ardupilot/libraries/AP_AHRS/AP_AHRS_DCM.cpp

/*
	APM_AHRS_DCM.cpp

	AHRS system using DCM matrices

	Based on DCM code by Doug Weibel, Jordi Mu<EFBFBD>oz and Jose Julio. DIYDrones.com

	Adapted for the general ArduPilot AHRS interface by Andrew Tridgell

	This library is free software; you can redistribute it and/or
	modify it under the terms of the GNU Lesser General Public License
	as published by the Free Software Foundation; either version 2.1
	of the License, or (at your option) any later version.
*/
#include <FastSerial.h>
#include <AP_AHRS.h>

// this is the speed in cm/s above which we first get a yaw lock with
// the GPS
#define GPS_SPEED_MIN 300

// this is the speed in cm/s at which we stop using drift correction
// from the GPS and wait for the ground speed to get above GPS_SPEED_MIN
#define GPS_SPEED_RESET 100

// the limit (in degrees/second) beyond which we stop integrating
// omega_I. At larger spin rates the DCM PI controller can get 'dizzy'
// which results in false gyro drift. See
// http://gentlenav.googlecode.com/files/fastRotations.pdf
#define SPIN_RATE_LIMIT 20

// table of user settable parameters
const AP_Param::GroupInfo AP_AHRS::var_info[] PROGMEM = {
	// @Param: YAW_P
	// @DisplayName: Yaw P
	// @Description: This controls the weight the compass has on the overall heading
	// @Range: 0 .4
	// @Increment: .01
    AP_GROUPINFO("YAW_P", 0, AP_AHRS_DCM, _kp_yaw),
    AP_GROUPINFO("RP_P",  1, AP_AHRS_DCM, _kp),
    AP_GROUPEND
};

// run a full DCM update round
void
AP_AHRS_DCM::update(void)
{
	float delta_t;

	// tell the IMU to grab some data
	_imu->update();

	// ask the IMU how much time this sensor reading represents
	delta_t = _imu->get_delta_time();

	// Get current values for gyros
	_gyro_vector  = _imu->get_gyro();
	_accel_vector = _imu->get_accel();

	// Integrate the DCM matrix using gyro inputs
	matrix_update(delta_t);

	// Normalize the DCM matrix
	normalize();

	// Perform drift correction
	drift_correction(delta_t);

	// paranoid check for bad values in the DCM matrix
	check_matrix();

	// Calculate pitch, roll, yaw for stabilization and navigation
	euler_angles();
}

// update the DCM matrix using only the gyros
void
AP_AHRS_DCM::matrix_update(float _G_Dt)
{
	// note that we do not include the P terms in _omega. This is
	// because the spin_rate is calculated from _omega.length(),
	// and including the P terms would give positive feedback into
	// the _P_gain() calculation, which can lead to a very large P
	// value
	_omega = _gyro_vector + _omega_I;

	_dcm_matrix.rotate((_omega + _omega_P + _omega_yaw_P) * _G_Dt);
}


/*
  reset the DCM matrix and omega. Used on ground start, and on
  extreme errors in the matrix
 */
void
AP_AHRS_DCM::reset(bool recover_eulers)
{
	// reset the integration terms
	_omega_I.zero();
	_omega_P.zero();
	_omega_yaw_P.zero();
	_omega.zero();

	// if the caller wants us to try to recover to the current
	// attitude then calculate the dcm matrix from the current
	// roll/pitch/yaw values
	if (recover_eulers && !isnan(roll) && !isnan(pitch) && !isnan(yaw)) {
		_dcm_matrix.from_euler(roll, pitch, yaw);
	} else {
		// otherwise make it flat
		_dcm_matrix.from_euler(0, 0, 0);
	}
}

/*
  check the DCM matrix for pathological values
 */
void
AP_AHRS_DCM::check_matrix(void)
{
	if (_dcm_matrix.is_nan()) {
		//Serial.printf("ERROR: DCM matrix NAN\n");
		SITL_debug("ERROR: DCM matrix NAN\n");
		renorm_blowup_count++;
		reset(true);
		return;
	}
	// some DCM matrix values can lead to an out of range error in
	// the pitch calculation via asin().  These NaN values can
	// feed back into the rest of the DCM matrix via the
	// error_course value.
	if (!(_dcm_matrix.c.x < 1.0 &&
	      _dcm_matrix.c.x > -1.0)) {
		// We have an invalid matrix. Force a normalisation.
		renorm_range_count++;
		normalize();

		if (_dcm_matrix.is_nan() ||
		    fabs(_dcm_matrix.c.x) > 10) {
			// normalisation didn't fix the problem! We're
			// in real trouble. All we can do is reset
			//Serial.printf("ERROR: DCM matrix error. _dcm_matrix.c.x=%f\n",
			//	   _dcm_matrix.c.x);
			SITL_debug("ERROR: DCM matrix error. _dcm_matrix.c.x=%f\n",
				   _dcm_matrix.c.x);
			renorm_blowup_count++;
			reset(true);
		}
	}
}

