LSM9DS0_AHRS.cpp

//
//  LSM9SDS0_AHRS.cpp
//  LSM9SDS0 AHRS
//
//  Created by Nicholas Robinson on 04/19/14.
//  Copyright (c) 2014 Nicholas Robinson. All rights reserved.
//

#include "LSM9DS0_AHRS.h"

LSM9DS0_AHRS::LSM9DS0_AHRS(UpdateMethod _updateMethod)
{
	marg = initializeMarg();
	
	updateMethod = _updateMethod;
	
	dt = 0.0f;
	lastUpdate = 0;
	
	q[0] = 1.0f;
	q[1] = 0.0f;
	q[2] = 0.0f;
	q[3] = 0.0f;
	
	mahonyErrors[0] = 0.0f;
	mahonyErrors[1] = 0.0f;
	mahonyErrors[2] = 0.0f;
}

void LSM9DS0_AHRS::update()
{
    readMarg();
	updateQuaternions();
	updateEulerAngles();
	tick();
}

LSM9DS0* LSM9DS0_AHRS::initializeMarg()
{
	marg = new LSM9DS0(MODE_I2C, LSM9DS0_G, LSM9DS0_XM);
	
	marg->begin();
	
	marg->setAccelScale(marg->A_SCALE_2G);
	marg->setAccelODR(marg->A_ODR_100);
	marg->setAccelABW(marg->A_ABW_50);
	
	marg->setGyroScale(marg->G_SCALE_245DPS);
	marg->setGyroODR(marg->G_ODR_190_BW_125);
	
	marg->setMagScale(marg->M_SCALE_2GS);
	marg->setMagODR(marg->M_ODR_125);
	
	return marg;
}

void LSM9DS0_AHRS::readMarg()
{
    marg->readAccel();
	ax = marg->calcAccel(marg->ax);
	ay = marg->calcAccel(marg->ay);
	az = marg->calcAccel(marg->az);

	marg->readGyro();
	gx = marg->calcGyro(marg->gx);
	gy = marg->calcGyro(marg->gy);
	gz = marg->calcGyro(marg->gz);

	marg->readMag();
	mx = marg->calcMag(marg->mx);
	my = marg->calcMag(marg->my);
	mz = marg->calcMag(marg->mz);
}

void LSM9DS0_AHRS::updateQuaternions()
{
	if (updateMethod == MADGWICK)
		madgwickQuaternionUpdate(ax, ay, az, gx * PI / 180.0f, gy * PI / 180.0f, gz * PI / 180.0f, mx, my, mz);
	else
		mahonyQuaternionUpdate(ax, ay, az, gx * PI / 180.0f, gy * PI / 180.0f, gz * PI / 180.0f, mx, my, mz);
}

void LSM9DS0_AHRS::updateEulerAngles()
{
	yaw = atan2(2.0f * (q[1] * q[2] + q[0] * q[3]), q[0] * q[0] + q[1] * q[1] - q[2] * q[2] - q[3] * q[3]);
	yaw *= 180.0f / PI - 13.8f; // Declination at Danville, California is 13 degrees 48 minutes and 47 seconds on 2014-04-04
	pitch = -asin(2.0f * (q[1] * q[3] - q[0] * q[2]));
	pitch *= 180.0f / PI;
	roll = atan2(2.0f * (q[0] * q[1] + q[2] * q[3]), q[0] * q[0] - q[1] * q[1] - q[2] * q[2] + q[3] * q[3]);
	roll *= 180.0f / PI;
}

void LSM9DS0_AHRS::tick()
{
	uint16_t now = micros();
	dt = (now - lastUpdate) / 1000000.0f;
	lastUpdate = now;
}

// Implementation of Sebastian Madgwick's "...efficient orientation filter for... inertial/magnetic sensor arrays"
// (see http://www.x-io.co.uk/category/open-source/ for examples and more details)
// which fuses acceleration, rotation rate, and magnetic moments to produce a quaternion-based estimate of absolute
// device orientation -- which can be converted to yaw, pitch, and roll. Useful for stabilizing quadcopters, etc.
// The performance of the orientation filter is at least as good as conventional Kalman-based filtering algorithms
// but is much less computationally intensive---it can be performed on a 3.3 V Pro Mini operating at 8 MHz!
void LSM9DS0_AHRS::madgwickQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
{
	float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
	float norm;
	float hx, hy, _2bx, _2bz;
	float s1, s2, s3, s4;
	float qDot1, qDot2, qDot3, qDot4;

