Networked Lagrangian Systems

This chapter moves from point models primarily adopted in distributed multi-agent coordination to more realistic Lagrangian models. A class of mechanical systems including autonomous vehicles, robotic manipulators, and walking robots are Lagrangian systems. We focus on fully-actuated Lagrangian systems. We first study distributed leaderless coordination algorithms for networked Lagrangian systems. The objective is to drive a team of agents modeled by Euler–Lagrange equations to achieve desired relative deviations on their vectors of generalized coordinates with local interaction. We then study distributed coordinated regulation and distributed coordinated tracking algorithms in the presence of a leader for networked Lagrangian systems under the constraints that the leader is a neighbor of only a subset of the followers and the followers have only local interaction. In the case of coordinated regulation, the leader has a constant vector of generalized coordinates. In the case of coordinated tracking, the leader has a varying vector of generalized coordinates. In both cases, the objective is to drive the vectors of generalized coordinates of a team of followers modeled by Euler–Lagrange equations to approach that of a leader. Simulation results show the effectiveness of the proposed algorithms.