Esempio n. 1
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 def __init__(self, R: Robot):
     self.origin = R.get_effector()
     self.R = R
     self.w = R.kin_eps
Esempio n. 2
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 def __init__(self, R: Robot):
     self.robot = R
     self.origin = R.get_effector()
Esempio n. 3
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 def moved_normally(R: Robot, target: Vector3):
     m = R.move_to(target)
     col = R.check_collisions()
     if col:
         log()['COLLISION'].log('collision detected')
     return m and not col
Esempio n. 4
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    def getstate(self):
        print("MapSize:{}x{}, Parking Number:{}".format(
            self.Height, self.Width, len(self.parkingdict)))


if __name__ == '__main__':

    from env.robot import Robot

    vision = Vision()
    vision.initwindows()
    vision.initrobot(2)
    vision.setrobot(1, 1)

    path = vision.astar(vision.imports, (0, 12))
    robot = Robot(0, vision.imports)
    robot.setpath(path)

    while not robot.IsArrive:
        step = robot.move()
        if tuple(step) == (0, 0):
            break
        vision.moverobot(1, step)

        vision.updatesim(0.5)

    stop = input('stop Y/n : ')
    if stop == 'y':
        vision.destroy()

    vision.mainloop()
Esempio n. 5
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class Planner(object):
    LENGTHS = [RobotSettings.LINK_1_LENGTH, RobotSettings.LINK_2_LENGTH]
    # Maximum step size between configurations
    MAX_STEP = 2.0
    MAX_PROXIMITY = 60.0  # magic constant - how close to connect configs
    X_MAX = WorkspaceSettings.WIDTH
    Y_MAX = WorkspaceSettings.HEIGHT
    MAX_ANGLE = 230.0
    MIN_ANGLE = -50.0
    N = 3  # Number of joints (inc. end effector)
    TIMEOUT = 30  # seconds
    SAFE_FACTOR = 1.0
    RISKY_FACTOR = 0.6
    SWEAT_FACTOR = 0.5

    def __init__(self):
        self.scene = Scene()
        self.robot = Robot()
        self.obstacles = []
        self.path = Path()
        self.sampler = Sampler(self.LENGTHS)
        self.validator = Validator()
        self.configs = []
        self.path_found = False
        self.super_path = SuperPath()
        self.safety = True
        self.all_paths_found = False

    def received_scene_string(self, scene_string):
        """
        Convert the string to a scene, process the scene,
        and return a path string.
        """
        self.__init__()
        self.scene.decode(scene_string)
        print("Can Move: ", self.scene.moveableBlocks)
        self.scene.render()

        if len(self.scene.pucks) > len(self.scene.holes):
            print("{0} pucks, {1} goals - can't do it".format(len(self.scene.pucks), len(self.scene.holes)))
            exit()

        self.scene.print_scene()
        self.set_obstacles(self.scene, pucks=True)
        if len(self.scene.moveableBlocks) > 0:
            print("ATTEMPTING TO MOVE A BLOCK")
            self.move_block()
        # return self.super_path.to_string()

        all_paths, costs = self.find_all_paths()

        goal_indices, goal_costs = self.find_puck_goal_mapping(costs)

        for i in range(len(goal_indices)):
            self.super_path.paths.append(all_paths[i][goal_indices[i]])

        # Show path(s) in simulator
        sim_paths = [
            np.array([list(cfg.positions[-1]) for cfg in path.path])
            for path in self.super_path.paths
        ]
        # print("Planner: sim paths are \n", sim_paths)
        self.scene.render(paths=sim_paths)

        return self.super_path.to_string()

    def move_block(self):

        push_behind = 50
        push_distance = 50
        max_push_distance = 150

        # Plan path with movable block removed until path found
        for block in self.scene.moveableBlocks:
            self.set_obstacles(self.scene, pucks=True)
            if block.y < 0:
                continue
            print("Attempting to remove block at ", block.x, block.y)
            print("Length before removal = ", len(self.obstacles))
            self.obstacles.remove(block.shape)
            print("Length after removal = ", len(self.obstacles))

            if len(self.scene.moveableBlocks) == 1:
                all_paths, costs = self.find_all_paths(impatient=False)
            else:
                all_paths, costs = self.find_all_paths(impatient=True)

            if self.all_paths_found:
                self.configs = []
                block_to_move = block
                x = block.x
                y = block.y
                if block.blockType == BlockSettings.CYLINDER:
                    push_behind = 40
                if block.blockType == BlockSettings.CUBE:
                    push_behind = 45
                elif block.blockType == BlockSettings.PRISM:
                    push_behind = 65
                break

            self.configs = []

        if not self.all_paths_found:
            print("Error: Couldn't find a path for block pushing")
            exit()

