Beispiel #1
0
class NNPlanner(Planner):
    """ A planner which uses
    a trained neural network. """
    def __init__(self, simulator, params):
        super(NNPlanner, self).__init__(simulator, params)
        self.goal_ego_config = SystemConfig(dt=self.params.dt, n=1, k=1)

    @staticmethod
    def parse_params(p):
        """
        Parse the parameters to add some additional helpful parameters.
        """
        return p

    def _raw_data(self, start_config):
        """
        Return a dictionary of raw_data from the simulator.
        To be passed to model.create_nn_inputs_and_outputs
        """
        simulator = self.simulator
        data = {}

        # Convert Goal to Egocentric Coordinates
        self.params.system_dynamics.to_egocentric_coordinates(
            start_config, simulator.goal_config, self.goal_ego_config)

        # Image Data
        if hasattr(self.params.model, 'occupancy_grid_positions_ego_1mk12'):
            kwargs = {
                'occupancy_grid_positions_ego_1mk12':
                self.params.model.occupancy_grid_positions_ego_1mk12
            }
        else:
            kwargs = {}
        data['img_nmkd'] = simulator.get_observation(config=start_config,
                                                     **kwargs)

        # Vehicle Data
        data['vehicle_state_nk3'] = start_config.position_and_heading_nk3(
        ).numpy()
        data[
            'vehicle_controls_nk2'] = start_config.speed_and_angular_speed_nk2(
            ).numpy()

        # Goal Data
        data['goal_position_n2'] = simulator.goal_config.position_nk2().numpy(
        )[:, 0, :]
        data['goal_position_ego_n2'] = self.goal_ego_config.position_nk2(
        ).numpy()[:, 0, :]

        # Dummy Labels
        data['optimal_waypoint_ego_n3'] = np.ones((1, 3), dtype=np.float32)
        data['waypoint_horizon_n1'] = np.ones((1, 1), dtype=np.float32)
        data['optimal_control_nk2'] = np.ones((1, 1, 2), dtype=np.float32)
        return data
Beispiel #2
0
class Simulator(SimulatorHelper):

    def __init__(self, params):
        self.params = params.simulator.parse_params(params)
        self.rng = np.random.RandomState(params.seed)
        self.obstacle_map = self._init_obstacle_map(self.rng)
        self.obj_fn = self._init_obj_fn()
        self.planner = self._init_planner()
        self.system_dynamics = self._init_system_dynamics()

    @staticmethod
    def parse_params(p):
        """
        Parse the parameters to add some additional helpful parameters.
        """
        # Parse the dependencies
        p.planner_params.planner.parse_params(p.planner_params)
        p.obstacle_map_params.obstacle_map.parse_params(p.obstacle_map_params)

        dt = p.planner_params.control_pipeline_params.system_dynamics_params.dt

        p.episode_horizon = int(np.ceil(p.episode_horizon_s / dt))
        p.control_horizon = int(np.ceil(p.control_horizon_s / dt))
        p.dt = dt
 
        return p

    # TODO: Varun. Dont clip the vehicle trajectory object,
    # but store the time index of when
    # the episode ends. Use this when plotting stuff
    def simulate(self):
        """ A function that simulates an entire episode. The agent starts at self.start_config, repeatedly
        calling _iterate to generate subtrajectories. Generates a vehicle_trajectory for the episode, calculates its
        objective value, and sets the episode_type (timeout, collision, success)"""
        config = self.start_config
        vehicle_trajectory = self.vehicle_trajectory
        vehicle_data = self.planner.empty_data_dict()
        end_episode = False
        commanded_actions_nkf = []
        while not end_episode:
            trajectory_segment, next_config, data, commanded_actions_1kf = self._iterate(config)

