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.