  In many applications, multi-robot systems are required to achieve multiple
objectives. For these multi-objective tasks, it is oftentimes hard to design a
single control policy that fulfills all the objectives simultaneously. In this
paper, we focus on multi-objective tasks that can be decomposed into a set of
simple subtasks. Controllers for these subtasks are individually designed and
then combined into a control policy for the entire team. One significant
feature of our work is that the subtask controllers are designed along with
their underlying manifolds. When a controller is combined with other
controllers, their associated manifolds are also taken into account. This
formulation yields a policy generation framework for multi-robot systems that
can combine controllers for a variety of objectives while implicitly handling
the interaction among robots and subtasks. To describe controllers on
manifolds, we adopt Riemannian Motion Policies (RMPs), and propose a collection
of RMPs for common multi-robot subtasks. Centralized and decentralized
algorithms are designed to combine these RMPs into a final control policy.
Theoretical analysis shows that the system under the control policy is stable.
Moreover, we prove that many existing multi-robot controllers can be closely
approximated by the framework. The proposed algorithms are validated through
both simulated tasks and robotic implementations.
