uas-ugv/main/MadgwickAHRS.cpp

//=============================================================================================
// MadgwickAHRS.c
//=============================================================================================
//
// Implementation of Madgwick's IMU and AHRS algorithms.
// 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
// 19/02/2012	SOH Madgwick	Magnetometer measurement is normalised
//
//=============================================================================================

//-------------------------------------------------------------------------------------------
// Header files

#include "MadgwickAHRS.h"
#include <math.h>
#include <string.h>

//-------------------------------------------------------------------------------------------
// Definitions

#define sampleFreqDef 512.0f  // sample frequency in Hz
#define betaDef 0.4f          // 2 * proportional gain

//============================================================================================
// Functions

//-------------------------------------------------------------------------------------------
// AHRS algorithm update

Madgwick::Madgwick() {
  beta = betaDef;
  q0 = 1.0f;
  q1 = 0.0f;
  q2 = 0.0f;
  q3 = 0.0f;
  invSampleFreq = 1.0f / sampleFreqDef;
  anglesComputed = 0;
}

void Madgwick::update(float gx, float gy, float gz, float ax, float ay,
                      float az, float mx, float my, float mz) {
  float recipNorm;
  float s0, s1, s2, s3;
  float qDot1, qDot2, qDot3, qDot4;
  float hx, hy;
  float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1,
      _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3,
      q2q2, q2q3, q3q3;

  // 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;

  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  // 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 = invSqrt(ax * ax + ay * ay + az * az);
    ax *= recipNorm;
    ay *= recipNorm;
    az *= recipNorm;

    // Normalise magnetometer measurement
    recipNorm = invSqrt(mx * mx + my * my + mz * mz);
    mx *= recipNorm;
    my *= recipNorm;
    mz *= recipNorm;

    // Auxiliary variables to avoid repeated arithmetic
    _2q0mx = 2.0f * q0 * mx;
    _2q0my = 2.0f * q0 * my;
    _2q0mz = 2.0f * q0 * mz;
    _2q1mx = 2.0f * q1 * mx;
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _2q0q2 = 2.0f * q0 * q2;
    _2q2q3 = 2.0f * q2 * q3;
    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 = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 +
         _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
    hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 +
         my * q2q2 + _2q2 * mz * q3 - my * q3q3;
    _2bx = sqrtf(hx * hx + hy * hy);
    _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 +
           _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
    _4bx = 2.0f * _2bx;
    _4bz = 2.0f * _2bz;

    // Gradient decent algorithm corrective step
    s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) +
         _2q1 * (2.0f * q0q1 + _2q2q3 - ay) -
         _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
         (-_2bx * q3 + _2bz * q1) *
             (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
         _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) +
         _2q0 * (2.0f * q0q1 + _2q2q3 - ay) -
         4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
         _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
         (_2bx * q2 + _2bz * q0) *
             (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
         (_2bx * q3 - _4bz * q1) *
             (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) +
         _2q3 * (2.0f * q0q1 + _2q2q3 - ay) -
         4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) +
         (-_4bx * q2 - _2bz * q0) *
             (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
         (_2bx * q1 + _2bz * q3) *
             (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
         (_2bx * q0 - _4bz * q2) *
             (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) +
         _2q2 * (2.0f * q0q1 + _2q2q3 - ay) +
         (-_4bx * q3 + _2bz * q1) *
             (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) +
         (-_2bx * q0 + _2bz * q2) *
             (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) +
         _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 +
                        s3 * s3);  // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * invSampleFreq;
  q1 += qDot2 * invSampleFreq;
  q2 += qDot3 * invSampleFreq;
  q3 += qDot4 * invSampleFreq;

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;
  anglesComputed = 0;
}

//-------------------------------------------------------------------------------------------
// IMU algorithm update

void Madgwick::updateIMU(float gx, float gy, float gz, float ax, float ay,
                         float az) {
  float recipNorm;
  float s0, s1, s2, s3;
  float qDot1, qDot2, qDot3, qDot4;
  float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2, _8q1, _8q2, q0q0, q1q1, q2q2,
      q3q3;

  // Convert gyroscope degrees/sec to radians/sec
  gx *= 0.0174533f;
  gy *= 0.0174533f;
  gz *= 0.0174533f;

  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  // 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 = invSqrt(ax * ax + ay * ay + az * az);
    ax *= recipNorm;
    ay *= recipNorm;
    az *= recipNorm;

    // Auxiliary variables to avoid repeated arithmetic
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _4q0 = 4.0f * q0;
    _4q1 = 4.0f * q1;
    _4q2 = 4.0f * q2;
    _8q1 = 8.0f * q1;
    _8q2 = 8.0f * q2;
    q0q0 = q0 * q0;
    q1q1 = q1 * q1;
    q2q2 = q2 * q2;
    q3q3 = q3 * q3;

    // Gradient decent algorithm corrective step
    s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
    s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 +
         _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
    s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 +
         _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
    s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 +
                        s3 * s3);  // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * invSampleFreq;
  q1 += qDot2 * invSampleFreq;
  q2 += qDot3 * invSampleFreq;
  q3 += qDot4 * invSampleFreq;

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;
  anglesComputed = 0;
}

//-------------------------------------------------------------------------------------------
// Fast inverse square-root
// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root

float Madgwick::invSqrt(float x) {
  float halfx = 0.5f * x;
  float y = x;
  // long  i     = *(long *)&y;
  long i;
  memcpy(&i, &y, sizeof(float));
  i = 0x5f3759df - (i >> 1);
  // y           = *(float *)&i;
  memcpy(&y, &i, sizeof(float));
  y = y * (1.5f - (halfx * y * y));
  y = y * (1.5f - (halfx * y * y));
  return y;
}

//-------------------------------------------------------------------------------------------

void Madgwick::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;
}