Distributed Time-varying Formation and Optimization for Uncertain Euler-Lagrange Systems

In this paper, we consider a distributed time varying formation and optimization problem for a group of robots with uncertain Euler-Lagrange dynamics. The robots arc required to keep a time-varying formation as well as optimizing a quadratic objective function that is composed of the state information of all the robots. The problem is first mathematically reformulated as a distributed time-varying optimization problem, where the time-varying formation task is viewed as a time-varying constraint. An inexact penalty function based method is proposed to estimate the optimal solution of the time-varying optimization problem. Lyapunov based analysis is developed, and asymptotical convergence to the estimated optimal solution is proven. A numerical example is provided to show the effectiveness and efficiency of the proposed methods.