rrt算法全称

 回答1：

*-connect是一种路径规划

，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

语言

的简单示例

：

 python 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

了一个简单的

*-connect

，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

_connect则是使用

*-connect

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

_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：

*-connect

是一种针对路径规划问题的改进型Rapidly-Exploring Random Tree (

)

。以下是一个简单的

*-connect的

示例：

 python 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

描述了

*-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。

还包含了绘制路径的部分，以便可视化显示结果。请注意，

中的碰撞检测部分需要根据具体的碰撞检测

进行

。

回答3：

*-connect是一种改进版的快速随机树（Rapidly-exploring Random Trees，

）

，用于路径规划。下面是一个使用

编写的简要

：

 python 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 RRT Connect: 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 = RRT Connect(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

*-connect

的

。

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。

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