为未知动态系统设计安全路径，确保在限定时间内到达目标且避开随时间变化的危险区。
Spatiotemporal Tubes for Temporal Reach-Avoid-Stay Tasks in Unknown Systems
- 用采样法构建时空管，将约束转为鲁棒优化问题
- 通过场景优化解决无限约束导致的不可行性，生成闭式控制器
- 适用于机器人、机械臂等需时序安全控制的复杂系统
本文研究具有未知动态特性的通用多输入多输出（MIMO）系统的控制器综合问题，旨在实现时间相关的“到达-避让-停留”任务：即在规定时间窗口内到达目标集，同时避开随时间变化的不安全区域。核心目标是利用基于采样的方法构造时空管（Spatiotemporal Tube, STT），进而设计无需近似、可直接应用的闭环控制策略，以保证系统轨迹在满足安全约束的前提下抵达目标。所提方案将STT要求转化为鲁棒优化程序（ROP），针对因无限约束导致的不可行问题，引入基于采样的场景优化程序（SOP）进行求解。最终通过求解SOP获得时空管与闭式控制器，保障系统满足时序可达-避让-停留规范。三个案例验证了该方法的有效性：全向移动机器人、SCARA机械臂和磁悬浮系统。
原文摘要 · Abstract (English)
The paper considers the controller synthesis problem for general MIMO systems with unknown dynamics, aiming to fulfill the temporal reach-avoid-stay task, where the unsafe regions are time-dependent, and the target must be reached within a specified time frame. The primary aim of the paper is to construct the spatiotemporal tube (STT) using a sampling-based approach and thereby devise a closed-form approximation-free control strategy to ensure that system trajectory reaches the target set while avoiding time-dependent unsafe sets. The proposed scheme utilizes a novel method involving STTs to provide controllers that guarantee both system safety and reachability. In our sampling-based framework, we translate the requirements of STTs into a Robust optimization program (ROP). To address the infeasibility of ROP caused by infinite constraints, we utilize the sampling-based Scenario optimization program (SOP). Subsequently, we solve the SOP to generate the tube and closed-form controller for an unknown system, ensuring the temporal reach-avoid-stay specification. Finally, the effectiveness of the proposed approach is demonstrated through three case studies: an omnidirectional robot, a SCARA manipulator, and a magnetic levitation system.
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