Energy shaping-based consensus control in networked underactuated Euler-Lagrange systems with communication and input delays

This paper aims to solve the problems of energy shaping -based consensus control in networked underactuated Euler-Lagrange systems (NUELSs) in the presence of communication and input delays. By appropriately introducing the auxiliary sliding mode variable describing local communication interaction among agents and the corresponding adaptive velocity observer in energy -shaping framework, two decentralized time -varying consensus tracking schemes are proposed for NUELSs. The developed schemes systematically integrate the energy of three parts: the system model energy of actuated and underactuated components, the energy of the controller dynamics and the energy of the adaptive update law, as the total energy. Then this total energy formulates the resultant Lyapunov function that can fully guarantee the distributed time -varying consensus tracking of NUELSs having time -varying communication and input delays. Furthermore, simulation examples of multiple flexible -joint manipulator systems characterized by NUELSs demonstrate the potential advantages of the proposed consensus schemes in stability, adaptability, and robustness. The effects of communication and input delays on cooperative tracking performance are also numerically investigated for NUELSs.