Sensor Coverage Control Using Robots Constrained to a Curve

In this paper we consider a constrained coverage control problem for a team of mobile robots. The robots are asked to provide sensor coverage over a two-dimensional domain, while being constrained to only move on a curve. The unconstrained coverage problem can be effectively solved by defining a locational cost to be minimized by the robots, in a decentralized fashion, using gradient descent. However, a direct projection of the solution to the unconstrained problem onto the curve may result in a very poor spatial allocation of the team within the two-dimensional domain. Therefore, we propose a modification to the locational cost, which incorporates the constraints, and a convex relaxation that allows us to efficiently minimize a convex approximation of the cost using a decentralized strategy. The resulting algorithm is implemented on a team of mobile robots.