How can I change the function calc_obstacle_map(self, ox, oy) to get an equivalent result that runs as fast as possible? The time complexity of O(n³) takes a huge amount of time to calculate the obstacle map for bigger arrays. I'm glad about every hint to improve the running time, including a version of this code with numpy arrays.

import math
import matplotlib.pyplot as plt
import numpy as np

show_animation = True

class AStarPlanner:

    def __init__(self, ox, oy, resolution, rr):
        Initialize grid map for a star planning

        ox: x position list of Obstacles [m]
        oy: y position list of Obstacles [m]
        resolution: grid resolution [m]
        rr: robot radius[m]

        self.resolution = resolution
        self.rr = rr
        self.min_x, self.min_y = 0, 0
        self.max_x, self.max_y = 0, 0
        self.obstacle_map = None
        self.x_width, self.y_width = 0, 0
        self.motion = self.get_motion_model()
        self.calc_obstacle_map(ox, oy)

    class Node:
        def __init__(self, x, y, cost, parent_index):
            self.x = x  # index of grid
            self.y = y  # index of grid
            self.cost = cost
            self.parent_index = parent_index

        def __str__(self):
            return str(self.x) + "," + str(self.y) + "," + str(
                self.cost) + "," + str(self.parent_index)

    def planning(self, sx, sy, gx, gy):
        A star path search

            s_x: start x position [m]
            s_y: start y position [m]
            gx: goal x position [m]
            gy: goal y position [m]

            rx: x position list of the final path
            ry: y position list of the final path

        start_node = self.Node(self.calc_xy_index(sx, self.min_x),
                               self.calc_xy_index(sy, self.min_y), 0.0, -1)
        goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
                              self.calc_xy_index(gy, self.min_y), 0.0, -1)

        open_set, closed_set = dict(), dict()
        open_set[self.calc_grid_index(start_node)] = start_node

        while 1:
            if len(open_set) == 0:
                print("Open set is empty..")

            c_id = min(
                key=lambda o: open_set[o].cost + self.calc_heuristic(goal_node,
            current = open_set[c_id]

            # show graph
            if show_animation:  # pragma: no cover
                plt.plot(self.calc_grid_position(current.x, self.min_x),
                         self.calc_grid_position(current.y, self.min_y), ".c")
                # for stopping simulation with the esc key.
                                             lambda event: [exit(
                                                 0) if event.key == 'escape' else None])
                #if len(closed_set.keys()) % 10 == 0:

            if current.x == goal_node.x and current.y == goal_node.y:
                print("Find goal")
                goal_node.parent_index = current.parent_index
                goal_node.cost = current.cost

            # Remove the item from the open set
            del open_set[c_id]

            # Add it to the closed set
            closed_set[c_id] = current

            # expand_grid search grid based on motion model
            for i, _ in enumerate(self.motion):
                node = self.Node(current.x + self.motion[i][0],
                                 current.y + self.motion[i][1],
                                 current.cost + self.motion[i][2], c_id)
                n_id = self.calc_grid_index(node)

                # If the node is not safe, do nothing
                if not self.verify_node(node):

                if n_id in closed_set:

                if n_id not in open_set:
                    open_set[n_id] = node  # discovered a new node
                    if open_set[n_id].cost > node.cost:
                        # This path is the best until now. record it
                        open_set[n_id] = node

        rx, ry = self.calc_final_path(goal_node, closed_set)

        return rx, ry

    def calc_final_path(self, goal_node, closed_set):
        # generate final course
        rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], [
            self.calc_grid_position(goal_node.y, self.min_y)]
        parent_index = goal_node.parent_index
        while parent_index != -1:
            n = closed_set[parent_index]
            rx.append(self.calc_grid_position(n.x, self.min_x))
            ry.append(self.calc_grid_position(n.y, self.min_y))
            parent_index = n.parent_index

        return rx, ry

    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 calc_grid_position(self, index, min_position):
        calc grid position

