The paper deals with the problem of coordinated goal-oriented target control for a group of control systems that are to realize a joint movement towards a given target set under collision avoidance. The members of the group are obliged to lie inside a virtual ellipsoidal container, which realizes a reference motion while also avoiding external obstacles specified in advance. We describe a general solution scheme based on decomposing the main problem into auxiliary subproblems, for which we indicate solution methods as well as the necessity of coordinating these solutions at the final stage.