paparazzi/sw/airborne/subsystems/nav.c

/*
 * Copyright (C) 2003-2005  Pascal Brisset, Antoine Drouin
 *
 * This file is part of paparazzi.
 *
 * paparazzi is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2, or (at your option)
 * any later version.
 *
 * paparazzi is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with paparazzi; see the file COPYING.  If not, write to
 * the Free Software Foundation, 59 Temple Place - Suite 330,
 * Boston, MA 02111-1307, USA.
 */

/**
 * @file subsystems/nav.c
 * Fixedwing functions to compute navigation.
 *
 */

#define NAV_C

#include <math.h>

#include "subsystems/nav.h"
#include "subsystems/gps.h"
#include "firmwares/fixedwing/stabilization/stabilization_attitude.h"
#include "firmwares/fixedwing/autopilot.h"
#include "inter_mcu.h"
#include "subsystems/navigation/traffic_info.h"

#define RCLost() bit_is_set(fbw_state->status, RADIO_REALLY_LOST)

enum oval_status oval_status;

float last_x, last_y;

/** Index of last waypoint. Used only in "go" stage in "route" horiz mode */
static uint8_t last_wp __attribute__ ((unused));

float rc_pitch;
float carrot_x, carrot_y;

/** Status on the current circle */
float nav_circle_radians; /* Cumulated */
float nav_circle_radians_no_rewind; /* Cumulated */
float nav_circle_trigo_qdr; /* Angle from center to mobile */
float nav_radius, nav_course, nav_climb, nav_shift;


/** Status on the current leg (percentage, 0. < < 1.) in route mode */
static float nav_leg_progress;

/** length of the current leg (m) */
static float nav_leg_length;

bool_t nav_in_circle = FALSE;
bool_t nav_in_segment = FALSE;
float nav_circle_x, nav_circle_y, nav_circle_radius;
float nav_segment_x_1, nav_segment_y_1, nav_segment_x_2, nav_segment_y_2;
uint8_t horizontal_mode;
float circle_bank = 0;

/** Dynamically adjustable, reset to nav_altitude when it is changing */
float flight_altitude;

float nav_glide_pitch_trim;
#ifndef NAV_GLIDE_PITCH_TRIM
#define NAV_GLIDE_PITCH_TRIM 0.
#endif



float nav_ground_speed_setpoint, nav_ground_speed_pgain;

/* Used in nav_survey_rectangle. Defined here for downlink and uplink */
float nav_survey_shift;
float nav_survey_west, nav_survey_east, nav_survey_north, nav_survey_south;
bool_t nav_survey_active;

int nav_mode;

void nav_init_stage( void ) {
  last_x = stateGetPositionEnu_f()->x;
  last_y = stateGetPositionEnu_f()->y;
  stage_time = 0;
  nav_circle_radians = 0;
  nav_circle_radians_no_rewind = 0;
  nav_in_circle = FALSE;
  nav_in_segment = FALSE;
  nav_shift = 0;
  nav_pitch = 0.;
}

#define PowerVoltage() (vsupply/10.)
#define RcRoll(travel) (fbw_state->channels[RADIO_ROLL]* (float)travel /(float)MAX_PPRZ)

#define MIN_DX ((int16_t)(MAX_PPRZ * 0.05))


/** Navigates around (x, y). Clockwise iff radius > 0 */
void nav_circle_XY(float x, float y, float radius) {
  struct EnuCoor_f* pos = stateGetPositionEnu_f();
  float last_trigo_qdr = nav_circle_trigo_qdr;
  nav_circle_trigo_qdr = atan2(pos->y - y, pos->x - x);
  float sign_radius = radius > 0 ? 1 : -1;

  if (nav_in_circle) {
    float trigo_diff = nav_circle_trigo_qdr - last_trigo_qdr;
    NormRadAngle(trigo_diff);
    nav_circle_radians += trigo_diff;
    trigo_diff *= - sign_radius;
    if (trigo_diff > 0) // do not rewind if the change in angle is in the opposite sense than nav_radius
      nav_circle_radians_no_rewind += trigo_diff;
  }

  float dist2_center = DistanceSquare(pos->x, pos->y, x, y);
  float dist_carrot = CARROT*NOMINAL_AIRSPEED;

  radius += -nav_shift;

  float abs_radius = fabs(radius);

