Distributed adaptive containment control of networked flexible-joint robots using neural networks

• This research is the first trial for networked Lagrangian systems with flexible joints.
• Simple local controllers are designed regardless of the order of followers and the complexity of communication links.
• Derivative terms of multiple dynamic leaders are not required to implement the controllers.

This study presents a distributed adaptive containment control approach for a group of uncertain flexible-joint (FJ) robots with multiple dynamic leaders under a directed communication graph. The leaders are neighbors of only a subset of the followers. The derivatives of the leaders are unknown, namely, the position information of the leaders is only available for implementing the proposed control approach. The local adaptive dynamic surface containment controller for each follower is designed using only neighbors’ information to guarantee that all followers converge to the dynamic convex hull spanned by the dynamic leaders. The function approximation technique using neural networks is employed to estimate the model uncertainties of each follower. It is proved that the containment control errors converge to an adjustable neighborhood of the origin regardless of model uncertainties and the lack of shared communication information. Simulation results for FJ manipulators are provided to illustrate the effectiveness of the proposed adaptive containment control scheme.