// renormalise one vector component of the DCM matrix
// this will return false if renormalization fails
bool
AP_AHRS_DCM::renorm(Vector3f const &a, Vector3f &result)
{
	float	renorm_val;

	// numerical errors will slowly build up over time in DCM,
	// causing inaccuracies. We can keep ahead of those errors
	// using the renormalization technique from the DCM IMU paper
	// (see equations 18 to 21).

	// For APM we don't bother with the taylor expansion
	// optimisation from the paper as on our 2560 CPU the cost of
	// the sqrt() is 44 microseconds, and the small time saving of
	// the taylor expansion is not worth the potential of
	// additional error buildup.

	// Note that we can get significant renormalisation values
	// when we have a larger delta_t due to a glitch eleswhere in
	// APM, such as a I2c timeout or a set of EEPROM writes. While
	// we would like to avoid these if possible, if it does happen
	// we don't want to compound the error by making DCM less
	// accurate.

	renorm_val = 1.0 / a.length();

	// keep the average for reporting
	_renorm_val_sum += renorm_val;
	_renorm_val_count++;

	if (!(renorm_val < 2.0 && renorm_val > 0.5)) {
		// this is larger than it should get - log it as a warning
		renorm_range_count++;
		if (!(renorm_val < 1.0e6 && renorm_val > 1.0e-6)) {
			// we are getting values which are way out of
			// range, we will reset the matrix and hope we
			// can recover our attitude using drift
			// correction before we hit the ground!
			//Serial.printf("ERROR: DCM renormalisation error. renorm_val=%f\n",
			//	   renorm_val);
			SITL_debug("ERROR: DCM renormalisation error. renorm_val=%f\n",
				   renorm_val);
			renorm_blowup_count++;
			return false;
		}
	}

	result = a * renorm_val;
	return true;
}

/*************************************************
Direction Cosine Matrix IMU: Theory
William Premerlani and Paul Bizard

Numerical errors will gradually reduce the orthogonality conditions expressed by equation 5
to approximations rather than identities. In effect, the axes in the two frames of reference no
longer describe a rigid body. Fortunately, numerical error accumulates very slowly, so it is a
simple matter to stay ahead of it.
We call the process of enforcing the orthogonality conditions <EFBFBD>renormalization<EFBFBD>.
*/
void
AP_AHRS_DCM::normalize(void)
{
	float error;
	Vector3f t0, t1, t2;

	error = _dcm_matrix.a * _dcm_matrix.b; 						// eq.18

	t0 = _dcm_matrix.a - (_dcm_matrix.b * (0.5f * error));		// eq.19
	t1 = _dcm_matrix.b - (_dcm_matrix.a * (0.5f * error));		// eq.19
	t2 = t0 % t1;					                // c= a x b // eq.20

	if (!renorm(t0, _dcm_matrix.a) ||
	    !renorm(t1, _dcm_matrix.b) ||
	    !renorm(t2, _dcm_matrix.c)) {
		// Our solution is blowing up and we will force back
		// to last euler angles
		reset(true);
	}
}


// produce a yaw error value. The returned value is proportional
// to sin() of the current heading error in earth frame
float
AP_AHRS_DCM::yaw_error_compass(void)
{
	Vector3f mag = Vector3f(_compass->mag_x, _compass->mag_y, _compass->mag_z);
	// get the mag vector in the earth frame
	Vector3f rb = _dcm_matrix * mag;

	rb.normalize();
	if (rb.is_inf()) {
		// not a valid vector
		return 0.0;
	}

	// get the earths magnetic field (only X and Y components needed)
	Vector3f mag_earth = Vector3f(cos(_compass->get_declination()),
				      sin(_compass->get_declination()), 0);

	// calculate the error term in earth frame
	Vector3f error = rb % mag_earth;

	return error.z;
}

// produce a yaw error value using the GPS. The returned value is proportional
// to sin() of the current heading error in earth frame
float
AP_AHRS_DCM::yaw_error_gps(void)
{
	return sin(ToRad(_gps->ground_course * 0.01) - yaw);
}


// the _P_gain raises the gain of the PI controller
// when we are spinning fast. See the fastRotations 
// paper from Bill. 
float
AP_AHRS_DCM::_P_gain(float spin_rate)
{
	if (spin_rate < ToDeg(50)) {
		return 1.0;
	}
	if (spin_rate > ToDeg(500)) {
		return 10.0;
	}
	return spin_rate/ToDeg(50);
}

