A Novel ℒ1 Gain Performance Based Multi-robot System Formulation Control Design Method

The time-varying formations are usually required in practice for multi-agent systems to track the trajectories generated by multiple leaders. The ability to maintain a stable formation property is helpful in terms of facilitating subsequent tasks such as collaborative detection, cooperative reconnaissance and performing other specific task like fetch and transport goods together as a team. However, most of existing methods, on the other hand, are fragile to the measurement noises and network sparsity. Moreover, it seems that few results are available that considering the internal and external control loop to arrive the consensus of position, the velocity and the attitude simultaneously. To overcome these limitations, in this paper, we proposed a novel scheme and developed a novel ℒ
₁
gain algorithm, where the integrated two loop robot control scheme is endowed with disturbance rejection ability, and it can maintain the formation structure during motion along a pre-determined or online generated geometric path, and to follow a timing law that dominates the rate of advancement of the group. Sufficient conditions are established to guarantee the stability, the invariant set property, the ℒ
₁
gain index, and also the initial tracking error bounding constraints, which are formulated and presented in terms of LMIs/BMIs and can be readily solved to obtain the controller. Extensive simulations are carried out to validate the effectiveness of the proposed method, and the five robots as well as the three robots formulation cases are detail analysis. It turns out that, in addition to providing a novel perspective of the formulation control problem with disturbance rejection ability, the approach adopted in this paper also paves the way to several extensions in relation to control of multi-agent systems in accordance with swarm intelligence principles, such as the collision avoidance, the delayed multi-agent system control, the incorporation of multiple simultaneous objectives and control design under communication constraints.