The estimation problem and heterogenous swarms of autonomous agents

We consider the situation of a homogeneous swarm of agents following a partially observable leader agent. The resulting, slightly heterogeneous swarm of agents is softly controlled by the leader. We study the swarm dynamics using a recently established connection existing between multi-agents dynamics and nonlinear optimal state estimation. For a whole class of nonlinear agents interactions, we are able to explicitly calculate the resulting swarm dynamics. We interpret the leader-follower dynamics as a nonlinear scalar feedback particle filtering problem which is closely related to the class of non-linear filters initially studied by V. E. Beneš. Despite its nonlinear character, the state estimation problem remains finite dimensional; it merely results from a change of measure in an underlying Ornstein-Uhlenbeck process. The agents interactions, which are driven by common observations of the randomly corrupted position of the leader, can be interpreted as the innovation kernel that underlies any Bayesian filtering issues. Numerical results fully corroborate our theoretical findings and intuition.