Merge pull request AtsushiSakai#313 from Guilyx/bidir-astar

Bidirectional A*

Author: AtsushiSakai

PathPlanning/AStar/a_star.py

@@ -271,6 +271,7 @@ def main():
     if show_animation:  # pragma: no cover
         plt.plot(rx, ry, "-r")
         plt.show()
+        plt.pause(0.001)
 
 
 if __name__ == '__main__':

PathPlanning/BidirectionalAStar/bidirectional_a_star.py

@@ -0,0 +1,342 @@
+"""
+
+Bidirectional A* grid planning
+
+author: Erwin Lejeune (@spida_rwin)
+
+See Wikipedia article (https://en.wikipedia.org/wiki/Bidirectional_search)
+
+"""
+
+import math
+
+import matplotlib.pyplot as plt
+
+show_animation = True
+
+
+class BidirectionalAStarPlanner:
+
+    def __init__(self, ox, oy, reso, rr):
+        """
+        Initialize grid map for a star planning
+
+        ox: x position list of Obstacles [m]
+        oy: y position list of Obstacles [m]
+        reso: grid resolution [m]
+        rr: robot radius[m]
+        """
+
+        self.reso = reso
+        self.rr = rr
+        self.calc_obstacle_map(ox, oy)
+        self.motion = self.get_motion_model()
+
+    class Node:
+        def __init__(self, x, y, cost, pind):
+            self.x = x  # index of grid
+            self.y = y  # index of grid
+            self.cost = cost
+            self.pind = pind
+
+        def __str__(self):
+            return str(self.x) + "," + str(self.y) + "," + str(
+                self.cost) + "," + str(self.pind)
+
+    def planning(self, sx, sy, gx, gy):
+        """
+        Bidirectional A star path search
+
+        input:
+            sx: start x position [m]
+            sy: start y position [m]
+            gx: goal x position [m]
+            gy: goal y position [m]
+
+        output:
+            rx: x position list of the final path
+            ry: y position list of the final path
+        """
+
+        nstart = self.Node(self.calc_xyindex(sx, self.minx),
+                           self.calc_xyindex(sy, self.miny), 0.0, -1)
+        ngoal = self.Node(self.calc_xyindex(gx, self.minx),
+                          self.calc_xyindex(gy, self.miny), 0.0, -1)
+
+        open_set_A, closed_set_A = dict(), dict()
+        open_set_B, closed_set_B = dict(), dict()
+        open_set_A[self.calc_grid_index(nstart)] = nstart
+        open_set_B[self.calc_grid_index(ngoal)] = ngoal
+
+        current_A = nstart
+        current_B = ngoal
+
+        while 1:
+            if len(open_set_A) == 0:
+                print("Open set A is empty..")
+                break
+
+            if len(open_set_B) == 0:
+                print("Open set B is empty..")
+                break
+
+            c_id_A = min(
+                open_set_A,
+                key=lambda o: self.find_total_cost(open_set_A, o, current_B))
+
+            current_A = open_set_A[c_id_A]
+
+            c_id_B = min(
+                open_set_B,
+                key=lambda o: self.find_total_cost(open_set_B, o, current_A))
+
+            current_B = open_set_B[c_id_B]
+
+            # show graph
+            if show_animation:  # pragma: no cover
+                plt.plot(self.calc_grid_position(current_A.x, self.minx),
+                         self.calc_grid_position(current_A.y, self.miny), "xc")
+                plt.plot(self.calc_grid_position(current_B.x, self.minx),
+                         self.calc_grid_position(current_B.y, self.miny), "xc")
+                # for stopping simulation with the esc key.
+                plt.gcf().canvas.mpl_connect('key_release_event',
+                                             lambda event: [exit(
+                                                 0) if event.key == 'escape' else None])
+                if len(closed_set_A.keys()) % 10 == 0:
+                    plt.pause(0.001)
+
+            if current_A.x == current_B.x and current_A.y == current_B.y:
