Bounded-rate multi-mode systems based motion planning

Abstract

Bounded-rate multi-mode systems are hybrid systems that can switch among a finite set of modes. Its dynamics is specified by a finite number of real-valued variables with modedependent rates that can vary within given bounded sets. Given an arbitrary piecewise linear trajectory, we study the problem of following the trajectory with arbitrary precision, using motion primitives given as bounded-rate multi-mode systems. We give an algorithm to solve the problem and show that the problem is co-NP complete. We further prove that the problem can be solved in polynomial time for multimode systems with fixed dimension. We study the problem with dwell-time requirement and show the decidability of the problem under certain positivity restriction on the rate vectors. Finally, we show that introducing structure to the multi-mode systems leads to undecidability, even when using only a single clock variable.

Global Almost-Sure Reachability in Stochastic Constant-Rate Multi-Mode Systems

“…These systems can be considered as constant-rate multi-mode systems with uncertainties. It is known [5,10] that the schedulability and reachability problems for bounded-rate multi-mode systems are, although intractable (co-NP-complete), decidable. To the best of our knowledge, there is no known result on stochastic extensions of multi-mode systems.…”