<p>Robotic manipulators are subject to parametric uncertainties and external disturbances, which complicate accurate trajectory tracking. Existing approaches may require accurate dynamic models, multiple adaptive networks, or conservative fixed switching gains. To address these issues, an adaptive terminal sliding-mode controller integrating a dual-feedback Improved-RNN with a barrier-function-based super-twisting mechanism is developed. A single Improved-RNN directly approximates the lumped equivalent control term, while the switching gain changes from a time-varying reaching gain to a state-dependent barrier-function gain. Lyapunov analysis establishes finite-time convergence of the overall closed-loop system under the proposed controller. Unified comparisons with two published fixed-time controllers and an RBFNN comparator are conducted under identical nominal and sudden payload-change conditions. The proposed method achieves the lowest nominal tracking RMSE and the shortest nominal settling times for both joints, and maintains small tracking errors after the sudden payload change without controller retuning.</p>