+                print("Found goal")
+                meetpointA = current_A
+                meetpointB = current_B
+                break
+
+            # Remove the item from the open set
+            del open_set_A[c_id_A]
+            del open_set_B[c_id_B]
+
+            # Add it to the closed set
+            closed_set_A[c_id_A] = current_A
+            closed_set_B[c_id_B] = current_B
+
+            # expand_grid search grid based on motion model
+            for i, _ in enumerate(self.motion):
+                continue_A = False
+                continue_B = False
+
+                child_node_A = self.Node(current_A.x + self.motion[i][0],
+                                         current_A.y + self.motion[i][1],
+                                         current_A.cost + self.motion[i][2], 
+                                         c_id_A)
+
+                child_node_B = self.Node(current_B.x + self.motion[i][0],
+                                         current_B.y + self.motion[i][1],
+                                         current_B.cost + self.motion[i][2], 
+                                         c_id_B)
+
+                n_id_A = self.calc_grid_index(child_node_A)
+                n_id_B = self.calc_grid_index(child_node_B)
+
+                # If the node is not safe, do nothing
+                if not self.verify_node(child_node_A):
+                    continue_A = True
+
+                if not self.verify_node(child_node_B):
+                    continue_B = True
+
+                if n_id_A in closed_set_A:
+                    continue_A = True
+
+                if n_id_B in closed_set_B:
+                    continue_B = True
+
+                if not continue_A:
+                    if n_id_A not in open_set_A:
+                        # discovered a new node
+                        open_set_A[n_id_A] = child_node_A
+                    else:
+                        if open_set_A[n_id_A].cost > child_node_A.cost:
+                            # This path is the best until now. record it
+                            open_set_A[n_id_A] = child_node_A
+
+                if not continue_B:
+                    if n_id_B not in open_set_B:
+                        # discovered a new node
+                        open_set_B[n_id_B] = child_node_B
+                    else:
+                        if open_set_B[n_id_B].cost > child_node_B.cost:
+                            # This path is the best until now. record it
+                            open_set_B[n_id_B] = child_node_B
+
+        rx, ry = self.calc_final_bidirectional_path(
+            meetpointA, meetpointB, closed_set_A, closed_set_B)
+
+        return rx, ry
+
+    def calc_final_bidirectional_path(self, meetnode_A, meetnode_B, closed_set_A, closed_set_B):
+        rx_A, ry_A = self.calc_final_path(meetnode_A, closed_set_A)
+        rx_B, ry_B = self.calc_final_path(meetnode_B, closed_set_B)
+
+        rx_A.reverse()
+        ry_A.reverse()
+
+        rx = rx_A + rx_B
+        ry = ry_A + ry_B
+
+        return rx, ry
+
+    def calc_final_path(self, ngoal, closedset):
+        # generate final course
+        rx, ry = [self.calc_grid_position(ngoal.x, self.minx)], [
+            self.calc_grid_position(ngoal.y, self.miny)]
+        pind = ngoal.pind
+        while pind != -1:
+            n = closedset[pind]
+            rx.append(self.calc_grid_position(n.x, self.minx))
+            ry.append(self.calc_grid_position(n.y, self.miny))
+            pind = n.pind
+
+        return rx, ry
+
+    @staticmethod
+    def calc_heuristic(n1, n2):
+        w = 1.0  # weight of heuristic
+        d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
+        return d
+
+    def find_total_cost(self, open_set, lambda_, n1):
+        g_cost = open_set[lambda_].cost
