An Online System Identification Algorithm for Spherical Robot Using the Koopman Theory

This letter proposes a novel linear online identification framework for the spherical robot to address the modeling difficulties posed by nonlinearity and time-varying characteristics. Firstly, the Koopman theory is applied to the spherical robot to build a linear model to approximate the nonlinearity. After selecting a set of observables based on spherical robots' dynamics, the model is identified from data. Then, a new online system identification algorithm based on the Kalman filter and noise estimation was presented, which updates the model in real time to track the time-varying system characteristics. Experiments demonstrate that the Koopman-based linear model meets the precision criteria for long-term forecasting of the nonlinear spherical robot. Through the Kalman filter online identification algorithm, the model parameters can achieve stable convergence, accurately tracking the system changes caused by elements like terrain, load, and actuators. The performance, robustness, and application potential of our algorithm significantly exceed those of traditional methods. After providing a foundation for the spherical robot's adaptive control, this study is also a useful reference for other robots' and nonlinear systems' online identification.