        # Goals are obstacles when it comes to pushing
        self.set_obstacles(self.scene, pucks=True, goals=True)
        self.obstacles.remove(block_to_move.shape)

        min_d1 = 1000000
        min_d2 = 1000000
        nearest_block1 = None
        nearest_block2 = None
        for block in self.scene.blocks:
            if block.y < 0:
                continue
            d = gm.distance((block.x, block.y), (x, y))
            if d < 0.5:
                # THIS IS THE BLOCK THATS MOVING. 0.5 IS ARBITRARY
                continue
            if d < min_d1:
                min_d2 = min_d1
                min_d1 = d
                nearest_block2 = nearest_block1
                nearest_block1 = (block.x, block.y)
            elif d < min_d2:
                min_d2 = d
                nearest_block2 = (block.x, block.y)

        # Check if block is closer to boundary than one of the nearest
        ww = WorkspaceSettings.WIDTH
        wh = WorkspaceSettings.HEIGHT
        bottom = gm.Line2D((-ww / 2, 0.0), (ww / 2, 0.0))
        right = gm.Line2D((ww / 2, 0.0), (ww / 2, wh))
        top = gm.Line2D((ww / 2, wh), (-ww / 2, wh))
        left = gm.Line2D((-ww / 2, wh), (-ww / 2, 0.0))
        boundaries = [bottom, right, top, left]
        # Make the boundary point one of the nearest if so
        min_db = 1000000
        for boundary in boundaries:
            p = boundary.p_point((x, y))
            d = boundary.p_distance((x, y))
            if d < min_d1:
                min_d2 = min_d1
                min_d1 = d
                nearest_block2 = nearest_block1
                nearest_block1 = p
            elif d < min_d2:
                min_d2 = d
                nearest_block2 = p

        if nearest_block1 is None or nearest_block2 is None:
            # Maybe there were not enought blocks or something?
            # This shouldn't happen, but if it does it will cause problems
            print("Planner: Error finding nearest blocks in moving blocks")
            return

        print("Found Nearest Blocks: ", nearest_block1, nearest_block2)

        nearest_block_line = gm.Line2D(nearest_block1, nearest_block2)

        m1, c1 = nearest_block_line.find_normal_at_point((x, y))
        print("Nearest block line: m,c: ", m1, c1)

        # Direction of push
        theta = math.atan2(m1, 1.0)
        print("Theta is ", theta)
        print("x,y is :", x, y)

        start_point = gm.point_from_polar((x, y), push_behind, theta + np.pi)
        start_point = (start_point[0], start_point[1] - 5.0)
        print("Start point is: ", start_point)
        start_cfg = self.config_from_point(start_point)
        max_point = gm.point_from_polar((x, y), max_push_distance, theta)
        max_cfg = self.config_from_point(max_point)

        # Move forward (~ along path)
        # Check each direction until not in collision

        # TODO: intersect functions for prism and cube
        nearest_collision = self.step_to_block(start_cfg, max_cfg)

        if nearest_collision is None:
            push_distance = max_push_distance
        else:
            push_distance = gm.distance((x, y), nearest_collision)
        print("Nearest collision for first direction: ", nearest_collision)

