Symmetry and structural balance play a fundamental role in the collective behavior of networked agent systems (NASs). In particular, cluster formation tracking, representing the emergence and maintenance of symmetric group structures, has attracted significant attention due to its wide applications in robotics and autonomous systems. However, most existing approaches assume autonomous leaders, which may not be applicable in scenarios where human intervention is required. With this in mind, this paper addresses the cluster formation tracking problem for NASs with collision avoidance, where the leader receives control inputs from a human-in-the-loop (HiTL), making the leader a non-autonomous system. A distributed control protocol is developed so that followers can track the trajectories of their designated leaders using only relative information from neighboring agents. Sufficient conditions are established to guarantee collision-free cluster formation tracking, and Lyapunov-based analysis is employed to prove the asymptotic convergence of the subgroup tracking errors. In the proposed framework, human intervention is incorporated through external commands applied to the leaders, which makes the leader dynamics non-autonomous while preserving the distributed nature of the follower controllers. Simulation studies on a 13-agent network with three subgroups show that all followers achieve the desired time-varying cluster formations under HiTL-driven leader motions, with convergence times ranging from 4.21 s to 5.12 s. Moreover, the final tracking errors of all followers are reduced below 9.07×10−5, while the minimum pairwise distances within each subgroup remain strictly above the prescribed safety threshold. These quantitative results verify both the effectiveness of the proposed protocol and the practical feasibility of integrating HiTL commands into collision-free cluster formation tracking.
Lu et al. (Sat,) studied this question.