px4_autopilot/l1/ecl_l1_pos_controller.cpp

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/**
 * @file ecl_l1_pos_controller.h
 * Implementation of L1 position control.
 * Authors and acknowledgements in header.
 *
 */

#include <float.h>

#include "ecl_l1_pos_controller.h"

using matrix::Vector2f;
using matrix::wrap_pi;

float ECL_L1_Pos_Controller::nav_roll()
{
	float ret = atanf(_lateral_accel * 1.0f / CONSTANTS_ONE_G);
	ret = math::constrain(ret, -_roll_lim_rad, _roll_lim_rad);
	return ret;
}

float ECL_L1_Pos_Controller::switch_distance(float wp_radius)
{
	/* following [2], switching on L1 distance */
	return math::min(wp_radius, _L1_distance);
}

void
ECL_L1_Pos_Controller::navigate_waypoints(const Vector2f &vector_A, const Vector2f &vector_B,
		const Vector2f &vector_curr_position, const Vector2f &ground_speed_vector)
{
	/* this follows the logic presented in [1] */
	float eta = 0.0f;
	float xtrack_vel = 0.0f;
	float ltrack_vel = 0.0f;

	/* get the direction between the last (visited) and next waypoint */
	_target_bearing = get_bearing_to_next_waypoint((double)vector_curr_position(0), (double)vector_curr_position(1), (double)vector_B(0), (double)vector_B(1));

	/* enforce a minimum ground speed of 0.1 m/s to avoid singularities */
	float ground_speed = math::max(ground_speed_vector.length(), 0.1f);

	/* calculate the L1 length required for the desired period */
	_L1_distance = _L1_ratio * ground_speed;

	/* calculate vector from A to B */
	Vector2f vector_AB = get_local_planar_vector(vector_A, vector_B);

	/*
	 * check if waypoints are on top of each other. If yes,
	 * skip A and directly continue to B
	 */
	if (vector_AB.length() < 1.0e-6f) {
		vector_AB = get_local_planar_vector(vector_curr_position, vector_B);
	}

	vector_AB.normalize();

	/* calculate the vector from waypoint A to the aircraft */
	Vector2f vector_A_to_airplane = get_local_planar_vector(vector_A, vector_curr_position);

	/* calculate crosstrack error (output only) */
	_crosstrack_error = vector_AB % vector_A_to_airplane;

	/*
	 * If the current position is in a +-135 degree angle behind waypoint A
	 * and further away from A than the L1 distance, then A becomes the L1 point.
	 * If the aircraft is already between A and B normal L1 logic is applied.
	 */
	float distance_A_to_airplane = vector_A_to_airplane.length();
	float alongTrackDist = vector_A_to_airplane * vector_AB;

	/* estimate airplane position WRT to B */
	Vector2f vector_B_to_P_unit = get_local_planar_vector(vector_B, vector_curr_position).normalized();

	/* calculate angle of airplane position vector relative to line) */

	// XXX this could probably also be based solely on the dot product
	float AB_to_BP_bearing = atan2f(vector_B_to_P_unit % vector_AB, vector_B_to_P_unit * vector_AB);

	/* extension from [2], fly directly to A */
	if (distance_A_to_airplane > _L1_distance && alongTrackDist / math::max(distance_A_to_airplane, 1.0f) < -0.7071f) {

		/* calculate eta to fly to waypoint A */

		/* unit vector from waypoint A to current position */
		Vector2f vector_A_to_airplane_unit = vector_A_to_airplane.normalized();
		/* velocity across / orthogonal to line */
		xtrack_vel = ground_speed_vector % (-vector_A_to_airplane_unit);
		/* velocity along line */
		ltrack_vel = ground_speed_vector * (-vector_A_to_airplane_unit);
		eta = atan2f(xtrack_vel, ltrack_vel);
		/* bearing from current position to L1 point */
		_nav_bearing = atan2f(-vector_A_to_airplane_unit(1), -vector_A_to_airplane_unit(0));

		/*
		 * If the AB vector and the vector from B to airplane point in the same
		 * direction, we have missed the waypoint. At +- 90 degrees we are just passing it.
		 */

	} else if (fabsf(AB_to_BP_bearing) < math::radians(100.0f)) {
		/*
		 * Extension, fly back to waypoint.
		 *
		 * This corner case is possible if the system was following
		 * the AB line from waypoint A to waypoint B, then is
		 * switched to manual mode (or otherwise misses the waypoint)
		 * and behind the waypoint continues to follow the AB line.
		 */

