Second-Order Consensus of Networked Thrust-Propelled Vehicles on Directed Graphs

This technical note addresses the second-order consensus problem of multiple underactuated thrust-propelled vehicles (TPVs) on directed graphs containing a directed spanning tree. We propose an adaptive control approach to resolve this problem, and the proposed controller does not rely on the commonly used backstepping methodology and the exact knowledge of the mass properties of the TPVs. In addition, the resultant complexity is reduced and the requirement on the interaction graph is relaxed. Using an input-output analysis, we show that the proposed controller realizes second-order consensus of the TPVs, i.e., the position and velocity consensus errors between the TPVs converge to zero, and moreover the velocities of the TPVs converge to the weighted average of their initial values. The performance of the proposed control approach is shown by a numerical simulation.