        # See if opposite direction is better
        print("Checking opposite push direction")
        start_point2 = gm.point_from_polar((x, y), push_behind, theta)
        start_point2 = (start_point2[0], start_point2[1] - 5.0)
        start_cfg2 = self.config_from_point(start_point2)
        max_point2 = gm.point_from_polar((x, y), max_push_distance, theta + np.pi)
        max_cfg2 = self.config_from_point(max_point)
        nearest_collision2 = self.step_to_block(start_cfg2, max_cfg2)
        print("Nearest collision for second direction: ", nearest_collision2)

        if nearest_collision2 is None:
            if nearest_collision is not None:
                # Opposite direction does not collide -> better
                theta += np.pi
                start_point = start_point2
                start_cfg = start_cfg2
                push_distance = max_push_distance
        # Both None -> go with first option
        elif nearest_collision is not None:
            # Both have collision -> choose longest available push
            push_distance2 = gm.distance((x, y), nearest_collision2)
            if push_distance2 > push_distance:
                print("Chose opposite direction")
                # Direction 2 is better
                theta += np.pi
                start_point = start_point2
                start_cfg = start_cfg2
                push_distance = push_distance2
        # Else no change, go with direction 1

        end_point = gm.point_from_polar((x, y), push_distance - 20, theta)
        end_point = (end_point[0], end_point[1] - 5.0)
        print("End point is: ", end_point)
        end_cfg = self.config_from_point(end_point)

        path = Path()
        path.path.append(start_cfg)
        path.path.append(end_cfg)
        path.movingPath = True
        self.super_path.paths.append(path)

        # Update block position after push (inaccurate)
        self.set_obstacles(self.scene, pucks=True)
        self.obstacles.remove(block_to_move.shape)
        block_to_move.x = end_point[0]
        block_to_move.y = end_point[1]
        block_to_move.find_shape()
        print("Adding back the moved block: ", block_to_move.shape)
        # Remove goals for path planning
        self.obstacles.append(block_to_move.shape)

    def config_from_point(self, pt):
        angles = list(self.robot.inverse_kinematics(pt[0], pt[1], None, 0.0))
        coordinates = self.robot.forward_kinematics(angles[0], angles[1],
                                                    angles[2], all_joints=True)
        return RobotConfig(coordinates[:-1], angles[:-1])

    def set_obstacles(self, scene, pucks=False, goals=False):
        """
        Retrieves the obstacles in the environment based on the scene data.
        :param scene: the scene representing the state of the workspace.
        :return: list<Shape2D>
        """
        self.obstacles = [block.shape for block in scene.blocks]
        if pucks:
            self.obstacles.extend([puck.shape for puck in self.scene.pucks])
        if goals:
            self.obstacles.extend([hole.shape for hole in self.scene.holes])

    # print("Planner: scene is:\n", scene.print_scene())

    def find_all_paths(self, impatient=False):
        """
        Find all the paths from pucks to holes
        """
        # TODO handle invalid end states with super path
        # TODO iterate through all root-goal combos after each PRM build
        print("\nPlanner: planning safely ({0}x puck enlargement)"
              .format(2 * self.SAFE_FACTOR))

        if impatient:
            timeout = self.TIMEOUT / 2
        else:
            timeout = self.TIMEOUT

        # Build and search roadmap with random samples until all paths found
        # or we run out of time
        t0 = time.time()
        all_paths = [[None for h in range(len(self.scene.holes))]
                     for p in range(len(self.scene.pucks))]
        costs = [[None for h in range(len(self.scene.holes))]
                 for p in range(len(self.scene.pucks))]
        self.all_paths_found = False
        sample_size = 2
        while time.time() - t0 < timeout and not self.all_paths_found:
            print("\nPlanner: building roadmap with {0} samples"
                  .format(sample_size))

            if sample_size == 1024:
                # print("Planner: visualising")
                # self.visualise_graph()
                self.validator.set_enlarge_factor(self.RISKY_FACTOR)
                print("\nPlanner: living dangerously " \
                      "({0}x puck enlargement)".format(2 * self.RISKY_FACTOR))
                self.safety = False
            elif sample_size == 4096 and len(self.scene.moveableBlocks) == 0:
                self.validator.set_enlarge_factor(self.SWEAT_FACTOR)
                print("\nPlanner: start sweating ({0}x puck enlargement)"
                      .format(2 * self.SWEAT_FACTOR))

            self.build_road_map(sample_size)

            for root_index in range(len(self.scene.pucks)):
                # Reset to block obstacles only
                self.obstacles.remove(self.scene.pucks[root_index].shape)

