mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
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348 lines
11 KiB
Python
348 lines
11 KiB
Python
"""
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Bidirectional A* grid planning
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author: Erwin Lejeune (@spida_rwin)
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See Wikipedia article (https://en.wikipedia.org/wiki/Bidirectional_search)
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"""
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import math
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import matplotlib.pyplot as plt
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show_animation = True
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class BidirectionalAStarPlanner:
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def __init__(self, ox, oy, resolution, rr):
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"""
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Initialize grid map for a star planning
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ox: x position list of Obstacles [m]
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oy: y position list of Obstacles [m]
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resolution: grid resolution [m]
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rr: robot radius[m]
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"""
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self.min_x, self.min_y = None, None
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self.max_x, self.max_y = None, None
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self.x_width, self.y_width, self.obstacle_map = None, None, None
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self.resolution = resolution
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self.rr = rr
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self.calc_obstacle_map(ox, oy)
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self.motion = self.get_motion_model()
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class Node:
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def __init__(self, x, y, cost, parent_index):
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self.x = x # index of grid
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self.y = y # index of grid
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self.cost = cost
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self.parent_index = parent_index
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def __str__(self):
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return str(self.x) + "," + str(self.y) + "," + str(
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self.cost) + "," + str(self.parent_index)
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def planning(self, sx, sy, gx, gy):
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"""
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Bidirectional A star path search
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input:
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s_x: start x position [m]
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s_y: start y position [m]
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gx: goal x position [m]
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gy: goal y position [m]
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output:
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rx: x position list of the final path
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ry: y position list of the final path
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"""
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start_node = self.Node(self.calc_xy_index(sx, self.min_x),
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self.calc_xy_index(sy, self.min_y), 0.0, -1)
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goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
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self.calc_xy_index(gy, self.min_y), 0.0, -1)
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open_set_A, closed_set_A = dict(), dict()
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open_set_B, closed_set_B = dict(), dict()
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open_set_A[self.calc_grid_index(start_node)] = start_node
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open_set_B[self.calc_grid_index(goal_node)] = goal_node
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current_A = start_node
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current_B = goal_node
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meet_point_A, meet_point_B = None, None
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while True:
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if len(open_set_A) == 0:
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print("Open set A is empty..")
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break
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if len(open_set_B) == 0:
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print("Open set B is empty..")
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break
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c_id_A = min(
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open_set_A,
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key=lambda o: self.find_total_cost(open_set_A, o, current_B))
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current_A = open_set_A[c_id_A]
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c_id_B = min(
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open_set_B,
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key=lambda o: self.find_total_cost(open_set_B, o, current_A))
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current_B = open_set_B[c_id_B]
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# show graph
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if show_animation: # pragma: no cover
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plt.plot(self.calc_grid_position(current_A.x, self.min_x),
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self.calc_grid_position(current_A.y, self.min_y),
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"xc")
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plt.plot(self.calc_grid_position(current_B.x, self.min_x),
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self.calc_grid_position(current_B.y, self.min_y),
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"xc")
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# for stopping simulation with the esc key.
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plt.gcf().canvas.mpl_connect(
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'key_release_event',
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lambda event: [exit(0) if event.key == 'escape' else None])
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if len(closed_set_A.keys()) % 10 == 0:
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plt.pause(0.001)
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if current_A.x == current_B.x and current_A.y == current_B.y:
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print("Found goal")
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meet_point_A = current_A
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meet_point_B = current_B
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break
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# Remove the item from the open set
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del open_set_A[c_id_A]
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del open_set_B[c_id_B]
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# Add it to the closed set
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closed_set_A[c_id_A] = current_A
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closed_set_B[c_id_B] = current_B
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# expand_grid search grid based on motion model
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for i, _ in enumerate(self.motion):
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c_nodes = [self.Node(current_A.x + self.motion[i][0],
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current_A.y + self.motion[i][1],
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current_A.cost + self.motion[i][2],
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c_id_A),
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self.Node(current_B.x + self.motion[i][0],
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current_B.y + self.motion[i][1],
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current_B.cost + self.motion[i][2],
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c_id_B)]
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n_ids = [self.calc_grid_index(c_nodes[0]),
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self.calc_grid_index(c_nodes[1])]
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# If the node is not safe, do nothing
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continue_ = self.check_nodes_and_sets(c_nodes, closed_set_A,
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closed_set_B, n_ids)
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if not continue_[0]:
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if n_ids[0] not in open_set_A:
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# discovered a new node
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open_set_A[n_ids[0]] = c_nodes[0]
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else:
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if open_set_A[n_ids[0]].cost > c_nodes[0].cost:
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# This path is the best until now. record it
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open_set_A[n_ids[0]] = c_nodes[0]
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if not continue_[1]:
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if n_ids[1] not in open_set_B:
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# discovered a new node
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open_set_B[n_ids[1]] = c_nodes[1]
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else:
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if open_set_B[n_ids[1]].cost > c_nodes[1].cost:
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# This path is the best until now. record it
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open_set_B[n_ids[1]] = c_nodes[1]
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rx, ry = self.calc_final_bidirectional_path(
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meet_point_A, meet_point_B, closed_set_A, closed_set_B)
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return rx, ry
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# takes two sets and two meeting nodes and return the optimal path
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def calc_final_bidirectional_path(self, n1, n2, setA, setB):
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rx_A, ry_A = self.calc_final_path(n1, setA)
