k-Color Multi-Robot Motion Planning

We present a simple and natural extension of the multi-robot motion planning problem where the robots are partitioned into groups (colors), such that in each group the robots are interchangeable. Every robot is no longer required to move to a specific target, but rather to some target placement that is assigned to its group. We call this problem k-color multi-robot motion planning and provide a sampling-based algorithm specifically designed for solving it. At the heart of the algorithm is a novel technique where the k-color problem is reduced to several discrete multi-robot motion planning problems. These reductions amplify basic samples into massive collections of free placements and paths for the robots. We demonstrate the performance of the algorithm by an implementation for the case of disc robots and polygonal robots translating in the plane. We show that the algorithm successfully and efficiently copes with a variety of challenging scenarios, involving many robots, while a simplified version of this algorithm, that can be viewed as an extension of a prevalent sampling-based algorithm for the k-color case, fails even on simple scenarios. Interestingly, our algorithm outperforms a well established implementation of PRM for the standard multi-robot problem, in which each robot has a distinct color.Comment: 2

Well-structured languages

SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Model checking coverability graphs of vector addition systems

A large number of properties of a vector addition system—for instance coverability, boundedness, or regularity—can be decided using its coverability graph, by looking for some characteristic pattern. We propose to unify the known exponential-space upper bounds on the complexity of such problems on vector addition systems, by seeing them as instances of the model-checking problem for a suitable extension of computation tree logic, which allows to check for the existence of these patterns. This provides new insights into what constitutes a “coverability-like ” property

Flat counter automata almost everywhere

Abstract. This paper argues that flatness appears as a central notion in the verification of counter automata. A counter automaton is called flat when its control graph can be “replaced”, equivalently w.r.t. reachability, by another one with no nested loops. From a practical view point, we show that flatness is a necessary and sufficient condition for termination of accelerated symbolic model checking, a generic semi-algorithmic technique implemented in successful tools like FAST,LASH or TREX. From a theoretical view point, we prove that many known semilinear subclasses of counter automata are flat: reversal bounded counter machines, lossy vector addition systems with states, reversible Petri nets, persistent and conflict-free Petri nets, etc. Hence, for these subclasses, the semilinear reachability set can be computed using a uniform accelerated symbolic procedure (whereas previous algorithms were specifically designed for each subclass).