Program Listing for File MahonyAHRS.cpp
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//=============================================================================================
// MahonyAHRS.c
//=============================================================================================
//
// Madgwick's implementation of Mayhony's AHRS algorithm.
// See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/
//
// From the x-io website "Open-source resources available on this website are
// provided under the GNU General Public Licence unless an alternative licence
// is provided in source."
//
// Date Author Notes
// 29/09/2011 SOH Madgwick Initial release
// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
// 09/06/2020 Matthew Arnold Update style, use safer casting
//
// Algorithm paper:
// http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934
//
//=============================================================================================
//-------------------------------------------------------------------------------------------
// Header files
#include "MahonyAHRS.h"
#include <cinttypes>
#include <cmath>
#include <cstring>
//-------------------------------------------------------------------------------------------
// Definitions
#define DEFAULT_SAMPLE_FREQ 500.0f // sample frequency in Hz
#define twoKpDef (2.0f * 0.5f) // 2 * proportional gain
#define twoKiDef (2.0f * 0.0f) // 2 * integral gain
//============================================================================================
// Functions
static float fastInvSqrt(float x);
//-------------------------------------------------------------------------------------------
// AHRS algorithm update
Mahony::Mahony()
{
twoKp = twoKpDef; // 2 * proportional gain (Kp)
twoKi = twoKiDef; // 2 * integral gain (Ki)
q0 = 1.0f;
q1 = 0.0f;
q2 = 0.0f;
q3 = 0.0f;
integralFBx = 0.0f;
integralFBy = 0.0f;
integralFBz = 0.0f;
anglesComputed = 0;
invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ;
roll = 0.0f;
pitch = 0.0f;
yaw = 0.0f;
}
void Mahony::update(
float gx,
float gy,
float gz,
float ax,
float ay,
float az,
float mx,
float my,
float mz)
{
float recipNorm;
float qa, qb, qc;
// Use IMU algorithm if magnetometer measurement invalid
// (avoids NaN in magnetometer normalisation)
if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f))
{
updateIMU(gx, gy, gz, ax, ay, az);
return;
}
// Convert gyroscope degrees/sec to radians/sec
gx *= 0.0174533f;
gy *= 0.0174533f;
gz *= 0.0174533f;
// Compute feedback only if accelerometer measurement valid
// (avoids NaN in accelerometer normalisation)
if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
{
// Normalise accelerometer measurement
recipNorm = fastInvSqrt(ax * ax + ay * ay + az * az);
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
// Normalise magnetometer measurement
recipNorm = fastInvSqrt(mx * mx + my * my + mz * mz);
mx *= recipNorm;
my *= recipNorm;
mz *= recipNorm;
float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
// 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;
float hx, hy, bx, bz;
// 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 = sqrtf(hx * hx + hy * hy);
bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2));
float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz;
float halfex, halfey, halfez;
// 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)
{
// integral error scaled by Ki
integralFBx += twoKi * halfex * invSampleFreq;
integralFBy += twoKi * halfey * invSampleFreq;
integralFBz += twoKi * halfez * invSampleFreq;
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 * invSampleFreq); // pre-multiply common factors
gy *= (0.5f * invSampleFreq);
gz *= (0.5f * invSampleFreq);
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
recipNorm = fastInvSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
anglesComputed = 0;
}
//-------------------------------------------------------------------------------------------
// IMU algorithm update
void Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az)
{
float recipNorm;
float qa, qb, qc;
// Convert gyroscope degrees/sec to radians/sec
gx *= 0.0174533f;
gy *= 0.0174533f;
gz *= 0.0174533f;
// Compute feedback only if accelerometer measurement valid
// (avoids NaN in accelerometer normalisation)
if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
{
// Normalise accelerometer measurement
recipNorm = fastInvSqrt(ax * ax + ay * ay + az * az);
ax *= recipNorm;
ay *= recipNorm;
az *= recipNorm;
float halfvx, halfvy, halfvz;
float halfex, halfey, halfez;
// Estimated direction of gravity
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)
{
// integral error scaled by Ki
integralFBx += twoKi * halfex * invSampleFreq;
integralFBy += twoKi * halfey * invSampleFreq;
integralFBz += twoKi * halfez * invSampleFreq;
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 * invSampleFreq); // pre-multiply common factors
gy *= (0.5f * invSampleFreq);
gz *= (0.5f * invSampleFreq);
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
recipNorm = fastInvSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
q0 *= recipNorm;
q1 *= recipNorm;
q2 *= recipNorm;
q3 *= recipNorm;
anglesComputed = 0;
}
//-------------------------------------------------------------------------------------------
void Mahony::computeAngles()
{
roll = atan2f(q0 * q1 + q2 * q3, 0.5f - q1 * q1 - q2 * q2);
pitch = asinf(-2.0f * (q1 * q3 - q0 * q2));
yaw = atan2f(q1 * q2 + q0 * q3, 0.5f - q2 * q2 - q3 * q3);
anglesComputed = 1;
}
template <typename From, typename To>
To reinterpretCopy(From from)
{
static_assert(sizeof(From) == sizeof(To), "can only reinterpret-copy types of the same size");
To result;
memcpy(static_cast<void*>(&result), static_cast<void*>(&from), sizeof(To));
return result;
}
float fastInvSqrt(float x)
{
static_assert(sizeof(float) == 4, "fast inverse sqrt requires 32-bit float");
float halfx = 0.5f * x;
float y = x;
int32_t i = reinterpretCopy<float, int32_t>(y);
i = 0x5f3759df - (i >> 1);
y = reinterpretCopy<int32_t, float>(i);
y = y * (1.5f - (halfx * y * y));
return y;
}
//============================================================================================
// END OF CODE
//============================================================================================