A Nonconservative Prescribed-Time Control Approach for Robotic Manipulation: Design and Experiment

Robotic manipulators play a crucial role in industrial automation, medical procedures, and space operations, where fast and precise trajectory tracking is essential for ensuring performance and reliability. This article addresses the challenge of prescribed-time tracking control for robotic manipulator systems. To achieve precise tracking within a prescribed time horizon, we propose a novel control framework that integrates two distinct design methodologies: 1) one based on error scaling and small-gain analysis; and 2) the other leveraging virtual error scaling with a backstepping design. Compared with existing approaches, the proposed methods significantly reduce conservatism while guaranteeing uniform boundedness of the control input, even in the presence of matched nonvanishing disturbances. Notably, the developed framework satisfies the small-gain theorem for arbitrary numerical gain selection, thereby reinforcing its theoretical rigor and practical applicability. Theoretical guarantees are rigorously established using Lyapunov-based analysis, proving that all tracking errors converge to zero within the prescribed time. Compared with existing prescribed-time control schemes, the proposed methods exhibit reduced conservatism in parameter selection and yield more user-friendly control inputs. Moreover, an in-depth analysis of the control law highlights an intuitive parameter selection process, facilitating practical implementation with minimal system modifications. To validate the effectiveness and robustness of the proposed control strategy, numerical simulations on a 2-DoF robotic manipulator and experiments on a real robotic platform are conducted, demonstrating its feasibility in practical applications.