                for goal_index in range(len(self.scene.holes)):
                    if all_paths[root_index][goal_index] is not None:
                        # Path already found; use that
                        continue
                    self.path = Path()
                    path_possible = self.do_query(root_index, goal_index)
                    if not path_possible:
                        continue
                    puck = self.scene.pucks[root_index]
                    hole = self.scene.holes[goal_index]
                    self.path.deltaTheta = puck.theta - hole.theta
                    # print("DELTA_ANGLE_IS: ", self.path.deltaTheta)
                    if self.path_found:
                        all_paths[root_index][goal_index] = self.path
                        costs[root_index][goal_index] = self.path.cost
                    self.path_found = False

                self.obstacles.append(self.scene.pucks[root_index].shape)

            if self.find_puck_goal_mapping(costs) is not None:
                self.all_paths_found = True

            # Extend the roadmap in the next iteration if paths were not found
            sample_size *= 2

        if time.time() - t0 > timeout:
            # TODO try again
            print("Planner: timeout at {0}s\n".format(time.time() - t0))
            return all_paths, costs

        if self.all_paths_found:
            print("Planner: found paths in {0}s\n".format(time.time() - t0))
            return all_paths, costs

    def do_query(self, root_index, goal_index):
        """
        Search for a path between the specified root and goal via the roadmap
        :return: True if a path was found
        """

        self.validator.set_enlarge_factor(0.5)
        print("Planner: finding path from puck {0} to goal {1}"
              .format(root_index, goal_index))

        root = self.get_end_state(0, index=root_index)
        goal = self.get_end_state(1, index=goal_index)
        if not self.validator.is_valid_sample(root, self.obstacles, debug=False) or \
                not self.validator.is_valid_sample(goal, self.obstacles, debug=False):
            print("Planner: ERROR: invalid end states")
            print("Valid root: ", self.validator.is_valid_sample(root, self.obstacles))
            print("Valid goal: ", self.validator.is_valid_sample(goal, self.obstacles))
            exit()

        if self.safety:
            self.validator.set_enlarge_factor(self.SAFE_FACTOR)
        else:
            self.validator.set_enlarge_factor(self.RISKY_FACTOR)

        # Try direct path
        direct_connection = self.make_steps(root, goal, check=True)[0]
        if direct_connection:
            self.path.set_path([root, goal])
            self.path_found = True
            self.path.cost = gm.distance(root.positions[-1],
                                         goal.positions[-1])
            print("Planner: goal found directly")
            return True

        # Find vertices nearest initial and goal configs
        connected_root = self.connect_configs(root)
        connected_goal = self.connect_configs(goal)

        # Check if root and goal were connected
        if not (connected_root and connected_goal):
            # Solution not possible
            return False

        # Initial and goal states are now in the roadmap
        # Search for a path
        ass = AStarSearch(root, goal)
        print("Planner: searching")
        ass.search()

        if ass.goal_found:
            # print("Planner: visualising")
            # self.visualise_graph()
            # Record solution
            path = ass.path
            full_path = []

            while len(path) > 1:
                cfg_0 = path.pop(0)
                # Uncomment below 4 lines to display/calculate curved paths
                # cfg_m = path[0]
                # steps = self.make_steps(cfg_0, cfg_m, check=False)[1]
                # steps.pop()
                # full_path += steps

                full_path.append(cfg_0)

            full_path.append(goal)
            self.path.set_path(full_path)
            self.path.cost = ass.total_cost
            self.path_found = True
            # Remove this root and goal from the roadmap, ready for the next
            for cfg in root.connectors:
                cfg.connectors.pop(root, False)
            for cfg in goal.connectors:
                cfg.connectors.pop(goal, False)
            return True

        return False

    def build_road_map(self, sample_size):
        """
        Add samples to the roadmap
        """
        while len(self.configs) < sample_size:
            self.sample_uniform()
        # print("Planner: Finished sampling, attempting to connect configs")
        self.connect_configs()

    def sample_uniform(self):
        """
        Sample a configuration uniformly at random.
        :return: True if the configuration was connected to any others
        """
        sample = self.sampler.sample_cart(self.N, 0.0, 0.0,
                                          self.X_MAX, self.Y_MAX,
                                          self.MIN_ANGLE, self.MAX_ANGLE)
        cfg = RobotConfig(sample[0], sample[1])
        if self.validator.is_valid_sample(cfg, self.obstacles):
            self.configs.append(cfg)

