An Insight on the Ratio of Transmission of Motion (RoToM) and its Relation to the Centroidal Inertia Matrix
This provides a deeper insight into centroidal dynamics for developing whole-body controllers in redundant robots, such as reducing joint torque effort for gravity compensation, but it is incremental as it builds on existing concepts of robot dynamics.
The paper tackles the problem of understanding how external forces applied to a robot's center of mass generate motion versus being dissipated by constraints, proposing the Ratio of Transmission of Motion (RoToM) as a novel indicator, with results showing it ranges from 0 to 1 and is used to derive a transmissibility ellipsoid and index for analyzing robot behavior across force directions.
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.