<p>High-precision dual-arm robotic manipulation is essential in applications such as railway overhead contact system maintenance, where motion–force coupling, nonlinear dynamics, and strict transient performance requirements arise simultaneously. This paper proposes a Lyapunov-barrier-enabled adaptive neural control framework that achieves coordinated motion and internal force regulation for a dual-arm robot subject to modeling uncertainties and external disturbances. Asymmetric time-varying barrier Lyapunov functions are constructed to encode prescribed transient and steady-state bounds on the task space tracking error, thereby guaranteeing constraint satisfaction throughout the motion. A unified dynamics-based controller is then developed, in which internal-force feedback is embedded into the dual-arm object model to suppress load deformation while tracking the desired trajectory. To cope with unknown dynamics, radial basis function neural networks are integrated with a smooth switching mechanism that blends data-driven approximation and robust compensation, and a Lyapunov-based analysis establishes global uniformly ultimately bounded stability of all closed-loop signals as well as convergence of the internal force to a small neighborhood of its reference. Simulation studies inspired by contact wire stagger adjustment demonstrate that the proposed method achieves faster convergence, smaller tracking and internal-force errors, and stronger disturbance rejection than traditional adaptive control, NN-only control, model predictive control, and sliding-mode control.</p>