In this paper, we propose a solution to the problem of herding by caging. Given a set of mobile robots (called herders) and a group of moving agents (called sheep), we move the latter to a 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” that push 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 caging, which is 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.