  /** Computes a prebank. Go straight if inside or outside the circle */
  circle_bank =
    (dist2_center > Square(abs_radius + dist_carrot)
     || dist2_center < Square(abs_radius - dist_carrot)) ?
    0 :
    atan((*stateGetHorizontalSpeedNorm_f())*(*stateGetHorizontalSpeedNorm_f()) / (NAV_GRAVITY*radius));

  float carrot_angle = dist_carrot / abs_radius;
  carrot_angle = Min(carrot_angle, M_PI/4);
  carrot_angle = Max(carrot_angle, M_PI/16);
  float alpha_carrot = nav_circle_trigo_qdr - sign_radius * carrot_angle;
  horizontal_mode = HORIZONTAL_MODE_CIRCLE;
  float radius_carrot = abs_radius;
  if (nav_mode == NAV_MODE_COURSE) {
    radius_carrot += (abs_radius / cos(carrot_angle) - abs_radius);
  }
  fly_to_xy(x+cos(alpha_carrot)*radius_carrot,
            y+sin(alpha_carrot)*radius_carrot);
  nav_in_circle = TRUE;
  nav_circle_x = x;
  nav_circle_y = y;
  nav_circle_radius = radius;
}


#define NavGlide(_last_wp, _wp) {                                       \
    float start_alt = waypoints[_last_wp].a;                            \
    float diff_alt = waypoints[_wp].a - start_alt;                      \
    float alt = start_alt + nav_leg_progress * diff_alt;                \
    float pre_climb = (*stateGetHorizontalSpeedNorm_f()) * diff_alt / nav_leg_length; \
    NavVerticalAltitudeMode(alt, pre_climb);                            \
  }




#define MAX_DIST_CARROT 250.
#define MIN_HEIGHT_CARROT 50.
#define MAX_HEIGHT_CARROT 150.

#define Goto3D(radius) {                                                \
    if (pprz_mode == PPRZ_MODE_AUTO2) {                                 \
      int16_t yaw = fbw_state->channels[RADIO_YAW];                     \
      if (yaw > MIN_DX || yaw < -MIN_DX) {                              \
        carrot_x += FLOAT_OF_PPRZ(yaw, 0, -20.);                        \
        carrot_x = Min(carrot_x, MAX_DIST_CARROT);                      \
        carrot_x = Max(carrot_x, -MAX_DIST_CARROT);                     \
      }                                                                 \
      int16_t pitch = fbw_state->channels[RADIO_PITCH];                 \
      if (pitch > MIN_DX || pitch < -MIN_DX) {                          \
        carrot_y += FLOAT_OF_PPRZ(pitch, 0, -20.);                      \
        carrot_y = Min(carrot_y, MAX_DIST_CARROT);                      \
        carrot_y = Max(carrot_y, -MAX_DIST_CARROT);                     \
      }                                                                 \
      v_ctl_mode = V_CTL_MODE_AUTO_ALT;                                 \
      int16_t roll =  fbw_state->channels[RADIO_ROLL];                  \
      if (roll > MIN_DX || roll < -MIN_DX) {                            \
        nav_altitude += FLOAT_OF_PPRZ(roll, 0, -1.0);                   \
        nav_altitude = Max(nav_altitude, MIN_HEIGHT_CARROT+ground_alt); \
        nav_altitude = Min(nav_altitude, MAX_HEIGHT_CARROT+ground_alt); \
      }                                                                 \
    }                                                                   \
    nav_circle_XY(carrot_x, carrot_y, radius);                          \
  }


#define NavFollow(_ac_id, _distance, _height)   \
  nav_follow(_ac_id, _distance, _height);


static unit_t unit __attribute__ ((unused));

static inline void nav_follow(uint8_t _ac_id, float _distance, float _height);

