ardupilot/libraries/AC_WPNav/AC_WPNav.cpp

#include <AP_HAL/AP_HAL.h>
#include "AC_WPNav.h"

extern const AP_HAL::HAL& hal;

const AP_Param::GroupInfo AC_WPNav::var_info[] = {
    // index 0 was used for the old orientation matrix

    // @Param: SPEED
    // @DisplayName: Waypoint Horizontal Speed Target
    // @Description: Defines the speed in cm/s which the aircraft will attempt to maintain horizontally during a WP mission
    // @Units: cm/s
    // @Range: 20 2000
    // @Increment: 50
    // @User: Standard
    AP_GROUPINFO("SPEED",       0, AC_WPNav, _wp_speed_cms, WPNAV_WP_SPEED),

    // @Param: RADIUS
    // @DisplayName: Waypoint Radius
    // @Description: Defines the distance from a waypoint, that when crossed indicates the wp has been hit.
    // @Units: cm
    // @Range: 100 1000
    // @Increment: 1
    // @User: Standard
    AP_GROUPINFO("RADIUS",      1, AC_WPNav, _wp_radius_cm, WPNAV_WP_RADIUS),

    // @Param: SPEED_UP
    // @DisplayName: Waypoint Climb Speed Target
    // @Description: Defines the speed in cm/s which the aircraft will attempt to maintain while climbing during a WP mission
    // @Units: cm/s
    // @Range: 10 1000
    // @Increment: 50
    // @User: Standard
    AP_GROUPINFO("SPEED_UP",    2, AC_WPNav, _wp_speed_up_cms, WPNAV_WP_SPEED_UP),

    // @Param: SPEED_DN
    // @DisplayName: Waypoint Descent Speed Target
    // @Description: Defines the speed in cm/s which the aircraft will attempt to maintain while descending during a WP mission
    // @Units: cm/s
    // @Range: 10 500
    // @Increment: 10
    // @User: Standard
    AP_GROUPINFO("SPEED_DN",    3, AC_WPNav, _wp_speed_down_cms, WPNAV_WP_SPEED_DOWN),

    // @Param: LOIT_SPEED
    // @DisplayName: Loiter Horizontal Maximum Speed
    // @Description: Defines the maximum speed in cm/s which the aircraft will travel horizontally while in loiter mode
    // @Units: cm/s
    // @Range: 20 2000
    // @Increment: 50
    // @User: Standard
    AP_GROUPINFO("LOIT_SPEED",  4, AC_WPNav, _loiter_speed_cms, WPNAV_LOITER_SPEED),

    // @Param: ACCEL
    // @DisplayName: Waypoint Acceleration 
    // @Description: Defines the horizontal acceleration in cm/s/s used during missions
    // @Units: cm/s/s
    // @Range: 50 500
    // @Increment: 10
    // @User: Standard
    AP_GROUPINFO("ACCEL",       5, AC_WPNav, _wp_accel_cms, WPNAV_ACCELERATION),

    // @Param: ACCEL_Z
    // @DisplayName: Waypoint Vertical Acceleration
    // @Description: Defines the vertical acceleration in cm/s/s used during missions
    // @Units: cm/s/s
    // @Range: 50 500
    // @Increment: 10
    // @User: Standard
    AP_GROUPINFO("ACCEL_Z",     6, AC_WPNav, _wp_accel_z_cms, WPNAV_WP_ACCEL_Z_DEFAULT),

    // @Param: LOIT_JERK
    // @DisplayName: Loiter maximum jerk
    // @Description: Loiter maximum jerk in cm/s/s/s
    // @Units: cm/s/s/s
    // @Range: 500 5000
    // @Increment: 1
    // @User: Advanced
    AP_GROUPINFO("LOIT_JERK",   7, AC_WPNav, _loiter_jerk_max_cmsss, WPNAV_LOITER_JERK_MAX_DEFAULT),

    // @Param: LOIT_MAXA
    // @DisplayName: Loiter maximum acceleration
    // @Description: Loiter maximum acceleration in cm/s/s.  Higher values cause the copter to accelerate and stop more quickly.
    // @Units: cm/s/s
    // @Range: 100 981
    // @Increment: 1
    // @User: Advanced
    AP_GROUPINFO("LOIT_MAXA",   8, AC_WPNav, _loiter_accel_cmss, WPNAV_LOITER_ACCEL),

    // @Param: LOIT_MINA
    // @DisplayName: Loiter minimum acceleration
    // @Description: Loiter minimum acceleration in cm/s/s. Higher values stop the copter more quickly when the stick is centered, but cause a larger jerk when the copter stops.
    // @Units: cm/s/s
    // @Range: 25 250
    // @Increment: 1
    // @User: Advanced
    AP_GROUPINFO("LOIT_MINA",   9, AC_WPNav, _loiter_accel_min_cmss, WPNAV_LOITER_ACCEL_MIN),

    // @Param: RFND_USE
    // @DisplayName: Use rangefinder for terrain following
    // @Description: This controls the use of a rangefinder for terrain following
    // @Values: 0:Disable,1:Enable
    // @User: Advanced
    AP_GROUPINFO("RFND_USE",   10, AC_WPNav, _rangefinder_use, 1),
    
    AP_GROUPEND
};

// Default constructor.
// Note that the Vector/Matrix constructors already implicitly zero
// their values.
//
AC_WPNav::AC_WPNav(const AP_InertialNav& inav, const AP_AHRS_View& ahrs, AC_PosControl& pos_control, const AC_AttitudeControl& attitude_control) :
    _inav(inav),
    _ahrs(ahrs),
    _pos_control(pos_control),
    _attitude_control(attitude_control),
    _pilot_accel_fwd_cms(0),
    _pilot_accel_rgt_cms(0),
    _wp_last_update(0),
    _wp_step(0),
    _track_length(0.0f),
    _track_length_xy(0.0f),
    _track_desired(0.0f),
    _limited_speed_xy_cms(0.0f),
    _track_accel(0.0f),
    _track_speed(0.0f),
    _track_leash_length(0.0f),
    _slow_down_dist(0.0f),
    _spline_time(0.0f),
    _spline_time_scale(0.0f),
    _spline_vel_scaler(0.0f),
    _yaw(0.0f)
{
    AP_Param::setup_object_defaults(this, var_info);

    // init flags
    _flags.reached_destination = false;
    _flags.fast_waypoint = false;
    _flags.slowing_down = false;
    _flags.recalc_wp_leash = false;
    _flags.new_wp_destination = false;
    _flags.segment_type = SEGMENT_STRAIGHT;

    // sanity check loiter speed
    _loiter_speed_cms = MAX(_loiter_speed_cms, WPNAV_LOITER_SPEED_MIN);
}

///
/// loiter controller
///

/// init_loiter_target in cm from home
void AC_WPNav::init_loiter_target(const Vector3f& position, bool reset_I)
{
    // initialise position controller
    _pos_control.init_xy_controller(reset_I);

