Skilled-motion plannings of multi-body systems based upon Riemannian distance

This paper focuses on the Riemannian distance and its application to skilled-motion plannings for the system. The Riemannian distance from one pose to another and vice versa is defined as the minimum curve-length measured by the Riemannian metric based upon the system inertia matrix among all curves connecting the two poses. The minimum-length curve in this meaning is called "geodesic" and reflects a movement of the system affected only by inertia-tensor-originated force (i.e., pure inertia, centrifugal, and Coriolis forces). In order to investigate in detail such a movement along the geodesic, some computer simulations are conducted in the cases of planar motions by a 4-DOF robot arm and biped walkings by a whole-body robot. It is shown through simulation results that movements attaining the Riemannian distance (natural movements in inertial actions) in the two cases tend to be similar to those in human skilled motions when human-scale robot models are chosen. Based upon the Riemannian distance, motion plannings for multi-body systems using physical properties inherent in their own physical structures are discussed.