常速率多模系统的Reach-Avoid问题
The Reach-Avoid Problem for Constant-Rate Multi-Mode Systems
摘要：
常速率多模态系统是一种能够在有限个模态之间自由切换的混合系统，其动态特性由有限个具有依赖于模态的常速率的实值变量来描述。Wojtczak和Trivedi已经证明，对于开和凸安全集的恒定速率多模式系统的可达性问题可以在多项式时间内解决。本文研究了非凸状态空间的可达性问题，并证明了该问题在一般情况下是不可判定的。我们通过对安全集做出某些假设来恢复可判定性。我们提出了一种新的算法来解决这个问题，并比较其性能与流行的基于采样的算法快速探索随机树（RRT）的开放运动规划库（OMPL）中实现。
英文摘要：
A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. Alur, Wojtczak, and Trivedi have shown that reachability problems for constant-rate multi-mode systems for open and convex safety sets can be solved in polynomial time. In this paper, we study the reachability problem for non-convex state spaces and show that this problem is in general undecidable. We recover decidability by making certain assumptions about the safety set. We present a new algorithm to solve this problem and compare its performance with the popular sampling based algorithm rapidly-exploring random tree (RRT) as implemented in the Open Motion Planning Library (OMPL).
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