Robot navigation functions on manifolds with boundary (Q803601)

Mathematically the authors are concerned with the construction of a class of scalar valued analytic maps (navigation functions) on analytic manifolds with boundary. The problem is of significance for robotics and control theory is here considered for a quite special manifold. An important property of the navigation functions constructed here is their deformation invariance (under analytic diffeomorphisms) rendering the construction more general. Arguments suggesting the existence of analytic navigation functions on general analytic manifolds are given and the connection to control theory/robotics is described.