Control of a self-balancing robot with two degrees of freedom via IDA-PBC.

This paper presents an interconnection and damping assignment passivity-based control (IDA-PBC) to drive a self-balancing robot restricted to two degrees of freedom including the dynamics of the actuators. The design of the control law, stability analysis and estimation of the domain of attraction are shown in detail. A convenient change of variables and an appropriate handling of the matching equations have been key to design the control law and to get the asymptotic stability analysis, respectively. Two scalar functions have been used in the design of the controller to underscore how different proposals for the desired potential energy can shape the behavior of the self-balancing robot in closed loop. Experimental results are presented in order to confirm the theoretical proposal and to illustrate the performance of the proposed control law in the regulation task and the practical robustness against external disturbances.