Stabilization of an underactuated 2-Dimensional TORA using passivity-based controllers

2-Dimensional Translational Oscillator with Rotational Actuator (2DTORA) consisting of an actuated rotational proof-mass and two unactuated translational carts is a novel underactuated system. In this paper, passivity-based stabilizing controllers are designed for 2DTORA based on its Euler-Lagrange structure and passivity property. Firstly, the dynamics of 2DTORA is described by Euler-Lagrange Equations. Motivated by constructing a damped close-loop Euler-Lagrange system, the controller dynamics are designed to shape the potential energy and inject required damping. The designed controller is with the feedback of the rotational actuator´s position only. Moreover, by modifying controller dynamics with a saturation function, the control input can be constraint to certain bounds. Finally, simulation results demonstrate the feasibility and effectiveness of the controllers.