	// Auxiliary variables to avoid repeated arithmetic
	float _2q1mx;
	float _2q1my;
	float _2q1mz;
	float _2q2mx;
	float _4bx;
	float _4bz;
	float _2q1 = 2.0f * q1;
	float _2q2 = 2.0f * q2;
	float _2q3 = 2.0f * q3;
	float _2q4 = 2.0f * q4;
	float _2q1q3 = 2.0f * q1 * q3;
	float _2q3q4 = 2.0f * q3 * q4;
	float q1q1 = q1 * q1;
	float q1q2 = q1 * q2;
	float q1q3 = q1 * q3;
	float q1q4 = q1 * q4;
	float q2q2 = q2 * q2;
	float q2q3 = q2 * q3;
	float q2q4 = q2 * q4;
	float q3q3 = q3 * q3;
	float q3q4 = q3 * q4;
	float q4q4 = q4 * q4;

	// Normalise accelerometer measurement
	norm = sqrt(ax * ax + ay * ay + az * az);
	if (norm == 0.0f) return; // handle NaN
	norm = 1.0f/norm;
	ax *= norm;
	ay *= norm;
	az *= norm;

	// Normalise magnetometer measurement
	norm = sqrt(mx * mx + my * my + mz * mz);
	if (norm == 0.0f) return; // handle NaN
	norm = 1.0f/norm;
	mx *= norm;
	my *= norm;
	mz *= norm;

	// Reference direction of Earth's magnetic field
	_2q1mx = 2.0f * q1 * mx;
	_2q1my = 2.0f * q1 * my;
	_2q1mz = 2.0f * q1 * mz;
	_2q2mx = 2.0f * q2 * mx;
	hx = mx * q1q1 - _2q1my * q4 + _2q1mz * q3 + mx * q2q2 + _2q2 * my * q3 + _2q2 * mz * q4 - mx * q3q3 - mx * q4q4;
	hy = _2q1mx * q4 + my * q1q1 - _2q1mz * q2 + _2q2mx * q3 - my * q2q2 + my * q3q3 + _2q3 * mz * q4 - my * q4q4;
	_2bx = sqrt(hx * hx + hy * hy);
	_2bz = -_2q1mx * q3 + _2q1my * q2 + mz * q1q1 + _2q2mx * q4 - mz * q2q2 + _2q3 * my * q4 - mz * q3q3 + mz * q4q4;
	_4bx = 2.0f * _2bx;
	_4bz = 2.0f * _2bz;

	// Gradient decent algorithm corrective step
	s1 = -_2q3 * (2.0f * q2q4 - _2q1q3 - ax) + _2q2 * (2.0f * q1q2 + _2q3q4 - ay) - _2bz * q3 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q4 + _2bz * q2) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q3 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
	s2 = _2q4 * (2.0f * q2q4 - _2q1q3 - ax) + _2q1 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q2 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + _2bz * q4 * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q3 + _2bz * q1) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q4 - _4bz * q2) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
	s3 = -_2q1 * (2.0f * q2q4 - _2q1q3 - ax) + _2q4 * (2.0f * q1q2 + _2q3q4 - ay) - 4.0f * q3 * (1.0f - 2.0f * q2q2 - 2.0f * q3q3 - az) + (-_4bx * q3 - _2bz * q1) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (_2bx * q2 + _2bz * q4) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + (_2bx * q1 - _4bz * q3) * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
	s4 = _2q2 * (2.0f * q2q4 - _2q1q3 - ax) + _2q3 * (2.0f * q1q2 + _2q3q4 - ay) + (-_4bx * q4 + _2bz * q2) * (_2bx * (0.5f - q3q3 - q4q4) + _2bz * (q2q4 - q1q3) - mx) + (-_2bx * q1 + _2bz * q3) * (_2bx * (q2q3 - q1q4) + _2bz * (q1q2 + q3q4) - my) + _2bx * q2 * (_2bx * (q1q3 + q2q4) + _2bz * (0.5f - q2q2 - q3q3) - mz);
	norm = sqrt(s1 * s1 + s2 * s2 + s3 * s3 + s4 * s4);    // normalise step magnitude
	norm = 1.0f/norm;
	s1 *= norm;
	s2 *= norm;
	s3 *= norm;
	s4 *= norm;

	// Compute rate of change of quaternion
	qDot1 = 0.5f * (-q2 * gx - q3 * gy - q4 * gz) - beta * s1;
	qDot2 = 0.5f * (q1 * gx + q3 * gz - q4 * gy) - beta * s2;
	qDot3 = 0.5f * (q1 * gy - q2 * gz + q4 * gx) - beta * s3;
	qDot4 = 0.5f * (q1 * gz + q2 * gy - q3 * gx) - beta * s4;

	// Integrate to yield quaternion
	q1 += qDot1 * dt;
	q2 += qDot2 * dt;
	q3 += qDot3 * dt;
	q4 += qDot4 * dt;
	norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);    // normalise quaternion
	norm = 1.0f/norm;
	q[0] = q1 * norm;
	q[1] = q2 * norm;
	q[2] = q3 * norm;
	q[3] = q4 * norm;
}
  