            # Append to Vehicle Data
            for key in vehicle_data.keys():
                vehicle_data[key].append(data[key])

            vehicle_trajectory.append_along_time_axis(trajectory_segment)
            commanded_actions_nkf.append(commanded_actions_1kf)
            config = next_config
            end_episode, episode_data = self._enforce_episode_termination_conditions(vehicle_trajectory,
                                                                                     vehicle_data,
                                                                                     commanded_actions_nkf)
        self.vehicle_trajectory = episode_data['vehicle_trajectory']
        self.vehicle_data = episode_data['vehicle_data']
        self.vehicle_data_last_step = episode_data['vehicle_data_last_step']
        self.last_step_data_valid = episode_data['last_step_data_valid']
        self.episode_type = episode_data['episode_type']
        self.valid_episode = episode_data['valid_episode']
        self.commanded_actions_1kf = episode_data['commanded_actions_1kf']
        self.obj_val = self._compute_objective_value(self.vehicle_trajectory)

    def _iterate(self, config):
        """ Runs the planner for one step from config to generate a
        subtrajectory, the resulting robot config after the robot executes
        the subtrajectory, and relevant planner data"""

        planner_data = self.planner.optimize(config)
        trajectory_segment, trajectory_data, commanded_actions_nkf = self._process_planner_data(config, planner_data)
        next_config = SystemConfig.init_config_from_trajectory_time_index(trajectory_segment, t=-1)
        return trajectory_segment, next_config, trajectory_data, commanded_actions_nkf

    def _process_planner_data(self, start_config, planner_data):
        """
        Process the planners current plan. This could mean applying
        open loop control or LQR feedback control on a system.
        """

        # The 'plan' is open loop control
        if 'trajectory' not in planner_data.keys():
            trajectory, commanded_actions_nkf = self.apply_control_open_loop(start_config,
                                                                             planner_data['optimal_control_nk2'],
                                                                             T=self.params.control_horizon-1,
                                                                             sim_mode=self.system_dynamics.simulation_params.simulation_mode)
        # The 'plan' is LQR feedback control
        else:
            # If we are using ideal system dynamics the planned trajectory
            # is already dynamically feasible. Clip it to the control horizon
            if self.system_dynamics.simulation_params.simulation_mode == 'ideal':
                trajectory = Trajectory.new_traj_clip_along_time_axis(planner_data['trajectory'],
                                                                      self.params.control_horizon,
                                                                      repeat_second_to_last_speed=True)
                _, commanded_actions_nkf = self.system_dynamics.parse_trajectory(trajectory)
            elif self.system_dynamics.simulation_params.simulation_mode == 'realistic':
                trajectory, commanded_actions_nkf = self.apply_control_closed_loop(start_config,
                                                                                   planner_data['spline_trajectory'],
                                                                                   planner_data['k_nkf1'],
                                                                                   planner_data['K_nkfd'],
                                                                                   T=self.params.control_horizon-1,
                                                                                   sim_mode='realistic')
            else:
                assert(False)

        self.planner.clip_data_along_time_axis(planner_data, self.params.control_horizon)
        return trajectory, planner_data, commanded_actions_nkf

    def get_observation(self, config=None, pos_n3=None, **kwargs):
        """
        Return the robot's observation from configuration config or
        pos_nk3.
        """
        return [None]*config.n

    def get_observation_from_data_dict_and_model(self, data_dict, model):
        """
        Returns the robot's observation from the data inside data_dict,
        using parameters specified by the model.
        """
        raise NotImplementedError

    def get_simulator_data_numpy_repr(self):
        """
        Convert the vehicle trajectory, vehicle data,
        and vehicle data last step to numpy representations
        and return them.
        """
        vehicle_trajectory = self.vehicle_trajectory.to_numpy_repr()
        vehicle_data = self.planner.convert_planner_data_to_numpy_repr(self.vehicle_data)
        vehicle_data_last_step = self.planner.convert_planner_data_to_numpy_repr(self.vehicle_data_last_step)
        vehicle_commanded_actions_1kf = self.commanded_actions_1kf.numpy()
        return vehicle_trajectory, vehicle_data, vehicle_data_last_step, vehicle_commanded_actions_1kf

    def _enforce_episode_termination_conditions(self, vehicle_trajectory, planner_data,
                                                commanded_actions_nkf):
        p = self.params
        time_idxs = []
        for condition in p.episode_termination_reasons:
            time_idxs.append(self._compute_time_idx_for_termination_condition(vehicle_trajectory,
                                                                              condition))
        try:
            idx = np.argmin(time_idxs)
        except ValueError:
            idx = np.argmin([time_idx.numpy() for time_idx in time_idxs])

