Adaptive Leader-Follower Coordination of Lagrangian Multi-Agent Systems under Transient Constraints

This paper presents a novel control methodology for the coordination of a multi-agent system with 2nd order uncertain Lagrangian dynamics, while guaranteeing collision and connectivity properties in the transient state. More specifically, we consider that a leader agent aims at tracking a desired pose, while all the agents must avoid collisions with each other. Motivated by cooperative tasks, we also consider that a subset of the initially connected agents must remain connected, in the sense of a connected sensing graph. We employ a key property of the incidence matrix and integrate potential fields with discontinuous adaptive control laws to compensate for unknown dynamic parameters of the model and external disturbances. Simulation results in a realistic dynamics engine illustrate the theoretical findings.