Discrete–Time Linear Quadratic Regulator for a NXT Ballbot System

In this paper, a Discrete-Time Linear Quadratic Regulator (DTLQR) is proposed to the control of a NXT ballbot (NXTB) system. The NXTB system is a nonlinear underactuated robotic system having four generalized coordinates and two generalized torques. Such a robotic system can be seen as a system whose mechanical configuration is given in the form of an inverted pendulum mounted on a ball. In our work, the nonlinear model of the NXTB is linearized around an operation point for which its body coincides with the upright position. The DTLQR is then designed from the linearized model, when considering distinct sets of values for the servomotors’ physical parameters, and whose performance is validated and contrasted with that from its respective version in continuous–time, i.e., a continuous–time LQR (CTLQR), via numerical simulations.