// yaw drift correction using the compass or GPS
// this function prodoces the _omega_yaw_P vector, and also
// contributes to the _omega_I.z long term yaw drift estimate
void
AP_AHRS_DCM::drift_correction_yaw(void)
{
	bool new_value = false;
	float yaw_error;
	float yaw_deltat;

	if (_compass && _compass->use_for_yaw()) {
		if (_compass->last_update != _compass_last_update) {
			yaw_deltat = (_compass->last_update - _compass_last_update) * 1.0e-6;
			_compass_last_update = _compass->last_update;
			if (!_have_initial_yaw) {
				float heading = _compass->calculate_heading(_dcm_matrix);
				_dcm_matrix.from_euler(roll, pitch, heading);
				_omega_yaw_P.zero();
				_have_initial_yaw = true;
			}
			new_value = true;
			yaw_error = yaw_error_compass();
		}
	} else if (_fly_forward && _gps && _gps->status() == GPS::GPS_OK) {
		if (_gps->last_fix_time != _gps_last_update &&
		    _gps->ground_speed >= GPS_SPEED_MIN) {
			yaw_deltat = (_gps->last_fix_time - _gps_last_update) * 1.0e-3;
			_gps_last_update = _gps->last_fix_time;
			if (!_have_initial_yaw) {
				_dcm_matrix.from_euler(roll, pitch, ToRad(_gps->ground_course*0.01));
				_omega_yaw_P.zero();
				_have_initial_yaw = true;
			}
			new_value = true;
			yaw_error = yaw_error_gps();
		}
	}

	if (!new_value) {
		// we don't have any new yaw information
		// slowly decay _omega_yaw_P to cope with loss
		// of our yaw source
		_omega_yaw_P *= 0.97;
		return;
	}

	// the yaw error is a vector in earth frame
	Vector3f error = Vector3f(0,0, yaw_error);

	// convert the error vector to body frame
	error = _dcm_matrix.mul_transpose(error);

	// the spin rate changes the P gain, and disables the
	// integration at higher rates
	float spin_rate = _omega.length();

	// update the proportional control to drag the
	// yaw back to the right value. We use a gain
	// that depends on the spin rate. See the fastRotations.pdf
	// paper from Bill Premerlani
	_omega_yaw_P = error * _P_gain(spin_rate) * _kp_yaw.get();

	// don't update the drift term if we lost the yaw reference
	// for more than 2 seconds
	if (yaw_deltat < 2.0 && spin_rate < ToRad(SPIN_RATE_LIMIT)) {
		// also add to the I term
		_omega_I_sum.z += error.z * _ki_yaw * yaw_deltat;
	}

	_error_yaw_sum += fabs(yaw_error);
	_error_yaw_count++;
}




// perform drift correction. This function aims to update _omega_P and
// _omega_I with our best estimate of the short term and long term
// gyro error. The _omega_P value is what pulls our attitude solution
// back towards the reference vector quickly. The _omega_I term is an
// attempt to learn the long term drift rate of the gyros.
//
// This drift correction implementation is based on a paper
// by Bill Premerlani from here:
//   http://gentlenav.googlecode.com/files/RollPitchDriftCompensation.pdf
void
AP_AHRS_DCM::drift_correction(float deltat)
{
    Vector3f velocity;
    uint32_t last_correction_time;

    // perform yaw drift correction if we have a new yaw reference
    // vector
    drift_correction_yaw();

    // integrate the accel vector in the earth frame between GPS readings
    _ra_sum += _dcm_matrix * (_accel_vector * deltat);

    // keep a sum of the deltat values, so we know how much time
    // we have integrated over
    _ra_deltat += deltat;

    if (_gps == NULL || _gps->status() != GPS::GPS_OK) {
        // no GPS, or no lock. We assume zero velocity. This at
        // least means we can cope with gyro drift while sitting
        // on a bench with no GPS lock
        if (_ra_deltat < 0.1) {
            // not enough time has accumulated
            return;
        }
        velocity.zero();
	_last_velocity.zero();
        last_correction_time = millis();
	_have_gps_lock = false;
    } else {
        if (_gps->last_fix_time == _ra_sum_start) {
            // we don't have a new GPS fix - nothing more to do
            return;
        }
        velocity = Vector3f(_gps->velocity_north(), _gps->velocity_east(), 0);
        last_correction_time = _gps->last_fix_time;
	if (_have_gps_lock == false) {
		// if we didn't have GPS lock in the last drift
		// correction interval then set the velocities equal
		_last_velocity = velocity;
	}
	_have_gps_lock = true;
    }