        try:
            termination_time = time_idxs[idx].numpy()
        except ValueError:
            termination_time = time_idxs[idx]

        if termination_time != np.inf:
            end_episode = True
            vehicle_trajectory.clip_along_time_axis(termination_time)
            planner_data, planner_data_last_step, last_step_data_valid = self.planner.mask_and_concat_data_along_batch_dim(planner_data,
                                                                                                                           k=termination_time)
            commanded_actions_1kf = tf.concat(commanded_actions_nkf, axis=1)[:, :termination_time]

            # If all of the data was masked then
            # the episode simulated is not valid
            valid_episode = True
            if planner_data['system_config'] is None:
                valid_episode = False
            episode_data = {'vehicle_trajectory': vehicle_trajectory,
                            'vehicle_data': planner_data,
                            'vehicle_data_last_step': planner_data_last_step,
                            'last_step_data_valid': last_step_data_valid,
                            'episode_type': idx,
                            'valid_episode': valid_episode,
                            'commanded_actions_1kf': commanded_actions_1kf}
        else:
            end_episode = False
            episode_data = {}

        return end_episode, episode_data

    def reset(self, seed=-1):
        """Reset the simulator. Optionally takes a seed to reset
        the simulator's random state."""
        if seed != -1:
            self.rng.seed(seed)

        # Note: Obstacle map must be reset independently of the fmm map.
        # Sampling start and goal may depend on the updated state of the
        # obstacle map. Updating the fmm map depends on the newly sampled goal.
        reset_start = True
        while reset_start:
            self._reset_obstacle_map(self.rng)
            self._reset_start_configuration(self.rng)
            reset_start = self._reset_goal_configuration(self.rng)
        self._update_fmm_map()

        self.vehicle_trajectory = Trajectory(dt=self.params.dt, n=1, k=0)
        self.obj_val = np.inf
        self.vehicle_data = {}

    def _reset_obstacle_map(self, rng):
        raise NotImplementedError

    def _update_fmm_map(self):
        raise NotImplementedError

    def _reset_start_configuration(self, rng):
        """
        Reset the starting configuration of the vehicle.
        """
        p = self.params.reset_params.start_config

        # Reset the position
        if p.position.reset_type == 'random':
            # Select a random position on the map that is at least obstacle margin
            # away from the nearest obstacle
            obs_margin = self.params.avoid_obstacle_objective.obstacle_margin1
            dist_to_obs = 0.
            while dist_to_obs <= obs_margin:
                start_112 = self.obstacle_map.sample_point_112(rng)
                dist_to_obs = tf.squeeze(self.obstacle_map.dist_to_nearest_obs(start_112))
        elif p.position.reset_type == 'custom':
            x, y = p.position.start_pos
            start_112 = np.array([[[x, y]]], dtype=np.float32)
            dist_to_obs = tf.squeeze(self.obstacle_map.dist_to_nearest_obs(start_112))
            assert(dist_to_obs.numpy() > 0.0)
        else:
            raise NotImplementedError('Unknown reset type for the vehicle starting position.')

        # Reset the heading
        if p.heading.reset_type == 'zero':
            heading_111 = np.zeros((1, 1, 1))
        elif p.heading.reset_type == 'random':
            heading_111 = rng.uniform(p.heading.bounds[0], p.heading.bounds[1], (1, 1, 1))
        elif p.position.reset_type == 'custom':
            theta = p.heading.start_heading
            heading_111 = np.array([[[theta]]], dtype=np.float32)
        else:
            raise NotImplementedError('Unknown reset type for the vehicle starting heading.')

        # Reset the speed
        if p.speed.reset_type == 'zero':
            speed_111 = np.zeros((1, 1, 1))
        elif p.speed.reset_type == 'random':
            speed_111 = rng.uniform(p.speed.bounds[0], p.speed.bounds[1], (1, 1, 1))
        elif p.speed.reset_type == 'custom':
            speed = p.speed.start_speed
            speed_111 = np.array([[[speed]]], dtype=np.float32)
        else:
            raise NotImplementedError('Unknown reset type for the vehicle starting speed.')

