Multi-Robot Control Using Coverage Over Time-Varying Non-Convex Domains

Abstract

This paper addresses the problem of a domain becoming non-convex while using coverage control of a multirobot system over time-varying domains. When the domain moves around in the workspace, its motion and the presence of obstacles might cause it to deform into some non-convex shape, and the robot team should act in a coordinating manner to maintain coverage. The proposed solution is based on a framework for constructing a diffeomorphism to transform a non-convex coverage problem into a convex one. A control law is developed to capture the effects of time variations (e.g., from a time-varying density, time-varying convex hull of the domain and time-varying diffeomorphism) in the system. Analytic expressions of each term in the control law are found for uniform density case. A simulation and robotic implementation are used to validate the proposed algorithm.