Reciprocal Neural State–Disturbance Observer for Model-Free Trajectory Tracking of Robotic Manipulators

High-precision trajectory tracking of robotic manipulators is fundamentally challenged by strong nonlinear dynamics, unmodeled uncertainties, and external disturbances. This paper proposes a Reciprocal Neural State–Disturbance Observer (RNSDO) featuring a neural activation mechanism for adaptive gain modulation and a reciprocally coupled state–disturbance estimation architecture. By reshaping the observer error dynamics through mutual feedback between state and disturbance estimation, the proposed structure alleviates the conflict between fast transient disturbance reconstruction and steady-state noise suppression, while requiring only position measurements. A decentralized position controller is designed based on RNSDO. The global asymptotic stability of the resulting closed-loop system is rigorously established via Lyapunov analysis. Extensive simulations on a PUMA 560 and experiments on a 7-DOF Franka FR3 robotic manipulator demonstrate highly consistent performance trends. The proposed method achieves improved state and disturbance estimation accuracy and enhanced robustness against unmodeled dynamics and payload variations compared with a linear Improved Extended State Observer (IESO), a classical Nonlinear Extended State Observer (NLESO), and a model-based Nonlinear Disturbance Observer-based Adaptive Robust Controller (NDO-ARC). Furthermore, the algorithm exhibits excellent real-time feasibility with a minimal computational footprint.