<p>This paper achieves the predefined-time task-space bipartite time-varying formation tracking problem for heterogeneous robot systems facing the case of kinematic redundancy and perturbations (namely, external disturbances and parameter uncertainties), considering matrix-weighted digraphs. Based on a novel nonsingular terminal sliding-mode control method, a predefined-time hierarchical control mechanism is designed to solve the foregoing issue. Meanwhile, to mitigate the impact of perturbations, neural networks are integrated into the method. Precisely, the estimator layer estimates the information of the leader, while the control layer ensures that all followers can achieve the control objectives. More noteworthy is that this study considers kinematic redundancy to enhance task allocation flexibility, and it enables the settling time to be preset according to actual requirements. Additionally, the convergence time is independent of system control parameters and initial conditions. Furthermore, the theoretical validity of the proposed control algorithm is rigorously established through Lyapunov stability analysis, which is further validated through numerical simulations.</p>