        :param index:
        :param min_position:
        pos = index * self.resolution + min_position
        return pos

    def calc_xy_index(self, position, min_pos):
        return round((position - min_pos) / self.resolution)

    def calc_grid_index(self, node):
        return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)

    def verify_node(self, node):
        px = self.calc_grid_position(node.x, self.min_x)
        py = self.calc_grid_position(node.y, self.min_y)

        if px < self.min_x:
            return False
        elif py < self.min_y:
            return False
        elif px >= self.max_x:
            return False
        elif py >= self.max_y:
            return False

        # collision check
        if self.obstacle_map[node.x][node.y]:
            return False

        return True

    def calc_obstacle_map(self, ox, oy):

        self.min_x = round(min(ox))
        self.min_y = round(min(oy))
        self.max_x = round(max(ox))
        self.max_y = round(max(oy))
        print("min_x:", self.min_x)
        print("min_y:", self.min_y)
        print("max_x:", self.max_x)
        print("max_y:", self.max_y)

        self.x_width = round((self.max_x - self.min_x) / self.resolution)
        self.y_width = round((self.max_y - self.min_y) / self.resolution)
        print("x_width:", self.x_width)
        print("y_width:", self.y_width)

        # obstacle map generation
        self.obstacle_map = [[False for _ in range(self.y_width)]
                             for _ in range(self.x_width)]
        for ix in range(self.x_width):
            x = self.calc_grid_position(ix, self.min_x)
            for iy in range(self.y_width):
                y = self.calc_grid_position(iy, self.min_y)
                for iox, ioy in zip(ox, oy):
                    d = math.hypot(iox - x, ioy - y)
                    if d <= self.rr:
                        self.obstacle_map[ix][iy] = True

    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):
    for i in range(-10, 60):
    for i in range(-10, 61):
    for i in range(-10, 61):
    for i in range(-10, 40):
    for i in range(0, 40):
        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, "xb")

    a_star = AStarPlanner(ox, oy, grid_size, robot_radius)
    rx, ry = a_star.planning(sx, sy, gx, gy)

    if show_animation:  # pragma: no cover
        plt.plot(rx, ry, "-r")

if __name__ == '__main__':

1 Answer 1


One idea that occurs to me is that you appear to be using circles to determine where your obstacles interfere with the grid cells.

Since the radius of the circle is the same for all obstacles (self.rr), why not simply compute the offsets of a circle with that radius, and store it?

If the robot radius can be changed, you may have to compute it once during your function. But if the radius is really a constant, you might be able to compute it now and store it as source code.

Something like:

def compute_robot_radius(self):
    """ Compute and store table of offsets of cells within a robot's radius.
    self.robot_radius = []
    for x in range(-self.rr, self.rr + 1):
        for y in range(-self.rr, self.rr + 1):
            if math.hypot(x, y) < self.rr:
               self.robot_radius.append((x, y))

Then you could just iterate over the obstacles, marking the cells according to the list you have pre-computed:

    obstacles = zip(ox, oy)
    for ox, oy in obstacles:
        for dx, dy in self.robot_radius:
            self.obstacle_map[ox + dx][oy + dy] = True

  • \$\begingroup\$ I think you could use a circle drawing algorithm in the first part of the code to just mark the perimeter of the circle. Because the bot would have to go thru the perimeter to get to the inside points. It would save work proportional to the size of the robot times the number of obstacles. \$\endgroup\$
    – RootTwo
    Jan 31, 2021 at 3:25
  • \$\begingroup\$ @RootTwo That would work as long as no diagonal paths are available into the circle. \$\endgroup\$
    – aghast
    Jan 31, 2021 at 21:03
  • \$\begingroup\$ Yes, you would need to modify the circle drawing routine to block the diagonal paths too. When ever the "slow" coordinate changes, also fill in a extra square to block the diagonal path. \$\endgroup\$
    – RootTwo
    Feb 1, 2021 at 7:44

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