Abstract (EN):
This work presents a mathematical toy model for a process of garbage collection encompassing the coordination of a vast array of autonomous devices, where each device needs only a few trajectory adjustments. This simplified conceptual model serves as a valuable tool for both educational and initial research purposes. In this model, each autonomous device is represented by a passive particle, while the environmental currents are depicted by the dynamic behavior of point vortices on a spherical surface. In order to maintain device autonomy, a system of piecewise constant controls is utilized, which involves a limited set of predetermined switching points to adjust the trajectory. Each control incurs an energy expense, and the model aims to minimize this cost by solving a nonlinear optimization problem. The preliminary findings suggest the presence of multiple potential trajectories for autonomous devices, each associated with different energy costs. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
Language:
English
Type (Professor's evaluation):
Scientific
No. of pages:
9