Limited range spatial load balancing for multiple robots

This paper generalizes a spatial load balancing deployment problem for multiple robots in convex environments to handle limited range agent constraints. Here, limited range is understood as imposing a reachability condition or limitation on the distance that an agent can move. The limited range helps in forming a distributed algorithm that restricts the neighbors of an agent. To account for limited ranges, two different cost functions are considered for minimization subject to a variable area constraint. This area constraint leads to a sub-partition of the environment which is dependent on a set of weights and is invariant under translation of the weights. For a fixed sub-partition, an agent position update law is given to decrease the corresponding cost function. Building on the update laws, a class of distributed algorithms are proposed to solve the limited range spatial load balancing problem. We present a result that shows convergence of the algorithm for the area-only cost function. Finally, we include simulations that show the convergent behavior of the algorithms for both cost functions.