Adaptive Modular Geometric Control of Robotic Manipulators

This paper proposes an adaptive modular geometric control framework for robotic manipulators. The proposed methodology decomposes the overall manipulator dynamics into individual modules, enabling the design of local geometric control laws at the module level. To address parametric uncertainties, geometric adaptation law is incorporated into the control structure, requiring only a single adaptation gain for the entire system while ensuring physically consistent and drift-free parameter estimates. Exponential stability of the proposed controller is established in the nominal case. Numerical simulations on a complex redundant robotic manipulator are conducted to evaluate the proposed approach against existing modular and geometric control methods. The results show that the proposed method reduces the RMS position error by at least 12.2% compared with state-of-the-art controllers under almost the same control effort. In addition, the adaptive extension demonstrates strong capability in compensating for parametric uncertainties and preserving high tracking performance.