### Geometric and Dynamic Sensing: Observation of Pose and Motion
through Contact

** Yan-Bin Jia **

* Abstract *

I investigate geometric and mechanical sensing strategies for objects of known
shapes. Examples include industrial parts and everyday desktop items. Based on
nonlinear control theory, I show that local observability from contact holds in
typical manipulation tasks, and present an approach for estimating the pose and
motion of a manipulated object from a small amount of tactile data.
The first part of the thesis describes two geometric strategies, namely *
inscription and point sampling*, for computing the pose of a polygonal part; both can
generalize to other shapes in two and three dimensions. These strategies use simple
geometric constraints to either immobilize the object or to distinguish its real pose
from a finite number of apparent poses. Computational complexity issues are
examined. Simulation results support their use in real applications.

The second and main part of the thesis introduces a sensing strategy called * pose
and motion from contact *. I look at two representative tasks: (1) a finger pushing
an object in the plane; and (2) a three-dimensional smooth object rolling on a
translating horizontal plane. I demonstrate that essential task information is often
hidden in mechanical interactions, and show how this information can be properly
revealed.

The thesis proves that the nonlinear dynamical system that governs pushing in the
first task is locally observable. Hence a sensing strategy can be realized as an
observer of the system. I have subsequently developed two nonlinear observers. The
first one determines its ``gain'' from the solution of a Lyapunov-like equation. The
second one solves for the initial (motionless) pose of the object from as few as
three intermediate contact points. Both observers have been simulated and a contact
sensor has been implemented using strain gauges.

Through cotangent space decomposition in the second task, I derive a sufficient
condition on local observability for the pose and motion of the rolling object from
its path in the plane. 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.