提出平滑时空管方法，实现快速避障追踪且控制更平稳。
Smooth Spatiotemporal Tube Synthesis for Prescribed-Time Reach-Avoid-Stay Control
- 构建绕静态危险区的光滑时空管，避免突变修正
- 无需近似即可导出闭式控制律，确保轨迹在管内
- 相比旧方法大幅降低控制代价，适合高精度时序任务
本文针对控制仿射非线性系统，在预定时间内满足到达-避让-驻留（RAS）规范的控制器设计问题。为改进现有基于时空管（STTs）的方法，该工作提出一种自适应框架，通过构造绕静态危险集的光滑时空管，实现连续避障并引导系统在规定时间内抵达目标。所提方法无需引入规避函数，从而避免了管结构的剧烈变化与过高控制能量。推导出无近似的闭式控制律，确保系统轨迹始终位于时空管内，并完成RAS任务。案例研究验证了该方法的有效性，相比先前方法显著降低了控制努力。
原文摘要 · Abstract (English)
In this work, we address the issue of controller synthesis for a control-affine nonlinear system to meet prescribed time reach-avoid-stay specifications. Our goal is to improve upon previous methods based on spatiotemporal tubes (STTs) by eliminating the need for circumvent functions, which often lead to abrupt tube modifications and high control effort. We propose an adaptive framework that constructs smooth STTs around static unsafe sets, enabling continuous avoidance while guiding the system toward the target within the prescribed time. A closed-form, approximation-free control law is derived to ensure the system trajectory remains within the tube and satisfies the RAS task. The effectiveness of the proposed approach is demonstrated through a case study, showing a significant reduction in control effort compared to prior methods.
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