Leader–follower and leaderless consensus in networks of flexible-joint manipulators

This work presents some first results on the consensus for networks of nonlinear under-actuated mechanical systems without assuming that the gravity effects are negligible or locally pre-compensated. In particular, the study is focused on networks composed of nonidentical flexible-joint robot manipulators. Through a straightforward Lyapunov stability analysis, it is established that a simple control law provides a solution to the leader–follower consensus problem, provided that at least one follower has a direct access to the leader׳s position, and to the leaderless consensus problem. The network is modeled as an undirected graph and the network interconnection can have variable time-delays. The proposed controller consists of two different terms, one that dynamically compensates the robot gravity and another which ensures the desired consensus objective. This last term is a simple Proportional plus damping scheme. Simulations, using a network with ten manipulators, and experiments, with three 3 degrees-of-freedom manipulators, are provided to support the theoretical contributions of this work.