Modelling and control of a spherical inverted pendulum on a five-bar mechanism

Abstract

This paper describes the kinematics and dynamics modelling of a mechanical system consisting of a spherical inverted pendulum whose base is mounted on a parallel planar mechanism, better known as a five-bar mechanism. The whole mechanism has four degrees of freedom, but it has only two actuators and so it is an under-actuated system. The nonlinear dynamics model of the complete system is first obtained using a non-minimal set of generalized coordinates, and then a reduced equivalent model is computed. To validate this approach, the reduced model is linearized and simulations are carried out, showing the stabilization of the system with a simple LQR controller. Experimental results on an academic prototype are also presented.