Nonlinear Discrete-Time Control Approaches for Underactuated Manipulators

In this paper, we propose two nonlinear discretetime control approaches for underactuated manipulators operating in the horizontal plane which are equipped with passive joints. The first control approach is based on an extended linearization. It can be applied to different kinds of underactuated systems such as a cart-pole system or a highly underactuated manipulator. A manipulator is called a highly underactuated manipulator if it has no braking mechanisms and more passive than active joints. However, the control approach mentioned above performs well only if the errors are sufficiently small. Therefore, a discrete-time feedback controller based on nonlinear online optimization is proposed also to counteract large trajectory deviations. In order to reduce the computation time, we present an initialization strategy of the nonlinear online optimization considering the relation between both controllers. Experimental results of both controller are reported to demonstrate advantages and drawbacks.