    def connect_configs(self, cfg_0=None):
        """
        Connect a new configuration to a maximum of k others in the state
        graph, if they are within a certain distance and there is a
        collision-free path between them.
        :param cfg_0: The new configuration to connect to
        :return: True if any connections were made
        """
        num_connections = 0
        if len(self.configs) == 0:
            return False
        elif len(self.configs) < 5:
            n_neighbors = len(self.configs)
        else:
            n_neighbors = 5
        # Make array of end effector positions
        # print("Planner: Building points")
        points = np.array([cfg.positions[-1] for cfg in self.configs])
        # print("Planner: Finding NearestNeighbors")
        neigh = NearestNeighbors(n_neighbors=n_neighbors,
                                 radius=self.MAX_PROXIMITY)
        # print("Planner: Fitting points")
        neigh.fit(points)
        # distances, indices = neigh.radius_neighbors([cfg_0.positions[-1]])
        if cfg_0 is not None:
            distances, indices = neigh.kneighbors([cfg_0.positions[-1]])
            for i in indices[0]:
                cfg_m = self.configs[i]
                # if cfg_m not in cfg_0.connectors.keys():
                num_connections += self.make_steps(cfg_0, cfg_m)[0]
            return num_connections > 0
        else:
            distances, indices = neigh.kneighbors(points)
            for i in indices:
                cfg_0 = self.configs[i[0]]
                for j in i[1:]:
                    cfg_m = self.configs[j]
                    if cfg_m not in cfg_0.connectors.keys():
                        self.make_steps(cfg_0, cfg_m)
            return False

    def make_steps(self, cfg_0, cfg_m, check=True):
        """
        Interpolate a straight-line path between configurations in C-space.
        :param cfg_0: the initial configuration
        :param cfg_m: the final configuration
        :param check: check if the path is collision free if True
        :return: a tuple; the first element is 1 if a connection is
        made and 0 otherwise; the second element is the interpolated
        configurations from the initial to the final state inclusive.
        """
        connection = 0  # 1 if valid connection is made
        steps = [cfg_0, cfg_m]
        end_loop = False
        max_step = 1000.0  # max of all iterations

        while True:
            old_steps = list(steps)
            current_max_step = 0  # max of current iteration
            end_index = len(steps) - 1
            for i in range(end_index):
                # Interpolate the midpoint configuration
                cfg_1 = old_steps[i]
                cfg_2 = old_steps[i + 1]
                cfg_nxt = self.midpoint(cfg_1, cfg_2)
                steps.insert(2 * i + 1, cfg_nxt)
                i_max_step = gm.distance(cfg_1.positions[-1],
                                         cfg_nxt.positions[-1])

                if i_max_step > current_max_step:
                    current_max_step = i_max_step

                if check and (self.validator.has_collision(cfg_nxt,
                                                           self.obstacles)
                              or not self.validator.fits_bounds(cfg_nxt)):
                    end_loop = True
                    break

            if current_max_step < max_step:
                max_step = current_max_step

            if max_step < self.MAX_STEP:
                # No collision and primitive step size has been reached
                if check:
                    # Connect vertices in state graph
                    jump = PathJump(cfg_0, cfg_m)
                    cfg_0.add_connector(cfg_m, jump)
                    cfg_m.add_connector(cfg_0, jump)
                    connection = 1
                break
            if end_loop:
                break
        return connection, steps

    def step_to_block(self, cfg_0, cfg_m):

        steps = [cfg_0, cfg_m]

        p0 = cfg_0.positions[-1]
        pm = cfg_m.positions[-1]
        d = gm.distance(p0, pm)
        # print(d)
        # print(p0, pm)
        theta = math.atan2(float(pm[1] - p0[1]), (pm[0] - p0[0]))
        # print(theta)
        num_steps = int(math.ceil(d * 1.0 / self.MAX_STEP))
        # print(num_steps)

        while len(steps) - 1 < num_steps:
            for i in range(num_steps - 1):
                cfg_1 = steps[i]
                cfg_nxt = self.config_from_point(gm.point_from_polar(
                    cfg_1.positions[-1], self.MAX_STEP, theta))
                steps.insert(i + 1, cfg_nxt)

                if (not self.validator.fits_bounds(cfg_nxt)) \
                        or self.validator.has_collision(
                        cfg_nxt, self.obstacles):
                    print(i)
                    print("hit block or out of bounds")
                    print(cfg_nxt.positions[-1])
                    return cfg_nxt.positions[-1]

