Design of a desirable trajectory and convergent control for 3-D.O.F manipulator with a nonholonomic constraint

Abstract

This paper is concerned with control of a 3 link planar underactuated manipulator whose most distal joint is unactuated. This system is known as a second order nonholonomic system. In a previous paper, we proposed a control law that guarantees the convergence of its state to a given desirable trajectory and to any desired final point. We also gave a design method of the desirable trajectory, but this method has a limitation on the location of the initial state. In the present paper, we propose a design method of a desirable trajectory that starts from any given initial point, converges to any given desired final point, and on the way passes through any given desired passing point that can be specifyed rather freely. By this new design method, we can derive a desirable trajectory that satisfies given requirements much better than the previous method.