  This study considers the control of parent-child systems where a parent
system is acted on by a set of controllable child systems (i.e. a swarm).
Examples of such systems include a swarm of robots pushing an object over a
surface, a swarm of aerial vehicles carrying a large load, or a set of end
effectors manipulating an object. In this paper, a general approach for
decoupling the swarm from the parent system through a low-dimensional abstract
state space is presented. The requirements of this approach are given along
with how constraints on both systems propagate through the abstract state and
impact the requirements of the controllers for both systems. To demonstrate,
several controllers with hard state constraints are designed to track a given
desired angle trajectory of a tilting plane with a swarm of robots driving on
top. Both homogeneous and heterogeneous swarms of varying sizes and properties
are considered to test the robustness of this architecture. The controllers are
shown to be locally asymptotically stable and are demonstrated in simulation.
