Design of a desirable trajectory and convergent control for 3-DOF manipulator with a nonholonomic constraint

This paper deals with the 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 (1996), we proposed a control law that guarantees the convergence of its state to a given desirable trajectory and to any desired final point, and we also gave a design method of the desirable trajectory. However, this method has a limitation on the location of the initial state. In this 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 specified rather freely. By this new design method, one can derive a desirable trajectory that satisfies given requirements much better than the previous method