        # print(steps)
        # print(len(steps))
        return None

    def midpoint(self, cfg_0, cfg_1):
        coordinates = []
        angles = []
        # p00 = cfg_0.get_positions()[0]
        # p10 = cfg_1.get_positions()[0]
        # p_mid_0 = ((p00[0] + p10[0])*1.0/2, (p00[1] + p10[1])*1.0/2)
        # Assume same base position
        coordinates.append(cfg_0.get_position(0))
        thetas_0 = cfg_0.get_angles()
        thetas_1 = cfg_1.get_angles()
        delta_thetas = self.delta_thetas(thetas_0, thetas_1)
        phi = 0
        for i in range(len(thetas_0)):
            p_ref = coordinates[i]
            # Rotation = preceding angle for mid config + this angle for
            # previous config + change in this angle
            theta_mid = thetas_0[i] + delta_thetas[i] * 1.0 / 2
            angles.append(theta_mid)
            phi += theta_mid
            p_mid = (p_ref[0] + self.LENGTHS[i] * math.cos(math.radians(phi)),
                     p_ref[1] + self.LENGTHS[i] * math.sin(math.radians(phi)))
            coordinates.append(p_mid)
        return RobotConfig(coordinates, angles)

    def delta_thetas(self, thetas_0, thetas_1):
        delta_thetas = []
        for i in range(self.N - 1):
            delta_theta = thetas_1[i] - thetas_0[i]
            if i == 0:
                delta_theta = self.normalise_angle(delta_theta)
            delta_thetas.append(delta_theta)
        return delta_thetas

    @staticmethod
    def normalise_angle(angle):
        """
        Normalises an angle to the range (-180, 180]
        :param angle: the angle to normalise
        :return: the normalised angle
        """
        while angle <= -180.0:
            angle += 2 * 180.0
        while angle > 180.0:
            angle -= 2 * 180.0
        return angle

    def get_end_state(self, state, index=0):
        """
        Get an end state where 
            state = 0 means puck
            state = 1 means goal

        if there are more than one puck or goal, index can
        be used to get the state of the i'th puck or goal
        """
        if state == 0:
            p = self.scene.pucks[index].shape
        elif state == 1:
            p = self.scene.holes[index].shape
        else:
            return None
        return self.config_from_point(p.centre)

    def visualise_graph(self):
        plt.ylim((-200, 400))
        plt.xlim((-400, 400))
        plotted = []
        for config in self.configs:
            end_pos1 = config.positions[-1]
            for config2 in config.get_connectors().keys():
                end_pos2 = config2.positions[-1]
                if end_pos2 not in plotted:
                    connection = np.array((end_pos1, end_pos2))
                    plt.plot(connection[:, 0], connection[:, 1], color='black',
                             marker='8', linewidth=0.5)
            plotted.append(end_pos1)
        plt.show()

    @staticmethod
    def find_puck_goal_mapping(costs):
        print("Planner: path costs:\n", costs)
        perms = permutations(range(len(costs[0])), len(costs))
        endCosts = []
        permList = []
        permCostList = []
        for i in perms:
            permList.append(i)
            permCosts = []
            for j in range(len(costs)):
                permCosts.append(costs[j][i[j]])

            if None in permCosts:
                endCosts.append(None)
            else:
                endCosts.append(sum(permCosts))

            permCostList.append(permCosts)

        minIndex = None
        minValue = sys.float_info.max
        for x in range(len(endCosts)):
            if endCosts[x] is None:
                continue
            if endCosts[x] < minValue:
                minIndex = x
                minValue = endCosts[x]

        if minIndex is None:
            return None
        return permList[minIndex], permCostList[minIndex]
Esempio n. 6
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class Simulator(object):

    def __init__(self):
        self.fig = plt.figure()
        self.ax = self.fig.add_subplot(111)
        # self.fig, self.ax = plt.subplots()
        self.robot = Robot()
        self.obstacles = []
        self.goals = []
        self.pucks = []

        self.endPoints = None
        self.elbowPoints = None
        self.pathPoints = None
        self.paths = []

        self.pathColour = 'black'
        self.goalColour = 'cyan'
        self.puckColour = 'gray'
        self.obstacleColour = 'red'
        self.workspaceFeatures = []
        self.workspaceColour = 'green'
        self.armColour = 'black'