#ifdef NAV_GROUND_SPEED_PGAIN
/** \brief Computes cruise throttle from ground speed setpoint
 */
static void nav_ground_speed_loop( void ) {
  if (MINIMUM_AIRSPEED < nav_ground_speed_setpoint
      && nav_ground_speed_setpoint < MAXIMUM_AIRSPEED) {
    float err = nav_ground_speed_setpoint - (*stateGetHorizontalSpeedNorm_f());
    v_ctl_auto_throttle_cruise_throttle += nav_ground_speed_pgain*err;
    Bound(v_ctl_auto_throttle_cruise_throttle, V_CTL_AUTO_THROTTLE_MIN_CRUISE_THROTTLE, V_CTL_AUTO_THROTTLE_MAX_CRUISE_THROTTLE);
  } else {
    /* Reset cruise throttle to nominal value */
    v_ctl_auto_throttle_cruise_throttle = V_CTL_AUTO_THROTTLE_NOMINAL_CRUISE_THROTTLE;
  }
}
#endif

static float baseleg_out_qdr;
static inline bool_t nav_compute_baseleg(uint8_t wp_af, uint8_t wp_td, uint8_t wp_baseleg, float radius ) {
  nav_radius = radius;

  float x_0 = waypoints[wp_td].x - waypoints[wp_af].x;
  float y_0 = waypoints[wp_td].y - waypoints[wp_af].y;

  /* Unit vector from AF to TD */
  float d = sqrt(x_0*x_0+y_0*y_0);
  float x_1 = x_0 / d;
  float y_1 = y_0 / d;

  waypoints[wp_baseleg].x = waypoints[wp_af].x + y_1 * nav_radius;
  waypoints[wp_baseleg].y = waypoints[wp_af].y - x_1 * nav_radius;
  waypoints[wp_baseleg].a = waypoints[wp_af].a;
  baseleg_out_qdr = M_PI - atan2(-y_1, -x_1);
  if (nav_radius < 0)
    baseleg_out_qdr += M_PI;

  return FALSE;
}

static inline bool_t nav_compute_final_from_glide(uint8_t wp_af, uint8_t wp_td, float glide ) {

  float x_0 = waypoints[wp_td].x - waypoints[wp_af].x;
  float y_0 = waypoints[wp_td].y - waypoints[wp_af].y;
  float h_0 = waypoints[wp_td].a - waypoints[wp_af].a;

  /* Unit vector from AF to TD */
  float d = sqrt(x_0*x_0+y_0*y_0);
  float x_1 = x_0 / d;
  float y_1 = y_0 / d;

  waypoints[wp_af].x = waypoints[wp_td].x + x_1 * h_0 * glide;
  waypoints[wp_af].y = waypoints[wp_td].y + y_1 * h_0 * glide;
  waypoints[wp_af].a = waypoints[wp_af].a;

  return FALSE;
}


/* For a landing UPWIND.
   Computes Top Of Descent waypoint from Touch Down and Approach Fix
   waypoints, using glide airspeed, glide vertical speed and wind */
static inline bool_t compute_TOD(uint8_t _af, uint8_t _td, uint8_t _tod, float glide_airspeed, float glide_vspeed) {
  struct FloatVect2* wind = stateGetHorizontalWindspeed_f();
  float td_af_x = WaypointX(_af) - WaypointX(_td);
  float td_af_y = WaypointY(_af) - WaypointY(_td);
  float td_af = sqrt( td_af_x*td_af_x + td_af_y*td_af_y);
  float td_tod = (WaypointAlt(_af) - WaypointAlt(_td)) / glide_vspeed * (glide_airspeed - sqrt(wind->x*wind->x + wind->y*wind->y));
  WaypointX(_tod) = WaypointX(_td) + td_af_x / td_af * td_tod;
  WaypointY(_tod) = WaypointY(_td) + td_af_y / td_af * td_tod;
  WaypointAlt(_tod) = WaypointAlt(_af);
  return FALSE;
}


#include "generated/flight_plan.h"


#ifndef LINE_START_FUNCTION
#define LINE_START_FUNCTION {}
#endif
#ifndef LINE_STOP_FUNCTION
#define LINE_STOP_FUNCTION {}
#endif



static inline void nav_follow(uint8_t _ac_id, float _distance, float _height) {
  struct ac_info_ * ac = get_ac_info(_ac_id);
  NavVerticalAutoThrottleMode(0.);
  NavVerticalAltitudeMode(Max(ac->alt + _height, ground_alt+SECURITY_HEIGHT), 0.);
  float alpha = M_PI/2 - ac->course;
  float ca = cos(alpha), sa = sin(alpha);
  float x = ac->east - _distance*ca;
  float y = ac->north - _distance*sa;
  fly_to_xy(x, y);
#ifdef NAV_FOLLOW_PGAIN
  float s = (stateGetPositionEnu_f()->x - x)*ca + (stateGetPositionEnu_f()->y - y)*sa;
  nav_ground_speed_setpoint = ac->gspeed + NAV_FOLLOW_PGAIN*s;
  nav_ground_speed_loop();
#endif
}

float nav_altitude = GROUND_ALT + MIN_HEIGHT_CARROT;
float desired_x, desired_y;
pprz_t nav_throttle_setpoint;
float nav_pitch; /* Rad */
float fp_pitch; /* deg */


