A Differential Game Approach to Optimal Intrinsic Formation Control

In this paper, the optimal formation control problem of a multi-agent system is investigated. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The formations are achieved in an intrinsic way in the sense that they are only attributed to the inter-agent interaction and geometric properties of the network, where the desired formations are not designated beforehand. Through the design of individual costs and network topology, regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria while inter-agent collisions are avoided. Finally, numerical simulations are provided in both two-dimensional and three-dimensional Euclidean space to demonstrate the effectiveness and feasibility of the proposed methods.QC 20190529