在将 CBS 算法应用于 AGV 路径规划时，AGV 的尺寸和角度（如方向、转弯半径）是关键的物理约束因素，必须在路径搜索与冲突检测阶段加以考虑。以下是在 Python 中实现 CBS 算法结合 AGV 尺寸和角度计算的方法。 ### 3.1 AGV 尺寸建模与地图预处理 AGV 的尺寸（宽度、长度）直接影响其在路径上的可通行性。为确保路径规划的安全性，需在地图预处理阶段对障碍物进行膨胀处理，生成适合 AGV 实际尺寸的可行走区域。例如，使用膨胀地图（inflated map）技术，将原本可通行的路径根据 AGV 的宽度进行收缩，避免 AGV 与障碍物发生碰撞[^2]。 ```python def inflate_obstacles(grid_map, agv_width): inflated_map = grid_map.copy() half_width = int(agv_width / 2) for y in range(len(grid_map)): for x in range(len(grid_map[0])): if grid_map[y][x] == 0: # 可通行区域 for dy in range(-half_width, half_width + 1): for dx in range(-half_width, half_width + 1): if 0 <= y + dy < len(grid_map) and 0 <= x + dx < len(grid_map[0]): if grid_map[y + dy][x + dx] == 1: inflated_map[y][x] = 1 break return inflated_map ``` ### 3.2 AGV 角度建模与路径方向约束 AGV 在移动过程中具有方向性，转弯半径限制决定了其能否顺利通过某些路径节点。在路径搜索中，需将 AGV 的朝向（角度）作为状态的一部分进行建模。A* 算法可扩展为包含方向的状态空间（如 (x, y, θ)），并在启发式函数中考虑转向代价。 ```python def a_star_with_orientation(map, start, goal, agv_turn_radius): from heapq import heappush, heappop open_set = [] came_from = {} g_score = {} f_score = {} start_state = (start[0], start[1], start[2]) # x, y, theta goal_state = (goal[0], goal[1], goal[2]) heappush(open_set, (0, start_state)) g_score[start_state] = 0 f_score[start_state] = heuristic(start_state, goal_state) while open_set: current = heappop(open_set)[1] if current[:2] == goal_state[:2]: return reconstruct_path(came_from, current) for neighbor in get_neighbors_with_orientation(current, agv_turn_radius): tentative_g = g_score[current] + cost_function(current, neighbor) if neighbor not in g_score or tentative_g < g_score[neighbor]: came_from[neighbor] = current g_score[neighbor] = tentative_g f_score[neighbor] = tentative_g + heuristic(neighbor, goal_state) heappush(open_set, (f_score[neighbor], neighbor)) return None # No path found ``` ### 3.3 CBS 算法中结合 AGV 尺寸与角度的冲突检测 CBS 算法的上层结构通过冲突检测与约束生成解决路径冲突。在引入 AGV 尺寸和角度后，冲突检测需考虑 AGV 实际占据的空间与方向变化，例如两个 AGV 在同一时间点是否可能因尺寸重叠而发生碰撞。 ```python def find_conflict(paths): time_steps = set() for path in paths.values(): for t, (x, y, theta) in enumerate(path): time_steps.add((t, x, y)) conflicts = [] for t, x, y in time_steps: agents_at_pos = [agent for agent, path in paths.items() if len(path) > t and (path[t][0], path[t][1]) == (x, y)] if len(agents_at_pos) > 1: conflicts.append((t, x, y, agents_at_pos)) return conflicts ``` ### 3.4 约束生成与路径重规划 在检测到冲突后，CBS 算法需为冲突的 AGV 添加时间或空间约束，并重新调用 A* 算法进行路径规划。约束可以是某个 AGV 在特定时间不能出现在某个坐标，或必须绕行特定方向。 ```python def generate_constraint(conflict): t, x, y, agents = conflict constraints = [] for agent in agents: constraints.append({'agent': agent, 'time': t, 'position': (x, y)}) return constraints ``` ### 3.5 路径冲突解决与迭代优化 CBS 算法通过迭代方式不断检测冲突并添加约束，直到所有 AGV 路径无冲突为止。该过程在 Python 中可通过递归或队列方式实现。 ```python def cbs_with_agv_constraints(agents, grid_map): paths = {} constraints = [] for agent in agents: path = a_star_with_orientation(grid_map, agent.start, agent.goal, agent.turn_radius) paths[agent] = path while True: conflict = find_conflict(paths) if not conflict: break for constraint in generate_constraint(conflict): constraints.append(constraint) for agent in conflict.agents: paths[agent] = a_star_with_orientation_with_constraints( grid_map, agent.start, agent.goal, agent.turn_radius, constraints ) return paths ``` ---