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    一文教你用python编写Dijkstra算法进行机器人路径规划

    前言

    为了机器人在寻路的过程中避障并且找到最短距离,我们需要使用一些算法进行路径规划(Path Planning),常用的算法有Djikstra算法、A*算法等等,在github上有一个非常好的项目叫做PythonRobotics,其中给出了源代码,参考代码,可以对Djikstra算法有更深的了解。

    一、算法原理

    如图所示,Dijkstra算法要解决的是一个有向权重图中最短路径的寻找问题,图中红色节点1代表起始节点,蓝色节点6代表目标结点。箭头上的数字代表两个结点中的的距离,也就是模型中所谓的代价(cost)。

    贪心算法需要设立两个集合,open_set(开集)和closed_set(闭集),然后根据以下程序进行操作:

    注意open_set中的代价是可变的,而closed_set中的代价已经是最小的代价了,这也是为什么叫做open和close的原因。

    至于为什么closed_set中的代价是最小的,是因为我们使用了贪心算法,既然已经把节点加入到了close中,那么初始点到close节点中的距离就比到open中的距离小了,无论如何也不可能找到比它更小的了。

    二、程序代码

    """
    
    Grid based Dijkstra planning
    
    author: Atsushi Sakai(@Atsushi_twi)
    
    """
    
    import matplotlib.pyplot as plt
    import math
    
    show_animation = True
    
    
    class Dijkstra:
    
        def __init__(self, ox, oy, resolution, robot_radius):
            """
            Initialize 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.min_x = None
            self.min_y = None
            self.max_x = None
            self.max_y = None
            self.x_width = None
            self.y_width = None
            self.obstacle_map = None
    
            self.resolution = resolution
            self.robot_radius = robot_radius
            self.calc_obstacle_map(ox, oy)
            self.motion = self.get_motion_model()
    
        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  # index of previous Node
    
            def __str__(self):
                return str(self.x) + "," + str(self.y) + "," + str(
                    self.cost) + "," + str(self.parent_index)
    
        def planning(self, sx, sy, gx, gy):
            """
            dijkstra path search
    
            input:
                s_x: start x position [m]
                s_y: start y position [m]
                gx: goal x position [m]
                gx: goal x position [m]
    
            output:
                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_index(start_node)] = start_node
    
            while 1:
                c_id = min(open_set, key=lambda o: open_set[o].cost)
                current = open_set[c_id]
    
                # show graph
                if show_animation:  # pragma: no cover
                    plt.plot(self.calc_position(current.x, self.min_x),
                             self.calc_position(current.y, self.min_y), "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.keys()) % 10 == 0:
                        plt.pause(0.001)
    
                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
                    break
    
                # Remove the item from the open set
                del open_set[c_id]
    
                # Add it to the closed set
                closed_set[c_id] = current
    
                # expand search grid based on motion model
                for move_x, move_y, move_cost in self.motion:
                    node = self.Node(current.x + move_x,
                                     current.y + move_y,
                                     current.cost + move_cost, c_id)
                    n_id = self.calc_index(node)
    
                    if n_id in closed_set:
                        continue
    
                    if not self.verify_node(node):
                        continue
    
                    if n_id not in open_set:
                        open_set[n_id] = node  # Discover a new node
                    else:
                        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_position(goal_node.x, self.min_x)], [
                self.calc_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_position(n.x, self.min_x))
                ry.append(self.calc_position(n.y, self.min_y))
                parent_index = n.parent_index
    
            return rx, ry
    
        def calc_position(self, index, minp):
            pos = index * self.resolution + minp
            return pos
    
        def calc_xy_index(self, position, minp):
            return round((position - minp) / self.resolution)
    
        def calc_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_position(node.x, self.min_x)
            py = self.calc_position(node.y, self.min_y)
    
            if px  self.min_x:
                return False
            if py  self.min_y:
                return False
            if px >= self.max_x:
                return False
            if py >= self.max_y:
                return False
    
            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_position(ix, self.min_x)
                for iy in range(self.y_width):
                    y = self.calc_position(iy, self.min_y)
                    for iox, ioy in zip(ox, oy):
                        d = math.hypot(iox - x, ioy - y)
                        if d = self.robot_radius:
                            self.obstacle_map[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 = -5.0  # [m]
        sy = -5.0  # [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, "xb")
            plt.grid(True)
            plt.axis("equal")
    
        dijkstra = Dijkstra(ox, oy, grid_size, robot_radius)
        rx, ry = dijkstra.planning(sx, sy, gx, gy)
    
        if show_animation:  # pragma: no cover
            plt.plot(rx, ry, "-r")
            plt.pause(0.01)
            plt.show()
    
    
    if __name__ == '__main__':
        main()
    
    

    三、运行结果

    四、 A*算法:Djikstra算法的改进

    Dijkstra算法实际上是贪心搜索算法,算法复杂度为O( n 2 n^2 n2),为了减少无效搜索的次数,我们可以增加一个启发式函数(heuristic),比如搜索点到终点目标的距离,在选择open_set元素的时候,我们将cost变成cost+heuristic,就可以给出搜索的方向性,这样就可以减少南辕北辙的情况。我们可以run一下PythonRobotics中的Astar代码,得到以下结果:

    总结

    到此这篇关于python编写Dijkstra算法进行机器人路径规划的文章就介绍到这了,更多相关python写Dijkstra算法内容请搜索脚本之家以前的文章或继续浏览下面的相关文章希望大家以后多多支持脚本之家!

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