betaDef;
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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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invSampleFreq = 1.0f / sampleFreqDef;
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anglesComputed = 0;
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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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@ -50,10 +54,15 @@ void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float
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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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MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
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updateIMU(gx, gy, gz, ax, ay, az);
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return;
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}
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// Convert gyroscope degrees/sec to radians/sec
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gx *= 0.0174533f;
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gy *= 0.0174533f;
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gz *= 0.0174533f;
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// Rate of change of quaternion from gyroscope
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qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
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qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
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@ -67,7 +76,7 @@ void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float
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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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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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@ -100,7 +109,7 @@ void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float
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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 = sqrt(hx * hx + hy * hy);
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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 = 2.0f * _2bx;
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_4bz = 2.0f * _2bz;
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@ -124,10 +133,10 @@ void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float
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}
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// Integrate rate of change of quaternion to yield quaternion
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q0 += qDot1 * (1.0f / sampleFreq);
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q1 += qDot2 * (1.0f / sampleFreq);
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q2 += qDot3 * (1.0f / sampleFreq);
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q3 += qDot4 * (1.0f / sampleFreq);
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q0 += qDot1 * invSampleFreq;
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q1 += qDot2 * invSampleFreq;
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q2 += qDot3 * invSampleFreq;
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q3 += qDot4 * invSampleFreq;
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// Normalise quaternion
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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@ -135,17 +144,23 @@ void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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anglesComputed = 0;
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}
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//---------------------------------------------------------------------------------------------------
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//-------------------------------------------------------------------------------------------
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// IMU algorithm update
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void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
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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 *= 0.0174533f;
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gy *= 0.0174533f;
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gz *= 0.0174533f;
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// Rate of change of quaternion from gyroscope
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qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
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qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
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@ -159,7 +174,7 @@ void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, flo
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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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az *= recipNorm;
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// Auxiliary variables to avoid repeated arithmetic
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_2q0 = 2.0f * q0;
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@ -195,10 +210,10 @@ void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, flo
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}
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// Integrate rate of change of quaternion to yield quaternion
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q0 += qDot1 * (1.0f / sampleFreq);
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q1 += qDot2 * (1.0f / sampleFreq);
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q2 += qDot3 * (1.0f / sampleFreq);
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q3 += qDot4 * (1.0f / sampleFreq);
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q0 += qDot1 * invSampleFreq;
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q1 += qDot2 * invSampleFreq;
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q2 += qDot3 * invSampleFreq;
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q3 += qDot4 * invSampleFreq;
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// Normalise quaternion
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recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
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@ -206,27 +221,30 @@ void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, flo
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q1 *= recipNorm;
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q2 *= recipNorm;
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q3 *= recipNorm;
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anglesComputed = 0;
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}
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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 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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float getPitch()
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{
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return asinf(-2.0f * (q1*q3 - q0*q2));
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}
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//-------------------------------------------------------------------------------------------
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//====================================================================================================
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// END OF CODE
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//====================================================================================================
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void Madgwick::computeAngles()
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{
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roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2);
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pitch = asinf(-2.0f * (q1*q3 - q0*q2));
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yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3);
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anglesComputed = 1;
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}
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@ -1,32 +1,71 @@
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//=====================================================================================================
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//=============================================================================================
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// MadgwickAHRS.h
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//=====================================================================================================
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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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// 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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//
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//=====================================================================================================
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//=============================================================================================
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#ifndef MadgwickAHRS_h
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#define MadgwickAHRS_h
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#include <math.h>
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//----------------------------------------------------------------------------------------------------
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//--------------------------------------------------------------------------------------------
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// Variable declaration
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class Madgwick{
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private:
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static float invSqrt(float x);
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float beta; // algorithm gain
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float q0;
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float q1;
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float q2;
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float q3; // quaternion of sensor frame relative to auxiliary frame
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float invSampleFreq;
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float roll;
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float pitch;
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float yaw;
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char anglesComputed;
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void computeAngles();
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extern volatile float beta; // algorithm gain
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extern volatile float q0, q1, q2, q3; // quaternion of sensor frame relative to auxiliary frame
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//---------------------------------------------------------------------------------------------------
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//-------------------------------------------------------------------------------------------
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// Function declarations
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void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
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void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az);
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float getPitch();
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#endif
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//=====================================================================================================
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// End of file
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//=====================================================================================================
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public:
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Madgwick(void);
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void begin(float sampleFrequency) { invSampleFreq = 1.0f / sampleFrequency; }
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void update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz);
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void updateIMU(float gx, float gy, float gz, float ax, float ay, float az);
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float getRoll() {
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if (!anglesComputed) computeAngles();
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return roll * 57.29578f;
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}
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float getPitch() {
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if (!anglesComputed) computeAngles();
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return pitch * 57.29578f;
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}
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float getYaw() {
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if (!anglesComputed) computeAngles();
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return yaw * 57.29578f + 180.0f;
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}
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float getRollRadians() {
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if (!anglesComputed) computeAngles();
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return roll;
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}
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float getPitchRadians() {
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if (!anglesComputed) computeAngles();
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return pitch;
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}
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float getYawRadians() {
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if (!anglesComputed) computeAngles();
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return yaw;
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}
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};
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#endif
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