Alex Mikhalev
6 years ago
10 changed files with 445 additions and 74 deletions
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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/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 "MadgwickAHRS.h" |
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#include <math.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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#define betaDef 0.1f // 2 * proportional gain
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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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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, |
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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, |
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_2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, |
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q2q2, q2q3, q3q3; |
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// Use IMU algorithm if magnetometer measurement invalid (avoids NaN in
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// 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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// 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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qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); |
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qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); |
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// Compute feedback only if accelerometer measurement valid (avoids NaN in
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// 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 * q0 * mx; |
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_2q0my = 2.0f * q0 * my; |
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_2q0mz = 2.0f * q0 * mz; |
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_2q1mx = 2.0f * q1 * mx; |
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_2q0 = 2.0f * q0; |
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_2q1 = 2.0f * q1; |
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_2q2 = 2.0f * q2; |
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_2q3 = 2.0f * q3; |
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_2q0q2 = 2.0f * q0 * q2; |
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_2q2q3 = 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 + |
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_2q1 * mz * q3 - mx * q2q2 - mx * q3q3; |
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hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + |
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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 + |
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_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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// Gradient decent algorithm corrective step
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s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + |
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_2q1 * (2.0f * q0q1 + _2q2q3 - ay) - |
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_2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + |
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(-_2bx * q3 + _2bz * q1) * |
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + |
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_2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); |
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s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + |
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_2q0 * (2.0f * q0q1 + _2q2q3 - ay) - |
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4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + |
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_2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + |
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(_2bx * q2 + _2bz * q0) * |
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + |
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(_2bx * q3 - _4bz * q1) * |
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(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); |
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s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + |
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_2q3 * (2.0f * q0q1 + _2q2q3 - ay) - |
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4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + |
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(-_4bx * q2 - _2bz * q0) * |
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(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + |
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(_2bx * q1 + _2bz * q3) * |
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + |
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(_2bx * q0 - _4bz * q2) * |
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(_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); |
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s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + |
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_2q2 * (2.0f * q0q1 + _2q2q3 - ay) + |
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(-_4bx * q3 + _2bz * q1) * |
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(_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + |
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(-_2bx * q0 + _2bz * q2) * |
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(_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + |
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_2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz); |
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recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + |
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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 * 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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q0 *= recipNorm; |
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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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// IMU algorithm update
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void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay, |
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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, |
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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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qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); |
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qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); |
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// Compute feedback only if accelerometer measurement valid (avoids NaN in
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// 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 * q0; |
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_2q1 = 2.0f * q1; |
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_2q2 = 2.0f * q2; |
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_2q3 = 2.0f * q3; |
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_4q0 = 4.0f * q0; |
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_4q1 = 4.0f * q1; |
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_4q2 = 4.0f * q2; |
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_8q1 = 8.0f * q1; |
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_8q2 = 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 + |
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_8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az; |
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s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + |
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_8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az; |
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s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay; |
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recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + |
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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 * 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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q0 *= recipNorm; |
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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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// 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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void Madgwick::computeAngles() { |
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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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} |
@ -0,0 +1,88 @@
@@ -0,0 +1,88 @@
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//=============================================================================================
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// MadgwickAHRS.h
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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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//
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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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// 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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//-------------------------------------------------------------------------------------------
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// Function declarations
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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, |
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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 getPitch(){return atan2f(2.0f * q2 * q3 - 2.0f * q0 * q1, 2.0f * q0 *
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// q0 + 2.0f * q3 * q3 - 1.0f);}; float getRoll(){return -1.0f * asinf(2.0f *
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// q1 * q3 + 2.0f * q0 * q2);}; float getYaw(){return atan2f(2.0f * q1 * q2
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// - 2.0f * q0 * q3, 2.0f * q0 * q0 + 2.0f * q1 * q1 - 1.0f);};
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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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