强化学习(Reinforcement Learning, RL)通过智能体(Agent)与环境(Environment)的动态交互学习最优策略。其核心要素包括:
马尔可夫决策过程(MDP)是RL的数学基础,定义为五元组<inline_LaTeX_Formula>langle S, A, P, R, gamma rangle<inline_LaTeX_Formula>,其中:
传统路径规划算法(如A*、Dijkstra)依赖静态环境建模,难以应对动态变化。强化学习的优势在于:
Q-Learning通过迭代更新动作值函数<inline_LaTeX_Formula>Q(s,a)<\inline_LaTeX_Formula>实现策略优化:
其中<inline_LaTeX_Formula>\alpha<\inline_LaTeX_Formula>为学习率,<inline_LaTeX_Formula>\gamma<\inline_LaTeX_Formula>
为折扣因子。
import numpy as np
class QLearningAgent:
def __init__(self, state_size, action_size, alpha=0.1, gamma=0.9, epsilon=0.1):
self.Q = np.zeros((state_size, action_size))
self.alpha = alpha
self.gamma = gamma
self.epsilon = epsilon
def act(self, state):
if np.random.rand() < self.epsilon:
return np.random.choice(action_size)
else:
return np.argmax(self.Q[state, :])
def update(self, state, action, reward, next_state):
target = reward + self.gamma * np.max(self.Q[next_state, :])
self.Q[state, action] += self.alpha * (target - self.Q[state, action])
针对高维状态空间,DQN(深度Q网络)通过神经网络近似Q函数:
其中<inline_LaTeX_Formula>\theta^-<\inline_LaTeX_Formula>
为目标网络参数。
import torch
import torch.nn as nn
class DQN(nn.Module):
def __init__(self, input_dim, hidden_dim, output_dim):
super().__init__()
self.layers = nn.Sequential(
nn.Linear(input_dim, hidden_dim),
nn.ReLU(),
nn.Linear(hidden_dim, output_dim)
)
def forward(self, x):
return self.layers(x)
状态定义:机器人坐标(x,y)、障碍物分布热图、目标点坐标 动作空间:8个方向移动(±dx, ±dy) 奖励函数:
class WarehouseEnv:
def __init__(self, grid_size):
self.grid = np.zeros(grid_size)
self.goal = (grid_size[0]-1, grid_size[1]-1)
self.obstacles = self._generate_obstacles()
def _generate_obstacles(self):
# 随机生成障碍物
return np.random.randint(0, 2, self.grid.shape)
def step(self, action):
# 更新位置,检查碰撞,计算奖励
pass
采用优先级经验回放(PER)优化训练稳定性:
from collections import deque
class ReplayBuffer:
def __init__(self, capacity):
self.buffer = deque(maxlen=capacity)
def add(self, experience):
self.buffer.append(experience)
def sample(self, batch_size):
return random.sample(self.buffer, batch_size)
将路径规划分解为全局规划(粗粒度)和局部避障(细粒度):
利用预训练策略初始化新任务:
通过多智能体并行探索加速收敛:
本文系统阐述了强化学习在机器人路径规划中的应用框架,通过代码解析展示了Q-Learning、DQN等算法的实现细节,并探讨了优化策略与前沿趋势。随着深度强化学习与机器人学的深度融合,动态环境下的自主导航将迈向更高智能化水平。