LQG Control Design for a Coupled Ballbot Dynamical System

Ballbot is an under-actuated mobile robot which possesses an omnidirectional mobility. It can maintain the self-balancing and transfer on a spherical ball. The position and orientation of the robot in a space can be determined by two sensors, an encoder and inertia measurement unit. The measurement and fusion data processes from sensors are inevitably effected noise. The noise profile presented in the system is modeled as an additive white gaussian noise (AWGN). In this paper, a linear quadratic gaussian (LQG) controller is developed for a 3D dynamics of a ballbot system. The LQG control design is a combination of linear optimal state-feedback controller and an optimal estimator. The optimal estimator is applied to estimate the outputs of the system which is assumed to be affected by AWGN. Numerical simulations are implemented to demonstrate the effectiveness of our approach for a coupled ballbot dynamics.