Geometric Sensing of Known Planar Shapes

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.