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This paper analyses the dynamic response of a robot when subject to anexternal force that is applied to its Center of Mass (CoM). The Ratio ofTransmission of Motion (RoToM) is proposed as a novel indicator of what part ofthe applied force generates motion, and what part is dissipated by the passiveforces due to mechanical constraints. It depends on the configuration of therobot and on the direction of the force, and is always between 0 and 1.Extending this concept, a transmissibility ellipsoid is used to describe thebehavior of the robot given a certain configuration, and varying the directionof the applied force. Another physical measure that is related to thetransmissibility ellipsoid is the transmissibility index: it provides anindication on how similarly the system behaves when subject to forces comingfrom different directions. The presented analysis aims to provide a deeperinsight on the centroidal dynamics of a robot, and on its dependence on theconfiguration. It can be beneficial for developing whole-body controllers ofredundant robots for e.g., reducing the effort in terms of joint torques tocompensate for gravity, and more in general for designing interaction controlarchitectures.

An Insight on the Ratio of Transmission of Motion (RoToM) and its Relation to the Centroidal Inertia Matrix