Finite-Time Formation Control without Collisions for Multiagent Systems with Communication Graphs Composed of Cyclic Paths

Abstract EN

This paper addresses the formation control problem without collisions for multiagent systems.

A general solution is proposed for the case of any number of agents moving on a plane subject to communication graph composed of cyclic paths.

The control law is designed attending separately the convergence to the desired formation and the noncollision problems.

First, a normalized version of the directed cyclic pursuit algorithm is proposed.

After this, the algorithm is generalized to a more general class of topologies, including all the balanced formation graphs.

Once the finite-time convergence problem is solved we focus on the noncollision complementary requirement adding a repulsive vector field to the previous control law.

The repulsive vector fields display an unstable focus structure suitably scaled and centered at the position of the rest of agents in a certain radius.

The proposed control law ensures that the agents reach the desired geometric pattern in finite time and that they stay at a distance greater than or equal to some prescribed lower bound for all times.

Moreover, the closed-loop system does not exhibit undesired equilibria.

Numerical simulations and real-time experiments illustrate the good performance of the proposed solution.