• swarm
• shape
• robotics
• lennard-jones
• potential
• robot
• lattice
• formation
• field
• comparison
• artificial
• apf
• analysis

The artificial potential fields method stands as a common methodology for guiding autonomous robots behavior. Despite its wide use, a critical gap exists in the literature regarding the impact of the potentials shape, especially in the context of swarm robotics. Five attractive-repulsive artificial potentials commonly used in literature, together with a newly introduced potential, have been experimentally evaluated for their ability to solve lattice formation in simulated robotic swarms under varying conditions of noise and levels of cognitive speed. Results highlight the crucial impact of potential shape in swarm tasks. Potentials that are not diverging and non-smooth around the equilibrium point are poorly effective even for small swarm sizes. Smooth but non-diverging potentials exhibit acceptable yet sub-optimal performance. Smooth and diverging potentials like Lennard-Jones consistently proved to be optimal across the vast majority of experimental conditions.