/** \brief Decide if the UAV is approaching the current waypoint.
 *  Computes \a dist2_to_wp and compare it to square \a carrot.
 *  Return true if it is smaller. Else computes by scalar products if
 *  uav has not gone past waypoint.
 *  Return true if it is the case.
 */
bool_t nav_approaching_xy(float x, float y, float from_x, float from_y, float approaching_time) {
  /** distance to waypoint in x */
  float pw_x = x - stateGetPositionEnu_f()->x;
  /** distance to waypoint in y */
  float pw_y = y - stateGetPositionEnu_f()->y;

  dist2_to_wp = pw_x*pw_x + pw_y *pw_y;
  float min_dist = approaching_time * (*stateGetHorizontalSpeedNorm_f());
  if (dist2_to_wp < min_dist*min_dist)
    return TRUE;

  float scal_prod = (x - from_x) * pw_x + (y - from_y) * pw_y;

  return (scal_prod < 0.);
}


/**
 *  \brief Computes \a desired_x, \a desired_y and \a desired_course.
 */
//static inline void fly_to_xy(float x, float y) {
void fly_to_xy(float x, float y) {
  struct EnuCoor_f* pos = stateGetPositionEnu_f();
  desired_x = x;
  desired_y = y;
  if (nav_mode == NAV_MODE_COURSE) {
    h_ctl_course_setpoint = atan2(x - pos->x, y - pos->y);
    if (h_ctl_course_setpoint < 0.)
      h_ctl_course_setpoint += 2 * M_PI;
    lateral_mode = LATERAL_MODE_COURSE;
  } else {
    float diff = atan2(x - pos->x, y - pos->y) - (*stateGetHorizontalSpeedDir_f());
    NormRadAngle(diff);
    BoundAbs(diff,M_PI/2.);
    float s = sin(diff);
    float speed = *stateGetHorizontalSpeedNorm_f();
    h_ctl_roll_setpoint = atan(2 * speed * speed * s * h_ctl_course_pgain / (CARROT * NOMINAL_AIRSPEED * 9.81) );
    BoundAbs(h_ctl_roll_setpoint, h_ctl_roll_max_setpoint);
    lateral_mode = LATERAL_MODE_ROLL;
  }
}

/**
 *  \brief Computes the carrot position along the desired segment.
 */
void nav_route_xy(float last_wp_x, float last_wp_y, float wp_x, float wp_y) {
  float leg_x = wp_x - last_wp_x;
  float leg_y = wp_y - last_wp_y;
  float leg2 = Max(leg_x * leg_x + leg_y * leg_y, 1.);
  nav_leg_progress = ((stateGetPositionEnu_f()->x - last_wp_x) * leg_x + (stateGetPositionEnu_f()->y - last_wp_y) * leg_y) / leg2;
  nav_leg_length = sqrt(leg2);

  /** distance of carrot (in meter) */
  float carrot = CARROT * NOMINAL_AIRSPEED;

  nav_leg_progress += Max(carrot / nav_leg_length, 0.);
  nav_in_segment = TRUE;
  nav_segment_x_1 = last_wp_x;
  nav_segment_y_1 = last_wp_y;
  nav_segment_x_2 = wp_x;
  nav_segment_y_2 = wp_y;
  horizontal_mode = HORIZONTAL_MODE_ROUTE;

  fly_to_xy(last_wp_x + nav_leg_progress*leg_x +nav_shift*leg_y/nav_leg_length, last_wp_y + nav_leg_progress*leg_y-nav_shift*leg_x/nav_leg_length);
}

#include "subsystems/navigation/common_nav.c"

