Modelling, controller design and implementation for spherical double inverted pendulum system

This paper design a nonlinear control law for stabilizing a spherical double inverted pendulum system (SDIPS). SDIPS is a typical 6DOF underactuated nonlinear system. The model of the SDIPS is builded and a new variable feedback gain nonlinear controller is designed to achieve high precision control based on Lyapunov function. The design of the controller is exhaustively discussed in this paper. The major feature of this control scheme is online solving the nonlinear algebraic Riccati equation and obtaining the dynamic feedback gain. Finally, the stabilization of the SDIPS demonstrates the effectiveness of the proposed control scheme. The results of simulation and physical experiments illustrate the proposed nonlinear regulator has good adaptivity and strong robustness.