        # plt.ion()

    def add_goal(self, xy, radius):
        circle = Circle(xy, radius)
        self.goals.append(circle)

    def add_puck(self, xy, radius):
        circle = Circle(xy, radius)
        self.pucks.append(circle)

    def add_obstacle_polygon(self, points):
        self.obstacles.append(Polygon(points))

    def add_obstacle_circle(self, xy, radius):
        circle = Circle(xy, radius)
        self.obstacles.append(circle)

    def set_axis_limits(self, x_limits, y_limits):
        plt.ylim(y_limits)
        plt.xlim(x_limits)

    def add_workspace(self, width, height):
        xleft = 0.0 - width/2
        xright = 0.0 + width/2
        ylower = 0.0
        yupper = height
        points = np.array([[xleft, ylower], [xright, ylower], [xright, yupper],
                           [xleft, yupper]])
        self.workspaceFeatures.append(Polygon(points))

    def add_arm(self, theta1, theta2, theta3=0):
        self.elbowPoints = self.robot.get_elbow_position(theta1)
        self.endPoints = self.robot.forward_kinematics(theta1, theta2, theta3)[0:2]
        
    def add_path(self, path):
        self.paths.append(path)

    def set_scene(self, scene=None):
        for puck in scene.pucks:
            self.add_puck(puck.shape.centre, puck.shape.radius)
        for hole in scene.holes:
            self.add_goal(hole.shape.centre, hole.shape.radius)

        for block in scene.blocks:
            shape = block.shape
            if shape is None:
                continue
            if shape.type == "circle":
                self.add_obstacle_circle(shape.centre, shape.radius)
            else:
                vertices = np.array([list(v) for v in shape.vertices])
                self.add_obstacle_polygon(vertices)

    def show_figure(self):
        # plt.figure(1)
        # plt.clf()
        # plt.close()

        # self.set_axis_limits((-400.0, 400.0), (-200.0, 400.0))
        # self.add_workspace(WorkspaceSettings.WIDTH, WorkspaceSettings.HEIGHT)
        # self.set_scene()

        # self.add_arm(180.0, -90.0, 0.0)

        # if len(self.paths) == 0:
        #      plt.close()
        p = PatchCollection(self.workspaceFeatures, alpha=0.1,
                            color=self.workspaceColour, edgecolor='black')
        self.ax.add_collection(p)

        p = PatchCollection(self.obstacles, alpha=0.9,
                            color=self.obstacleColour, edgecolor='black')
        self.ax.add_collection(p)

        p = PatchCollection(self.goals, alpha=0.9, color=self.goalColour,
                            edgecolor='black')
        self.ax.add_collection(p)

        p = PatchCollection(self.pucks, alpha=0.9, color=self.puckColour,
                            edgecolor='black')
        self.ax.add_collection(p)

        if len(self.paths) > 0:
            i = 0
            for path in self.paths:
                plt.plot(path[:, 0], path[:, 1],
                         color=COLORS[i], solid_capstyle='round', alpha=0.2,
                         linewidth=BlockSettings.PUCK_DIAMETER/2)
                plt.plot(path[:, 0], path[:, 1],
                         color=self.armColour, linestyle='--', linewidth=2)
                i += 1

        if self.elbowPoints is not None:
            plt.plot([0, self.elbowPoints[0], self.endPoints[0]],
                     [-150, self.elbowPoints[1], self.endPoints[1]],
                     color=self.armColour, linestyle='-', linewidth=5)
        # plt.pause(0.00001)
        # self.fig.canvas.draw()
        # plt.draw()
        # plt.pause(1)
        
        plt.show()