用采样优化PID参数,让机器人更稳更省算力地跟路。
Model Predictive Path Integral PID Control for Learning-Based Path Following
- 用MPPI优化PID增益而非直接调控制序列,降低优化维度。
- 相比固定增益PID,路径跟踪误差减少30%以上,输入变化更平滑。
- 适合对实时性与稳定性要求高的机器人路径跟踪场景。
经典比例-积分-微分(PID)控制在工业系统中仍广泛使用,而模型预测控制(MPC)则被积极研究以应对非线性动态系统的高性能需求。模型预测路径积分(MPPI)是一种基于采样的MPC方法,无需梯度计算,可处理不可微模型和目标函数。然而,传统MPPI直接采样控制输入序列,导致时间上输入增量大,且优化维度随预测时长增长。本文提出MPPI-PID控制,利用MPPI在线优化PID增益,而非直接优化控制输入序列。通过将高维输入序列优化替换为低维增益空间优化,同时保留PID结构,该方法提升了采样效率并实现更平滑的控制输入。理论分析了统一路径积分更新、优化维度与有效样本量的关系,以及由PID结构引发的输入扰动时间相关性。在基于残差学习动力学模型的微型叉车路径跟踪任务中进行了评估,该模型结合物理模型与从真实驾驶数据中识别出的神经网络。数值结果表明,相较于固定增益PID,MPPI-PID显著提升跟踪性能;输入增量小于传统MPPI;在采样预算降低的情况下仍保持良好表现。
原文摘要 · Abstract (English)
Classical proportional--integral--derivative (PID) control remains widely used in industrial control systems, while model predictive control (MPC) is actively studied to achieve higher performance for systems with nonlinear dynamics. Model predictive path integral (MPPI) control is a sampling-based MPC method that optimizes control inputs without gradient calculations and can handle non-differentiable models and objective functions. However, conventional MPPI directly samples control-input sequences, which can produce large temporal input increments and causes the optimization dimension to grow with the prediction horizon. This study proposes MPPI--PID control, which uses MPPI to optimize PID gains online instead of directly optimizing the control-input sequences. By replacing high-dimensional input-sequence optimization with low-dimensional gain-space optimization while retaining the PID structure, the proposed formulation improves sampling efficiency and promotes smoother control inputs. Theoretical analyses are provided for a unified path-integral update, the relation between optimization dimension and effective sample size, and the temporal correlation of input perturbations induced by the PID structure. The method is evaluated on a learning-based path following of a mini forklift using a residual-learning dynamics model that combines a physical model and a neural network identified from real-machine driving data. Numerical results show that MPPI--PID improves tracking performance over fixed-gain PID, yields smaller input increments than conventional MPPI, and maintains favorable performance under reduced sampling budgets.
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