Density Control of Large-Scale Particles Swarm Through PDE-Constrained Optimization

In this article, we describe an optimal control strategy for shaping a large-scale swarm of particles using boundary global actuation. This problem arises as key challenge in many robotics applications, especially when the robots are passive that need to be guided by external fields. The system is and underactuated, making at microscopic particle level infeasible. We consider Kolmogorov forward equation associated stochastic process single encode macroscopic behavior swarm. inputs shape velocity field density dynamics according physical model actuators. find actuation considering whose state governed linear parabolic advection–diffusion where induces transport field. From theoretical standpoint, show existence solution resulting nonlinear problem. numerical employ discrete adjoint method accurately compute reduced gradient how it commutes with optimize-then-discretize approach. Finally, simulations effectiveness driving sufficiently close target.