We consider a controllability problem for the evolution of a set in V(t). This problem was originally motivated by a model where a dog controls a flock of sheep. Here, V(t) is the region occupied by the sheep and the position of the dog is regarded as a control function. We will discuss necessary conditions and sufficient conditions on the “scare function”, for the global exact controllability of the problem. This result is closely related to the approximation of the trajectories of a sweeping process. This talk is based on a joint work with Alberto Bressan and Khai T. Nguyen.