    // initialise pos controller speed, acceleration and jerk
    _pos_control.set_speed_xy(_loiter_speed_cms);
    _pos_control.set_accel_xy(_loiter_accel_cmss);
    _pos_control.set_jerk_xy(_loiter_jerk_max_cmsss);

    // set target position
    _pos_control.set_xy_target(position.x, position.y);

    // initialise feed forward velocity to zero
    _pos_control.set_desired_velocity_xy(0,0);

    // initialise desired accel and add fake wind
    _loiter_desired_accel.x = 0;
    _loiter_desired_accel.y = 0;

    // initialise pilot input
    _pilot_accel_fwd_cms = 0;
    _pilot_accel_rgt_cms = 0;
}

/// init_loiter_target - initialize's loiter position and feed-forward velocity from current pos and velocity
void AC_WPNav::init_loiter_target()
{
    const Vector3f& curr_pos = _inav.get_position();
    const Vector3f& curr_vel = _inav.get_velocity();

    // initialise position controller
    _pos_control.init_xy_controller();

    // sanity check loiter speed
    _loiter_speed_cms = MAX(_loiter_speed_cms, WPNAV_LOITER_SPEED_MIN);

    // initialise pos controller speed and acceleration
    _pos_control.set_speed_xy(_loiter_speed_cms);
    _pos_control.set_accel_xy(_loiter_accel_cmss);
    _pos_control.set_jerk_xy(_loiter_jerk_max_cmsss);

    // set target position
    _pos_control.set_xy_target(curr_pos.x, curr_pos.y);

    // move current vehicle velocity into feed forward velocity
    _pos_control.set_desired_velocity_xy(curr_vel.x, curr_vel.y);

    // initialise desired accel and add fake wind
    _loiter_desired_accel.x = (_loiter_accel_cmss)*curr_vel.x/_loiter_speed_cms;
    _loiter_desired_accel.y = (_loiter_accel_cmss)*curr_vel.y/_loiter_speed_cms;

    // initialise pilot input
    _pilot_accel_fwd_cms = 0;
    _pilot_accel_rgt_cms = 0;
}

/// loiter_soften_for_landing - reduce response for landing
void AC_WPNav::loiter_soften_for_landing()
{
    const Vector3f& curr_pos = _inav.get_position();

    // set target position to current position
    _pos_control.set_xy_target(curr_pos.x, curr_pos.y);
    _pos_control.freeze_ff_xy();
}

/// set_pilot_desired_acceleration - sets pilot desired acceleration from roll and pitch stick input
void AC_WPNav::set_pilot_desired_acceleration(float control_roll, float control_pitch)
{
    // convert pilot input to desired acceleration in cm/s/s
    _pilot_accel_fwd_cms = -control_pitch * _loiter_accel_cmss / 4500.0f;
    _pilot_accel_rgt_cms = control_roll * _loiter_accel_cmss / 4500.0f;
}

/// get_loiter_stopping_point_xy - returns vector to stopping point based on a horizontal position and velocity
void AC_WPNav::get_loiter_stopping_point_xy(Vector3f& stopping_point) const
{
	_pos_control.get_stopping_point_xy(stopping_point);
}

/// calc_loiter_desired_velocity - updates desired velocity (i.e. feed forward) with pilot requested acceleration and fake wind resistance
///		updated velocity sent directly to position controller
void AC_WPNav::calc_loiter_desired_velocity(float nav_dt, float ekfGndSpdLimit)
{
    // calculate a loiter speed limit which is the minimum of the value set by the WPNAV_LOITER_SPEED
    // parameter and the value set by the EKF to observe optical flow limits
    float gnd_speed_limit_cms = MIN(_loiter_speed_cms,ekfGndSpdLimit*100.0f);
    gnd_speed_limit_cms = MAX(gnd_speed_limit_cms, WPNAV_LOITER_SPEED_MIN);

    // range check nav_dt
    if( nav_dt < 0 ) {
        return;
    }

    _pos_control.set_speed_xy(gnd_speed_limit_cms);
    _pos_control.set_accel_xy(_loiter_accel_cmss);
    _pos_control.set_jerk_xy(_loiter_jerk_max_cmsss);

    // rotate pilot input to lat/lon frame
    Vector2f desired_accel;
    desired_accel.x = (_pilot_accel_fwd_cms*_ahrs.cos_yaw() - _pilot_accel_rgt_cms*_ahrs.sin_yaw());
    desired_accel.y = (_pilot_accel_fwd_cms*_ahrs.sin_yaw() + _pilot_accel_rgt_cms*_ahrs.cos_yaw());

    // calculate the difference
    Vector2f des_accel_diff = (desired_accel - _loiter_desired_accel);

    // constrain and scale the desired acceleration
    float des_accel_change_total = norm(des_accel_diff.x, des_accel_diff.y);
    float accel_change_max = _loiter_jerk_max_cmsss * nav_dt;
    
    if (_loiter_jerk_max_cmsss > 0.0f && des_accel_change_total > accel_change_max && des_accel_change_total > 0.0f) {
        des_accel_diff.x = accel_change_max * des_accel_diff.x/des_accel_change_total;
        des_accel_diff.y = accel_change_max * des_accel_diff.y/des_accel_change_total;
    }
    
    // adjust the desired acceleration
    _loiter_desired_accel += des_accel_diff;

    // get pos_control's feed forward velocity
    const Vector3f &desired_vel_3d = _pos_control.get_desired_velocity();
    Vector2f desired_vel(desired_vel_3d.x,desired_vel_3d.y);

    // add pilot commanded acceleration
    desired_vel.x += _loiter_desired_accel.x * nav_dt;
    desired_vel.y += _loiter_desired_accel.y * nav_dt;

    float desired_speed = desired_vel.length();

    if (!is_zero(desired_speed)) {
        Vector2f desired_vel_norm = desired_vel/desired_speed;
        float drag_speed_delta = -_loiter_accel_cmss*nav_dt*desired_speed/gnd_speed_limit_cms;

        if (_pilot_accel_fwd_cms == 0 && _pilot_accel_rgt_cms == 0) {
            drag_speed_delta = MIN(drag_speed_delta,MAX(-_loiter_accel_min_cmss*nav_dt, -2.0f*desired_speed*nav_dt));
        }

        desired_speed = MAX(desired_speed+drag_speed_delta,0.0f);
        desired_vel = desired_vel_norm*desired_speed;
    }

    // Apply EKF limit to desired velocity -  this limit is calculated by the EKF and adjusted as required to ensure certain sensor limits are respected (eg optical flow sensing)
    float horizSpdDem = sqrtf(sq(desired_vel.x) + sq(desired_vel.y));
    if (horizSpdDem > gnd_speed_limit_cms) {
        desired_vel.x = desired_vel.x * gnd_speed_limit_cms / horizSpdDem;
        desired_vel.y = desired_vel.y * gnd_speed_limit_cms / horizSpdDem;
    }

