Decentralized route-planning for multi-vehicle teams to satisfy a subclass of linear temporal logic specifications

Abstract

Linear temporal logic (LTL) formulae are widely used to provide high level behavioral specifications on mobile robots. We propose a decentralized route-planning method for a networked team of mobile robots to satisfy a common (global) LTL specification. The global specification is assumed to be a conjunction of multiple formulae, each of which is treated as a task to be assigned to one or more vehicles. The vehicle kinematic model consists of two modes: a hover mode and a constant-speed forward motion mode with bounded steering rate. The proposed method leverages the consensus-based bundle algorithm for decentralized task assignment, thereby decomposing the global specification into local specifications for each vehicle. We develop a new algorithm to assign collaborative tasks: those simultaneously assigned to multiple vehicles. Rewards in the proposed task assignment algorithm are computed using the so-called lifted graph, which ensures the satisfaction of minimum turn radius constraints on vehicular motion. This algorithm synchronizes the vehicles’ routes with minimum waiting durations. The proposed method is compared against a multi-vehicle task assignment algorithm from the literature, which we extend to apply for satisfying LTL specifications. The proposed route-planning method is demonstrated via numerical simulation examples and a hardware implementation on networked single-board computers.