Coordination of multi-agent Euler–Lagrange systems via energy-shaping: Networking improves robustness

In this paper, the robust coordination of multi-agent systems via energy-shaping is studied. The agents are nonidentical, Euler–Lagrange systems with uncertain parameters which are regulated (with and without exchange of information between the agents) by the classical energy-based controller where the potential energy function is shaped such that, if the parameters are known, all agents converge globally to the same desired constant equilibrium. Under parameter uncertainty, the globally asymptotically stable (GAS) equilibrium point is shifted away from its desired value and this paper shows that adding information exchange between the agents to the decentralized control policy improves the steady-state performance. More precisely, it proves that if the undirected communication graph is connected, the equilibrium of the networked controller is always closer (in a suitable metric) to the desired one than that of the decentralized controller. The result holds for all interconnection gains if the potential energy functions are quadratic, else, it is true for sufficiently large gains. An additional advantage of networking is that the asymptotic stabilization objective can be achieved by using lower gains into the loop. Some experimental results (using two nonlinear manipulators) given support to the main results of the paper.