    // Limit the velocity to prevent fence violations
    if (_avoid != nullptr) {
        _avoid->adjust_velocity(_pos_control.get_pos_xy_kP(), _loiter_accel_cmss, desired_vel);
    }

    // send adjusted feed forward velocity back to position controller
    _pos_control.set_desired_velocity_xy(desired_vel.x,desired_vel.y);
}

/// get_bearing_to_target - get bearing to loiter target in centi-degrees
int32_t AC_WPNav::get_loiter_bearing_to_target() const
{
    return get_bearing_cd(_inav.get_position(), _pos_control.get_pos_target());
}

// update_loiter - run the loiter controller - gets called at 100hz (APM) or 400hz (PX4)
void AC_WPNav::update_loiter(float ekfGndSpdLimit, float ekfNavVelGainScaler)
{
    // calculate dt
    float dt = _pos_control.time_since_last_xy_update();

    // run at poscontrol update rate.
    // TODO: run on user input to reduce latency, maybe if (user_input || dt >= _pos_control.get_dt_xy())
    if (dt >= _pos_control.get_dt_xy()) {
        // sanity check dt
        if (dt >= 0.2f) {
            dt = 0.0f;
        }

        // initialise pos controller speed and acceleration
        _pos_control.set_speed_xy(_loiter_speed_cms);
        _pos_control.set_accel_xy(_loiter_accel_cmss);
        _pos_control.set_jerk_xy(_loiter_jerk_max_cmsss);

        calc_loiter_desired_velocity(dt,ekfGndSpdLimit);
        _pos_control.update_xy_controller(AC_PosControl::XY_MODE_POS_LIMITED_AND_VEL_FF, ekfNavVelGainScaler, true);
    }
}

/// init_brake_target - initializes stop position from current position and velocity
void AC_WPNav::init_brake_target(float accel_cmss)
{
    const Vector3f& curr_vel = _inav.get_velocity();
    Vector3f stopping_point;

    // initialise position controller
    _pos_control.init_xy_controller();

    // initialise pos controller speed and acceleration
    _pos_control.set_speed_xy(curr_vel.length());
    _pos_control.set_accel_xy(accel_cmss);
    _pos_control.set_jerk_xy(_loiter_jerk_max_cmsss);
    _pos_control.calc_leash_length_xy();

    _pos_control.get_stopping_point_xy(stopping_point);

    // set target position
    init_loiter_target(stopping_point);
}

// update_brake - run the stop controller - gets called at 400hz
void AC_WPNav::update_brake(float ekfGndSpdLimit, float ekfNavVelGainScaler)
{
    // calculate dt
    float dt = _pos_control.time_since_last_xy_update();

    // run at poscontrol update rate.
    if (dt >= _pos_control.get_dt_xy()) {

        // send adjusted feed forward velocity back to position controller
        _pos_control.set_desired_velocity_xy(0,0);
        _pos_control.update_xy_controller(AC_PosControl::XY_MODE_POS_LIMITED_AND_VEL_FF, ekfNavVelGainScaler, false);
    }
}

///
/// waypoint navigation
///

/// wp_and_spline_init - initialise straight line and spline waypoint controllers
///     updates target roll, pitch targets and I terms based on vehicle lean angles
///     should be called once before the waypoint controller is used but does not need to be called before subsequent updates to destination
void AC_WPNav::wp_and_spline_init()
{
    // check _wp_accel_cms is reasonable
    if (_wp_accel_cms <= 0) {
        _wp_accel_cms.set_and_save(WPNAV_ACCELERATION);
    }

    // also limit the accel using the maximum lean angle. This
    // prevents the navigation controller from trying to move the
    // target point at an unachievable rate
    float accel_limit_cms = GRAVITY_MSS * 100 * tanf(radians(_attitude_control.lean_angle_max()*0.01f));
    if (_wp_accel_cms > accel_limit_cms) {
        _wp_accel_cms.set(accel_limit_cms);
    }

    // initialise position controller
    _pos_control.init_xy_controller();
    _pos_control.clear_desired_velocity_ff_z();

    // initialise position controller speed and acceleration
    _pos_control.set_speed_xy(_wp_speed_cms);
    _pos_control.set_accel_xy(_wp_accel_cms);
    _pos_control.set_jerk_xy_to_default();
    _pos_control.set_speed_z(-_wp_speed_down_cms, _wp_speed_up_cms);
    _pos_control.set_accel_z(_wp_accel_z_cms);
    _pos_control.calc_leash_length_xy();
    _pos_control.calc_leash_length_z();

    // initialise yaw heading to current heading target
    _flags.wp_yaw_set = false;
}

/// set_speed_xy - allows main code to pass target horizontal velocity for wp navigation
void AC_WPNav::set_speed_xy(float speed_cms)
{
    // range check new target speed and update position controller
    if (speed_cms >= WPNAV_WP_SPEED_MIN) {
        _wp_speed_cms = speed_cms;
        _pos_control.set_speed_xy(_wp_speed_cms);
        // flag that wp leash must be recalculated
        _flags.recalc_wp_leash = true;
    }
}

/// set_wp_destination waypoint using location class
///     returns false if conversion from location to vector from ekf origin cannot be calculated
bool AC_WPNav::set_wp_destination(const Location_Class& destination)
{
    bool terr_alt;
    Vector3f dest_neu;

    // convert destination location to vector
    if (!get_vector_NEU(destination, dest_neu, terr_alt)) {
        return false;
    }

    // set target as vector from EKF origin
    return set_wp_destination(dest_neu, terr_alt);
}

/// set_wp_destination waypoint using position vector (distance from home in cm)
///     terrain_alt should be true if destination.z is a desired altitude above terrain
bool AC_WPNav::set_wp_destination(const Vector3f& destination, bool terrain_alt)
{
	Vector3f origin;

    // if waypoint controller is active use the existing position target as the origin
    if ((AP_HAL::millis() - _wp_last_update) < 1000) {
        origin = _pos_control.get_pos_target();
    } else {
        // if waypoint controller is not active, set origin to reasonable stopping point (using curr pos and velocity)
        _pos_control.get_stopping_point_xy(origin);
        _pos_control.get_stopping_point_z(origin);
    }

    // convert origin to alt-above-terrain
    if (terrain_alt) {
        float origin_terr_offset;
        if (!get_terrain_offset(origin_terr_offset)) {
            return false;
        }
        origin.z -= origin_terr_offset;
    }

    // set origin and destination
    return set_wp_origin_and_destination(origin, destination, terrain_alt);
}

/// set_origin_and_destination - set origin and destination waypoints using position vectors (distance from home in cm)
///     terrain_alt should be true if origin.z and destination.z are desired altitudes above terrain (false if these are alt-above-ekf-origin)
///     returns false on failure (likely caused by missing terrain data)
bool AC_WPNav::set_wp_origin_and_destination(const Vector3f& origin, const Vector3f& destination, bool terrain_alt)
{
    // store origin and destination locations
    _origin = origin;
    _destination = destination;
    _terrain_alt = terrain_alt;
    Vector3f pos_delta = _destination - _origin;

