Local Observability of Rolling
Yan-Bin Jia and Michael Erdmann
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.