【启发式算法】RRT算法详细介绍（Python）

def RRT(q_start, q_goal, N, Δq):
    T = Tree(q_start)
    for i in range(N):
        q_rand = random_sample()
        q_nearest = nearest_node(T, q_rand)
        q_new = steer(q_nearest, q_rand, Δq)
        if is_valid(q_nearest, q_new):
            T.add_node(q_new, parent=q_nearest)
            if distance(q_new, q_goal) < threshold:
                return extract_path(T, q_new)
    return failure

"""《RRT算法》
    时间：2025.06.16
    作者：不去幼儿园
"""
import numpy as np
import matplotlib.pyplot as plt
import random

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

def distance(n1, n2):
    return np.hypot(n1.x - n2.x, n1.y - n2.y)

def get_random_node(goal_sample_rate, goal):
    if random.random() < goal_sample_rate:
        return Node(goal.x, goal.y)
    return Node(random.uniform(0, 100), random.uniform(0, 100))

def steer(from_node, to_node, extend_length=5.0):
    dist = distance(from_node, to_node)
    theta = np.arctan2(to_node.y - from_node.y, to_node.x - from_node.x)
    new_x = from_node.x + extend_length * np.cos(theta)
    new_y = from_node.y + extend_length * np.sin(theta)
    new_node = Node(new_x, new_y)
    new_node.parent = from_node
    return new_node

def is_collision(node):
    # 简化处理：假设无障碍物
    return False

def rrt(start, goal, max_iter=500, goal_sample_rate=0.05):
    nodes = [start]
    for _ in range(max_iter):
        rnd = get_random_node(goal_sample_rate, goal)
        nearest = min(nodes, key=lambda n: distance(n, rnd))
        new_node = steer(nearest, rnd)

        if not is_collision(new_node):
            nodes.append(new_node)
            if distance(new_node, goal) < 5.0:
                goal.parent = new_node
                nodes.append(goal)
                break
    return nodes

def draw_path(last_node):
    path = []
    node = last_node
    while node:
        path.append((node.x, node.y))
        node = node.parent
    path = path[::-1]
    plt.plot([x for x, y in path], [y for x, y in path], '-r')

def draw_tree(nodes):
    for node in nodes:
        if node.parent:
            plt.plot([node.x, node.parent.x], [node.y, node.parent.y], '-g')

start = Node(10, 10)
goal = Node(90, 90)

nodes = rrt(start, goal)
draw_tree(nodes)
draw_path(goal)
plt.plot(start.x, start.y, "bs", label="Start")
plt.plot(goal.x, goal.y, "gs", label="Goal")
plt.legend()
plt.grid(True)
plt.axis([0, 100, 0, 100])
plt.title("RRT Path Planning (No Obstacles)")
plt.show()

​# 环境配置
Python                  3.11.5
torch                   2.1.0
torchvision             0.16.0
gym                     0.26.2