		/* calculate eta to fly to waypoint B */

		/* velocity across / orthogonal to line */
		xtrack_vel = ground_speed_vector % (-vector_B_to_P_unit);
		/* velocity along line */
		ltrack_vel = ground_speed_vector * (-vector_B_to_P_unit);
		eta = atan2f(xtrack_vel, ltrack_vel);
		/* bearing from current position to L1 point */
		_nav_bearing = atan2f(-vector_B_to_P_unit(1), -vector_B_to_P_unit(0));

	} else {

		/* calculate eta to fly along the line between A and B */

		/* velocity across / orthogonal to line */
		xtrack_vel = ground_speed_vector % vector_AB;
		/* velocity along line */
		ltrack_vel = ground_speed_vector * vector_AB;
		/* calculate eta2 (angle of velocity vector relative to line) */
		float eta2 = atan2f(xtrack_vel, ltrack_vel);
		/* calculate eta1 (angle to L1 point) */
		float xtrackErr = vector_A_to_airplane % vector_AB;
		float sine_eta1 = xtrackErr / math::max(_L1_distance, 0.1f);
		/* limit output to 45 degrees */
		sine_eta1 = math::constrain(sine_eta1, -0.7071f, 0.7071f); //sin(pi/4) = 0.7071
		float eta1 = asinf(sine_eta1);
		eta = eta1 + eta2;
		/* bearing from current position to L1 point */
		_nav_bearing = atan2f(vector_AB(1), vector_AB(0)) + eta1;

	}

	/* limit angle to +-90 degrees */
	eta = math::constrain(eta, (-M_PI_F) / 2.0f, +M_PI_F / 2.0f);
	_lateral_accel = _K_L1 * ground_speed * ground_speed / _L1_distance * sinf(eta);

	/* flying to waypoints, not circling them */
	_circle_mode = false;

	/* the bearing angle, in NED frame */
	_bearing_error = eta;
}

void
ECL_L1_Pos_Controller::navigate_loiter(const Vector2f &vector_A, const Vector2f &vector_curr_position, float radius,
				       int8_t loiter_direction, const Vector2f &ground_speed_vector)
{
	/* the complete guidance logic in this section was proposed by [2] */

	/* calculate the gains for the PD loop (circle tracking) */
	float omega = (2.0f * M_PI_F / _L1_period);
	float K_crosstrack = omega * omega;
	float K_velocity = 2.0f * _L1_damping * omega;

	/* update bearing to next waypoint */
	_target_bearing = get_bearing_to_next_waypoint((double)vector_curr_position(0), (double)vector_curr_position(1), (double)vector_A(0), (double)vector_A(1));

	/* ground speed, enforce minimum of 0.1 m/s to avoid singularities */
	float ground_speed = math::max(ground_speed_vector.length(), 0.1f);

	/* calculate the L1 length required for the desired period */
	_L1_distance = _L1_ratio * ground_speed;

	/* calculate the vector from waypoint A to current position */
	Vector2f vector_A_to_airplane = get_local_planar_vector(vector_A, vector_curr_position);

	Vector2f vector_A_to_airplane_unit;

	/* prevent NaN when normalizing */
	if (vector_A_to_airplane.length() > FLT_EPSILON) {
		/* store the normalized vector from waypoint A to current position */
		vector_A_to_airplane_unit = vector_A_to_airplane.normalized();

	} else {
		vector_A_to_airplane_unit = vector_A_to_airplane;
	}

	/* calculate eta angle towards the loiter center */

	/* velocity across / orthogonal to line from waypoint to current position */
	float xtrack_vel_center = vector_A_to_airplane_unit % ground_speed_vector;
	/* velocity along line from waypoint to current position */
	float ltrack_vel_center = - (ground_speed_vector * vector_A_to_airplane_unit);
	float eta = atan2f(xtrack_vel_center, ltrack_vel_center);
	/* limit eta to 90 degrees */
	eta = math::constrain(eta, -M_PI_F / 2.0f, +M_PI_F / 2.0f);

	/* calculate the lateral acceleration to capture the center point */
	float lateral_accel_sp_center = _K_L1 * ground_speed * ground_speed / _L1_distance * sinf(eta);

	/* for PD control: Calculate radial position and velocity errors */

	/* radial velocity error */
	float xtrack_vel_circle = -ltrack_vel_center;
	/* radial distance from the loiter circle (not center) */
	float xtrack_err_circle = vector_A_to_airplane.length() - radius;

	/* cross track error for feedback */
	_crosstrack_error = xtrack_err_circle;

	/* calculate PD update to circle waypoint */
	float lateral_accel_sp_circle_pd = (xtrack_err_circle * K_crosstrack + xtrack_vel_circle * K_velocity);

	/* calculate velocity on circle / along tangent */
	float tangent_vel = xtrack_vel_center * loiter_direction;

