Bergerman, M.; Xu, Y. "Robust joint and Cartesian control of underactuated manipulators." Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, vol. 118, no. 3, Sep. 1996, pp. 557-565.

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Underactuated manipulators are robot manipulators composed of both active and passive joints in serial chain mechanisms. For mechanisms with large degrees of freedom, such as hyper-redundant snake-like robots and multi-legged machines, the underactuated structure allows a more compact design, weight decrease and energy saving. When one or more joints of a standard manipulator fail, it becomes an underactuated mechanism; a control technique for such system will increase the reliability and fault-tolerance of current and future robots. The study of underactuation is also significant for the control of a variety of rigid-body systems, such as free-floating robots in space and gymnasts, whose structure include some passive joints. In this paper, we present a robust control method to control underactuated manipulators subject to modelling errors and uncertainties. Because an accurate modelling of the underactuated system is more critical for control issues than it is for standard manipulators, this method is significant in practice. Variable structure controllers are proposed in both joint space and Cartesian space, and a comprehensive simulation study is presented to address issues such as computation, robustness, and feasibility of the methods. Experimental results are shown to demonstrate the actual applicability of the proposed methods in a real two degrees-of-freedom underactuated manipulator.