    _track_length = pos_delta.length(); // get track length
    _track_length_xy = safe_sqrt(sq(pos_delta.x)+sq(pos_delta.y));  // get horizontal track length (used to decide if we should update yaw)

    // calculate each axis' percentage of the total distance to the destination
    if (is_zero(_track_length)) {
        // avoid possible divide by zero
        _pos_delta_unit.x = 0;
        _pos_delta_unit.y = 0;
        _pos_delta_unit.z = 0;
    }else{
        _pos_delta_unit = pos_delta/_track_length;
    }

    // calculate leash lengths
    calculate_wp_leash_length();

    // get origin's alt-above-terrain
    float origin_terr_offset = 0.0f;
    if (terrain_alt) {
        if (!get_terrain_offset(origin_terr_offset)) {
            return false;
        }
    }

    // initialise intermediate point to the origin
    _pos_control.set_pos_target(origin + Vector3f(0,0,origin_terr_offset));
    _track_desired = 0;             // target is at beginning of track
    _flags.reached_destination = false;
    _flags.fast_waypoint = false;   // default waypoint back to slow
    _flags.slowing_down = false;    // target is not slowing down yet
    _flags.segment_type = SEGMENT_STRAIGHT;
    _flags.new_wp_destination = true;   // flag new waypoint so we can freeze the pos controller's feed forward and smooth the transition
    _flags.wp_yaw_set = false;

    // initialise the limited speed to current speed along the track
    const Vector3f &curr_vel = _inav.get_velocity();
    // get speed along track (note: we convert vertical speed into horizontal speed equivalent)
    float speed_along_track = curr_vel.x * _pos_delta_unit.x + curr_vel.y * _pos_delta_unit.y + curr_vel.z * _pos_delta_unit.z;
    _limited_speed_xy_cms = constrain_float(speed_along_track,0,_wp_speed_cms);

    return true;
}

/// shift_wp_origin_to_current_pos - shifts the origin and destination so the origin starts at the current position
///     used to reset the position just before takeoff
///     relies on set_wp_destination or set_wp_origin_and_destination having been called first
void AC_WPNav::shift_wp_origin_to_current_pos()
{
    // return immediately if vehicle is not at the origin
    if (_track_desired > 0.0f) {
        return;
    }

    // get current and target locations
    const Vector3f curr_pos = _inav.get_position();
    const Vector3f pos_target = _pos_control.get_pos_target();

    // calculate difference between current position and target
    Vector3f pos_diff = curr_pos - pos_target;

    // shift origin and destination
    _origin += pos_diff;
    _destination += pos_diff;

    // move pos controller target and disable feed forward
    _pos_control.set_pos_target(curr_pos);
    _pos_control.freeze_ff_xy();
    _pos_control.freeze_ff_z();
}

/// get_wp_stopping_point_xy - returns vector to stopping point based on a horizontal position and velocity
void AC_WPNav::get_wp_stopping_point_xy(Vector3f& stopping_point) const
{
	_pos_control.get_stopping_point_xy(stopping_point);
}

/// get_wp_stopping_point - returns vector to stopping point based on 3D position and velocity
void AC_WPNav::get_wp_stopping_point(Vector3f& stopping_point) const
{
    _pos_control.get_stopping_point_xy(stopping_point);
    _pos_control.get_stopping_point_z(stopping_point);
}

/// advance_wp_target_along_track - move target location along track from origin to destination
bool AC_WPNav::advance_wp_target_along_track(float dt)
{
    float track_covered;        // distance (in cm) along the track that the vehicle has traveled.  Measured by drawing a perpendicular line from the track to the vehicle.
    Vector3f track_error;       // distance error (in cm) from the track_covered position (i.e. closest point on the line to the vehicle) and the vehicle
    float track_desired_max;    // the farthest distance (in cm) along the track that the leash will allow
    float track_leash_slack;    // additional distance (in cm) along the track from our track_covered position that our leash will allow
    bool reached_leash_limit = false;   // true when track has reached leash limit and we need to slow down the target point

    // get current location
    Vector3f curr_pos = _inav.get_position();

    // calculate terrain adjustments
    float terr_offset = 0.0f;
    if (_terrain_alt && !get_terrain_offset(terr_offset)) {
        return false;
    }

    // calculate 3d vector from segment's origin
    Vector3f curr_delta = (curr_pos - Vector3f(0,0,terr_offset)) - _origin;

    // calculate how far along the track we are
    track_covered = curr_delta.x * _pos_delta_unit.x + curr_delta.y * _pos_delta_unit.y + curr_delta.z * _pos_delta_unit.z;

    // calculate the point closest to the vehicle on the segment from origin to destination
    Vector3f track_covered_pos = _pos_delta_unit * track_covered;

    // calculate the distance vector from the vehicle to the closest point on the segment from origin to destination
    track_error = curr_delta - track_covered_pos;

    // calculate the horizontal error
    float track_error_xy = norm(track_error.x, track_error.y);

    // calculate the vertical error
    float track_error_z = fabsf(track_error.z);

    // get up leash if we are moving up, down leash if we are moving down
    float leash_z = track_error.z >= 0 ? _pos_control.get_leash_up_z() : _pos_control.get_leash_down_z();

    // use pythagoras's theorem calculate how far along the track we could move the intermediate target before reaching the end of the leash
    //   track_desired_max is the distance from the vehicle to our target point along the track.  It is the "hypotenuse" which we want to be no longer than our leash (aka _track_leash_length)
    //   track_error is the line from the vehicle to the closest point on the track.  It is the "opposite" side
    //   track_leash_slack is the line from the closest point on the track to the target point.  It is the "adjacent" side.  We adjust this so the track_desired_max is no longer than the leash
    float track_leash_length_abs = fabsf(_track_leash_length);
    float track_error_max_abs = MAX(_track_leash_length*track_error_z/leash_z, _track_leash_length*track_error_xy/_pos_control.get_leash_xy());
    track_leash_slack = (track_leash_length_abs > track_error_max_abs) ? safe_sqrt(sq(_track_leash_length) - sq(track_error_max_abs)) : 0;
    track_desired_max = track_covered + track_leash_slack;

    // check if target is already beyond the leash
    if (_track_desired > track_desired_max) {
        reached_leash_limit = true;
    }

    // get current velocity
    const Vector3f &curr_vel = _inav.get_velocity();
    // get speed along track
    float speed_along_track = curr_vel.x * _pos_delta_unit.x + curr_vel.y * _pos_delta_unit.y + curr_vel.z * _pos_delta_unit.z;

    // calculate point at which velocity switches from linear to sqrt
    float linear_velocity = _wp_speed_cms;
    float kP = _pos_control.get_pos_xy_kP();
    if (kP >= 0.0f) {   // avoid divide by zero
        linear_velocity = _track_accel/kP;
    }