        # Reset the angular speed
        if p.ang_speed.reset_type == 'zero':
            ang_speed_111 = np.zeros((1, 1, 1))
        elif p.ang_speed.reset_type == 'random':
            ang_speed_111 = rng.uniform(p.ang_speed.bounds[0], p.ang_speed.bounds[1], (1, 1, 1))
        elif p.ang_speed.reset_type == 'gaussian':
            ang_speed_111 = rng.normal(p.ang_speed.gaussian_params[0],
                                       p.ang_speed.gaussian_params[1], (1, 1, 1))
        elif p.ang_speed.reset_type == 'custom':
            ang_speed = p.ang_speed.start_ang_speed
            ang_speed_111 = np.array([[[ang_speed]]], dtype=np.float32)
        else:
            raise NotImplementedError('Unknown reset type for the vehicle starting angular speed.')

        # Initialize the start configuration
        self.start_config = SystemConfig(dt=p.dt, n=1, k=1,
                                         position_nk2=start_112,
                                         heading_nk1=heading_111,
                                         speed_nk1=speed_111,
                                         angular_speed_nk1=ang_speed_111)

        # The system dynamics may need the current starting position for
        # coordinate transforms (i.e. realistic simulation)
        self.system_dynamics.reset_start_state(self.start_config)

    def _reset_goal_configuration(self, rng):
        p = self.params.reset_params.goal_config
        goal_norm = self.params.goal_dist_norm
        goal_radius = self.params.goal_cutoff_dist
        start_112 = self.start_config.position_nk2()
        obs_margin = self.params.avoid_obstacle_objective.obstacle_margin1

        # Reset the goal position
        if p.position.reset_type == 'random':
            # Select a random position on the map that is at least obstacle margin away from the nearest obstacle, and
            # not within the goal margin of the start position.
            dist_to_obs = 0.
            dist_to_goal = 0.
            while dist_to_obs <= obs_margin or dist_to_goal <= goal_radius:
                goal_112 = self.obstacle_map.sample_point_112(rng)
                dist_to_obs = tf.squeeze(self.obstacle_map.dist_to_nearest_obs(goal_112))
                dist_to_goal = np.linalg.norm((start_112 - goal_112)[0], ord=goal_norm)
        elif p.position.reset_type == 'custom':
            x, y = p.position.goal_pos
            goal_112 = np.array([[[x, y]]], dtype=np.float32)
            dist_to_obs = tf.squeeze(self.obstacle_map.dist_to_nearest_obs(goal_112))
            assert(dist_to_obs.numpy() > 0.0)
        elif p.position.reset_type == 'random_v1':
            assert self.obstacle_map.name == 'SBPDMap'
            # Select a random position on the map that is at least obs_margin away from the
            # nearest obstacle, and not within the goal margin of the start position.
            # Additionaly the goal position must satisfy:
            # fmm_dist(start, goal) - l2_dist(start, goal) > fmm_l2_gap (goal should not be
            # fmm_dist(start, goal) < max_dist (goal should not be too far away)

            # Construct an fmm map where the 0 level set is the start position
            start_fmm_map = self._init_fmm_map(goal_pos_n2=self.start_config.position_nk2()[:, 0]) 
            # enforce fmm_dist(start, goal) < max_fmm_dist
            free_xy = np.where(start_fmm_map.fmm_distance_map.voxel_function_mn <
                               p.position.max_fmm_dist)
            free_xy = np.array(free_xy).T
            free_xy = free_xy[:, ::-1]
            free_xy_pts_m2 = self.obstacle_map._map_to_point(free_xy)
            
            # enforce dist_to_nearest_obstacle > obs_margin
            dist_to_obs = tf.squeeze(self.obstacle_map.dist_to_nearest_obs(free_xy_pts_m2[:, None])).numpy()

            dist_to_obs_valid_mask = dist_to_obs > obs_margin

            # enforce dist_to_goal > goal_radius
            fmm_dist_to_goal = np.squeeze(start_fmm_map.fmm_distance_map.compute_voxel_function(free_xy_pts_m2[:, None]).numpy())
            fmm_dist_to_goal_valid_mask = fmm_dist_to_goal > goal_radius

