Problem of Collision Avoidance for a Team Motion with Obstacles

The paper deals with the problem of coordinated control for a flock of control systems that are to realize a joint motion towards a target set under collision avoidance. We consider one of its subproblems, which is formulated as follows. During the motion to the target, the members of the group are obliged to lie within a virtual ellipsoidal container, which realizes a reference motion (a "tube"). The container avoids obstacles, which are known in advance, by means of reconfigurations. In response, the flock must rearrange itself within the container, avoiding collisions between its members. The present paper concerns the behavior of the flock within the container, when the flock coordinates its motions with the evolution of the container.