Distributed coordinated tracking with a dynamic leader for multiple Euler–Lagrange systems

Abstract—In this note, we study a distributed coordinated tracking problem for multiple networked Euler–Lagrange systems. The objective is for a team of followers modeled by full-actuated Euler–Lagrange equa-tions to track a dynamic leader whose vector of generalized coordinates is time varying under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. We consider two cases: i) The leader has a constant vector of generalized coordinate derivatives, and ii) The leader has a varying vector of gener-alized coordinate derivatives. In the first case, we propose a distributed continuous estimator and an adaptive control law to account for para-metric uncertainties. In the second case, we propose a model-independent sliding mode control algorithm. Simulation results on multiple networked two-link revolute joint arms are provided to show the effectiveness of the proposed control algorithms. Index Terms—Cooperative control, coordinated tracking, distributed control, Euler–Lagrange system, multi-agent systems. I