            # enforce fmm_dist - l2_dist > fmm_l2_gap
            fmm_l2_gap = rng.uniform(0.0, p.position.max_dist_diff)
            l2_dist_to_goal = np.linalg.norm((start_112 - free_xy_pts_m2[:, None]), axis=2)[:, 0]
            fmm_dist_to_goal = np.squeeze(start_fmm_map.fmm_distance_map.compute_voxel_function(free_xy_pts_m2[:, None]).numpy())
            fmm_l2_gap_valid_mask = fmm_dist_to_goal - l2_dist_to_goal > fmm_l2_gap

            valid_mask = np.logical_and.reduce((dist_to_obs_valid_mask,
                                                fmm_dist_to_goal_valid_mask,
                                                fmm_l2_gap_valid_mask))
            free_xy = free_xy[valid_mask]
            if len(free_xy) == 0:
                # there are no goal points within the max_fmm_dist of start
                # return True so the start is reset
                return True

            goal_112 = self.obstacle_map.sample_point_112(rng, free_xy_map_m2=free_xy)
        else:
            raise NotImplementedError('Unknown reset type for the vehicle goal position.')

        # Initialize the goal configuration
        self.goal_config = SystemConfig(dt=p.dt, n=1, k=1,
                                        position_nk2=goal_112)
        return False

    def _compute_objective_value(self, vehicle_trajectory):
        p = self.params.objective_fn_params
        if p.obj_type == 'valid_mean':
            vehicle_trajectory.update_valid_mask_nk()
        else:
            assert(p.obj_type in ['valid_mean', 'mean'])
        obj_val = tf.squeeze(self.obj_fn.evaluate_function(vehicle_trajectory))
        return obj_val

    def _update_obj_fn(self):
        """
        Update the objective function to use a new
        obstacle_map and fmm map
        """
        for objective in self.obj_fn.objectives:
            if isinstance(objective, ObstacleAvoidance):
                objective.obstacle_map = self.obstacle_map
            elif isinstance(objective, GoalDistance):
                objective.fmm_map = self.fmm_map
            elif isinstance(objective, AngleDistance):
                objective.fmm_map = self.fmm_map
            else:
                assert(False)

    def _init_obstacle_map(self, obstacle_params=None):
        """ Initializes a new obstacle map."""
        raise NotImplementedError

    def _init_system_dynamics(self):
        """
        If there is a control pipeline (i.e. model based method)
        return its system_dynamics. Else create a new system_dynamics
        instance.
        """
        try:
            return self.planner.control_pipeline.system_dynamics
        except AttributeError:
            p = self.params.planner_params.control_pipeline_params.system_dynamics_params
            return p.system(dt=p.dt, params=p)

    def _init_obj_fn(self):
        """
        Initialize the objective function.
        Use fmm_map = None as this is undefined
        until a goal configuration is specified.
        """
        p = self.params

        obj_fn = ObjectiveFunction(p.objective_fn_params)
        if not p.avoid_obstacle_objective.empty():
            obj_fn.add_objective(ObstacleAvoidance(
                params=p.avoid_obstacle_objective,
                obstacle_map=self.obstacle_map))
        if not p.goal_distance_objective.empty():
            obj_fn.add_objective(GoalDistance(
                params=p.goal_distance_objective,
                fmm_map=None))
        if not p.goal_angle_objective.empty():
            obj_fn.add_objective(AngleDistance(
                params=p.goal_angle_objective,
                fmm_map=None))
        return obj_fn

    def _init_fmm_map(self, goal_pos_n2=None):
        p = self.params
        self.obstacle_occupancy_grid = self.obstacle_map.create_occupancy_grid_for_map()

        if goal_pos_n2 is None:
            goal_pos_n2 = self.goal_config.position_nk2()[0]

        return FmmMap.create_fmm_map_based_on_goal_position(
            goal_positions_n2=goal_pos_n2,
            map_size_2=np.array(p.obstacle_map_params.map_size_2),
            dx=p.obstacle_map_params.dx,
            map_origin_2=p.obstacle_map_params.map_origin_2,
            mask_grid_mn=self.obstacle_occupancy_grid)

    def _init_planner(self):
        p = self.params
        return p.planner_params.planner(simulator=self,
                                        params=p.planner_params)

