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MahonyAHRS.cpp
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#include "MahonyAHRS.h"
#include <math.h>
#include "util.h"
//#define twoKpDef (2.0f * 0.5f) // 2 * proportional gain
#define twoKpDef (2.0f * 5.0f) // 2 * proportional gain
#define twoKiDef (2.0f * 0.0f) // 2 * integral gain
volatile float twoKp = twoKpDef; // 2 * proportional gain (Kp)
volatile float twoKi = twoKiDef; // 2 * integral gain (Ki)
volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
volatile float integralFBx = 0.0f, integralFBy = 0.0f, integralFBz = 0.0f; // integral error terms scaled by Ki
void imu_MahonyAHRSupdate9DOF(int bUseAccel, int bUseMag, float dt, float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
float invNorm;
float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
float hx, hy, bx, bz;
float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
float halfex, halfey, halfez;
float qa, qb, qc;
// Use 6dof algorithm if magnetometer measurement invalid
if(!bUseMag) {
imu_MahonyAHRSupdate6DOF(bUseAccel,dt, gx, gy, gz, ax, ay, az);
return;
}
if(bUseAccel) {
// Normalise accelerometer measurement
invNorm = 1.0f/sqrt(ax * ax + ay * ay + az * az);
ax *= invNorm;
ay *= invNorm;
az *= invNorm;
// Normalise magnetometer measurement
invNorm = 1.0f/sqrt(mx * mx + my * my + mz * mz);
mx *= invNorm;
my *= invNorm;
mz *= invNorm;
// Auxiliary variables to avoid repeated arithmetic
q0q0 = q0 * q0;
q0q1 = q0 * q1;
q0q2 = q0 * q2;
q0q3 = q0 * q3;
q1q1 = q1 * q1;
q1q2 = q1 * q2;
q1q3 = q1 * q3;
q2q2 = q2 * q2;
q2q3 = q2 * q3;
q3q3 = q3 * q3;
// Reference direction of Earth's magnetic field
hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2));
hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1));
bx = sqrt(hx * hx + hy * hy);
bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
// Estimated direction of gravity and magnetic field
halfvx = q1q3 - q0q2;
halfvy = q0q1 + q2q3;
halfvz = q0q0 - 0.5f + q3q3;
halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2);
halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3);
halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2);
// Error is sum of cross product between estimated direction and measured direction of field vectors
halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy);
halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz);
halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx);
// Compute and apply integral feedback if enabled
if(twoKi > 0.0f) {
integralFBx += twoKi * halfex * dt; // integral error scaled by Ki
integralFBy += twoKi * halfey * dt;
integralFBz += twoKi * halfez * dt;
gx += integralFBx; // apply integral feedback
gy += integralFBy;
gz += integralFBz;
}
else {
integralFBx = 0.0f; // prevent integral windup
integralFBy = 0.0f;
integralFBz = 0.0f;
}
// Apply proportional feedback
gx += twoKp * halfex;
gy += twoKp * halfey;
gz += twoKp * halfez;
}
// Integrate rate of change of quaternion
gx *= (0.5f * dt); // pre-multiply common factors
gy *= (0.5f * dt);
gz *= (0.5f * dt);
qa = q0;
qb = q1;
qc = q2;
q0 += (-qb * gx - qc * gy - q3 * gz);
q1 += (qa * gx + qc * gz - q3 * gy);
q2 += (qa * gy - qb * gz + q3 * gx);
q3 += (qa * gz + qb * gy - qc * gx);
// Normalise quaternion
invNorm = 1.0f/sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= invNorm;
q1 *= invNorm;
q2 *= invNorm;
q3 *= invNorm;
}
void imu_MahonyAHRSupdate6DOF(int bUseAccel, float dt, float gx, float gy, float gz, float ax, float ay, float az) {
float invNorm;
float halfvx, halfvy, halfvz;
float halfex, halfey, halfez;
float qa, qb, qc;
// Compute feedback only if accelerometer measurement valid )
if(bUseAccel) {
// Normalise accelerometer measurement
invNorm = 1.0f/sqrt(ax * ax + ay * ay + az * az);
ax *= invNorm;
ay *= invNorm;
az *= invNorm;
// Estimated direction of gravity and vector perpendicular to magnetic flux
halfvx = q1 * q3 - q0 * q2;
halfvy = q0 * q1 + q2 * q3;
halfvz = q0 * q0 - 0.5f + q3 * q3;
// Error is sum of cross product between estimated and measured direction of gravity
halfex = (ay * halfvz - az * halfvy);
halfey = (az * halfvx - ax * halfvz);
halfez = (ax * halfvy - ay * halfvx);
// Compute and apply integral feedback if enabled
if(twoKi > 0.0f) {
integralFBx += twoKi * halfex * dt; // integral error scaled by Ki
integralFBy += twoKi * halfey * dt;
integralFBz += twoKi * halfez * dt;
gx += integralFBx; // apply integral feedback
gy += integralFBy;
gz += integralFBz;
}
else {
integralFBx = 0.0f; // prevent integral windup
integralFBy = 0.0f;
integralFBz = 0.0f;
}
// Apply proportional feedback
gx += twoKp * halfex;
gy += twoKp * halfey;
gz += twoKp * halfez;
}
// Integrate rate of change of quaternion
gx *= (0.5f * dt); // pre-multiply common factors
gy *= (0.5f * dt);
gz *= (0.5f * dt);
qa = q0;
qb = q1;
qc = q2;
q0 += (-qb * gx - qc * gy - q3 * gz);
q1 += (qa * gx + qc * gz - q3 * gy);
q2 += (qa * gy - qb * gz + q3 * gx);
q3 += (qa * gz + qb * gy - qc * gx);
// Normalise quaternion
invNorm = 1.0f/sqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= invNorm;
q1 *= invNorm;
q2 *= invNorm;
q3 *= invNorm;
}
// HN
void imu_Quaternion2YawPitchRoll(float q0, float q1, float q2, float q3, float* pYawDeg, float* pPitchDeg, float* pRollDeg) {
float invNorm = 1.0f/sqrt(q0*q0 + q1*q1 + q2*q2 + q3*q3);
q0 *= invNorm;
q1 *= invNorm;
q2 *= invNorm;
q3 *= invNorm;
*pYawDeg = _180_DIV_PI * atan2(2.0f * (q1*q2 + q0*q3), q0*q0 + q1*q1 - q2*q2 - q3*q3);
*pPitchDeg = _180_DIV_PI * -asin(2.0f * (q1*q3 - q0*q2));
*pRollDeg = _180_DIV_PI * atan2(2.0f * (q0*q1 + q2*q3), q0*q0 - q1*q1 - q2*q2 + q3*q3);
}
float imu_GravityCompensatedAccel(float ax, float ay, float az, float q0, float q1, float q2, float q3) {
float acc = 2.0*(q1*q3 - q0*q2)*ax + 2.0f*(q0*q1 + q2*q3)*ay + (q0*q0 - q1*q1 - q2*q2 + q3*q3)*az - 1000.0f;
acc *= 0.98f; // in cm/s/s, assuming ax, ay, az are in milli-Gs
return acc;
}