Modeling and Control of a Ballbot: A Systematic Approach

The ballbot is a type of mobile robot that achieves dynamic stability by maintaining balance on a spherical ball. Its control poses significant challenges due to its nonlinear and unstable nature, as well as its five degrees of freedom and underactuated system dynamics with dynamic constraints. To the authors’ knowledge, there is a lack of a systematic approach in the literature that addresses these considerations, particularly when it comes to the parameter identification problem. This paper aims to provide a complete and straightforward approach for developing a model-based control of the ballbot, including hardware design and fabrication, detailed system modeling, advanced parameter identification, and control algorithm design. A planar dynamic model is adopted in this work to reduce system complexity and enable real-time control feasibility, serving as a tractable foundation for future extension to a fully coupled 3D dynamic model. The proposed approach is validated through several real-time experiments, demonstrating its robustness and validity. For instance, the identified model achieved a root mean square error (RMSE) of 0.0091 for the yz-plane and 0.0495 for the xy-plane, demonstrating accurate predictive performance, and the controller successfully maintained a tilt angle within ±1° under disturbances. The approach demonstrates a modular, low-complexity framework suitable for both research and educational platforms. Future work may explore extending this approach to more complex dynamic environments, advanced hardware, and nonlinear intelligent control strategies such as fuzzy logic and model predictive control.