  In this paper, we study the cooperative set tracking problem for a group of
Lagrangian systems. Each system observes a convex set as its local target. The
intersection of these local sets is the group aggregation target. We first
propose a control law based on each system's own target sensing and information
exchange with neighbors. With necessary connectivity for both cases of fixed
and switching communication graphs, multiple Lagrangian systems are shown to
achieve rendezvous on the intersection of all the local target sets while the
vectors of generalized coordinate derivatives are driven to zero. Then, we
introduce the collision avoidance control term into set aggregation control to
ensure group dispersion. By defining an ultimate bound on the final generalized
coordinate between each system and the intersection of all the local target
sets, we show that multiple Lagrangian systems approach a bounded region near
the intersection of all the local target sets while the collision avoidance is
guaranteed during the movement. In addition, the vectors of generalized
coordinate derivatives of all the mechanical systems are shown to be driven to
zero. Simulation results are given to validate the theoretical results.
