Stabilization of a mobile inverted pendulum with IDA-PBC and experimental verification

Mobile inverted pendulums are expected to be applied to personal mobility and robots which are used in human living space. Although this mobility always needs to be stabilized, previous approaches were based on a linearized model or feedback linearization. In this study, interconnection and damping assignment passivity-based control (IDA-PBC) is applied. The IDA-PBC is a nonlinear control method which has been shown to be powerful to stabilize underactuated mechanical systems. Although partial differential equation (PDE) must be solved to derive the IDA-PBC controller and it is a difficult task in general, we show that the controller for the mobile inverted pendulum can be constructed. A systematic graphical method to select controller parameters which guarantee asymptotic stability and estimate the domain of attraction is also proposed. Simulation results show that the IDA-PBC controller performs fast responses theoretically ensuring sufficient domain of attraction. The effectiveness of the IDA-PBC controller is also verified in experiments. Especially control performance under an impulsive disturbance on the mobile inverted pendulum is verified. The IDA-PBC achieves as fast transient performance as a linear-quadratic regulator (LQR). In addition, we show that when the pendulum inclines quickly and largely due to the disturbance, the IDA-PBC controller can stabilize it whereas the LQR can not.