Group-weighted oscillatory containment for multiple robots under heterogeneous cooperation and competition

The group-weighted containment (GWC) problem is studied for swarms of robots, where the information flow among agents is heterogeneous (weighted) cooperative-competitive and the whole networked systems are composed of multiple different groups. Each group is formed by multiple harmonic oscillator leaders and multiple robot followers governed by Euler-Lagrange (EL) equations. After introducing the definition of group-weighted containment to the networked robot systems, the control algorithms for the agents containing followers and leaders are formulated over newly weighted cooperative-competitive network. Some necessary conditions for solving the weighted containment control problem are established. It is shown that the followers in every group can achieve a kind of novel coordinated behaviors. Specifically, the followers can converge to the dynamic convex hull spanned by the corresponding leaders' weighted coordinates under some conditions. Simulation results are provided to illustrate the effectiveness of the proposed control schemes.