    // let the limited_speed_xy_cms be some range above or below current velocity along track
    if (speed_along_track < -linear_velocity) {
        // we are traveling fast in the opposite direction of travel to the waypoint so do not move the intermediate point
        _limited_speed_xy_cms = 0;
    }else{
        // increase intermediate target point's velocity if not yet at the leash limit
        if(dt > 0 && !reached_leash_limit) {
            _limited_speed_xy_cms += 2.0f * _track_accel * dt;
        }
        // do not allow speed to be below zero or over top speed
        _limited_speed_xy_cms = constrain_float(_limited_speed_xy_cms, 0.0f, _track_speed);

        // check if we should begin slowing down
        if (!_flags.fast_waypoint) {
            float dist_to_dest = _track_length - _track_desired;
            if (!_flags.slowing_down && dist_to_dest <= _slow_down_dist) {
                _flags.slowing_down = true;
            }
            // if target is slowing down, limit the speed
            if (_flags.slowing_down) {
                _limited_speed_xy_cms = MIN(_limited_speed_xy_cms, get_slow_down_speed(dist_to_dest, _track_accel));
            }
        }

        // if our current velocity is within the linear velocity range limit the intermediate point's velocity to be no more than the linear_velocity above or below our current velocity
        if (fabsf(speed_along_track) < linear_velocity) {
            _limited_speed_xy_cms = constrain_float(_limited_speed_xy_cms,speed_along_track-linear_velocity,speed_along_track+linear_velocity);
        }
    }
    // advance the current target
    if (!reached_leash_limit) {
    	_track_desired += _limited_speed_xy_cms * dt;

    	// reduce speed if we reach end of leash
        if (_track_desired > track_desired_max) {
        	_track_desired = track_desired_max;
        	_limited_speed_xy_cms -= 2.0f * _track_accel * dt;
        	if (_limited_speed_xy_cms < 0.0f) {
        	    _limited_speed_xy_cms = 0.0f;
        	}
    	}
    }

    // do not let desired point go past the end of the track unless it's a fast waypoint
    if (!_flags.fast_waypoint) {
        _track_desired = constrain_float(_track_desired, 0, _track_length);
    } else {
        _track_desired = constrain_float(_track_desired, 0, _track_length + WPNAV_WP_FAST_OVERSHOOT_MAX);
    }

    // recalculate the desired position
    Vector3f final_target = _origin + _pos_delta_unit * _track_desired;
    // convert final_target.z to altitude above the ekf origin
    final_target.z += terr_offset;
    _pos_control.set_pos_target(final_target);

    // check if we've reached the waypoint
    if( !_flags.reached_destination ) {
        if( _track_desired >= _track_length ) {
            // "fast" waypoints are complete once the intermediate point reaches the destination
            if (_flags.fast_waypoint) {
                _flags.reached_destination = true;
            }else{
                // regular waypoints also require the copter to be within the waypoint radius
                Vector3f dist_to_dest = (curr_pos - Vector3f(0,0,terr_offset)) - _destination;
                if( dist_to_dest.length() <= _wp_radius_cm ) {
                    _flags.reached_destination = true;
                }
            }
        }
    }

    // update the target yaw if origin and destination are at least 2m apart horizontally
    if (_track_length_xy >= WPNAV_YAW_DIST_MIN) {
        if (_pos_control.get_leash_xy() < WPNAV_YAW_DIST_MIN) {
            // if the leash is short (i.e. moving slowly) and destination is at least 2m horizontally, point along the segment from origin to destination
            set_yaw_cd(get_bearing_cd(_origin, _destination));
        } else {
            Vector3f horiz_leash_xy = final_target - curr_pos;
            horiz_leash_xy.z = 0;
            if (horiz_leash_xy.length() > MIN(WPNAV_YAW_DIST_MIN, _pos_control.get_leash_xy()*WPNAV_YAW_LEASH_PCT_MIN)) {
                set_yaw_cd(RadiansToCentiDegrees(atan2f(horiz_leash_xy.y,horiz_leash_xy.x)));
            }
        }
    }

    // successfully advanced along track
    return true;
}

/// get_wp_distance_to_destination - get horizontal distance to destination in cm
float AC_WPNav::get_wp_distance_to_destination() const
{
    // get current location
    Vector3f curr = _inav.get_position();
    return norm(_destination.x-curr.x,_destination.y-curr.y);
}

/// get_wp_bearing_to_destination - get bearing to next waypoint in centi-degrees
int32_t AC_WPNav::get_wp_bearing_to_destination() const
{
    return get_bearing_cd(_inav.get_position(), _destination);
}

/// update_wpnav - run the wp controller - should be called at 100hz or higher
bool AC_WPNav::update_wpnav()
{
    // calculate dt
    float dt = _pos_control.time_since_last_xy_update();
    bool ret = true;

    // update at poscontrol update rate
    if (dt >= _pos_control.get_dt_xy()) {
        // allow the accel and speed values to be set without changing
        // out of auto mode. This makes it easier to tune auto flight
        _pos_control.set_accel_xy(_wp_accel_cms);
        _pos_control.set_jerk_xy_to_default();
        _pos_control.set_accel_z(_wp_accel_z_cms);
    
        // sanity check dt
        if (dt >= 0.2f) {
            dt = 0.0f;
        }

        // advance the target if necessary
        if (!advance_wp_target_along_track(dt)) {
            // To-Do: handle inability to advance along track (probably because of missing terrain data)
            ret = false;
        }

        // freeze feedforwards during known discontinuities
        // TODO: why always consider Z axis discontinuous?
        if (_flags.new_wp_destination) {
            _flags.new_wp_destination = false;
            _pos_control.freeze_ff_xy();
        }
        _pos_control.freeze_ff_z();

        _pos_control.update_xy_controller(AC_PosControl::XY_MODE_POS_ONLY, 1.0f, false);
        check_wp_leash_length();

        _wp_last_update = AP_HAL::millis();
    }

    return ret;
}

// check_wp_leash_length - check if waypoint leash lengths need to be recalculated
//  should be called after _pos_control.update_xy_controller which may have changed the position controller leash lengths
void AC_WPNav::check_wp_leash_length()
{
    // exit immediately if recalc is not required
    if (_flags.recalc_wp_leash) {
        calculate_wp_leash_length();
    }
}

/// calculate_wp_leash_length - calculates horizontal and vertical leash lengths for waypoint controller
void AC_WPNav::calculate_wp_leash_length()
{
    // length of the unit direction vector in the horizontal
    float pos_delta_unit_xy = norm(_pos_delta_unit.x, _pos_delta_unit.y);
    float pos_delta_unit_z = fabsf(_pos_delta_unit.z);

    float speed_z;
    float leash_z;
    if (_pos_delta_unit.z >= 0.0f) {
        speed_z = _wp_speed_up_cms;
        leash_z = _pos_control.get_leash_up_z();
    }else{
        speed_z = _wp_speed_down_cms;
        leash_z = _pos_control.get_leash_down_z();
    }

