Potential-Based Swarm

Problem Statement

Potential-field swarm control combines attractive and repulsive fields to produce distributed collision-avoiding collective motion.

Model and Formulation

Agent force model:

$$F_i=-\mathrm{\nabla }{U}_{goal}(p_i)-\sum _{j\ne i}\mathrm{\nabla }{U}_{ij}(p_i,p_j)$$

where U_{ij} can be Lennard-Jones-like or quadratic barrier potentials.

Practical Notes

• Saturate the goal attraction. Unsaturated linear attraction is thousands of times stronger than the lattice forces at the start of a long transit, so the swarm crosses the map as a disordered blob and only forms up on arrival. Capping it at a fixed radius keeps formation-keeping and navigation comparable throughout.

• Clamp the obstacle repulsion. The 1/d² term is unbounded, so an agent that clips an obstacle receives an infinite kick and leaves the world. Floor the surface distance and cap the total force.

• Score the centroid, not the agents. A lattice converges with each agent one spacing away from the goal by construction, so mean agent-to-goal distance never goes to zero and reads like a failure. The meaningful numbers are centroid-to-goal error and nearest-neighbour spacing against d_des.

• Potential shape determines spacing and rigidity.

• Local minima are a known issue in cluttered environments.

• Add damping terms to prevent oscillatory interactions.

Implementation and Execution

python -m uav_sim.simulations.swarm.potential_swarm

Evidence

References

• Spears et al., Distributed Physics-Based Control of Swarms (2004)
• Khatib, Real-Time Obstacle Avoidance for Manipulators and Mobile Robots (1986)

Related Algorithms

• Reynolds Flocking
• Voronoi Coverage