Shaping up crowd of agents through controlling their statistical moments

TL;DR

This paper proposes a method to control a crowd of agents by manipulating their statistical moments instead of exact positions, enabling real-time shaping of the group based on moments.

Contribution

It introduces a moment-based control approach using a modified HJB equation, improving real-time applicability over position-based methods.

Findings

Efficient online control of agent groups using moments.

Modified HJB equation enables real-time moment tracking.

Shape of the crowd can be controlled via statistical moments.

Abstract

In a crowd model based on leader-follower interactions, where positions of the leaders are viewed as the control input, up-to-date solutions rely on knowledge of the agents' coordinates. In practice, it is more realistic to exploit knowledge of statistical properties of the group of agents, rather than their exact positions. In order to shape the crowd, we study thus the problem of controlling the moments instead, since it is well known that shape can be determined by moments. An optimal control for the moments tracking problem is obtained by solving a modified Hamilton-Jacobi-Bellman (HJB) equation, which only uses the moments and leaders' states as feedback. The optimal solution can be solved fast enough for on-line implementations.