    // calculate the maximum acceleration, maximum velocity, and leash length in the direction of travel
    if(is_zero(pos_delta_unit_z) && is_zero(pos_delta_unit_xy)){
        _track_accel = 0;
        _track_speed = 0;
        _track_leash_length = WPNAV_LEASH_LENGTH_MIN;
    }else if(is_zero(_pos_delta_unit.z)){
        _track_accel = _wp_accel_cms/pos_delta_unit_xy;
        _track_speed = _wp_speed_cms/pos_delta_unit_xy;
        _track_leash_length = _pos_control.get_leash_xy()/pos_delta_unit_xy;
    }else if(is_zero(pos_delta_unit_xy)){
        _track_accel = _wp_accel_z_cms/pos_delta_unit_z;
        _track_speed = speed_z/pos_delta_unit_z;
        _track_leash_length = leash_z/pos_delta_unit_z;
    }else{
        _track_accel = MIN(_wp_accel_z_cms/pos_delta_unit_z, _wp_accel_cms/pos_delta_unit_xy);
        _track_speed = MIN(speed_z/pos_delta_unit_z, _wp_speed_cms/pos_delta_unit_xy);
        _track_leash_length = MIN(leash_z/pos_delta_unit_z, _pos_control.get_leash_xy()/pos_delta_unit_xy);
    }

    // calculate slow down distance (the distance from the destination when the target point should begin to slow down)
    calc_slow_down_distance(_track_speed, _track_accel);

    // set recalc leash flag to false
    _flags.recalc_wp_leash = false;
}

// returns target yaw in centi-degrees (used for wp and spline navigation)
float AC_WPNav::get_yaw() const
{
    if (_flags.wp_yaw_set) {
        return _yaw;
    } else {
        // if yaw has not been set return attitude controller's current target
        return _attitude_control.get_att_target_euler_cd().z;
    }
}

// set heading used for spline and waypoint navigation
void AC_WPNav::set_yaw_cd(float heading_cd)
{
    _yaw = heading_cd;
    _flags.wp_yaw_set = true;
}

///
/// spline methods
///

/// set_spline_destination waypoint using location class
///     returns false if conversion from location to vector from ekf origin cannot be calculated
///     stopped_at_start should be set to true if vehicle is stopped at the origin
///     seg_end_type should be set to stopped, straight or spline depending upon the next segment's type
///     next_destination should be set to the next segment's destination if the seg_end_type is SEGMENT_END_STRAIGHT or SEGMENT_END_SPLINE
bool AC_WPNav::set_spline_destination(const Location_Class& destination, bool stopped_at_start, spline_segment_end_type seg_end_type, Location_Class next_destination)
{
    // convert destination location to vector
    Vector3f dest_neu;
    bool dest_terr_alt;
    if (!get_vector_NEU(destination, dest_neu, dest_terr_alt)) {
        return false;
    }

    // make altitude frames consistent
    if (!next_destination.change_alt_frame(destination.get_alt_frame())) {
        return false;
    }

    // convert next destination to vector
    Vector3f next_dest_neu;
    bool next_dest_terr_alt;
    if (!get_vector_NEU(next_destination, next_dest_neu, next_dest_terr_alt)) {
        return false;
    }

    // set target as vector from EKF origin
    return set_spline_destination(dest_neu, dest_terr_alt, stopped_at_start, seg_end_type, next_dest_neu);
}

/// set_spline_destination waypoint using position vector (distance from home in cm)
///     returns false if conversion from location to vector from ekf origin cannot be calculated
///     terrain_alt should be true if destination.z is a desired altitudes above terrain (false if its desired altitudes above ekf origin)
///     stopped_at_start should be set to true if vehicle is stopped at the origin
///     seg_end_type should be set to stopped, straight or spline depending upon the next segment's type
///     next_destination should be set to the next segment's destination if the seg_end_type is SEGMENT_END_STRAIGHT or SEGMENT_END_SPLINE
bool AC_WPNav::set_spline_destination(const Vector3f& destination, bool terrain_alt, bool stopped_at_start, spline_segment_end_type seg_end_type, const Vector3f& next_destination)
{
    Vector3f origin;

    // if waypoint controller is active and copter has reached the previous waypoint use current pos target as the origin
    if ((AP_HAL::millis() - _wp_last_update) < 1000) {
        origin = _pos_control.get_pos_target();
    }else{
        // otherwise calculate origin from the current position and velocity
        _pos_control.get_stopping_point_xy(origin);
        _pos_control.get_stopping_point_z(origin);
    }

    // convert origin to alt-above-terrain
    if (terrain_alt) {
        float terr_offset;
        if (!get_terrain_offset(terr_offset)) {
            return false;
        }
        origin.z -= terr_offset;
    }

    // set origin and destination
    return set_spline_origin_and_destination(origin, destination, terrain_alt, stopped_at_start, seg_end_type, next_destination);
}

/// set_spline_origin_and_destination - set origin and destination waypoints using position vectors (distance from home in cm)
///     terrain_alt should be true if origin.z and destination.z are desired altitudes above terrain (false if desired altitudes above ekf origin)
///     seg_type should be calculated by calling function based on the mission
bool AC_WPNav::set_spline_origin_and_destination(const Vector3f& origin, const Vector3f& destination, bool terrain_alt, bool stopped_at_start, spline_segment_end_type seg_end_type, const Vector3f& next_destination)
{
    // mission is "active" if wpnav has been called recently and vehicle reached the previous waypoint
    bool prev_segment_exists = (_flags.reached_destination && ((AP_HAL::millis() - _wp_last_update) < 1000));
    float dt = _pos_control.get_dt_xy();

    // check _wp_accel_cms is reasonable to avoid divide by zero
    if (_wp_accel_cms <= 0) {
        _wp_accel_cms.set_and_save(WPNAV_ACCELERATION);
    }

    // segment start types
    // stop - vehicle is not moving at origin
    // straight-fast - vehicle is moving, previous segment is straight.  vehicle will fly straight through the waypoint before beginning it's spline path to the next wp
    //     _flag.segment_type holds whether prev segment is straight vs spline but we don't know if it has a delay
    // spline-fast - vehicle is moving, previous segment is splined, vehicle will fly through waypoint but previous segment should have it flying in the correct direction (i.e. exactly parallel to position difference vector from previous segment's origin to this segment's destination)

