Hierarchical Consensus of Constrained Second-Order Multiagent Systems With Application to Formation of Multiple Mobile Robots

In this paper, the consensus problem is studied for leader-follower second-order multi-agent systems subject to velocity constraints. To solve the problem, an innovative hierarchical distributed control scheme is built, which consists of two main layers. In the upper layer, for the followers, a constrained distributed reference signal generator is developed with fractional differential gains to produce suitable references converging to the leader while maintaining velocity constraints. In the lower layer, via a nonlinear mapping control method, some constrained tracking controllers are designed for the followers to track the references produced by the generator. By means of bidirectional signal flows in the two layers, the followers asymptotically achieve consensus with the leader in the presence of velocity constraints. Moreover, the proposed control scheme is also applied to formation control of multiple mobile robots. Simulations and experiments demonstrate the effectiveness and advantages of the proposed hierarchical constrained distributed control scheme.