Continuous Control of Lagrangian Data

This paper addresses the challenging problem of globally controlling several (and possibly independent) moving agents that together form a whole, generally called swarm, which may display interesting properties. Applications are numerous and can be related either to robotics or computer animation. Assuming the agents are driven by their own dynamics (such act as Newtonian particles), controlling this swarm is known as the particle swarm control problem. In this paper, the theory of an original approach to solve this issue, where we rely on a centralized control rather than focusing on designing individual and simple rules for the agents, is presented. To that end, we propose a framework to control several particles with constraints either expressed on a per-particle basis, or expressed as a function of their environment. We refer to these two categories as respectively Lagrangian or Eulerian constraints.