请用python语言写一段双向RRT路径规划算法

好的，下面是一个简单的双向 RRT（Rapidly-exploring Random Tree）路径规划算法的 Python 实现：

import numpy as np
import matplotlib.pyplot as plt

# 定义节点类
class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.parent = None

# 定义 RRT 类
class RRT:
    def __init__(self, start, goal, obstacle_list, step_size=0.1, max_iter=500):
        self.start = Node(*start)
        self.goal = Node(*goal)
        self.obstacle_list = obstacle_list
        self.step_size = step_size
        self.max_iter = max_iter
        self.node_list = [self.start]

    # 判断是否与障碍物相交
    def is_collision(self, n1, n2):
        for (ox, oy, size) in self.obstacle_list:
            dx = n2.x - n1.x
            dy = n2.y - n1.y
            d = np.hypot(dx, dy)
            if d == 0:
                return True
            if size >= d:
                return True
            theta = np.arctan2(dy, dx)
            nx = n1.x + size * np.cos(theta)
            ny = n1.y + size * np.sin(theta)
            if (ox - nx)**2 + (oy - ny)**2 <= size**2:
                return True
        return False

    # 根据目标点生成随机点
    def get_random_node(self):
        if np.random.rand() < 0.5:
            return Node(np.random.uniform(-5, 5), np.random.uniform(-5, 5))
        else:
            return Node(self.goal.x, self.goal.y)

    # 寻找最近的节点
    def nearest_node(self, n):
        dlist = [(node.x - n.x)**2 + (node.y - n.y)**2 for node in self.node_list]
        return self.node_list[np.argmin(dlist)]

    # 扩展树
    def expand_tree(self, n):
        new_node = Node(n.x, n.y)
        theta = np.random.uniform(-np.pi, np.pi)
        new_node.x += self.step_size * np.cos(theta)
        new_node.y += self.step_size * np.sin(theta)
        new_node.parent = n
        if not self.is_collision(n, new_node):
            self.node_list.append(new_node)

    # 搜索路径
    def search_path(self):
        for i in range(self.max_iter):
            rnd_node = self.get_random_node()
            nearest_node = self.nearest_node(rnd_node)
            self.expand_tree(nearest_node)
            # 反向搜索
            rnd_node = self.get_random_node()
            nearest_node = self.nearest_node(rnd_node)
            self.expand_tree(nearest_node)

            # 检查是否到达目标点
            dx = self.node_list[-1].x - self.goal.x
            dy = self.node_list[-1].y - self.goal.y
            d = np.hypot(dx, dy)
            if d <= self.step_size:
                return self.generate_path(len(self.node_list) - 1)

        return None

    # 生成路径
    def generate_path(self, goal_index):
        path = [[self.goal.x, self.goal.y]]
        node = self.node_list[goal_index]
        while node.parent is not None:
            path.append([node.x, node.y])
            node = node.parent
        path.append([node.x, node.y])
        return np.array(path)

# 测试
def main():
    obstacle_list = [(1, 1, 1), (2, 3, 1), (4, 4, 1), (4, 2, 1)]
    start = (-4, -4)
    goal = (4, 4)
    rrt = RRT(start, goal, obstacle_list)
    path = rrt.search_path()

    if path is None:
        print("No path found")
    else:
        print("Found path with %d nodes" % len(path))
        plt.plot(path[:,0], path[:,1], '-r')
        for (ox, oy, size) in obstacle_list:
            circle = plt.Circle((ox, oy), size, color='k')
            plt.gca().add_patch(circle)
        plt.axis('equal')
        plt.show()

if __name__ == '__main__':
    main()

这个实现是基于 Python 的 NumPy 和 Matplotlib 库的。其中，Node 类表示节点，RRT 类表示 RRT 路径规划算法，包括判断是否与障碍物相交、生成随机点、寻找最近的节点、扩展树、搜索路径和生成路径等方法。在主函数中，我们定义了起点、终点和障碍物列表，然后创建 RRT 实例并搜索路径，最后绘制路径和障碍物。