Multiple time-varying formation tracking of multiple heterogeneous Euler–Lagrange systems via prescribed-time hierarchical control algorithms in task space

This paper aims at addressing the multiple time-varying formation tracking (MTVFT) problem for multiple heterogeneous Euler–Lagrange systems (MHELSs) in the scenario of uncertain dynamic terms and external disturbances within a prescribed time in the task space. A prescribed-time hierarchical control protocol is proposed to tackle above-mentioned problem. To be specific, a distributed prescribed-time estimator algorithm ensures that each agent can derive the accurate information of their corresponding leaders. In the local control layer, the prescribed-time controller is employed to verify MTVFT problem of the MHELSs, where the settling time is irrelevant to the initial conditions and control parameters of the system. With the help of the Lyapunov stability, the corresponding sufficient conditions for fulfilling the MTVFT in task space are derived. Eventually, the simulations results are performed to illustrate the feasibility and effectiveness of the main results.