Moving a Robot Arm: An interesting application of the Direct method of Lyapunov

Jito Vanualailai; Bibhya Sharma

Authors

Jito Vanualailai Department of Mathematics and Computing Science, University of the South Pacific, Suva, FIJI.
Bibhya Sharma Department of Mathematics and Computing Science, University of the South Pacific, Suva, FIJI.

Keywords:

Lyapunov stability, Lyapunov function, Robot Dynamics and Control, Findpath Problem Motion Planning

Abstract

In this paper, we explore the fundamentals of an emerging technique applicable, at least, in principle, to robot navigation, or motion planning. Termed the second method of Lyapunov, it is currently a powerful mathematical technique used to study the qualitative behaviour of natural or man-made systems that could be modeled, in an approximate way, by differential equations. We review the Lyapunov method and then in a simple and direct way, we use it to propose a theoretical technique to control the motion of a planar arm in a constrained environment. The controllers are mathematical entities which are nonlinear in nature. Computer simulations are used to illustrate the effectiveness of the proposed controllers.