Leader-following consensus of uncertain Euler-Lagrange multi-agent systems

What is it about?

The leader-following consensus problem for multiple Euler-lagrange systems has been extensively studied for various scenarios. Under the assumption that the communication graph is jointly connected, one of our recent papers gave the solution for the case where the leader system can generate a combination of arbitrary step signal, arbitrary ramp signal, and arbitrary sinusoidal signals. In practice, it is desirable to enable the control law the capability of maintaining the connectivity of the communication graph, thus achieving the leader-following consensus without assuming the connectivity of the communication graph. We call such a problem as leader-following consensus with connectivity preservation. By combining the adaptive control technique and potential function technique, we will show that such a problem is solvable. By employing different potential functions, our approach may also lead to the solution of such problems as rendezvous, flocking and swarming.

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Why is it important?

Euler-lagrange systems can describe some practical systems such as mobile robots with unknown mass and damping forces, under-actuated robotic vehicles, robot manipulators, rigid bodies, just name a few. This paper solved the rendezvous problem of multiple Euler-lagrange systems, and this problem is much more challenging than the mere consensus problem since our task does not only include consensus, but also maintaining the connectivity of the initially connected communication network.

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