    // calculate spline velocity at origin
    if (stopped_at_start || !prev_segment_exists) {
    	// if vehicle is stopped at the origin, set origin velocity to 0.02 * distance vector from origin to destination
    	_spline_origin_vel = (destination - origin) * dt;
    	_spline_time = 0.0f;
    	_spline_vel_scaler = 0.0f;
    }else{
    	// look at previous segment to determine velocity at origin
        if (_flags.segment_type == SEGMENT_STRAIGHT) {
            // previous segment is straight, vehicle is moving so vehicle should fly straight through the origin
            // before beginning it's spline path to the next waypoint. Note: we are using the previous segment's origin and destination
            _spline_origin_vel = (_destination - _origin);
            _spline_time = 0.0f;	// To-Do: this should be set based on how much overrun there was from straight segment?
            _spline_vel_scaler = _pos_control.get_vel_target().length();    // start velocity target from current target velocity
        }else{
            // previous segment is splined, vehicle will fly through origin
            // we can use the previous segment's destination velocity as this segment's origin velocity
            // Note: previous segment will leave destination velocity parallel to position difference vector
            //       from previous segment's origin to this segment's destination)
            _spline_origin_vel = _spline_destination_vel;
            if (_spline_time > 1.0f && _spline_time < 1.1f) {    // To-Do: remove hard coded 1.1f
                _spline_time -= 1.0f;
            }else{
                _spline_time = 0.0f;
            }
            // Note: we leave _spline_vel_scaler as it was from end of previous segment
        }
    }

    // calculate spline velocity at destination
    switch (seg_end_type) {

    case SEGMENT_END_STOP:
        // if vehicle stops at the destination set destination velocity to 0.02 * distance vector from origin to destination
        _spline_destination_vel = (destination - origin) * dt;
        _flags.fast_waypoint = false;
        break;

    case SEGMENT_END_STRAIGHT:
        // if next segment is straight, vehicle's final velocity should face along the next segment's position
        _spline_destination_vel = (next_destination - destination);
        _flags.fast_waypoint = true;
        break;

    case SEGMENT_END_SPLINE:
        // if next segment is splined, vehicle's final velocity should face parallel to the line from the origin to the next destination
        _spline_destination_vel = (next_destination - origin);
        _flags.fast_waypoint = true;
        break;
    }

    // code below ensures we don't get too much overshoot when the next segment is short
    float vel_len = _spline_origin_vel.length() + _spline_destination_vel.length();
    float pos_len = (destination - origin).length() * 4.0f;
    if (vel_len > pos_len) {
        // if total start+stop velocity is more than twice position difference
        // use a scaled down start and stop velocityscale the  start and stop velocities down
        float vel_scaling = pos_len / vel_len;
        // update spline calculator
        update_spline_solution(origin, destination, _spline_origin_vel * vel_scaling, _spline_destination_vel * vel_scaling);
    }else{
        // update spline calculator
        update_spline_solution(origin, destination, _spline_origin_vel, _spline_destination_vel);
    }

    // store origin and destination locations
    _origin = origin;
    _destination = destination;
    _terrain_alt = terrain_alt;

    // calculate slow down distance
    calc_slow_down_distance(_wp_speed_cms, _wp_accel_cms);

    // get alt-above-terrain
    float terr_offset = 0.0f;
    if (terrain_alt) {
        if (!get_terrain_offset(terr_offset)) {
            return false;
        }
    }

    // initialise intermediate point to the origin
    _pos_control.set_pos_target(origin + Vector3f(0,0,terr_offset));
    _flags.reached_destination = false;
    _flags.segment_type = SEGMENT_SPLINE;
    _flags.new_wp_destination = true;   // flag new waypoint so we can freeze the pos controller's feed forward and smooth the transition
    _flags.wp_yaw_set = false;

    // initialise yaw related variables
    _track_length_xy = safe_sqrt(sq(_destination.x - _origin.x)+sq(_destination.y - _origin.y));  // horizontal track length (used to decide if we should update yaw)

    return true;
}

/// update_spline - update spline controller
bool AC_WPNav::update_spline()
{
    // exit immediately if this is not a spline segment
    if (_flags.segment_type != SEGMENT_SPLINE) {
        return false;
    }

    float dt = _pos_control.time_since_last_xy_update();
    bool ret = true;

    // run at poscontrol update rate
    if (dt >= _pos_control.get_dt_xy()) {
        // sanity check dt
        if (dt >= 0.2f) {
            dt = 0.0f;
        }

        // advance the target if necessary
        if (!advance_spline_target_along_track(dt)) {
            // To-Do: handle failure to advance along track (due to missing terrain data)
            ret = false;
        }

        // freeze feedforwards during known discontinuities
        // TODO: why always consider Z axis discontinuous?
        if (_flags.new_wp_destination) {
            _flags.new_wp_destination = false;
            _pos_control.freeze_ff_xy();
        }
        _pos_control.freeze_ff_z();

        // run horizontal position controller
        _pos_control.update_xy_controller(AC_PosControl::XY_MODE_POS_ONLY, 1.0f, false);

        _wp_last_update = AP_HAL::millis();
    }
    return ret;
}

/// update_spline_solution - recalculates hermite_spline_solution grid
///		relies on _spline_origin_vel, _spline_destination_vel and _origin and _destination
void AC_WPNav::update_spline_solution(const Vector3f& origin, const Vector3f& dest, const Vector3f& origin_vel, const Vector3f& dest_vel)
{
    _hermite_spline_solution[0] = origin;
    _hermite_spline_solution[1] = origin_vel;
    _hermite_spline_solution[2] = -origin*3.0f -origin_vel*2.0f + dest*3.0f - dest_vel;
    _hermite_spline_solution[3] = origin*2.0f + origin_vel -dest*2.0f + dest_vel;
 }

/// advance_spline_target_along_track - move target location along track from origin to destination
bool AC_WPNav::advance_spline_target_along_track(float dt)
{
    if (!_flags.reached_destination) {
        Vector3f target_pos, target_vel;

        // update target position and velocity from spline calculator
        calc_spline_pos_vel(_spline_time, target_pos, target_vel);

        _pos_delta_unit = target_vel/target_vel.length();
        calculate_wp_leash_length();

        // get current location
        Vector3f curr_pos = _inav.get_position();

        // get terrain altitude offset for origin and current position (i.e. change in terrain altitude from a position vs ekf origin)
        float terr_offset = 0.0f;
        if (_terrain_alt && !get_terrain_offset(terr_offset)) {
            return false;
        }

        // calculate position error
        Vector3f track_error = curr_pos - target_pos;
        track_error.z -= terr_offset;

        // calculate the horizontal error
        float track_error_xy = norm(track_error.x, track_error.y);

        // calculate the vertical error
        float track_error_z = fabsf(track_error.z);

        // get position control leash lengths
        float leash_xy = _pos_control.get_leash_xy();
        float leash_z;
        if (track_error.z >= 0) {
            leash_z = _pos_control.get_leash_up_z();
        }else{
            leash_z = _pos_control.get_leash_down_z();
        }

        // calculate how far along the track we could move the intermediate target before reaching the end of the leash
        float track_leash_slack = MIN(_track_leash_length*(leash_z-track_error_z)/leash_z, _track_leash_length*(leash_xy-track_error_xy)/leash_xy);
        if (track_leash_slack < 0.0f) {
            track_leash_slack = 0.0f;
        }

        // update velocity
        float spline_dist_to_wp = (_destination - target_pos).length();
        float vel_limit = _wp_speed_cms;
        if (!is_zero(dt)) {
            vel_limit = MIN(vel_limit, track_leash_slack/dt);
        }

