Stabilization of underactuated four-link gymnast robot using torque-coupled method

• A coupled relationship between control toques is constructed for an underactuated four-link gymnast robot (UFGR). It changes the nonlinear UFGR system into a cascade-connected system.
• We transform the stabilization of the UFGR into that of an underactuated two-link acrobot.
• An energy-based stabilizing controller is designed for the two-link acrobot.
• The structure of the proposed control system is simple. And our proposed strategy is easy to extend to the stabilization control of n-DOF (n>4)(n>4) underactuated manipulator.

In this paper, we use an underactuated four-link gymnast robot (UFGR) with a passive first joint to model a gymnast on the bar, and consider the stabilization of the UFGR at the straight-up position. First, we introduce a coupled relationship between control torques for the UFGR. It decouples some state variables of the UFGR from others and changes the nonlinear UFGR system into a cascade-connected system. And then, we use an energy-based method to design a stabilizing controller for the zero dynamics of the cascade-connected system. And the triangle lemma guarantees the control objective of the UFGR to be achieved. The torque-coupled method transforms the stabilization of an underactuated four-link manipulator into that of an underactuated two-link acrobot. This makes the structure of the control system simple. Moreover, our proposed control strategy is easy to extend to the stabilization control of other multi-input nonlinear underactuated systems. Simulation results using the characteristics parameters of a gymnast demonstrate the validity of the proposed method.