  This paper analyses the dynamic response of a robot when subject to an
external force that is applied to its Center of Mass (CoM). The Ratio of
Transmission of Motion (RoToM) is proposed as a novel indicator of what part of
the applied force generates motion, and what part is dissipated by the passive
forces due to mechanical constraints. It depends on the configuration of the
robot and on the direction of the force, and is always between 0 and 1.
Extending this concept, a transmissibility ellipsoid is used to describe the
behavior of the robot given a certain configuration, and varying the direction
of the applied force. Another physical measure that is related to the
transmissibility ellipsoid is the transmissibility index: it provides an
indication on how similarly the system behaves when subject to forces coming
from different directions. The presented analysis aims to provide a deeper
insight on the centroidal dynamics of a robot, and on its dependence on the
configuration. It can be beneficial for developing whole-body controllers of
redundant robots for e.g., reducing the effort in terms of joint torques to
compensate for gravity, and more in general for designing interaction control
architectures.
