Verification of agent navigation in partially-known environments

Abstract

This paper establishes a framework based on logic and automata theory in which to model and automatically verify systems of multiple mobile agents moving in environments with partially-known topologies, i.e., ones which are not completely known at design time. Examples include physical agents designed to be used in many spatial environments and not tailored for a specific one, robots in environments not reachable by humans, and software exploring partially-mapped networks. We model spatial environments as graphs whose edges are labelled with directions. We model agents as finite-state machines that move on the graphs by issuing commands of the form “go in direction X”, that can communicate their internal state to other agents, and that can sense agent positions (including current and visited positions). We treat the incomplete information about the spatial environment by studying the decision problem that asks whether a given collection of agents achieve their tasks on all graphs from a class of graphs — this is called the parameterised verification problem. The framework also introduces a new logical language based on Linear Temporal Logic that is tailored for expressing agent navigation tasks in such environments.Although the parameterised verification problem is undecidable, we identify two key dimensions that need to be limited in order to regain decidability, namely, the set of graph-environments and the amount of sensing and communication between agents. In particular, one should limit the families of graphs to exclude grids, and there should be a bound on the number of times an agent senses the position of another agent or communicates its own state to another agent. We prove that dropping either of these assumptions results in undecidability, even for agents with severe restrictions on their abilities (e.g., with very limited sensing abilities and no communication abilities). The importance of this work is that a) it provides a general computational model for mobile multi-agent systems in environments with partially-known topologies, b) it identifies, for the first time, the precise causes of undecidability of these systems and presents minimal restrictions to alleviate this problem, and c) it provides a generic sound and complete procedure for solving the parameterised verification problem over a broad range of spatial-environments and for agents with very powerful sensing and communication abilities.