    # Functions for computing relevant metrics
    # on robot trajectories
    def _dist_to_goal(self, trajectory):
        """Calculate the FMM distance between
        each state in trajectory and the goal."""
        for objective in self.obj_fn.objectives:
            if isinstance(objective, GoalDistance):
                dist_to_goal_nk = objective.compute_dist_to_goal_nk(trajectory)
        return dist_to_goal_nk

    def _calculate_min_obs_distances(self, vehicle_trajectory):
        """Returns an array of dimension 1k where each element is the distance to the closest
        obstacle at each time step."""
        pos_1k2 = vehicle_trajectory.position_nk2()
        obstacle_dists_1k = self.obstacle_map.dist_to_nearest_obs(pos_1k2)
        return obstacle_dists_1k

    def _calculate_trajectory_collisions(self, vehicle_trajectory):
        """Returns an array of dimension 1k where each element is a 1 if the robot collided with an
        obstacle at that time step or 0 otherwise. """
        pos_1k2 = vehicle_trajectory.position_nk2()
        obstacle_dists_1k = self.obstacle_map.dist_to_nearest_obs(pos_1k2)
        return tf.cast(obstacle_dists_1k < 0.0, tf.float32)

    def get_metrics(self):
        """After the episode is over, call the get_metrics function to get metrics
        per episode.  Returns a structure, lists of which are passed to accumulate
        metrics static function to generate summary statistics."""
        dists_1k = self._dist_to_goal(self.vehicle_trajectory)
        init_dist = dists_1k[0, 0].numpy()
        final_dist = dists_1k[0, -1].numpy()
        collisions_mu = np.mean(self._calculate_trajectory_collisions(self.vehicle_trajectory))
        min_obs_distances = self._calculate_min_obs_distances(self.vehicle_trajectory)
        return np.array([self.obj_val,
                         init_dist,
                         final_dist,
                         self.vehicle_trajectory.k,
                         collisions_mu,
                         np.min(min_obs_distances),
                         self.episode_type])

    @staticmethod
    def collect_metrics(ms, termination_reasons=['Timeout', 'Collision', 'Success']):
        ms = np.array(ms)
        if len(ms) == 0:
            return None, None
        obj_vals, init_dists, final_dists, episode_length, collisions, min_obs_distances, episode_types = ms.T
        keys = ['Objective Value', 'Initial Distance', 'Final Distance',
                'Episode Length', 'Collisions_Mu', 'Min Obstacle Distance']
        vals = [obj_vals, init_dists, final_dists,
                episode_length, collisions, min_obs_distances]

        # mean, 25 percentile, median, 75 percentile
        fns = [np.mean, lambda x: np.percentile(x, q=25), lambda x:
               np.percentile(x, q=50), lambda x: np.percentile(x, q=75)]
        fn_names = ['mu', '25', '50', '75']
        out_vals, out_keys = [], []
        for k, v in zip(keys, vals):
            for fn, name in zip(fns, fn_names):
                _ = fn(v)
                out_keys.append('{:s}_{:s}'.format(k, name))
                out_vals.append(_)

        # Log the number of episodes
        num_episodes = len(episode_types)
        out_keys.append('Number Episodes')
        out_vals.append(num_episodes)

        # Log Percet Collision, Timeout, Success, Etc.
        for i, reason in enumerate(termination_reasons):
            out_keys.append('Percent {:s}'.format(reason))
            out_vals.append(1.*np.sum(episode_types == i) / num_episodes)

