Fixed-time adaptive gradient neural networks for error-tracking repetitive motion planning of redundant manipulators

Existing repetitive motion planning (RMP) schemes are designed without considering initial shifts, resulting in a transient response of the end-effector lacking a smoothness guarantee. To overcome this limitation, an error-tracking RMP scheme is proposed to regulate the transient behavior of the manipulator, in which an error transition function with adjustable smoothness is constructed to achieve smooth transient motion of the end-effector. As a time-varying optimization problem, an efficient solution to the proposed error-tracking RMP scheme is of critical importance. To this end, fixed-time convergent adaptive gradient neural networks (FxAGNNs) are developed as neural solvers, allowing the end-effector error to follow the user-defined error trajectory. In the presence of practical disturbances, observer-based FxAGNNs are further developed to enhance robustness and maintain fixed-time tracking of the prescribed error trajectory. Theoretical analysis together with numerical and experimental results validates the effectiveness of the proposed schemes.