	/* prevent PD output from turning the wrong way */
	if (tangent_vel < 0.0f) {
		lateral_accel_sp_circle_pd = math::max(lateral_accel_sp_circle_pd, 0.0f);
	}

	/* calculate centripetal acceleration setpoint */
	float lateral_accel_sp_circle_centripetal = tangent_vel * tangent_vel / math::max((0.5f * radius),
			(radius + xtrack_err_circle));

	/* add PD control on circle and centripetal acceleration for total circle command */
	float lateral_accel_sp_circle = loiter_direction * (lateral_accel_sp_circle_pd + lateral_accel_sp_circle_centripetal);

	/*
	 * Switch between circle (loiter) and capture (towards waypoint center) mode when
	 * the commands switch over. Only fly towards waypoint if outside the circle.
	 */

	// XXX check switch over
	if ((lateral_accel_sp_center < lateral_accel_sp_circle && loiter_direction > 0 && xtrack_err_circle > 0.0f) ||
	    (lateral_accel_sp_center > lateral_accel_sp_circle && loiter_direction < 0 && xtrack_err_circle > 0.0f)) {
		_lateral_accel = lateral_accel_sp_center;
		_circle_mode = false;
		/* angle between requested and current velocity vector */
		_bearing_error = eta;
		/* bearing from current position to L1 point */
		_nav_bearing = atan2f(-vector_A_to_airplane_unit(1), -vector_A_to_airplane_unit(0));

	} else {
		_lateral_accel = lateral_accel_sp_circle;
		_circle_mode = true;
		_bearing_error = 0.0f;
		/* bearing from current position to L1 point */
		_nav_bearing = atan2f(-vector_A_to_airplane_unit(1), -vector_A_to_airplane_unit(0));
	}
}

void ECL_L1_Pos_Controller::navigate_heading(float navigation_heading, float current_heading,
		const Vector2f &ground_speed_vector)
{
	/* the complete guidance logic in this section was proposed by [2] */

	/*
	 * As the commanded heading is the only reference
	 * (and no crosstrack correction occurs),
	 * target and navigation bearing become the same
	 */
	_target_bearing = _nav_bearing = wrap_pi(navigation_heading);

	float eta = wrap_pi(_target_bearing - wrap_pi(current_heading));

	/* consequently the bearing error is exactly eta: */
	_bearing_error = eta;

	/* ground speed is the length of the ground speed vector */
	float ground_speed = ground_speed_vector.length();

	/* adjust L1 distance to keep constant frequency */
	_L1_distance = ground_speed / _heading_omega;
	float omega_vel = ground_speed * _heading_omega;

	/* not circling a waypoint */
	_circle_mode = false;

	/* navigating heading means by definition no crosstrack error */
	_crosstrack_error = 0;

	/* limit eta to 90 degrees */
	eta = math::constrain(eta, (-M_PI_F) / 2.0f, +M_PI_F / 2.0f);
	_lateral_accel = 2.0f * sinf(eta) * omega_vel;
}

void ECL_L1_Pos_Controller::navigate_level_flight(float current_heading)
{
	/* the logic in this section is trivial, but originally proposed by [2] */

	/* reset all heading / error measures resulting in zero roll */
	_target_bearing = current_heading;
	_nav_bearing = current_heading;
	_bearing_error = 0;
	_crosstrack_error = 0;
	_lateral_accel = 0;

	/* not circling a waypoint when flying level */
	_circle_mode = false;
}

Vector2f ECL_L1_Pos_Controller::get_local_planar_vector(const Vector2f &origin, const Vector2f &target) const
{
	/* this is an approximation for small angles, proposed by [2] */
	Vector2f out(math::radians((target(0) - origin(0))),
		     math::radians((target(1) - origin(1))*cosf(math::radians(origin(0)))));

	return out * static_cast<float>(CONSTANTS_RADIUS_OF_EARTH);
}

void ECL_L1_Pos_Controller::set_l1_period(float period)
{
	_L1_period = period;

	/* calculate the ratio introduced in [2] */
	_L1_ratio = 1.0f / M_PI_F * _L1_damping * _L1_period;

	/* calculate normalized frequency for heading tracking */
	_heading_omega = sqrtf(2.0f) * M_PI_F / _L1_period;
}

void ECL_L1_Pos_Controller::set_l1_damping(float damping)
{
	_L1_damping = damping;

	/* calculate the ratio introduced in [2] */
	_L1_ratio = 1.0f / M_PI_F * _L1_damping * _L1_period;

	/* calculate the L1 gain (following [2]) */
	_K_L1 = 4.0f * _L1_damping * _L1_damping;
}