The Reach-Avoid Problem for Constant-Rate Multi-Mode Systems
This addresses a theoretical and practical problem in hybrid systems verification for researchers and engineers, but is incremental as it builds on prior work for convex sets.
The paper tackles the reachability problem for constant-rate multi-mode systems with non-convex state spaces, showing it is generally undecidable but becomes decidable under certain assumptions, and presents a new algorithm that outperforms RRT in performance comparisons.
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).