#ifndef FAILSAFE_HOME_RADIUS
#define FAILSAFE_HOME_RADIUS DEFAULT_CIRCLE_RADIUS
#endif

static void nav_set_altitude(void) {
  static float last_nav_altitude;
  if (fabs(nav_altitude - last_nav_altitude) > 1.) {
    flight_altitude = nav_altitude;
    last_nav_altitude = nav_altitude;
  }
  v_ctl_altitude_setpoint = flight_altitude;
}

/** \brief Home mode navigation (circle around HOME) */
void nav_home(void) {
  NavCircleWaypoint(WP_HOME, FAILSAFE_HOME_RADIUS);
  /** Nominal speed */
  nav_pitch = 0.;
  v_ctl_mode = V_CTL_MODE_AUTO_ALT;
  nav_altitude = ground_alt+HOME_MODE_HEIGHT;
  compute_dist2_to_home();
  dist2_to_wp = dist2_to_home;
  nav_set_altitude();
}

/**
 *  \brief Navigation main: call to the code generated from the XML flight
 * plan
 */
void nav_periodic_task(void) {
  nav_survey_active = FALSE;

  compute_dist2_to_home();
  dist2_to_wp = 0.;

  auto_nav(); /* From flight_plan.h */

  h_ctl_course_pre_bank = nav_in_circle ? circle_bank : 0;

#ifdef AGR_CLIMB
  if ( v_ctl_mode == V_CTL_MODE_AUTO_CLIMB)
    v_ctl_auto_throttle_submode =  V_CTL_AUTO_THROTTLE_STANDARD;
#endif

  nav_set_altitude();
}

/**
 * \brief Periodic telemetry
 */
#if DOWNLINK
#include "subsystems/datalink/telemetry.h"

static void send_nav_ref(void) {
  DOWNLINK_SEND_NAVIGATION_REF(DefaultChannel, DefaultDevice,
      &nav_utm_east0, &nav_utm_north0, &nav_utm_zone0);
}

static void send_nav(void) {
  SEND_NAVIGATION(DefaultChannel, DefaultDevice);
}

static void send_wp_moved(void) {
  static uint8_t i;
  i++; if (i >= nb_waypoint) i = 0;
  DownlinkSendWp(DefaultChannel, DefaultDevice, i);
}

static void send_circle(void) {
  if (nav_in_circle) {
    DOWNLINK_SEND_CIRCLE(DefaultChannel, DefaultDevice,
        &nav_circle_x, &nav_circle_y, &nav_circle_radius);
  }
}

static void send_segment(void) {
  if (nav_in_segment) {
    DOWNLINK_SEND_SEGMENT(DefaultChannel, DefaultDevice,
        &nav_segment_x_1, &nav_segment_y_1, &nav_segment_x_2, &nav_segment_y_2);
  }
}

static void send_survey(void) {
  if (nav_survey_active) {
    DOWNLINK_SEND_SURVEY(DefaultChannel, DefaultDevice,
        &nav_survey_east, &nav_survey_north, &nav_survey_west, &nav_survey_south);
  }
}
#endif

/**
 *  \brief Navigation Initialisation
 */
void nav_init(void) {
  nav_block = 0;
  nav_stage = 0;
  ground_alt = GROUND_ALT;
  nav_glide_pitch_trim = NAV_GLIDE_PITCH_TRIM;
  nav_radius = DEFAULT_CIRCLE_RADIUS;
  nav_survey_shift = 2*DEFAULT_CIRCLE_RADIUS;
  nav_mode = NAV_MODE_COURSE;

#ifdef NAV_GROUND_SPEED_PGAIN
  nav_ground_speed_pgain = ABS(NAV_GROUND_SPEED_PGAIN);
  nav_ground_speed_setpoint = NOMINAL_AIRSPEED;
#endif

#if DOWNLINK
  register_periodic_telemetry(DefaultPeriodic, "NAVIGATION_REF", send_nav_ref);
  register_periodic_telemetry(DefaultPeriodic, "NAVIGATION", send_nav);
  register_periodic_telemetry(DefaultPeriodic, "WP_MOVED", send_wp_moved);
  register_periodic_telemetry(DefaultPeriodic, "CIRCLE", send_circle);
  register_periodic_telemetry(DefaultPeriodic, "SEGMENT", send_segment);
  register_periodic_telemetry(DefaultPeriodic, "SURVEY", send_survey);
#endif
}

