帮我写利用RRT算法实现垂直车位自动泊车的代码，需满足车辆运动学约束，要求输出泊车轨迹并绘制泊车轨迹

好的，下面是一个基于Python的RRT算法实现垂直车位自动泊车的代码，包括车辆的运动学约束和泊车轨迹的输出和绘制。

import matplotlib.pyplot as plt
import numpy as np

# 定义车辆运动学参数
MAX_SPEED = 5.0     # 最大速度
MAX_STEER = np.pi/4 # 最大转角
MAX_ACC = 2.0       # 最大加速度

# 定义RRT算法参数
MAX_ITER = 5000     # 最大迭代次数
GOAL_RADIUS = 0.5   # 目标半径
STEP_SIZE = 0.5     # 步长

class Node:
    def __init__(self, x, y, theta):
        self.x = x
        self.y = y
        self.theta = theta
        self.parent = None
        
class RRT:
    def __init__(self, start, goal, obstacles):
        self.start = Node(start[0], start[1], start[2])
        self.goal = Node(goal[0], goal[1], goal[2])
        self.obstacles = obstacles
        self.nodes = [self.start]
        
    def planning(self):
        for i in range(MAX_ITER):
            rand_node = self.generate_random_node()
            nearest_node = self.find_nearest_node(rand_node)
            new_node = self.steer(nearest_node, rand_node)
            if self.check_collision(new_node):
                self.nodes.append(new_node)
                if self.calc_distance(new_node, self.goal) < GOAL_RADIUS:
                    self.goal.parent = new_node
                    return self.generate_path()
        return None
    
    def generate_random_node(self):
        if np.random.rand() < 0.5:
            x = np.random.uniform(-2.0, 2.0)
            y = np.random.choice([-6.0, 6.0])
            theta = np.random.choice([-np.pi/2, np.pi/2])
        else:
            x = np.random.choice([-2.0, 2.0])
            y = np.random.uniform(-6.0, 6.0)
            theta = np.random.choice([0, np.pi])
        return Node(x, y, theta)
    
    def find_nearest_node(self, rand_node):
        nearest_node = self.nodes[0]
        min_dist = self.calc_distance(rand_node, nearest_node)
        for node in self.nodes:
            dist = self.calc_distance(rand_node, node)
            if dist < min_dist:
                nearest_node = node
                min_dist = dist
        return nearest_node
    
    def steer(self, nearest_node, rand_node):
        delta_x = rand_node.x - nearest_node.x
        delta_y = rand_node.y - nearest_node.y
        delta_theta = np.arctan2(delta_y, delta_x)
        delta_theta = self.normalize_angle(delta_theta - nearest_node.theta)
        steer = np.clip(delta_theta, -MAX_STEER, MAX_STEER)
        delta_dist = np.sqrt(delta_x**2 + delta_y**2)
        delta_dist = np.clip(delta_dist, -MAX_SPEED, MAX_SPEED)
        new_x = nearest_node.x + delta_dist * np.cos(nearest_node.theta)
        new_y = nearest_node.y + delta_dist * np.sin(nearest_node.theta)
        new_theta = nearest_node.theta + delta_dist / np.tan(steer)
        new_node = Node(new_x, new_y, new_theta)
        new_node.parent = nearest_node
        return new_node
    
    def check_collision(self, node):
        for obs in self.obstacles:
            if self.calc_distance(node, obs) < 1.0:
                return False
        return True
    
    def generate_path(self):
        path = []
        node = self.goal
        while node is not None:
            path.append(node)
            node = node.parent
        return path[::-1]
    
    def calc_distance(self, node1, node2):
        dx = node1.x - node2.x
        dy = node1.y - node2.y
        return np.sqrt(dx**2 + dy**2)
    
    def normalize_angle(self, angle):
        while angle < -np.pi:
            angle += 2*np.pi
        while angle > np.pi:
            angle -= 2*np.pi
        return angle
    
    def plot(self, path):
        plt.figure(figsize=(8,8))
        plt.xlim(-8.0, 8.0)
        plt.ylim(-8.0, 8.0)
        plt.plot([node.x for node in self.nodes], [node.y for node in self.nodes], 'bo', markersize=3)
        plt.plot([obs[0] for obs in self.obstacles], [obs[1] for obs in self.obstacles], 'rs', markersize=6)
        plt.plot([node.x for node in path], [node.y for node in path], 'r-', linewidth=2)
        plt.plot(self.start.x, self.start.y, 'go', markersize=8)
        plt.plot(self.goal.x, self.goal.y, 'yo', markersize=8)
        plt.show()

# 定义场景参数
start = [-1.0, -7.0, np.pi/2]
goal = [1.0, 7.0, -np.pi/2]
obstacles = [[0.0, 0.0], [-2.0, 2.0], [2.0, 2.0], [-2.0, -2.0], [2.0, -2.0]]

# 进行路径规划
rrt = RRT(start, goal, obstacles)
path = rrt.planning()

# 输出泊车轨迹和绘制泊车轨迹
if path is not None:
    print("泊车轨迹长度：", len(path))
    for node in path:
        print(node.x, node.y, node.theta)
    rrt.plot(path)
else:
    print("无法找到合适的泊车轨迹！")

在上述代码中，我们定义了一个Node类来表示状态，包括车辆的位置和方向。然后，我们定义了一个RRT类来实现RRT算法，包括搜索空间、运动模型、随机采样、碰撞检测、路径回溯等操作。最后，我们利用RRT算法搜索泊车路径，并绘制泊车轨迹。

需要注意的是，上述代码只是一个简单的示例，实际应用中需要根据具体场景进行调整和优化。