+        h_cost = self.calc_heuristic(n1, open_set[lambda_])
+        f_cost = g_cost + h_cost
+        return f_cost
+
+    def calc_grid_position(self, index, minp):
+        """
+        calc grid position
+
+        :param index:
+        :param minp:
+        :return:
+        """
+        pos = index * self.reso + minp
+        return pos
+
+    def calc_xyindex(self, position, min_pos):
+        return round((position - min_pos) / self.reso)
+
+    def calc_grid_index(self, node):
+        return (node.y - self.miny) * self.xwidth + (node.x - self.minx)
+
+    def verify_node(self, node):
+        px = self.calc_grid_position(node.x, self.minx)
+        py = self.calc_grid_position(node.y, self.miny)
+
+        if px < self.minx:
+            return False
+        elif py < self.miny:
+            return False
+        elif px >= self.maxx:
+            return False
+        elif py >= self.maxy:
+            return False
+
+        # collision check
+        if self.obmap[node.x][node.y]:
+            return False
+
+        return True
+
+    def calc_obstacle_map(self, ox, oy):
+
+        self.minx = round(min(ox))
+        self.miny = round(min(oy))
+        self.maxx = round(max(ox))
+        self.maxy = round(max(oy))
+        print("minx:", self.minx)
+        print("miny:", self.miny)
+        print("maxx:", self.maxx)
+        print("maxy:", self.maxy)
+
+        self.xwidth = round((self.maxx - self.minx) / self.reso)
+        self.ywidth = round((self.maxy - self.miny) / self.reso)
+        print("xwidth:", self.xwidth)
+        print("ywidth:", self.ywidth)
+
+        # obstacle map generation
+        self.obmap = [[False for _ in range(self.ywidth)]
+                      for _ in range(self.xwidth)]
+        for ix in range(self.xwidth):
+            x = self.calc_grid_position(ix, self.minx)
+            for iy in range(self.ywidth):
+                y = self.calc_grid_position(iy, self.miny)
+                for iox, ioy in zip(ox, oy):
+                    d = math.hypot(iox - x, ioy - y)
+                    if d <= self.rr:
+                        self.obmap[ix][iy] = True
+                        break
+
+    @staticmethod
+    def get_motion_model():
+        # dx, dy, cost
+        motion = [[1, 0, 1],
+                  [0, 1, 1],
+                  [-1, 0, 1],
+                  [0, -1, 1],
+                  [-1, -1, math.sqrt(2)],
+                  [-1, 1, math.sqrt(2)],
+                  [1, -1, math.sqrt(2)],
+                  [1, 1, math.sqrt(2)]]
+
+        return motion
+
+
+def main():
+    print(__file__ + " start!!")
+
+    # start and goal position
+    sx = 10.0  # [m]
+    sy = 10.0  # [m]
+    gx = 50.0  # [m]
+    gy = 50.0  # [m]
+    grid_size = 2.0  # [m]
+    robot_radius = 1.0  # [m]
+
+    # set obstacle positions
+    ox, oy = [], []
+    for i in range(-10, 60):
+        ox.append(i)
+        oy.append(-10.0)
+    for i in range(-10, 60):
+        ox.append(60.0)
+        oy.append(i)
+    for i in range(-10, 61):
+        ox.append(i)
+        oy.append(60.0)
+    for i in range(-10, 61):
+        ox.append(-10.0)
+        oy.append(i)
+    for i in range(-10, 40):
+        ox.append(20.0)
+        oy.append(i)
+    for i in range(0, 40):
+        ox.append(40.0)
+        oy.append(60.0 - i)
+
+    if show_animation:  # pragma: no cover
+        plt.plot(ox, oy, ".k")
+        plt.plot(sx, sy, "og")
+        plt.plot(gx, gy, "ob")
+        plt.grid(True)
+        plt.axis("equal")
+
+    bidir_a_star = BidirectionalAStarPlanner(ox, oy, grid_size, robot_radius)
+    rx, ry = bidir_a_star.planning(sx, sy, gx, gy)
+
+    if show_animation:  # pragma: no cover
+        plt.plot(rx, ry, "-r")
+        plt.pause(.0001)
+        plt.show()
+
+
+if __name__ == '__main__':
+    main()