        // if within the stopping distance from destination, set target velocity to sqrt of distance * 2 * acceleration
        if (!_flags.fast_waypoint && spline_dist_to_wp < _slow_down_dist) {
            _spline_vel_scaler = safe_sqrt(spline_dist_to_wp * 2.0f * _wp_accel_cms);
        }else if(_spline_vel_scaler < vel_limit) {
            // increase velocity using acceleration
            _spline_vel_scaler += _wp_accel_cms * dt;
        }

        // constrain target velocity
        _spline_vel_scaler = constrain_float(_spline_vel_scaler, 0.0f, vel_limit);

        // scale the spline_time by the velocity we've calculated vs the velocity that came out of the spline calculator
        float target_vel_length = target_vel.length();
        if (!is_zero(target_vel_length)) {
            _spline_time_scale = _spline_vel_scaler/target_vel_length;
        }

        // update target position
        target_pos.z += terr_offset;
        _pos_control.set_pos_target(target_pos);

        // update the target yaw if origin and destination are at least 2m apart horizontally
        if (_track_length_xy >= WPNAV_YAW_DIST_MIN) {
            if (_pos_control.get_leash_xy() < WPNAV_YAW_DIST_MIN) {
                // if the leash is very short (i.e. flying at low speed) use the target point's velocity along the track
                if (!is_zero(target_vel.x) && !is_zero(target_vel.y)) {
                    set_yaw_cd(RadiansToCentiDegrees(atan2f(target_vel.y,target_vel.x)));
                }
            } else {
                // point vehicle along the leash (i.e. point vehicle towards target point on the segment from origin to destination)
                float track_error_xy_length = safe_sqrt(sq(track_error.x)+sq(track_error.y));
                if (track_error_xy_length > MIN(WPNAV_YAW_DIST_MIN, _pos_control.get_leash_xy()*WPNAV_YAW_LEASH_PCT_MIN)) {
                    // To-Do: why is track_error sign reversed?
                    set_yaw_cd(RadiansToCentiDegrees(atan2f(-track_error.y,-track_error.x)));
                }
            }
        }

        // advance spline time to next step
        _spline_time += _spline_time_scale*dt;

        // we will reach the next waypoint in the next step so set reached_destination flag
        // To-Do: is this one step too early?
        if (_spline_time >= 1.0f) {
            _flags.reached_destination = true;
        }
    }
    return true;
}

// calc_spline_pos_vel_accel - calculates target position, velocity and acceleration for the given "spline_time"
/// 	relies on update_spline_solution being called when the segment's origin and destination were set
void AC_WPNav::calc_spline_pos_vel(float spline_time, Vector3f& position, Vector3f& velocity)
{
    float spline_time_sqrd = spline_time * spline_time;
    float spline_time_cubed = spline_time_sqrd * spline_time;

    position = _hermite_spline_solution[0] + \
               _hermite_spline_solution[1] * spline_time + \
               _hermite_spline_solution[2] * spline_time_sqrd + \
               _hermite_spline_solution[3] * spline_time_cubed;

    velocity = _hermite_spline_solution[1] + \
               _hermite_spline_solution[2] * 2.0f * spline_time + \
               _hermite_spline_solution[3] * 3.0f * spline_time_sqrd;
}

// get terrain's altitude (in cm above the ekf origin) at the current position (+ve means terrain below vehicle is above ekf origin's altitude)
bool AC_WPNav::get_terrain_offset(float& offset_cm)
{
#if AP_TERRAIN_AVAILABLE
    // use range finder if connected
    if (_rangefinder_available && _rangefinder_use) {
        if (_rangefinder_healthy) {
            offset_cm = _inav.get_altitude() - _rangefinder_alt_cm;
            return true;
        } else {
            return false;
        }
    }

    // use terrain database
    float terr_alt = 0.0f;
    if (_terrain != nullptr && _terrain->height_above_terrain(terr_alt, true)) {
        offset_cm = _inav.get_altitude() - (terr_alt * 100.0f);
        return true;
    }
#endif
    return false;
}

// convert location to vector from ekf origin.  terrain_alt is set to true if resulting vector's z-axis should be treated as alt-above-terrain
//      returns false if conversion failed (likely because terrain data was not available)
bool AC_WPNav::get_vector_NEU(const Location_Class &loc, Vector3f &vec, bool &terrain_alt)
{
    // convert location to NEU vector3f
    Vector3f res_vec;
    if (!loc.get_vector_xy_from_origin_NEU(res_vec)) {
        return false;
    }

    // convert altitude
    if (loc.get_alt_frame() == Location_Class::ALT_FRAME_ABOVE_TERRAIN) {
        int32_t terr_alt;
        if (!loc.get_alt_cm(Location_Class::ALT_FRAME_ABOVE_TERRAIN, terr_alt)) {
            return false;
        }
        vec.z = terr_alt;
        terrain_alt = true;
    } else {
        terrain_alt = false;
        int32_t temp_alt;
        if (!loc.get_alt_cm(Location_Class::ALT_FRAME_ABOVE_ORIGIN, temp_alt)) {
            return false;
        }
        vec.z = temp_alt;
        terrain_alt = false;
    }

    // copy xy (we do this to ensure we do not adjust vector unless the overall conversion is successful
    vec.x = res_vec.x;
    vec.y = res_vec.y;

    return true;
}

///
/// shared methods
///

// get_bearing_cd - return bearing in centi-degrees between two positions
// To-Do: move this to math library
float AC_WPNav::get_bearing_cd(const Vector3f &origin, const Vector3f &destination) const
{
    float bearing = 9000 + atan2f(-(destination.x-origin.x), destination.y-origin.y) * 5729.57795f;
    if (bearing < 0) {
        bearing += 36000;
    }
    return bearing;
}

/// calc_slow_down_distance - calculates distance before waypoint that target point should begin to slow-down assuming it is travelling at full speed
void AC_WPNav::calc_slow_down_distance(float speed_cms, float accel_cmss)
{
	// protect against divide by zero
	if (accel_cmss <= 0.0f) {
		_slow_down_dist = 0.0f;
		return;
	}
    // To-Do: should we use a combination of horizontal and vertical speeds?
    // To-Do: update this automatically when speed or acceleration is changed
    _slow_down_dist = speed_cms * speed_cms / (4.0f*accel_cmss);
}

/// get_slow_down_speed - returns target speed of target point based on distance from the destination (in cm)
float AC_WPNav::get_slow_down_speed(float dist_from_dest_cm, float accel_cmss)
{
    // return immediately if distance is zero (or less)
    if (dist_from_dest_cm <= 0) {
        return WPNAV_WP_TRACK_SPEED_MIN;
    }

    // calculate desired speed near destination
    float target_speed = safe_sqrt(dist_from_dest_cm * 4.0f * accel_cmss);

    // ensure desired speed never becomes too low
    if (target_speed < WPNAV_WP_TRACK_SPEED_MIN) {
        return WPNAV_WP_TRACK_SPEED_MIN;
    } else {
        return target_speed;
    }
}