rrt*-connect的python代码

### 回答1：
rrt*-connect是一种路径规划算法，用于在给定的环境中找到两个已知点之间的最优路径。下面是一个基于Python语言实现的简单示例代码：

import numpy as np
import matplotlib.pyplot as plt

# 初始化rrt*-connect算法的节点类
class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.parent = None

# 计算两个节点之间的距离
def distance(node1, node2):
    return np.sqrt((node1.x - node2.x)**2 + (node1.y - node2.y)**2)

# 检查两个节点之间是否存在障碍物
def check_obstacle(node1, node2, obstacle_list):
    for obstacle in obstacle_list:
        distance_to_obstacle = np.sqrt((obstacle[0] - node1.x)**2 + (obstacle[1] - node1.y)**2)
        if distance_to_obstacle <= 1.0:
            return True

    return False

# 使用rrt*-connect算法搜索路径
def rrt_connect(start, goal, obstacle_list):
    nodes_start = [start]
    nodes_goal = [goal]

    while True:
        # 从起点开始扩展树
        random_node = Node(np.random.uniform(0, 10), np.random.uniform(0, 10))
        nearest_node = nodes_start[0]
        for node in nodes_start:
            if distance(node, random_node) < distance(nearest_node, random_node):
                nearest_node = node
        
        if check_obstacle(nearest_node, random_node, obstacle_list):
            continue

        new_node = Node(random_node.x, random_node.y)
        new_node.parent = nearest_node
        nodes_start.append(new_node)

        # 从终点开始扩展树
        random_node = Node(np.random.uniform(0, 10), np.random.uniform(0, 10))
        nearest_node = nodes_goal[0]
        for node in nodes_goal:
            if distance(node, random_node) < distance(nearest_node, random_node):
                nearest_node = node
        
        if check_obstacle(nearest_node, random_node, obstacle_list):
            continue

        new_node = Node(random_node.x, random_node.y)
        new_node.parent = nearest_node
        nodes_goal.append(new_node)

        # 检查两颗树是否连接
        for node1 in nodes_start:
            for node2 in nodes_goal:
                if distance(node1, node2) <= 1.0 and not check_obstacle(node1, node2, obstacle_list):
                    return nodes_start, nodes_goal
    
    return None, None

# 测试代码
start_node = Node(1, 1)
goal_node = Node(9, 9)
obstacles = [(5, 5), (6, 6), (7, 7)]

path_start, path_goal = rrt_connect(start_node, goal_node, obstacles)

if path_start is not None and path_goal is not None:
    path_start.append(path_goal[-1])
    path = []
    current_node = path_start[-1]
    while current_node is not None:
        path.append((current_node.x, current_node.y))
        current_node = current_node.parent
    path.reverse()
    print("找到路径：", path)
else:
    print("未找到路径")

这段代码实现了一个简单的rrt*-connect算法，用于寻找起点和终点之间的最优路径。其中通过定义Node类表示路径上的节点，distance函数计算两个节点间的距离，check_obstacle函数用于检查两个节点间是否存在障碍物。主函数rrt_connect则是使用rrt*-connect算法进行路径搜索，并返回两个树的根节点列表。
最后进行测试，通过rrt_connect函数得到的路径点列表，再逆向遍历节点的parent指针，获取完整的路径。如果找到路径，则将其打印输出，否则输出未找到路径的信息。

### 回答2：
rrt*-connect算法是一种针对路径规划问题的改进型Rapidly-Exploring Random Tree (RRT) 算法。以下是一个简单的rrt*-connect的Python代码示例：

import numpy as np
import matplotlib.pyplot as plt

class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.parent = None

def distance(node1, node2):
    return np.sqrt((node1.x - node2.x)**2 + (node1.y - node2.y)**2)

def generate_random_node(x_range, y_range):
     x = np.random.uniform(x_range[0], x_range[1])
     y = np.random.uniform(y_range[0], y_range[1])
     return Node(x, y)

def find_nearest_node(node_list, random_node):
    distances = [distance(node, random_node) for node in node_list]
    nearest_index = np.argmin(distances)
    return node_list[nearest_index]

def is_collision_free(node1, node2, obstacles):
    # 检查路径上是否有碰撞
    # 如果有碰撞，返回False；否则返回True
    # 这里省略碰撞检测的具体实现代码
    return not collision_detected

def rrt_connect(start, goal, x_range, y_range, obstacles):
    nodes = [start]
    while True:
        random_node = generate_random_node(x_range, y_range)
        nearest_node = find_nearest_node(nodes, random_node)
        new_node = Node(nearest_node.x + 0.1 * (random_node.x - nearest_node.x),
                        nearest_node.y + 0.1 * (random_node.y - nearest_node.y))
        if is_collision_free(nearest_node, new_node, obstacles):
            nodes.append(new_node)
            if distance(new_node, goal) < 0.1:
                return True, nodes
        if len(nodes) % 2 == 0:
            nodes = nodes[::-1]

start = Node(1, 1)
goal = Node(5, 5)
x_range = [0, 10]
y_range = [0, 10]
obstacles = [[3, 3], [4, 4]]  # 障碍物的位置
success, path = rrt_connect(start, goal, x_range, y_range, obstacles)

if success:
    x = [node.x for node in path]
    y = [node.y for node in path]
    plt.plot(x, y, '-r')
    plt.xlim(x_range)
    plt.ylim(y_range)
    plt.show()

