Solving the three-dimensional findpath problem via Liapunov's method

Abstract

This paper presents a method for solving the findpath problem. Commonly known as the second or direct method of Liapunov, the method is used to solve this geometric problem of finding collision-free trajectories of moving solid objects amongst other fixed and moving solid objects. A Liapunov function is proposed for a n-point dynamical system in three-space. Computer simulations are carried out to show the effectiveness of the proposed Liapunov function-based feedback controllers.