Composing Navigation Functions on Cartesian Products of Manifolds with Boundary

Abstract

Given two compact, simply connected manifolds with boundary, and a navigation function (NF) on each manifold, this paper presents a simple composition law that yields a new NF on the cross product space. The method provides tunable “hooks” for shaping the new potential function while still guaranteeing obstacle avoidance and essentially global convergence. The composition law is associative, and successive compositions fold into a single, computational simple expression, enabling the practical construction of NFs on the Cartesian product of several manifolds.