Control and Extended Kalman Filter based Estimation for a Ballbot Robotic System

Control and estimation are carried out in this paper for a ballbot underactuated robotic system. Under position measurements, the Extended Kalman Filter (EKF) is used as an asymptotic estimator in order to estimate the unavailable state vector of the robotic system. Then, the estimated state vector is used by a Linear Quadratic Regulator (LQR) that steers the ballbot to its upright position. It is demonstrated that the closed loop system that includes the ballbot, the LQR, and the EKF remains locally asymptotically stable. Numerical results corroborate the viability of the proposed control and estimation scheme.