Stabilization of Stiff Formations with a Mix of Direction and Distance Constraints

Abstract

Heterogenous formation shape control with a mix of inter-agent distance and bearing constraints involves the design of distributed control laws that ensure the formation moves such that these inter-agent constraints are achieved and maintained. This paper looks at the design of a distributed control scheme to solve the mixed constraint formation control problem with an arbitrary number of agents. A gradient control law is proposed based on the mathematical notion of a stiff formation structure and a corresponding stiff constraint matrix (which has origins in graph theory). This work provides an interesting and novel contrast to much of the existing work in formation control where distance-only or bearing-only constraints are typically maintained. A stability analysis is sketched and a number of other technical results are given.