Networking improves robustness in flexible-joint multi-robot systems with only joint position measurements

This paper studies the robustness in the coordination—via energy-shaping—of multiple nonidentical flexible-joint robots with only joint position measurements. The control objective is to drive all manipulators link positions to the same constant equilibrium. If the physical parameters are exactly known, then a classical decentralized energy-shaping controller solves the desired control objective. However, under parameter uncertainty, the globally asymptotically stable equilibrium point is shifted away from the desired value. The main contribution of the paper is to show that the steady-state performance is improved adding to the decentralized control policy information exchange between the agents. More precisely, it is proven that the equilibrium with the networked controller is always closer (in a suitable metric) to the desired one than that using the decentralized controller, provided the communication graph representing the network is undirected and connected. This result holds globally for sufficiently large interconnection gains and locally (in a suitably defined sense) for all values of the gains. An additional advantage of networking is that the asymptotic stabilization objective can be achieved injecting lower gains into the loop. The paper also provides simulation and experimental evidence, which illustrate the fact that networking improves robustness with respect to parameter uncertainty.