            # Log the Mean Episode Length for Each Episode Type
            episode_idxs = np.where(episode_types == i)[0]
            episode_length_for_this_episode_type = episode_length[episode_idxs]
            if len(episode_length_for_this_episode_type) > 0:
                mean_episode_length_for_this_episode_type = np.mean(episode_length_for_this_episode_type)
                out_keys.append('Mean Episode Length for {:s} Episodes'.format(reason))
                out_vals.append(mean_episode_length_for_this_episode_type)

        return out_keys, out_vals

    def start_recording_video(self, video_number):
        """ By default the simulator does not support video capture."""
        return None

    def stop_recording_video(self, video_number, video_filename):
        """ By default the simulator does not support video capture."""
        return None

    def render(self, axs, freq=4, render_velocities=False, prepend_title=''):
        if type(axs) is list or type(axs) is np.ndarray:
            self._render_trajectory(axs[0], freq)

            if render_velocities:
                self._render_velocities(axs[1], axs[2])
            [ax.set_title('{:s}{:s}'.format(prepend_title, ax.get_title())) for ax in axs]
        else:
            self._render_trajectory(axs, freq)
            axs.set_title('{:s}{:s}'.format(prepend_title, axs.get_title()))

    def _render_obstacle_map(self, ax):
        raise NotImplementedError

    def _render_trajectory(self, ax, freq=4):
        p = self.params

        self._render_obstacle_map(ax)

        if 'waypoint_config' in self.vehicle_data.keys():
            self.vehicle_trajectory.render([ax], freq=freq, plot_quiver=False)
            self._render_waypoints(ax)
        else:
            self.vehicle_trajectory.render([ax], freq=freq, plot_quiver=True)

        boundary_params = {'norm': p.goal_dist_norm, 'cutoff':
                           p.goal_cutoff_dist, 'color': 'g'}
        self.start_config.render(ax, batch_idx=0, marker='o', color='blue')
        self.goal_config.render_with_boundary(ax, batch_idx=0, marker='*', color='black',
                                              boundary_params=boundary_params)

        goal = self.goal_config.position_nk2()[0, 0]
        start = self.start_config.position_nk2()[0, 0]
        text_color = p.episode_termination_colors[self.episode_type]
        ax.set_title('Start: [{:.2f}, {:.2f}] '.format(*start) +
                     'Goal: [{:.2f}, {:.2f}]'.format(*goal), color=text_color)

        final_pos = self.vehicle_trajectory.position_nk2()[0, -1]
        ax.set_xlabel('Cost: {cost:.3f} '.format(cost=self.obj_val) +
                      'End: [{:.2f}, {:.2f}]'.format(*final_pos), color=text_color)

    def _render_waypoints(self, ax):
        # Plot the system configuration and corresponding
        # waypoint produced in the same color
        system_configs = self.vehicle_data['system_config']
        waypt_configs = self.vehicle_data['waypoint_config']
        cmap = matplotlib.cm.get_cmap(self.params.waypt_cmap)
        for i, (system_config, waypt_config) in enumerate(zip(system_configs, waypt_configs)):
            color = cmap(i / system_configs.n)
            system_config.render(ax, batch_idx=0, plot_quiver=True,
                                 marker='o', color=color)

            # Render the waypoint's number at each
            # waypoint's location
            pos_2 = waypt_config.position_nk2()[0, 0].numpy()
            ax.text(pos_2[0], pos_2[1], str(i), color=color)

    def _render_velocities(self, ax0, ax1):
        speed_k = self.vehicle_trajectory.speed_nk1()[0, :, 0].numpy()
        angular_speed_k = self.vehicle_trajectory.angular_speed_nk1()[0, :, 0].numpy()

        time = np.r_[:self.vehicle_trajectory.k]*self.vehicle_trajectory.dt

        if self.system_dynamics.simulation_params.simulation_mode == 'realistic':
            ax0.plot(time, speed_k, 'r--', label='Applied')
            ax0.plot(time, self.commanded_actions_1kf[0, :,  0], 'b--', label='Commanded')
            ax0.set_title('Linear Velocity')
            ax0.legend()

            ax1.plot(time, angular_speed_k, 'r--', label='Applied')
            ax1.plot(time, self.commanded_actions_1kf[0, :,  1], 'b--', label='Commanded')
            ax1.set_title('Angular Velocity')
            ax1.legend()
        else:

            ax0.plot(time, speed_k, 'r--')
            ax0.set_title('Linear Velocity')

            ax1.plot(time, angular_speed_k, 'r--')
            ax1.set_title('Angular Velocity')