Python 机器人大脑构建指南：路径规划与决策算法深度解析

路径规划与决策算法概述

路径规划与决策算法是机器人大脑的核心模块，涉及从环境感知到目标驱动的动态决策过程。常见方法包括基于图搜索的全局规划（如A*、Dijkstra）、局部避障算法（如动态窗口法DWA），以及结合机器学习的端到端决策模型（如强化学习）。

全局路径规划算法

A*算法：结合启发式函数与代价函数，平衡搜索效率与最优性。公式表示为：
$$f(n) = g(n) + h(n)$$
其中，$g(n)$为起点到当前节点的实际代价，$h(n)$为当前节点到终点的启发式估计（如欧氏距离）。

Dijkstra算法：适用于无权图的最短路径搜索，通过广度优先遍历保证最优性，但计算复杂度较高。

代码示例（Python实现A）*：

import heapq def a_star(start, goal, heuristic): open_set = [(0, start)] came_from = {} g_score = {start: 0} while open_set: _, current = heapq.heappop(open_set) if current == goal: return reconstruct_path(came_from, current) for neighbor in get_neighbors(current): tentative_g = g_score[current] + distance(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 = tentative_g + heuristic(neighbor, goal) heapq.heappush(open_set, (f_score, neighbor))

局部避障与动态决策

动态窗口法（DWA）：基于机器人运动学模型，在速度空间中采样可行轨迹，评估代价函数（如接近目标、避障、速度平滑）选择最优解。

代价函数设计：
$$cost(v, \omega) = \alpha \cdot \text{heading}(v, \omega) + \beta \cdot \text{dist}(v, \omega) + \gamma \cdot \text{velocity}(v, \omega)$$
参数$\alpha$, $\beta$, $\gamma$权重调节目标朝向、障碍距离与速度的优先级。

代码片段（DWA核心逻辑）：

def evaluate_trajectory(v, w, obstacles, goal): trajectory = simulate_motion(v, w) heading_cost = angle_to_goal(trajectory[-1], goal) obstacle_cost = min_distance_to_obstacles(trajectory, obstacles) return heading_cost + 10 * obstacle_cost # 权重示例

机器学习驱动的决策

强化学习（RL）：通过Q-Learning或深度Q网络（DQN）训练策略，直接映射状态到动作。状态可包含激光雷达数据、目标位置，动作为线速度与角速度。

PPO算法示例：

import torch from stable_baselines3 import PPO model = PPO("MlpPolicy", env, verbose=1) model.learn(total_timesteps=10000)

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