Predefined-Time Bipartite Formation Control for Networked Robotic Systems Under Directed and Matrix-Weighted Topology

This paper primarily delves into the pre-defined-time bipartite formation control (PTBFC) for networked robotic systems (NRSs) under directed and matrix-weighted topology, taking into account external disturbances and the directed topology incorporates interactive dynamics involving both cooperative and adversarial engagements. In order to address the aforementioned issues, presenting a hierarchical control algorithm grounded in the utilization of estimators, allowing for a systematic analysis of the system. Of note, the determination of settling time can be approached stochastically, tailored to specific practical needs. Subsequently, a set of sufficient conditions for implementing PTBFC was derived by leveraging Lyapunov stability analysis and the properties of the matrix-weighted Laplacian. Finally, the feasibility of the developed control strategy is validated through simulation experiments.