#if 1
    /* 
       NOTE: The barometric vertical acceleration correction is disabled 
       until we work out how to filter it sufficiently to be usable
       on ArduCopter
    */
    if (_barometer != NULL) {
	    // Z velocity is down
	    velocity.z = - _barometer->get_climb_rate();
    }
#endif

    // see if this is our first time through - in which case we
    // just setup the start times and return
    if (_ra_sum_start == 0) {
        _ra_sum_start = last_correction_time;
        _last_velocity = velocity;
        return;
    }

    // equation 9: get the corrected acceleration vector in earth frame. Units
    // are m/s/s
    Vector3f GA_e;
    float v_scale = 1.0/(_ra_deltat*_gravity);
    GA_e = Vector3f(0, 0, -1.0) + ((velocity - _last_velocity) * v_scale);
    GA_e.normalize();
    if (GA_e.is_inf()) {
	    // wait for some non-zero acceleration information
	    return;
    }

    // calculate the error term in earth frame.
    Vector3f GA_b = _ra_sum / _ra_deltat;
    GA_b.normalize();
    Vector3f error = GA_b % GA_e;
    
    // step 2 calculate earth_error_Z
    float earth_error_Z = error.z;

    // equation 10
    float tilt = sqrt(sq(GA_e.x) + sq(GA_e.y));

    // equation 11
    float theta = atan2(GA_b.y, GA_b.x);
    
    // equation 12
    Vector3f GA_e2 = Vector3f(cos(theta)*tilt, sin(theta)*tilt, GA_e.z);

    // step 6
    error = GA_b % GA_e2;
    error.z = earth_error_Z;

    // convert the error term to body frame
    error = _dcm_matrix.mul_transpose(error);

    _error_rp_sum += error.length();
    _error_rp_count++;

    // base the P gain on the spin rate
    float spin_rate = _omega.length();

    // we now want to calculate _omega_P and _omega_I. The
    // _omega_P value is what drags us quickly to the
    // accelerometer reading.
    _omega_P = error * _P_gain(spin_rate) * _kp;

    // accumulate some integrator error
    if (spin_rate < ToRad(SPIN_RATE_LIMIT)) {
	    _omega_I_sum += error * _ki * _ra_deltat;
	    _omega_I_sum_time += _ra_deltat;
    }

    if (_omega_I_sum_time >= 5) {
	    // limit the rate of change of omega_I to the hardware
	    // reported maximum gyro drift rate. This ensures that
	    // short term errors don't cause a buildup of omega_I
	    // beyond the physical limits of the device
	    float change_limit = _gyro_drift_limit * _omega_I_sum_time;
	    _omega_I_sum.x = constrain(_omega_I_sum.x, -change_limit, change_limit);
	    _omega_I_sum.y = constrain(_omega_I_sum.y, -change_limit, change_limit);
	    _omega_I_sum.z = constrain(_omega_I_sum.z, -change_limit, change_limit);
	    _omega_I += _omega_I_sum;
	    _omega_I_sum.zero();
	    _omega_I_sum_time = 0;
    }

    // zero our accumulator ready for the next GPS step
    _ra_sum.zero();
    _ra_deltat = 0;
    _ra_sum_start = last_correction_time;

    // remember the velocity for next time
    _last_velocity = velocity;
}


// calculate the euler angles which will be used for high level
// navigation control
void
AP_AHRS_DCM::euler_angles(void)
{
	_dcm_matrix.to_euler(&roll, &pitch, &yaw);

	roll_sensor 	= degrees(roll)  * 100;
	pitch_sensor 	= degrees(pitch) * 100;
	yaw_sensor 	= degrees(yaw)   * 100;

	if (yaw_sensor < 0)
		yaw_sensor += 36000;
}

/* reporting of DCM state for MAVLink */

// average error_roll_pitch since last call
float AP_AHRS_DCM::get_error_rp(void)
{
	if (_error_rp_count == 0) {
		// this happens when telemetry is setup on two
		// serial ports
		return _error_rp_last;
	}
	_error_rp_last = _error_rp_sum / _error_rp_count;
	_error_rp_sum = 0;
	_error_rp_count = 0;
	return _error_rp_last;
}

// average error_yaw since last call
float AP_AHRS_DCM::get_error_yaw(void)
{
	if (_error_yaw_count == 0) {
		// this happens when telemetry is setup on two
		// serial ports
		return _error_yaw_last;
	}
	_error_yaw_last = _error_yaw_sum / _error_yaw_count;
	_error_yaw_sum = 0;
	_error_yaw_count = 0;
	return _error_yaw_last;
}