Chattering elimination in the hybrid control of constrained manipulators via first/second order sliding mode control

This paper deals with the hybrid position/force control problem for constrained manipulators subjected to uncertainties and disturbance of various natures. This problem can be formulated in terms of the solution to differential algebraic equations with a structure which allows the separation of the force and position control when the system is perfectly known. A solution for the uncertain case has been carried out based on sliding mode control theory which has been shown to be highly effective in counteracting uncertainties and disturbances for some classes of uncertain, nonlinear systems. Specific problems related to this technique are chattering elimination and the algebraic coupling between constraint forces and possibly discontinuous control signals. This paper presents a solution to the particular case of a manipulator with n degrees of freedom and n-1 holonomic constraints, leaving the solution to the general problem for further investigations. The main contribution is the use of a new second order sliding mode control algorithm which is proved to yield the solution of the problem after a transient of finite duration without requiring the availability of the acceleration vector.