这段代码描述了rrt*-connect的主要逻辑。它通过生成随机节点，寻找最近邻节点，并尝试从最近邻节点朝随机节点延伸，然后检查路径是否与障碍物相碰撞。如果延伸的路径安全，则将新节点添加到节点列表中。最终，如果找到一条从起始节点到目标节点的路径，则返回路径节点列表。如果找不到路径，则返回False。代码还包含了绘制路径的部分，以便可视化显示结果。请注意，代码中的碰撞检测部分需要根据具体的碰撞检测算法进行实现。

### 回答3：
rrt*-connect是一种改进版的快速随机树（Rapidly-exploring Random Trees，RRT）算法，用于路径规划。下面是一个使用Python编写的简要实现代码：

import numpy as np
import matplotlib.pyplot as plt

class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        self.parent = None
    
    def dist(self, other):
        return np.sqrt((self.x - other.x)**2 + (self.y - other.y)**2)

class RRTConnect:
    def __init__(self, start, goal, obstacles, step_size=0.5, max_iters=1000):
        self.start = Node(*start)
        self.goal = Node(*goal)
        self.obstacles = obstacles
        self.step_size = step_size
        self.max_iters = max_iters
    
    def generate_random_point(self):
        x = np.random.uniform(0, 10)  # 计划空间的x范围
        y = np.random.uniform(0, 10)  # 计划空间的y范围
        return Node(x, y)
    
    def find_nearest_node(self, tree, point):
        distances = [node.dist(point) for node in tree]
        return tree[np.argmin(distances)]
    
    def generate_new_node(self, nearest_node, random_node):
        distance = nearest_node.dist(random_node)
        if distance <= self.step_size:
            return random_node
        else:
            scale = self.step_size / distance
            x = nearest_node.x + (random_node.x - nearest_node.x) * scale
            y = nearest_node.y + (random_node.y - nearest_node.y) * scale
            return Node(x, y)
    
    def is_collision_free(self, node1, node2):
        for obstacle in self.obstacles:
            if obstacle[0] < node1.x < obstacle[1] and obstacle[2] < node1.y < obstacle[3]:
                return False
            if obstacle[0] < node2.x < obstacle[1] and obstacle[2] < node2.y < obstacle[3]:
                return False
        return True
    
    def rrt_connect(self):
        tree1 = [self.start]
        tree2 = [self.goal]
        for _ in range(self.max_iters):
            random_node = self.generate_random_point()
            nearest_node1 = self.find_nearest_node(tree1, random_node)
            nearest_node2 = self.find_nearest_node(tree2, random_node)
            new_node1 = self.generate_new_node(nearest_node1, random_node)
            new_node2 = self.generate_new_node(nearest_node2, random_node)
            
            if self.is_collision_free(nearest_node1, new_node1):
                tree1.append(new_node1)
                if self.is_collision_free(nearest_node2, new_node1):
                    path = self.connect_trees(tree1, tree2, nearest_node1, new_node2)
                    if path:
                        return path
            
            if self.is_collision_free(nearest_node2, new_node2):
                tree2.append(new_node2)
                if self.is_collision_free(nearest_node1, new_node2):
                    path = self.connect_trees(tree1, tree2, nearest_node1, new_node2)
                    if path:
                        return path
        
        return None
    
    def connect_trees(self, tree1, tree2, node1, node2):
        path = []
        while node1.parent:
            path.append([node1.x, node1.y])
            node1 = node1.parent
        path.append([self.start.x, self.start.y])
        path = path[::-1]
        while node2.parent:
            path.append([node2.x, node2.y])
            node2 = node2.parent
        path.append([self.goal.x, self.goal.y])
        return path

# Usage example:
start = [1, 1]  # 起点
goal = [9, 9]   # 终点
obstacles = [[3, 4, 2, 5], [7, 9, 6, 8]]  # 障碍物坐标范围，例如[x1, x2, y1, y2]
rrt = RRTConnect(start, goal, obstacles)
path = rrt.rrt_connect()
print("路径点坐标：", path)

# 绘制路径
if path:
    path = np.array(path)
    plt.plot(path[:,0], path[:,1], '-o')
    for obstacle in obstacles:
        plt.fill([obstacle[0], obstacle[0], obstacle[1], obstacle[1]],
                 [obstacle[2], obstacle[3], obstacle[3], obstacle[2]],
                 'r')
    plt.xlim(0, 10)
    plt.ylim(0, 10)
    plt.show()

以上是一个简单的RRT*-connect算法的Python实现。代码实现了通过随机扩展树的方式来寻找起点到终点的路径，并考虑了障碍物的碰撞检测。