Kinematic finite-time control of robotic manipulators

This paper addresses the kinematic control problem of the non-redundant and/or redundant manipulators. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. These controllers use a new non-singular Terminal Sliding Mode (TSM) manifold, as being a non-linear integral mapping of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, Jacobian transpose control schemes proposed are shown to be finite-time stable provided that some reasonable assumptions are fulfilled during the manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a planar non-redundant manipulator of two revolute kinematic pairs which accomplishes trajectory tracking by the end-effector in a two-dimensional task space.