Spheres in motion: Adaptive dynamic programming for robotic intelligence

Controlling spherical robots is challenging due to their nonlinear dynamics, underactuated characteristics, and non-holonomic constraints. These challenges become more pronounced in the presence of parameter variations and external disturbances. To address these issues, this paper proposes an Adaptive Dynamic Programming (ADP)-based control framework for spherical robot dynamics. The stability properties of the proposed method are analyzed using Lyapunov theory. The kinematic control layer is designed based on the feedback linearization approach, while the dynamic controller employs ADP to compensate for uncertainties and disturbances. The effectiveness of the proposed method is evaluated through two simulation case studies involving trajectory-tracking tasks under parametric uncertainties and external disturbances. The simulation results show that the proposed controller is capable of achieving accurate trajectory tracking while maintaining stable system performance. To provide a comparative assessment, a Sliding Mode Control (SMC) scheme is also implemented under the same conditions. The obtained results indicate that the ADP-based controller can reduce tracking errors and power consumption compared with the considered SMC approach. In one case study, the tracking error integral achieved by the ADP controller is approximately 36% lower than that of SMC, while the corresponding power consumption is reduced by about 23%. These results demonstrate the potential of the proposed ADP framework for improving trajectory-tracking performance in spherical robots under uncertain operating conditions.