Adaptive tracking control of robotic manipulators with unknown kinematics and uncertain dynamics

This paper addresses a long-standing yet well-documented open problem on trajectory tracking control of manipulators, which is simultaneously affected by unknown kinematics and uncertain dynamics. A theoretical framework for implementing exponential tracking control is established by unifying two novel controllers, i.e., the Jacobian matrix adaption (JMA) controller and the observer-based estimation law, into an integrated control system. The proposed JMA controller converts internal, implicit and immeasurable model information to external, explicit and measurable input-output information for adaptive learning of unknown kinematics. The proposed observer-based estimation law can guarantee the global exponential stability of the estimation error for accurately estimating uncertain dynamics. In addition, the inherent measurement noise, hard nonlinearity, and limited sampling period lead to chattering phenomenon and accumulated errors occur during convergence process. Hence, an improved simple model-free adaptive sliding mode control (ASMC) scheme is proposed to compensate these limitations, which has fast adaptability and powerful tracking and chattering suppression capabilities. It is theoretically proved that the integrated control system is globally exponentially stable. Simulation, experiments and comparison verify the convergence performance of the proposed integrated control system.

Note to Practitioners - Despite the enormous advantages provided by advanced robotic manipulators, developing effective tracking control schemes remains a challenging problem Unfortunately, however, the assumption of precise kinematic and dynamic parameters during tracking control is practically unrealistic due to the absence of precise parameters and measurements of the interaction between robotic manipulators and external environment. This uncertainty will reduce the control performance of manipulators, such as accuracy and repeatability. It is of practical significance to further solve the tracking control of manipulators while considering both the uncertain kinematics and the uncertain dynamics. Therefore, this paper addresses the tracking control problem of manipulators, which is simultaneously affected by unknown kinematics and uncertain dynamics. By unifying the two novel controllers into an integrated control system, a theoretical framework for implementing exponential tracking control is established. In addition, an improved scheme is proposed to compensate chattering phenomenon and accumulated errors during the convergence process. The superior convergence performance of the integrated control system are verified by the simulation and experiments.