Scalable time-constrained planning of multi-robot systems

Abstract

This paper presents a scalable procedure for time-constrained planning of a class of uncertain nonlinear multi-robot systems. In particular, we consider N robotic agents operating in a workspace which contains regions of interest (RoI), in which atomic propositions for each robot are assigned. The main goal is to design decentralized and robust control laws so that each robot meets an individual high-level specification given as a metric interval temporal logic (MITL), while using only local information based on a limited sensing radius. Furthermore, the robots need to fulfill certain desired transient constraints such as collision avoidance between them. The controllers, which guarantee the transition between regions, consist of two terms: a nominal control input, which is computed online and is the solution of a decentralized finite-horizon optimal control problem (DFHOCP); and an additive state feedback law which is computed offline and guarantees that the real trajectories of the system will belong to a hyper-tube centered along the nominal trajectory. The controllers serve as actions for the individual weighted transition system (WTS) of each robot, and the time duration required for the transition between regions is modeled by a weight. The DFHOCP is solved at every sampling time by each robot and then necessary information is exchanged between neighboring robots. The proposed approach is scalable since it does not require a product computation among the WTS of the robots. The proposed framework is experimentally tested and the results show that the proposed framework is promising for solving real-life robotic as well as industrial applications.