// Similar to Madgwick scheme but uses proportional and integral filtering on the error between estimated reference vectors and
// measured ones. 
void LSM9DS0_AHRS::mahonyQuaternionUpdate(float ax, float ay, float az, float gx, float gy, float gz, float mx, float my, float mz)
{
  float q1 = q[0], q2 = q[1], q3 = q[2], q4 = q[3];   // short name local variable for readability
  float norm;
  float hx, hy, bx, bz;
  float vx, vy, vz, wx, wy, wz;
  float ex, ey, ez;
  float pa, pb, pc;

  // Auxiliary variables to avoid repeated arithmetic
  float q1q1 = q1 * q1;
  float q1q2 = q1 * q2;
  float q1q3 = q1 * q3;
  float q1q4 = q1 * q4;
  float q2q2 = q2 * q2;
  float q2q3 = q2 * q3;
  float q2q4 = q2 * q4;
  float q3q3 = q3 * q3;
  float q3q4 = q3 * q4;
  float q4q4 = q4 * q4;   

  // Normalise accelerometer measurement
  norm = sqrt(ax * ax + ay * ay + az * az);
  if (norm == 0.0f) return; // handle NaN
  norm = 1.0f / norm;        // use reciprocal for division
  ax *= norm;
  ay *= norm;
  az *= norm;

  // Normalise magnetometer measurement
  norm = sqrt(mx * mx + my * my + mz * mz);
  if (norm == 0.0f) return; // handle NaN
  norm = 1.0f / norm;        // use reciprocal for division
  mx *= norm;
  my *= norm;
  mz *= norm;

  // Reference direction of Earth's magnetic field
  hx = 2.0f * mx * (0.5f - q3q3 - q4q4) + 2.0f * my * (q2q3 - q1q4) + 2.0f * mz * (q2q4 + q1q3);
  hy = 2.0f * mx * (q2q3 + q1q4) + 2.0f * my * (0.5f - q2q2 - q4q4) + 2.0f * mz * (q3q4 - q1q2);
  bx = sqrt((hx * hx) + (hy * hy));
  bz = 2.0f * mx * (q2q4 - q1q3) + 2.0f * my * (q3q4 + q1q2) + 2.0f * mz * (0.5f - q2q2 - q3q3);

  // Estimated direction of gravity and magnetic field
  vx = 2.0f * (q2q4 - q1q3);
  vy = 2.0f * (q1q2 + q3q4);
  vz = q1q1 - q2q2 - q3q3 + q4q4;
  wx = 2.0f * bx * (0.5f - q3q3 - q4q4) + 2.0f * bz * (q2q4 - q1q3);
  wy = 2.0f * bx * (q2q3 - q1q4) + 2.0f * bz * (q1q2 + q3q4);
  wz = 2.0f * bx * (q1q3 + q2q4) + 2.0f * bz * (0.5f - q2q2 - q3q3);  

  // Error is cross product between estimated direction and measured direction of gravity
  ex = (ay * vz - az * vy) + (my * wz - mz * wy);
  ey = (az * vx - ax * vz) + (mz * wx - mx * wz);
  ez = (ax * vy - ay * vx) + (mx * wy - my * wx);
  if (Ki > 0.0f)
  {
    mahonyErrors[0] += ex;      // accumulate integral error
    mahonyErrors[1] += ey;
    mahonyErrors[2] += ez;
  }
  else
  {
    mahonyErrors[0] = 0.0f;     // prevent integral wind up
    mahonyErrors[1] = 0.0f;
    mahonyErrors[2] = 0.0f;
  }

  // Apply feedback terms
  gx = gx + Kp * ex + Ki * mahonyErrors[0];
  gy = gy + Kp * ey + Ki * mahonyErrors[1];
  gz = gz + Kp * ez + Ki * mahonyErrors[2];

  // Integrate rate of change of quaternion
  pa = q2;
  pb = q3;
  pc = q4;
  q1 = q1 + (-q2 * gx - q3 * gy - q4 * gz) * (0.5f * dt);
  q2 = pa + (q1 * gx + pb * gz - pc * gy) * (0.5f * dt);
  q3 = pb + (q1 * gy - pa * gz + pc * gx) * (0.5f * dt);
  q4 = pc + (q1 * gz + pa * gy - pb * gx) * (0.5f * dt);

  // Normalise quaternion
  norm = sqrt(q1 * q1 + q2 * q2 + q3 * q3 + q4 * q4);
  norm = 1.0f / norm;
  q[0] = q1 * norm;
  q[1] = q2 * norm;
  q[2] = q3 * norm;
  q[3] = q4 * norm;
}