TABLE OF CONTENTS Yan-Bin Jia, Carnegie Mellon University, Pittsburgh, PA, USA
Michael Erdmann, Carnegie Mellon University, Pittsburgh, PA, USA
This paper investigates local observability of the pose and motion of a curved 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.
Geometry and mechanics are always closely tied to each other in a manipulation task. The states (or configurations) of an object and its manipulator evolve under the laws of mechanics and subject to the geometric constraints of contact. Such interaction often yields simple information into which the geometry and motions of the object and manipulator are encoded by the mechanics of the manipulation. For example, the contact between the object and the manipulator is a form...
