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275 lines
8.2 KiB
275 lines
8.2 KiB
//============================================================================================= |
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// MahonyAHRS.c |
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//============================================================================================= |
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// |
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// Madgwick's implementation of Mayhony's AHRS algorithm. |
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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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// Algorithm paper: |
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// http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934 |
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// |
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//============================================================================================= |
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//------------------------------------------------------------------------------------------- |
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// Header files |
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#include "MahonyAHRS.h" |
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#include <math.h> |
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//------------------------------------------------------------------------------------------- |
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// Definitions |
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#define DEFAULT_SAMPLE_FREQ 512.0f // sample frequency in Hz |
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#define twoKpDef (2.0f * 0.5f) // 2 * proportional gain |
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#define twoKiDef (2.0f * 0.0f) // 2 * integral 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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Mahony::Mahony() |
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{ |
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twoKp = twoKpDef; // 2 * proportional gain (Kp) |
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twoKi = twoKiDef; // 2 * integral gain (Ki) |
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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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integralFBx = 0.0f; |
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integralFBy = 0.0f; |
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integralFBz = 0.0f; |
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anglesComputed = 0; |
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invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ; |
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} |
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void Mahony::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) |
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{ |
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float recipNorm; |
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float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; |
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float hx, hy, bx, bz; |
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float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz; |
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float halfex, halfey, halfez; |
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float qa, qb, qc; |
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// Use IMU algorithm if magnetometer measurement invalid |
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// (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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// 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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// Compute feedback only if accelerometer measurement valid |
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// (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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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 = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2)); |
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hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1)); |
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bx = sqrtf(hx * hx + hy * hy); |
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bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2)); |
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// Estimated direction of gravity and magnetic field |
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halfvx = q1q3 - q0q2; |
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halfvy = q0q1 + q2q3; |
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halfvz = q0q0 - 0.5f + q3q3; |
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halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2); |
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halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3); |
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halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2); |
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// Error is sum of cross product between estimated direction |
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// and measured direction of field vectors |
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halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy); |
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halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz); |
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halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx); |
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// Compute and apply integral feedback if enabled |
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if(twoKi > 0.0f) { |
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// integral error scaled by Ki |
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integralFBx += twoKi * halfex * invSampleFreq; |
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integralFBy += twoKi * halfey * invSampleFreq; |
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integralFBz += twoKi * halfez * invSampleFreq; |
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gx += integralFBx; // apply integral feedback |
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gy += integralFBy; |
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gz += integralFBz; |
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} else { |
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integralFBx = 0.0f; // prevent integral windup |
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integralFBy = 0.0f; |
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integralFBz = 0.0f; |
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} |
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// Apply proportional feedback |
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gx += twoKp * halfex; |
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gy += twoKp * halfey; |
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gz += twoKp * halfez; |
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} |
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// Integrate rate of change of quaternion |
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gx *= (0.5f * invSampleFreq); // pre-multiply common factors |
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gy *= (0.5f * invSampleFreq); |
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gz *= (0.5f * invSampleFreq); |
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qa = q0; |
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qb = q1; |
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qc = q2; |
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q0 += (-qb * gx - qc * gy - q3 * gz); |
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q1 += (qa * gx + qc * gz - q3 * gy); |
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q2 += (qa * gy - qb * gz + q3 * gx); |
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q3 += (qa * gz + qb * gy - qc * gx); |
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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 Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) |
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{ |
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float recipNorm; |
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float halfvx, halfvy, halfvz; |
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float halfex, halfey, halfez; |
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float qa, qb, qc; |
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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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// Compute feedback only if accelerometer measurement valid |
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// (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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// Estimated direction of gravity |
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halfvx = q1 * q3 - q0 * q2; |
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halfvy = q0 * q1 + q2 * q3; |
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halfvz = q0 * q0 - 0.5f + q3 * q3; |
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// Error is sum of cross product between estimated |
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// and measured direction of gravity |
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halfex = (ay * halfvz - az * halfvy); |
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halfey = (az * halfvx - ax * halfvz); |
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halfez = (ax * halfvy - ay * halfvx); |
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// Compute and apply integral feedback if enabled |
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if(twoKi > 0.0f) { |
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// integral error scaled by Ki |
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integralFBx += twoKi * halfex * invSampleFreq; |
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integralFBy += twoKi * halfey * invSampleFreq; |
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integralFBz += twoKi * halfez * invSampleFreq; |
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gx += integralFBx; // apply integral feedback |
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gy += integralFBy; |
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gz += integralFBz; |
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} else { |
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integralFBx = 0.0f; // prevent integral windup |
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integralFBy = 0.0f; |
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integralFBz = 0.0f; |
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} |
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// Apply proportional feedback |
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gx += twoKp * halfex; |
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gy += twoKp * halfey; |
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gz += twoKp * halfez; |
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} |
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// Integrate rate of change of quaternion |
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gx *= (0.5f * invSampleFreq); // pre-multiply common factors |
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gy *= (0.5f * invSampleFreq); |
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gz *= (0.5f * invSampleFreq); |
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qa = q0; |
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qb = q1; |
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qc = q2; |
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q0 += (-qb * gx - qc * gy - q3 * gz); |
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q1 += (qa * gx + qc * gz - q3 * gy); |
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q2 += (qa * gy - qb * gz + q3 * gx); |
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q3 += (qa * gz + qb * gy - qc * gx); |
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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 Mahony::invSqrt(float x) |
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{ |
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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 Mahony::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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//============================================================================================ |
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// END OF CODE |
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//============================================================================================ |
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© 2021 GitHub, Inc. |