Consensus in networks of uncertain euler-lagrange agents using adaptive gravity compensation
Résumé
The leaderless and the leader-follower consensus are the most basic synchronization behaviors for multi-agent systems. For networks of Euler-Lagrange (EL) agents different controllers have been proposed to achieve consensus, requiring in all cases, either the cancellation or the estimation of the gravity forces. While, in the first case, it is shown that a simple Proportional plus damping (P+d) scheme with exact gravity cancellation can achieve consensus, in the latter case, it is necessary to estimate, not just the gravity forces, but the parameters of the whole dynamics. This requires the computation of a complicated regressor matrix, that grows in complexity as the degrees-of-freedom of the EL-agents increase. To simplify the controller implementation we propose in this paper a simple P+d scheme with only adaptive gravity compensation. In particular, two adaptive controllers that solve both consensus problems by only estimating the gravitational term of the agents and hence without requiring the complete regressor matrix are reported. The first controller is a simple P+d scheme that does not require to exchange velocity information between the agents but requires centralized information. The second controller is a Proportional-Derivative plus damping (PD+d) scheme that is fully decentralized but requires exchanges of speed information between the agents. Simulation results demonstrate the performance of the proposed controllers.