A Directed Spanning Tree Adaptive Control Framework for Time-Varying Formations

In this paper, the time-varying formation and time-varying formation tracking problems are solved for linear multi-agent systems over digraphs without the knowledge of the eigenvalues of the Laplacian matrix associated to the digraph. The solution to these problems relies on a framework that generalizes the directed spanning tree adaptive method, which was originally limited to consensus problems. Necessary and sufficient conditions for the existence of solutions to the formation problems are derived. Asymptotic convergence of the formation errors is proved via graph theory and Lyapunov analysis

Fault-Tolerant Formation Tracking of Heterogeneous Multi-Agent Systems with Time-Varying Actuator Faults and Its Application to Task-Space Cooperative Tracking of Manipulators

This paper addresses a formation tracking problem for nonlinear multi-agent systems with time-varying actuator faults, in which only a subset of agents has access to the leader's information over the directed leader-follower network with a spanning tree. Both the amplitudes and signs of control coefficients induced by actuator faults are unknown and time-varying. The aforementioned setting improves the practical relevance of the problem to be investigated, and meanwhile, it poses technical challenges to distributed controller design and asymptotic stability analysis. By introducing a distributed estimation and control framework, a novel distributed control law based on a Nussbaum gain technique is developed to achieve robust fault-tolerant formation tracking for heterogeneous nonlinear multi-agent systems with time-varying actuator faults. It can be proved that the asymptotic convergence is guaranteed. In addition, the proposed approach is applied to task-space cooperative tracking of networked manipulators irrespective of the uncertain kinematics, dynamics, and actuator faults. Numerical simulation results are presented to verify the effectiveness of the proposed designs