SAC强化学习进行机器人轨迹规划的完整指南

轨迹规划是机器人控制中的核心问题，SAC(Soft Actor-Critic)因其出色的探索能力和稳定性，特别适合解决复杂的连续控制类轨迹规划问题。下面我将详细介绍如何用SAC实现高效的轨迹规划。

1. 轨迹规划问题建模

1.1 状态空间设计

对于机器人轨迹规划，典型的状态表示包括：

python

state = {
    'joint_positions': [q1, q2, ..., qn],  # 关节角度
    'joint_velocities': [dq1, dq2, ..., dqn],  # 关节速度
    'end_effector_pos': [x, y, z],  # 末端执行器位置
    'target_pos': [x_t, y_t, z_t],  # 目标位置
    'obstacle_info': [obs1_x, obs1_y, obs1_r, ...]  # 障碍物信息
}

1.2 动作空间设计

python

action = [τ1, τ2, ..., τn]  # 各关节的扭矩控制量
# 通常需要归一化到[-1, 1]范围

1.3 奖励函数设计

多目标奖励函数示例：

python

def compute_reward(state, action, next_state):
    # 1. 到达目标奖励
    dist_to_target = np.linalg.norm(next_state['end_effector_pos'] - state['target_pos'])
    reach_reward = -10.0 * dist_to_target  # 距离惩罚
    
    # 2. 碰撞惩罚
    collision_penalty = 0.0
    for obs in state['obstacle_info']:
        obs_dist = np.linalg.norm(next_state['end_effector_pos'] - obs[:3])
        if obs_dist < obs[3]:  # 障碍物半径
            collision_penalty -= 50.0
    
    # 3. 动作平滑惩罚
    action_diff = np.linalg.norm(action - state['last_action'])
    smooth_penalty = -0.1 * action_diff
    
    # 4. 能量消耗惩罚
    energy_penalty = -0.01 * np.sum(np.square(action))
    
    # 5. 成功奖励
    success_bonus = 100.0 if dist_to_target < 0.02 else 0.0  # 2cm内视为成功
    
    return reach_reward + collision_penalty + smooth_penalty + energy_penalty + success_bonus

2. SAC实现轨迹规划的关键技术

2.1 网络架构设计

增强的SAC网络实现：

python

class EnhancedSAC(nn.Module):
    def __init__(self, state_dim, action_dim, max_action):
        super().__init__()
        
        # 状态编码器(处理高维输入)
        self.encoder = nn.Sequential(
            nn.Linear(state_dim, 512),
            nn.LayerNorm(512),
            nn.ReLU(),
            nn.Linear(512, 256),
            nn.LayerNorm(256),
            nn.ReLU()
        )
        
        # 策略网络
        self.actor_mean = nn.Linear(256, action_dim)
        self.actor_log_std = nn.Linear(256, action_dim)
        
        # 双Q网络
        self.critic1 = nn.Sequential(
            nn.Linear(256 + action_dim, 256),
            nn.ReLU(),
            nn.Linear(256,