Temporal Logic Planning and Control of Robotic Swarms by Hierarchical Abstractions

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We develop a hierarchical framework for planning and control of arbitrarily large groups (swarms) of fully actuated robots with polyhedral velocity bounds moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high-dimensional control system of the swarm into a small-dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model-checking problem. In the obtained hierarchical framework, high-level specifications given in natural language, such as linear temporal logic formulas over linear predicates in the essential features, are automatically mapped to provably correct robot control laws. For the particular case of an abstraction based on centroid and variance, we show that swarm cohesion, interrobot collision avoidance, and environment containment can also be specified and automatically guaranteed in our framework. The obtained communication architecture is centralized. </para>