Local Observability of Rolling

Yan-Bin Jia and Michael Erdmann

Abstract

This paper investigates local observability of the pose and motion of a smooth three-dimensional object rolling on a rough horizontal plane. The plane models a controllable robotic palm imbued with tactile sensors. The palm can accelerate in arbitrary translational directions and the tactile sensors can determine the contact location between the palm and the rolling object at every instant in time. The object and contact motions are governed by a nonlinear system derived from the kinematics and dynamics of rolling. Through cotangent space decomposition, a sufficient condition on local observability of the system is obtained. This condition depends only on the differential geometry of contact and on the object's angular inertia matrix; it is satisfied by all but some degenerate shapes such as a sphere.

The above result demonstrates that the geometric and dynamic information of a manipulation task is often encoded in a small amount of tactile data.