差速车hybirdA*

差速车hybrid A*是一种路径规划算法，它结合了A*算法和差速车模型，用于在二维或三维空间中规划差速车的最优路径。下面是一个演示差速车hybrid A*算法的示例：

import math

# 定义差速车模型
class DifferentialDriveModel:
    def __init__(self, length, max_steering_angle):
        self.length = length
        self.max_steering_angle = max_steering_angle

    def move(self, x, y, theta, steering_angle, distance):
        new_x = x + distance * math.cos(theta)
        new_y = y + distance * math.sin(theta)
        new_theta = theta + (distance / self.length) * math.tan(steering_angle)
        return new_x, new_y, new_theta

# 定义节点类
class Node:
    def __init__(self, x, y, theta, g_cost, h_cost, parent=None):
        self.x = x
        self.y = y
        self.theta = theta
        self.g_cost = g_cost
        self.h_cost = h_cost
        self.parent = parent

    def f_cost(self):
        return self.g_cost + self.h_cost

# 定义差速车hybrid A*算法
def hybrid_a_star(start, goal, obstacles, map_resolution, car_length, max_steering_angle):
    # 初始化起点和终点节点
    start_node = Node(start[0], start[1], start[2], 0, heuristic(start, goal), None)
    goal_node = Node(goal[0], goal[1], goal[2], float('inf'), 0, None)

    # 初始化open和closed列表
    open_list = [start_node]
    closed_list = []

    # 初始化差速车模型
    car_model = DifferentialDriveModel(car_length, max_steering_angle)

    while open_list:
        # 从open列表中选择f_cost最小的节点
        current_node = min(open_list, key=lambda node: node.f_cost())

        # 如果当前节点是终点节点，则返回路径
        if current_node.x == goal_node.x and current_node.y == goal_node.y and current_node.theta == goal_node.theta:
            return reconstruct_path(current_node)

        # 将当前节点从open列表中移除，并加入closed列表
        open_list.remove(current_node)
        closed_list.append(current_node)

        # 生成当前节点的邻居节点
        neighbors = generate_neighbors(current_node, car_model, map_resolution)

        for neighbor in neighbors:
            # 如果邻居节点已经在closed列表中，则跳过
            if neighbor in closed_list:
                continue

            # 计算邻居节点的g_cost和h_cost
            g_cost = current_node.g_cost + distance(current_node, neighbor)
            h_cost = heuristic(neighbor, goal)

            # 如果邻居节点不在open列表中，则加入open列表
            if neighbor not in open_list:
                open_list.append(neighbor)
            # 如果邻居节点已经在open列表中，并且新的g_cost更小，则更新邻居节点的g_cost和parent
            elif g_cost < neighbor.g_cost:
                neighbor.g_cost = g_cost
                neighbor.parent = current_node

    # 如果open列表为空，则表示无法找到路径
    return None

# 重构路径
def reconstruct_path(node):
    path = []
    while node:
        path.append((node.x, node.y, node.theta))
        node = node.parent
    return list(reversed(path))

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

# 计算启发式函数（欧几里得距离）
def heuristic(node, goal):
    return math.sqrt((node.x - goal[0]) ** 2 + (node.y - goal[1]) ** 2)

# 生成邻居节点
def generate_neighbors(node, car_model, map_resolution):
    neighbors = []
    steering_angles = [-car_model.max_steering_angle, 0, car_model.max_steering_angle]
    distances = [map_resolution, 2 * map_resolution]

    for steering_angle in steering_angles:
        for distance in distances:
            new_x, new_y, new_theta = car_model.move(node.x, node.y, node.theta, steering_angle, distance)
            neighbors.append(Node(new_x, new_y, new_theta, float('inf'), float('inf'), None))

    return neighbors

# 示例使用
start = (0, 0, 0)
goal = (5, 5, math.pi / 2)
obstacles = [(2, 2), (3, 3), (4, 4)]
map_resolution = 1
car_length = 1
max_steering_angle = math.pi / 4

path = hybrid_a_star(start, goal, obstacles, map_resolution, car_length, max_steering_angle)
print("Path:", path)

这个示例演示了如何使用差速车hybrid A*算法规划差速车的最优路径。你可以根据自己的需求修改起点、终点、障碍物等参数，并获取到规划的路径。希望对你有帮助！