Motion Planning in Topologically Complex Environments via Hybrid Feedback

In this article we consider the motion planning problem in an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i>-dimensional Euclidean space, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n \geq 2$</tex-math></inline-formula>, containing finitely many obstacles with boundaries possessing a smooth structure. Obstacle boundaries are assumed to be compact and connected embedded submanifolds of the ambient Euclidean space of codimension 1. The proposed solution guarantees both global asymptotic stability of a target configuration and avoidance of the obstacles. The controller is based on a switching scheme between two modes of operation: 1) a free space mode; and 2) an avoidance mode. A simulation study illustrates and clarifies the theoretical results in a 3-D workspace.