Tracking the Kinematically Optimal Trajectories by Mobile Manipulators

This paper addresses the kinematically optimal control problem of the mobile manipulators. Dynamic equations of the mobile manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the mobile manipulator when tracking the trajectory by the end-effector. A computationally simple class of the Jacobian transpose control algorithms is proposed for the end-effector trajectory tracking. Such controllers apply a new non-singular Terminal Sliding Mode (TSM) manifold defined by a non-linear integral equality of the second order with respect to the task space tracking error. Based on the Lyapunov stability theory, the proposed Jacobian transpose control schemes are proved to be finite-time stable provided that some well-founded assumptions are fulfilled during the mobile manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a mobile manipulator that attains trajectory tracking by the end-effector in a two-dimensional task space and simultaneously minimises some objective function.