2D Density Control of Micro-Particles using Kernel Density Estimation

We address the challenge of controlling the density of particles in two dimensions by manipulating the electric field acting on the particles immersed in a dielectric fluid. An array of electrodes is used to control the electric field, which applies dielectrophoretic forces to achieve the desired pattern of particle density. To model the motion of a particle, we use a lumped, 2D, capacitive-based, and nonlinear model. We estimate the spatial dependence of the capacitances using electrostatic COMSOL simulations. We formulate an optimal control problem to determine the electrode potentials that will produce the desired particle density pattern. The loss function is defined in terms of the difference between the target density and the particle density at a specific final time. To estimate the particle density, we use a kernel density estimator (KDE) computed from the particle positions that vary with the electrode potentials. The effectiveness of our approach is demonstrated through numerical simulations that illustrate how the particle positions and electrode potentials change when shaping the particle density from a uniform to a Gaussian distribution.