Micro-scale chiplet assembly control with chiplet-to-chiplet potential interaction

We address the problem of simultaneous control of micro-objects (chiplets) immersed in dielectric fluid. An electric field, shaped by an array of thousands of electrodes, is used to transport and position chiplets using dielectrophoretic forces. We use a lumped, 2D, capacitive based (nonlinear) model of motion for the chiplets behavior that include chiplet to chiplet interactions. The chiplet positions are tracked using a high speed camera and image processing algorithms. We use a model predictive control (MPC) approach to derive control inputs (i.e., electrode potentials) that shape the chiplets into a desired pattern. To scale the problem with the number of inputs, the control inputs are parameterized as smooth time and space dependent functions avoiding the need to consider each electrode potential as a separate control input. We use automatic differentiation to compute gradients of the chiplet potential energy, and of the MPC loss and constrain functions. We demonstrate our approach on a scenario where nine chiplets are transported to a set a final positions while a tenth one is kept stationary.