Merge pull request AtsushiSakai#151 from toolleeo/improved_arm_obstacle_navigation__visualization

Added modified version of the arm obstacle avoidance simulation.

Author: AtsushiSakai

ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation_2.py

@@ -0,0 +1,277 @@
+"""
+Obstacle navigation using A* on a toroidal grid
+
+Author: Daniel Ingram (daniel-s-ingram)
+        Tullio Facchinetti ([email protected])
+"""
+from math import pi
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.colors import from_levels_and_colors
+import sys
+
+plt.ion()
+
+# Simulation parameters
+M = 100
+obstacles = [[1.75, 0.75, 0.6], [0.55, 1.5, 0.5], [0, -1, 0.7]]
+
+
+def press(event):
+    """Exit from the simulation."""
+    if event.key == 'q' or event.key == 'Q':
+        print('Quitting upon request.')
+        sys.exit(0)
+
+def main():
+    # Arm geometry in the working space
+    link_length = [0.5, 1.5]
+    initial_link_angle = [0, 0]
+    arm = NLinkArm(link_length, initial_link_angle)
+    # (x, y) co-ordinates in the joint space [cell]
+    start = (10, 50)
+    goal = (58, 56)
+    grid = get_occupancy_grid(arm, obstacles)
+    route = astar_torus(grid, start, goal)
+    if len(route) >= 0:
+        animate(grid, arm, route)
+
+
+def animate(grid, arm, route):
+    fig, axs = plt.subplots(1, 2)
+    fig.canvas.mpl_connect('key_press_event', press)
+    colors = ['white', 'black', 'red', 'pink', 'yellow', 'green', 'orange']
+    levels = [0, 1, 2, 3, 4, 5, 6, 7]
+    cmap, norm = from_levels_and_colors(levels, colors)
+    for i, node in enumerate(route):
+        plt.subplot(1, 2, 1)
+        grid[node] = 6
+        plt.cla()
+        plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
+        theta1 = 2 * pi * node[0] / M - pi
+        theta2 = 2 * pi * node[1] / M - pi
+        arm.update_joints([theta1, theta2])
+        plt.subplot(1, 2, 2)
+        arm.plot(plt, obstacles=obstacles)
+        plt.show()
+        # Uncomment here to save the sequence of frames
+        #plt.savefig('frame{:04d}.png'.format(i))
+        plt.pause(0.1)
+
+
+def detect_collision(line_seg, circle):
+    """
+    Determines whether a line segment (arm link) is in contact
+    with a circle (obstacle).
+    Credit to: http://doswa.com/2009/07/13/circle-segment-intersectioncollision.html
+    Args:
+        line_seg: List of coordinates of line segment endpoints e.g. [[1, 1], [2, 2]]
+        circle: List of circle coordinates and radius e.g. [0, 0, 0.5] is a circle centered
+                at the origin with radius 0.5
+
+    Returns:
+        True if the line segment is in contact with the circle
+        False otherwise
+    """
+    a_vec = np.array([line_seg[0][0], line_seg[0][1]])
+    b_vec = np.array([line_seg[1][0], line_seg[1][1]])
+    c_vec = np.array([circle[0], circle[1]])
+    radius = circle[2]
+    line_vec = b_vec - a_vec
+    line_mag = np.linalg.norm(line_vec)
+    circle_vec = c_vec - a_vec
+    proj = circle_vec.dot(line_vec / line_mag)
+    if proj <= 0:
+        closest_point = a_vec
+    elif proj >= line_mag:
+        closest_point = b_vec
+    else:
+        closest_point = a_vec + line_vec * proj / line_mag
+    if np.linalg.norm(closest_point - c_vec) > radius:
+        return False
+    else:
+        return True
+
+
+def get_occupancy_grid(arm, obstacles):
+    """
+    Discretizes joint space into M values from -pi to +pi
+    and determines whether a given coordinate in joint space
+    would result in a collision between a robot arm and obstacles
+    in its environment.
+
+    Args:
+        arm: An instance of NLinkArm
+        obstacles: A list of obstacles, with each obstacle defined as a list
+                   of xy coordinates and a radius. 
+
+    Returns:
+        Occupancy grid in joint space
+    """
+    grid = [[0 for _ in range(M)] for _ in range(M)]
+    theta_list = [2 * i * pi / M for i in range(-M // 2, M // 2 + 1)]
+    for i in range(M):
+        for j in range(M):
+            arm.update_joints([theta_list[i], theta_list[j]])
+            points = arm.points
+            collision_detected = False
+            for k in range(len(points) - 1):
+                for obstacle in obstacles:
+                    line_seg = [points[k], points[k + 1]]
+                    collision_detected = detect_collision(line_seg, obstacle)
+                    if collision_detected:
+                        break
+                if collision_detected:
+                    break
+            grid[i][j] = int(collision_detected)
+    return np.array(grid)
+
+
+def astar_torus(grid, start_node, goal_node):
+    """
+    Finds a path between an initial and goal joint configuration using
+    the A* Algorithm on a tororiadal grid.
+
+    Args:
+        grid: An occupancy grid (ndarray)
+        start_node: Initial joint configuation (tuple)
