### RRT*算法在三维空间中的Python实现 对于三维空间内的路径规划，RRT*（快速随机树星型）是一种有效的采样方法。该算法不仅能够找到可行路径，而且随着迭代次数增加可以渐近地接近最优解。 下面是一个简单的RRT*算法用于三维空间路径规划的Python实现： ```python import numpy as np from scipy.spatial import KDTree class Node: def __init__(self, x, y, z): self.x = x self.y = y self.z = z self.path_to_node = [] self.cost = 0.0 def distance(node1, node2): return ((node1.x - node2.x)**2 + (node1.y - node2.y)**2 + (node1.z - node2.z)**2) ** 0.5 def steer(from_node, to_node, extend_length=0.5): new_node = Node(to_node.x, to_node.y, to_node.z) d = distance(from_node, to_node) if d >= extend_length: theta_x = np.arctan2((to_node.x - from_node.x), max(abs(to_node.x - from_node.x), 1e-8)) theta_y = np.arctan2((to_node.y - from_node.y), max(abs(to_node.y - from_node.y), 1e-8)) theta_z = np.arctan2((to_node.z - from_node.z), max(abs(to_node.z - from_node.z), 1e-8)) new_node.x = from_node.x + extend_length * np.cos(theta_x) new_node.y = from_node.y + extend_length * np.sin(theta_y) new_node.z = from_node.z + extend_length * np.sin(theta_z) new_node.path_to_node = [new_node.x, new_node.y, new_node.z] return new_node def get_random_point(min_val=-10, max_val=10): return Node(np.random.uniform(min_val, max_val), np.random.uniform(min_val, max_val), np.random.uniform(min_val, max_val)) def rrt_star(start_position, goal_position, obstacle_list, expand_dis=0.5, goal_sample_rate=20, max_iter=500): start_node = Node(start_position[0], start_position[1], start_position[2]) end_node = Node(goal_position[0], goal_position[1], goal_position[2]) node_list = [start_node] for i in range(max_iter): # 随机选取目标点或者随机点 if np.random.randint(0, 100) > goal_sample_rate: rnd = get_random_point() else: rnd = end_node nearest_ind = KDTree([[nd.x, nd.y, nd.z] for nd in node_list]).query([rnd.x, rnd.y, rnd.z])[1] nearest_node = node_list[nearest_ind] new_node = steer(nearest_node, rnd, extend_length=expand_dis) if not check_collision(new_node, obstacle_list): # 假设有一个碰撞检测函数check_collision near_inds = find_near_nodes(new_node, node_list) node_with_updated_parent = choose_parent( new_node, near_inds, node_list) if node_with_updated_parent: node_list.append(node_with_updated_parent) rewire(node_with_updated_parent, near_inds, node_list) last_index = search_best_goal_node(end_node, node_list) if last_index is not None and distance(node_list[last_index], end_node) <= expand_dis: final_course = generate_final_course(last_index, node_list) break return final_course ``` 此代码片段展示了如何构建基本框架来执行三维空间里的RRT*搜索[^1]。需要注意的是，在实际应用中还需要定义`check_collision()`、`find_near_nodes()`、`choose_parent()`以及`rewire()`等功能辅助完成整个过程，并且要根据具体应用场景调整参数设置和处理细节[^3]。