/**
 *  \brief Failsafe navigation without position estimation
 *
 * Just set attitude and throttle to FAILSAFE values
 * to prevent the plane from crashing.
 */
void nav_without_gps(void) {
  lateral_mode = LATERAL_MODE_ROLL;
  v_ctl_mode = V_CTL_MODE_AUTO_THROTTLE;

#ifdef SECTION_FAILSAFE
  h_ctl_roll_setpoint = FAILSAFE_DEFAULT_ROLL;
  nav_pitch = FAILSAFE_DEFAULT_PITCH;
  nav_throttle_setpoint = TRIM_UPPRZ((FAILSAFE_DEFAULT_THROTTLE)*MAX_PPRZ);
#else
  h_ctl_roll_setpoint = 0;
  nav_pitch = 0;
  nav_throttle_setpoint = TRIM_UPPRZ((V_CTL_AUTO_THROTTLE_NOMINAL_CRUISE_THROTTLE)*MAX_PPRZ);
#endif
}


/**************** 8 Navigation **********************************************/


enum eight_status { R1T, RT2, C2, R2T, RT1, C1 };

static enum eight_status eight_status;
void nav_eight_init( void ) {
  eight_status = C1;
}

/** Navigation along a figure 8. The cross center is defined by the waypoint
    [target], the center of one of the circles is defined by [c1]. Altitude is
    given by [target].
    The navigation goes through 6 states: C1 (circle around [c1]), R1T, RT2
    (route from circle 1 to circle 2 over [target]), C2 and R2T, RT1.
    If necessary, the [c1] waypoint is moved in the direction of [target]
    to be not far than [2*radius].
*/
void nav_eight(uint8_t target, uint8_t c1, float radius) {
  float aradius = fabs(radius);
  float alt = waypoints[target].a;
  waypoints[c1].a = alt;

  float target_c1_x = waypoints[c1].x - waypoints[target].x;
  float target_c1_y = waypoints[c1].y - waypoints[target].y;
  float d = sqrt(target_c1_x*target_c1_x+target_c1_y*target_c1_y);
  d = Max(d, 1.); /* To prevent a division by zero */

  /* Unit vector from target to c1 */
  float u_x = target_c1_x / d;
  float u_y = target_c1_y / d;

  /* Move [c1] closer if needed */
  if (d > 2 * aradius) {
    d = 2*aradius;
    waypoints[c1].x = waypoints[target].x + d*u_x;
    waypoints[c1].y = waypoints[target].y + d*u_y;
  }

  /* The other center */
  struct point c2 = {
    waypoints[target].x - d*u_x,
    waypoints[target].y - d*u_y,
    alt };

  struct point c1_in = {
    waypoints[c1].x + radius * -u_y,
    waypoints[c1].y + radius * u_x,
    alt };
  struct point c1_out = {
    waypoints[c1].x - radius * -u_y,
    waypoints[c1].y - radius * u_x,
    alt };

  struct point c2_in = {
    c2.x + radius * -u_y,
    c2.y + radius * u_x,
    alt };
  struct point c2_out = {
    c2.x - radius * -u_y,
    c2.y - radius * u_x,
    alt };

  float qdr_out = M_PI - atan2(u_y, u_x);
  if (radius < 0)
    qdr_out += M_PI;

  switch (eight_status) {
  case C1 :
    NavCircleWaypoint(c1, radius);
    if (NavQdrCloseTo(DegOfRad(qdr_out)-10)) {
      eight_status = R1T;
      InitStage();
    }
    return;

  case R1T:
    nav_route_xy(c1_out.x, c1_out.y, c2_in.x, c2_in.y);
    if (nav_approaching_xy(waypoints[target].x, waypoints[target].y, c1_out.x, c1_out.y, 0)) {
      eight_status = RT2;
      InitStage();
    }
    return;

  case RT2:
    nav_route_xy(c1_out.x, c1_out.y, c2_in.x, c2_in.y);
    if (nav_approaching_xy(c2_in.x, c2_in.y, c1_out.x, c1_out.y, CARROT)) {
      eight_status = C2;
      InitStage();
    }
    return;

  case C2 :
    nav_circle_XY(c2.x, c2.y, -radius);
    if (NavQdrCloseTo(DegOfRad(qdr_out)+10)) {
      eight_status = R2T;
      InitStage();
    }
    return;

