Herding by Caging: a Topological Approach towards Guiding Moving Agents via Mobile Robots
Abstract
In this paper, we propose a solution to the problem of {\it herding by caging}: given a set of mobile robots (called herders) and a group of moving agents (called sheep), we move the latter to some predefined location in such a way that they cannot escape from the robots while moving. We model the interaction between the herders and the sheep by assuming that the former exert virtual ``repulsive forces" pushing the sheep away from them. These forces induce a potential field, in which the sheep move in a way that does not increase their potential. This enables the robots to partially control the motion of the sheep. We formalize this behavior geometrically by applying the notion of {\it caging}, widely used in robotic grasping. We show that our approach is provably correct in the sense that the sheep cannot escape from the robots. We propose an RRT-based motion planning algorithm, demonstrate its probabilistic completeness, and evaluate it in simulations.