Achieving overlap of multiple, arbitrarily shaped footprints using rendezvous cones

Abstract

This paper addresses the problem of achieving the overlap of footprints of unmanned aerial vehicles used for search and surveillance or for establishing communication between remote areas. The need of the footprints to overlap is dictated by the requirement that no part of the sensed area is left uncovered in a search and surveillance operation or by the need to position a relay unmanned aerial vehicle in the overlap region of two distant unmanned aerial vehicles in order to enable them to communicate with each other. The problem is generalized by considering arbitrarily shaped footprints that can arise in various applications. The concept of a rendezvous cone, which invokes several notions from hyperbolic geometry and collision dynamics in the relative velocity framework, is used as the basis for the development of nonlinear analytical guidance laws that enable the overlap of footprints to the requisite depth. Simulations are presented that demonstrate the effectiveness of the developed guidance laws.