Chattering free sliding modes in robotic manipulators control

In this paper the sliding mode motion design is considered for the nonlinear plants which are linear with respect to the control input. The dynamics of the robotic manipulators is treated with and without the dynamics of the actuators. When the dynamics of the actuators is included a design of the sliding modes for the systems with discontinuous control is performed. If actuators’ dynamics is neglected the control is assumed to be continuous quantity. By combining the variable structure systems and Lyapunov designs a new algorithm is developed which posses all good properties of the sliding mode systems while avoiding unnecessary discontinuity of the control and thus eliminating chattering. Neither the explicit calculation of the equivalent control nor high gain inside the boundary layer are used. The parameters of the control depend on the plant’s gain matrix, and the gradients of the sliding mode manifold. This control method is then applied to develop a unified control strategy for the motion c ontrol systems including the path tracking control, the impedance control and the force control of a robotic manipulator. It is shown that all these tasks can be formulated in the same mathematical form in which selected socalled sliding mode functions, must track their references. In this way the systems state is forced to remain on the selected manifold in the state space after reaching it. The solution is interpreted in both the Joint space and the Work space for ndegrees of freedom robotic manipulator.