233 lines
7.9 KiB
C
233 lines
7.9 KiB
C
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//=====================================================================================================
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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/node/8#open_source_ahrs_and_imu_algorithms
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//
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// Date Author Notes
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// 29/09/2011 SOH Madgwick Initial release
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// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
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//
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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 sampleFreq 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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// Variable definitions
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volatile float twoKp = twoKpDef; // 2 * proportional gain (Kp)
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volatile float twoKi = twoKiDef; // 2 * integral gain (Ki)
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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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volatile float integralFBx = 0.0f, integralFBy = 0.0f, integralFBz = 0.0f; // integral error terms scaled by Ki
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//---------------------------------------------------------------------------------------------------
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// Function declarations
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float invSqrt(float x);
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//====================================================================================================
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// Functions
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//---------------------------------------------------------------------------------------------------
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// AHRS algorithm update
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void MahonyAHRSupdate(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 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 (avoids NaN in magnetometer normalisation)
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if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
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MahonyAHRSupdateIMU(gx, gy, gz, ax, ay, az);
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return;
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}
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// Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
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if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
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// Normalise accelerometer measurement
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recipNorm = invSqrt(ax * ax + ay * ay + az * az);
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ax *= recipNorm;
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ay *= recipNorm;
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az *= recipNorm;
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// Normalise magnetometer measurement
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recipNorm = invSqrt(mx * mx + my * my + mz * mz);
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mx *= recipNorm;
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my *= recipNorm;
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mz *= recipNorm;
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// Auxiliary variables to avoid repeated arithmetic
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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 = sqrt(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 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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integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
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integralFBy += twoKi * halfey * (1.0f / sampleFreq);
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integralFBz += twoKi * halfez * (1.0f / sampleFreq);
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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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}
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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 * (1.0f / sampleFreq)); // pre-multiply common factors
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gy *= (0.5f * (1.0f / sampleFreq));
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gz *= (0.5f * (1.0f / sampleFreq));
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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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}
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//---------------------------------------------------------------------------------------------------
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// IMU algorithm update
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void MahonyAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
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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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// 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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// Estimated direction of gravity and vector perpendicular to magnetic flux
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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 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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integralFBx += twoKi * halfex * (1.0f / sampleFreq); // integral error scaled by Ki
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integralFBy += twoKi * halfey * (1.0f / sampleFreq);
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integralFBz += twoKi * halfez * (1.0f / sampleFreq);
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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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}
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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 * (1.0f / sampleFreq)); // pre-multiply common factors
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gy *= (0.5f * (1.0f / sampleFreq));
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gz *= (0.5f * (1.0f / sampleFreq));
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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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}
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//---------------------------------------------------------------------------------------------------
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// Fast inverse square-root
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// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
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float invSqrt(float x) {
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float halfx = 0.5f * x;
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float y = x;
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long i = *(long*)&y;
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i = 0x5f3759df - (i>>1);
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y = *(float*)&i;
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y = y * (1.5f - (halfx * y * y));
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return y;
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}
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//====================================================================================================
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// END OF CODE
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//====================================================================================================
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