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 constra ined manipulators subjected to uncertainties and disturbance of various nat ures. This problem can be formulated in terms of the solution to differenti al algebraic equations with a structure which allows the separation of the force and position control when the system is perfectly known. A solution f or the uncertain case has been carried out based on sliding mode control th eory which has been shown to be highly effective in counteracting uncertain ties and disturbances for some classes of uncertain, nonlinear systems. Spe cific problems related to this technique are chattering elimination and the algebraic coupling between constraint forces and possibly discontinuous co ntrol signals. This paper presents a solution to the particular case of a m anipulator with n degrees of freedom and n - 1 holonomic constraints, leavi ng the solution to the general problem for further investigations. The main contribution is the use of a new second order sliding mode control algorit hm which is proved to yield the solution of the problem after a transient o f finite duration without requiring the availability of the acceleration ve ctor.