Optimal Control of Several Motion Models

TL;DR

This paper develops optimal control strategies for multiple crowd motion models in planar environments, deriving necessary conditions, proposing algorithms, and demonstrating their effectiveness through simulations.

Contribution

It introduces new optimal control conditions for crowd motion models with multiple agents and obstacles, along with effective algorithms and illustrative examples.

Findings

Derived necessary optimality conditions for crowd motion control.

Proposed algorithms successfully solve complex motion planning problems.

Validated models through simulations and provided implementation resources.

Abstract

This paper is devoted to the study of the dynamic optimization of several controlled crowd motion models in the general planar settings, which is an application of a class of optimal control problems involving a general nonconvex sweeping process with perturbations. A set of necessary optimality conditions for such optimal control problems involving the crowd motion models with multiple agents and obstacles is obtained and analyzed. Several effective algorithms based on such necessary optimality conditions are proposed and various nontrivial illustrative examples together with their simulations are also presented. The implementation of all the considered motion models can be found via the link: https://github.com/tancao1128/Optimal_Control_of_Several_Motion_Models with the instruction and demonstration video uploaded at https://www.youtube.com/watch?v=B8DQ0wvCtIQ.