+        goal_node: Goal joint configuration (tuple)
+
+    Returns:
+        Obstacle-free route in joint space from start_node to goal_node
+    """
+    grid[start_node] = 4
+    grid[goal_node] = 5
+
+    parent_map = [[() for _ in range(M)] for _ in range(M)]
+
+    X, Y = np.meshgrid([i for i in range(M)], [i for i in range(M)])
+    heuristic_map = np.abs(X - goal_node[1]) + np.abs(Y - goal_node[0])
+    for i in range(heuristic_map.shape[0]):
+        for j in range(heuristic_map.shape[1]):
+            heuristic_map[i, j] = min(heuristic_map[i, j],
+                                      i + 1 + heuristic_map[M - 1, j],
+                                      M - i + heuristic_map[0, j],
+                                      j + 1 + heuristic_map[i, M - 1],
+                                      M - j + heuristic_map[i, 0]
+                                      )
+
+    explored_heuristic_map = np.full((M, M), np.inf)
+    distance_map = np.full((M, M), np.inf)
+    explored_heuristic_map[start_node] = heuristic_map[start_node]
+    distance_map[start_node] = 0
+    while True:
+        grid[start_node] = 4
+        grid[goal_node] = 5
+
+        current_node = np.unravel_index(
+            np.argmin(explored_heuristic_map, axis=None), explored_heuristic_map.shape)
+        min_distance = np.min(explored_heuristic_map)
+        if (current_node == goal_node) or np.isinf(min_distance):
+            break
+
+        grid[current_node] = 2
+        explored_heuristic_map[current_node] = np.inf
+
+        i, j = current_node[0], current_node[1]
+
+        neighbors = []
+        if i - 1 >= 0:
+            neighbors.append((i - 1, j))
+        else:
+            neighbors.append((M - 1, j))
+
+        if i + 1 < M:
+            neighbors.append((i + 1, j))
+        else:
+            neighbors.append((0, j))
+
+        if j - 1 >= 0:
+            neighbors.append((i, j - 1))
+        else:
+            neighbors.append((i, M - 1))
+
+        if j + 1 < M:
+            neighbors.append((i, j + 1))
+        else:
+            neighbors.append((i, 0))
+
+        for neighbor in neighbors:
+            if grid[neighbor] == 0 or grid[neighbor] == 5:
+                distance_map[neighbor] = distance_map[current_node] + 1
+                explored_heuristic_map[neighbor] = heuristic_map[neighbor]
+                parent_map[neighbor[0]][neighbor[1]] = current_node
+                grid[neighbor] = 3
+        '''
+        plt.cla()
+        plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
+        plt.show()
+        plt.pause(1e-5)
+        '''
+
+    if np.isinf(explored_heuristic_map[goal_node]):
+        route = []
+        print("No route found.")
+    else:
+        route = [goal_node]
+        while parent_map[route[0][0]][route[0][1]] is not ():
+            route.insert(0, parent_map[route[0][0]][route[0][1]])
+
+        print("The route found covers %d grid cells." % len(route))
+    return route
+
+
+class NLinkArm(object):
+    """
+    Class for controlling and plotting a planar arm with an arbitrary number of links.
+    """
+
+    def __init__(self, link_lengths, joint_angles):
+        self.n_links = len(link_lengths)
+        if self.n_links != len(joint_angles):
+            raise ValueError()
+
+        self.link_lengths = np.array(link_lengths)
+        self.joint_angles = np.array(joint_angles)
+        self.points = [[0, 0] for _ in range(self.n_links + 1)]
+
+        self.lim = sum(link_lengths)
+        self.update_points()
+
+    def update_joints(self, joint_angles):
+        self.joint_angles = joint_angles
+        self.update_points()
+
+    def update_points(self):
+        for i in range(1, self.n_links + 1):
+            self.points[i][0] = self.points[i - 1][0] + \
+                self.link_lengths[i - 1] * \
+                np.cos(np.sum(self.joint_angles[:i]))
+            self.points[i][1] = self.points[i - 1][1] + \
+                self.link_lengths[i - 1] * \
+                np.sin(np.sum(self.joint_angles[:i]))
+
+        self.end_effector = np.array(self.points[self.n_links]).T
+
+    def plot(self, myplt, obstacles=[]):
+        myplt.cla()
+
+        for obstacle in obstacles:
+            circle = myplt.Circle(
+                (obstacle[0], obstacle[1]), radius=0.5 * obstacle[2], fc='k')
+            myplt.gca().add_patch(circle)
+
+        for i in range(self.n_links + 1):
+            if i is not self.n_links:
+                myplt.plot([self.points[i][0], self.points[i + 1][0]],
+                         [self.points[i][1], self.points[i + 1][1]], 'r-')
+            myplt.plot(self.points[i][0], self.points[i][1], 'k.')
+
+        myplt.xlim([-self.lim, self.lim])
+        myplt.ylim([-self.lim, self.lim])
+        myplt.draw()
+        #myplt.pause(1e-5)
+
+
+if __name__ == '__main__':
+    main()