  case R2T:
    nav_route_xy(c2_out.x, c2_out.y, c1_in.x, c1_in.y);
    if (nav_approaching_xy(waypoints[target].x, waypoints[target].y, c2_out.x, c2_out.y, 0)) {
      eight_status = RT1;
      InitStage();
    }
    return;

  case RT1:
    nav_route_xy(c2_out.x, c2_out.y, c1_in.x, c1_in.y);
    if (nav_approaching_xy(c1_in.x, c1_in.y, c2_out.x, c2_out.y, CARROT)) {
      eight_status = C1;
      InitStage();
    }
    return;

  default:/* Should not occur !!! Doing nothing */
    return;
  } /* switch */
}

/************** Oval Navigation **********************************************/

/** Navigation along a figure O. One side leg is defined by waypoints [p1] and
    [p2].
    The navigation goes through 4 states: OC1 (half circle next to [p1]),
    OR21 (route [p2] to [p1], OC2 (half circle next to [p2]) and OR12
    (opposite leg).

    Initial state is the route along the desired segment (OC2).
*/

uint8_t nav_oval_count;

void nav_oval_init( void ) {
  oval_status = OC2;
  nav_oval_count = 0;
}

void nav_oval(uint8_t p1, uint8_t p2, float radius) {
  radius = - radius; /* Historical error ? */

  float alt = waypoints[p1].a;
  waypoints[p2].a = alt;

  float p2_p1_x = waypoints[p1].x - waypoints[p2].x;
  float p2_p1_y = waypoints[p1].y - waypoints[p2].y;
  float d = sqrt(p2_p1_x*p2_p1_x+p2_p1_y*p2_p1_y);

  /* Unit vector from p1 to p2 */
  float u_x = p2_p1_x / d;
  float u_y = p2_p1_y / d;

  /* The half circle centers and the other leg */
  struct point p1_center = { waypoints[p1].x + radius * -u_y,
                             waypoints[p1].y + radius * u_x,
                             alt  };
  struct point p1_out = { waypoints[p1].x + 2*radius * -u_y,
                          waypoints[p1].y + 2*radius * u_x,
                          alt  };

  struct point p2_in = { waypoints[p2].x + 2*radius * -u_y,
                         waypoints[p2].y + 2*radius * u_x,
                         alt  };
  struct point p2_center = { waypoints[p2].x + radius * -u_y,
                             waypoints[p2].y + radius * u_x,
                             alt  };

  float qdr_out_2 = M_PI - atan2(u_y, u_x);
  float qdr_out_1 = qdr_out_2 + M_PI;
  if (radius < 0) {
    qdr_out_2 += M_PI;
    qdr_out_1 += M_PI;
  }
  float qdr_anticipation = (radius > 0 ? -15 : 15);

  switch (oval_status) {
  case OC1 :
    nav_circle_XY(p1_center.x,p1_center.y, -radius);
    if (NavQdrCloseTo(DegOfRad(qdr_out_1)-qdr_anticipation)) {
      oval_status = OR12;
      InitStage();
      LINE_START_FUNCTION;
    }
    return;

  case OR12:
    nav_route_xy(p1_out.x, p1_out.y, p2_in.x, p2_in.y);
    if (nav_approaching_xy(p2_in.x, p2_in.y, p1_out.x, p1_out.y, CARROT)) {
      oval_status = OC2;
      nav_oval_count++;
      InitStage();
      LINE_STOP_FUNCTION;
    }
    return;

  case OC2 :
    nav_circle_XY(p2_center.x, p2_center.y, -radius);
    if (NavQdrCloseTo(DegOfRad(qdr_out_2)-qdr_anticipation)) {
      oval_status = OR21;
      InitStage();
      LINE_START_FUNCTION;
    }
    return;

  case OR21:
    nav_route_xy(waypoints[p2].x, waypoints[p2].y, waypoints[p1].x, waypoints[p1].y);
    if (nav_approaching_xy(waypoints[p1].x, waypoints[p1].y, waypoints[p2].x, waypoints[p2].y, CARROT)) {
      oval_status = OC1;
      InitStage();
      LINE_STOP_FUNCTION;
    }
    return;

  default: /* Should not occur !!! Doing nothing */
    return;
  }
}