用物理神经网络学习时空管，让机器人在干扰下精准完成时序避障任务。
Learning Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks using Physics-Informed Neural Networks
- 用物理信息神经网络联合学习随时间变化的时空管中心与半径。
- 训练后通过李普希茨条件验证，确保全时段满足约束。
- 无需近似直接生成控制器，适合复杂动态系统的实时控制。
本文提出一种基于时空管（STT）的控制框架，用于处理具有未知动力学的通用控制仿射多输入多输出非线性纯反馈系统，在外部干扰下实现预设时间的到达-避让-停留（T-RAS）任务。时空管定义为随时间变化的球体，其中心与半径由物理信息神经网络（PINN）联合逼近。将时空管约束转化为PINN的损失函数，并提出训练算法以最小化整体违反程度。在特定采样点上训练PINN后，提出基于李普希茨的验证条件，形式化保证学习到的PINN在整个连续时间范围内满足约束。基于学习到的时空管表示，定义了无需近似的闭式控制器，可确保满足T-RAS规范。最后通过两个案例研究验证了该框架的有效性与可扩展性：移动机器人和飞行器在杂乱环境中的导航。
原文摘要 · Abstract (English)
This paper presents a Spatiotemporal Tube (STT)-based control framework for general control-affine MIMO nonlinear pure-feedback systems with unknown dynamics to satisfy prescribed time reach-avoid-stay tasks under external disturbances. The STT is defined as a time-varying ball, whose center and radius are jointly approximated by a Physics-Informed Neural Network (PINN). The constraints governing the STT are first formulated as loss functions of the PINN, and a training algorithm is proposed to minimize the overall violation. The PINN being trained on certain collocation points, we propose a Lipschitz-based validity condition to formally verify that the learned PINN satisfies the conditions over the continuous time horizon. Building on the learned STT representation, an approximation-free closed-form controller is defined to guarantee satisfaction of the T-RAS specification. Finally, the effectiveness and scalability of the framework are validated through two case studies involving a mobile robot and an aerial vehicle navigating through cluttered environments.
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