Socially Fair Coverage Control

Abstract

We investigate and develop algorithms for social fairness in coverage control problems. Existing coverage control methods are efficient, optimizing the average expected distance from any event to the nearest robot. However, in societal applications like disaster response or transportation, these conventional objectives lead to disparate coverage costs with respect to different groups within a population. We formulate social fairness for coverage control as the minimization of the maximum coverage cost among a set of groups within a population. Our approach uses Voronoi iteration to solve this novel problem by approximating the non-differentiable objective with the log-sum-exp and defining a gradient based controller that prioritizes fairness while also optimizing average performance when disparities between groups are low. We show convergence properties of this proposed control law and demonstrate the approach in simulations of randomly generated population densities as well as environments generated from U.S. census data on population rates and demographics. Our approach provides greater fairness than existing methods while maintaining similar computational time and convergence properties.