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.