Distributed Attraction-Repulsion Potential for Multi-Agent Formation Control

A new paper on arXiv by Hemanta Ban, Seddik M. Djouadi, and Kevin Tomsovic tackles a fundamental challenge in multi-agent systems: ensuring agents coordinate without colliding. Their approach uses the Lennard-Jones potential—a physics model of atomic interactions—to control attraction and repulsion between agents. The authors prove that if agents start in a collision-free configuration, they will never collide during motion. This is mathematically guaranteed by a uniform lower bound on all inter-agent distances. Using total energy as a Lyapunov function and LaSalle's invariance principle, they show that every trajectory converges to an equilibrium formation, modulo translations. The key insight is that the Lennard-Jones potential provides both repulsion (to prevent collisions) and attraction (to maintain formation), and the authors prove this works even in distributed settings where agents only have local information. Numerical simulations confirm the theory.

The work is significant for real-world applications like drone swarms, autonomous vehicle fleets, or satellite clusters. Existing formation control methods often rely on potential fields that can lead to undesired collisions or deadlocks. This paper provides rigorous guarantees that the system will avoid collisions and converge to a stable formation without centralized coordination. The authors also avoid the issue of agents getting stuck at saddle points by leveraging the analytic nature of the energy function along trajectories. This research appears in the Systems and Control area of arXiv (eess.SY) and has implications for both robotics and dynamical systems theory. It's a step toward safer, more reliable multi-agent systems in complex environments.