Information patterns and Hedging Brockett´s theorem in controlling vehicle formations

Efforts to apply computer vision and various optical and acoustic proximity sensors for distributed/ coordinated motion control of a small group of autonomous vehicles has led us to consider a number of natural feedback control laws which utilize realtime measurements of relative distances between the vehicles. Unfortunately, none of the feedback laws satisfies Brockett´s necessary conditions for asymptotic stabilization. They do appear to provide a basis for practical solutions to a number of interesting vehicle control problems, however. Part of the rationale for proposing feedback laws which are not asymptotically stabilizing is that in a number of cases of practical interest, one may show that the set of initial conditions which are not driven to the prescribed rest point is either small (in some sense) or uninteresting (in the problem context) or both. In some cases, one can also show that by choosing feedback gains in terms of the problem´s initial conditions-using say a table look-up-it is possible to steer from any given initial state into an arbitrarily small neighborhood of the desired goal state. The aim of the research here is to develop a large catalogue of simple controlled motions which in appropriate sequential combinations permit autonomous nonholonomic vehicles to assemble themselves and execute coordinated motions in highly structured formations.