Multi-robot Implicit Control of Herds

Abstract

This paper solves the problem of herding countless evaders by means of a few robots. The objective is to steer all the evaders towards a desired tracking reference while avoiding escapes. The problem is very challenging due to the highly complex repulsive evaders' dynamics and the underdetermined states to control. We propose a solution that is based on Implicit Control and a novel dynamic assignment strategy to select the evaders to be directly controlled. The former is a general technique that explicitly computes control inputs even in highly complex input-nonaffine dynamics. The latter is built upon a convex-hull dynamic clustering inspired by the Voronoi tessellation problem. The combination of both allows to choose the best evaders to directly control, while the others are indirectly controlled by exploiting the repulsive interactions among them. Simulations show that massive herds can be herd throughout complex patterns by means of a few herders.

Noncooperative Herding With Control Barrier Functions: Theory and Experiments

“…Several prior works have considered the problem of noncooperative shepherding using robots. Some of these include [11], [14], [15], [16], [17], [18]. They refer to the shepherding problem as noncooperative because the flock agents are not necessarily adversarial i.e.…”

“…In the following discussion, we prove that for the one dog v/s one sheep case, ( 17) is always feasible: Theorem 1. If there is one dog and one sheep, then (17) always has a solution.…”

“…The only case when (17) does not have a solution is when the defending constraint is infeasible i.e. when A H u D ≤ b H is infeasible.…”

“…For the robots representing the sheep, ũ is obtained from (1) while for the robots representing the dog, ũ is obtained from (17). In Fig.…”

“…The protected zone is highlighted in green and the goal and center of the protected zone are the black dot. We use (17) to compute the velocity of the dog robot and convert it to angular speed and forward translational speed using (29). As can be noted from the snapshots, the dog robot is able successfully defend the zone from the sheep.…”