Parameter Identification and LQR/MPC Balancing Control of a Ballbot

This paper presents a method for identifying the parameters of a ballbot (a robot balancing on a ball) from proper input/output measurements and by exploiting available information about its model structure. To avoid biased parameter estimations, the method adopts a so-called indirect closed-loop identification, where a linearized model of the system dynamics is identified. Owing to the special structure of the linearized model, the parameters of the nonlinear model, which are nonlinear combinations of it physical parameters, can be extracted by solving a set of linear equations. These identified parameters could be used to initialize any suitable optimization tool for further enhancing their values. One important feature of the method is that it allows the use of highly developed off-the-shelf algorithms of system identification, which can give unbiased/consistent estimates. For evaluating the identified model, it has been employed to design a combination of two controllers, a linear quadratic regulator (LQR) and a model predictive control (MPC) for balancing the ballbot. The experimental results demonstrate that the ballbot can be balanced with such a composition control based on the identified model.