Gradient-based control with the Lennard-Jones potential yields global well-posedness, a strict lower bound on inter-agent distances, and convergence to equilibria modulo translations for collision-free initial conditions.
Convergence of solutions of second- order gradient-like systems with analytic nonlinearities,
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Distributed Attraction-Repulsion Potential for Multi-Agent Formation Control
Gradient-based control with the Lennard-Jones potential yields global well-posedness, a strict lower bound on inter-agent distances, and convergence to equilibria modulo translations for collision-free initial conditions.