  This paper considers the integration of rigid cooperative manipulation with
rigidity theory. Motivated by rigid models of cooperative manipulation systems,
i.e., where the grasping contacts are rigid, we introduce first the notion of
bearing and distance rigidity for graph frameworks in SE(3). Next, we associate
the nodes of these frameworks to the robotic agents of rigid cooperative
manipulation schemes and we express the object-agent interaction forces by
using the graph rigidity matrix, which encodes the infinitesimal rigid body
motions of the system. Moreover, we show that the associated cooperative
manipulation grasp matrix is related to the rigidity matrix via a
range-nullspace relation, based on which we provide novel results on the
relation between the arising interaction and internal forces and consequently
on the energy-optimal force distribution on a cooperative manipulation system.
Finally, simulation results on a realistic environment enhance the validity of
the theoretical findings.