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rx_B, ry_B = self.calc_final_path(n2, setB)
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rx_A.reverse()
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ry_A.reverse()
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rx = rx_A + rx_B
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ry = ry_A + ry_B
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return rx, ry
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def calc_final_path(self, goal_node, closed_set):
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# generate final course
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rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], \
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[self.calc_grid_position(goal_node.y, self.min_y)]
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parent_index = goal_node.parent_index
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while parent_index != -1:
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n = closed_set[parent_index]
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rx.append(self.calc_grid_position(n.x, self.min_x))
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ry.append(self.calc_grid_position(n.y, self.min_y))
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parent_index = n.parent_index
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return rx, ry
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def check_nodes_and_sets(self, c_nodes, closedSet_A, closedSet_B, n_ids):
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continue_ = [False, False]
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if not self.verify_node(c_nodes[0]) or n_ids[0] in closedSet_A:
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continue_[0] = True
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if not self.verify_node(c_nodes[1]) or n_ids[1] in closedSet_B:
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continue_[1] = True
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return continue_
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@staticmethod
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def calc_heuristic(n1, n2):
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w = 1.0 # weight of heuristic
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d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
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return d
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def find_total_cost(self, open_set, lambda_, n1):
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g_cost = open_set[lambda_].cost
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h_cost = self.calc_heuristic(n1, open_set[lambda_])
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f_cost = g_cost + h_cost
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return f_cost
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def calc_grid_position(self, index, min_position):
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"""
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calc grid position
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:param index:
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:param min_position:
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:return:
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"""
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pos = index * self.resolution + min_position
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return pos
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def calc_xy_index(self, position, min_pos):
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return round((position - min_pos) / self.resolution)
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def calc_grid_index(self, node):
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return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
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def verify_node(self, node):
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px = self.calc_grid_position(node.x, self.min_x)
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py = self.calc_grid_position(node.y, self.min_y)
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if px < self.min_x:
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return False
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elif py < self.min_y:
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return False
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elif px >= self.max_x:
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return False
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elif py >= self.max_y:
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return False
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# collision check
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if self.obstacle_map[node.x][node.y]:
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return False
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return True
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def calc_obstacle_map(self, ox, oy):
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self.min_x = round(min(ox))
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self.min_y = round(min(oy))
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self.max_x = round(max(ox))
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self.max_y = round(max(oy))
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print("min_x:", self.min_x)
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print("min_y:", self.min_y)
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print("max_x:", self.max_x)
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print("max_y:", self.max_y)
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self.x_width = round((self.max_x - self.min_x) / self.resolution)
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self.y_width = round((self.max_y - self.min_y) / self.resolution)
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print("x_width:", self.x_width)
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print("y_width:", self.y_width)
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# obstacle map generation
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self.obstacle_map = [[False for _ in range(self.y_width)]
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for _ in range(self.x_width)]
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for ix in range(self.x_width):
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x = self.calc_grid_position(ix, self.min_x)
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for iy in range(self.y_width):
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y = self.calc_grid_position(iy, self.min_y)
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for iox, ioy in zip(ox, oy):
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d = math.hypot(iox - x, ioy - y)
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if d <= self.rr:
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self.obstacle_map[ix][iy] = True
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break
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@staticmethod
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def get_motion_model():
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# dx, dy, cost
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motion = [[1, 0, 1],
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[0, 1, 1],
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[-1, 0, 1],
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[0, -1, 1],
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[-1, -1, math.sqrt(2)],
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[-1, 1, math.sqrt(2)],
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[1, -1, math.sqrt(2)],
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[1, 1, math.sqrt(2)]]
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return motion
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def main():
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print(__file__ + " start!!")
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# start and goal position
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sx = 10.0 # [m]
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sy = 10.0 # [m]
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gx = 50.0 # [m]
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gy = 50.0 # [m]
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grid_size = 2.0 # [m]
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robot_radius = 1.0 # [m]
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# set obstacle positions
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ox, oy = [], []
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for i in range(-10, 60):
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ox.append(i)
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oy.append(-10.0)
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for i in range(-10, 60):
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ox.append(60.0)
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oy.append(i)
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for i in range(-10, 61):
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ox.append(i)
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oy.append(60.0)
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for i in range(-10, 61):
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ox.append(-10.0)
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oy.append(i)
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for i in range(-10, 40):
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ox.append(20.0)
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oy.append(i)
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for i in range(0, 40):
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ox.append(40.0)
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oy.append(60.0 - i)
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if show_animation: # pragma: no cover
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plt.plot(ox, oy, ".k")
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plt.plot(sx, sy, "og")
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plt.plot(gx, gy, "ob")
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plt.grid(True)
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plt.axis("equal")
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bidir_a_star = BidirectionalAStarPlanner(ox, oy, grid_size, robot_radius)
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rx, ry = bidir_a_star.planning(sx, sy, gx, gy)
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if show_animation: # pragma: no cover
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plt.plot(rx, ry, "-r")
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plt.pause(.0001)
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plt.show()
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if __name__ == '__main__':
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main()
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