Collisions-Free Distributed Optimal Coordination for Multiple Euler-Lagrangian Systems

Multiagent distributed optimal coordination (DOC) involves the motion conflicts of a large numbers of physical systems, which lead to significant safety challenges in terms of collision avoidance. This article studies the problem of
secure
DOC for multiple uncertain Euler–Lagrangian (EL) systems. The objective is to steer each EL agent to achieve the optimization task while avoiding collisions with other agents. The main challenge focuses on the co-design of optimal coordination strategy and collision avoidance mechanism. The safety barrier certificates in the closed form of path integrals are constructed, which generate provably collisions-free behaviors. With convex optimization and adaptive nonlinear control, a fully distributed protocol is proposed. Based on Lyapunov method and boundedness analysis for the barrier functions, it is proved that the protocol simultaneously guarantees the global convergence and collision avoidance of the EL systems in the presence of parametric uncertainties .