Passivity-based Nonlinear Control for a Ballbot to Balance and Transfer

Ballbot is a robot that can transfer to a given position while maintaining a self-balanced upright posture on a spherical ball. This paper proposes a nonlinear control of a ballbot using three omnidirectional wheels in the driving mechanism. Assuming a small swing angle for balance, the full dynamics of the ballbot can be decomposed into three, which are two underactuated dynamics for two orthogonal vertical planes and the fully actuated dynamics for one horizontal plane. The passivity of closed-loop systems of vertical planes is derived from the modified potential energy function. The proposed controller is designed to control the balancing and transferring of the system based on Lyapunov theory and the passivity of the system. A proportional-derivative feedforward controller is applied to regulate the heading motion in the horizontal plane. Experiments are performed with a real ballbot system to validate the effectiveness of system modeling and to show the controllability of the proposed algorithm.