Estimation and inference for grasping and manipulation tasks using vision and kinesthetic sensors

This thesis presents a novel framework for state estimation in the context of robotic grasping and manipulation. The overall estimation approach is based on fusing various visual cues for manipulator tracking, namely appearance and feature-based, shape-based, and silhouette-based visual cues. Similarly, a framework is developed to fuse the above visual cues, but also kinesthetic cues such as force-torque and tactile measurements, for in-hand object pose estimation. The cues are extracted from multiple sensor modalities and are fused in a variety of Kalman filters.

A hybrid estimator is developed to estimate both a continuous state (robot and object states) and discrete states, called contact modes, which specify how each finger contacts a particular object surface. A static multiple model estimator is used to compute and maintain this mode probability. The thesis also develops an estimation framework for estimating model parameters associated with object grasping. Dual and joint state-parameter estimation is explored for parameter estimation of a grasped object's mass and center of mass. Experimental results demonstrate simultaneous object localization and center of mass estimation.

Dual-arm estimation is developed for two arm robotic manipulation tasks. Two types of filters are explored; the first is an augmented filter that contains both arms in the state vector while the second runs two filters in parallel, one for each arm. These two frameworks and their performance is compared in a dual-arm task of removing a wheel from a hub.

This thesis also presents a new method for action selection involving touch. This next best touch method selects an available action for interacting with an object that will gain the most information. The algorithm employs information theory to compute an information gain metric that is based on a probabilistic belief suitable for the task. An estimation framework is used to maintain this belief over time. Kinesthetic measurements such as contact and tactile measurements are used to update the state belief after every interactive action. Simulation and experimental results are demonstrated using next best touch for object localization, specifically a door handle on a door. The next best touch theory is extended for model parameter determination. Since many objects within a particular object category share the same rough shape, principle component analysis may be used to parametrize the object mesh models. These parameters can be estimated using the action selection technique that selects the touching action which best both localizes and estimates these parameters. Simulation results are then presented involving localizing and determining a parameter of a screwdriver.

Lastly, the next best touch theory is further extended to model classes. Instead of estimating parameters, object class determination is incorporated into the information gain metric calculation. The best touching action is selected in order to best discern between the possible model classes. Simulation results are presented to validate the theory.

Molecular mechanisms of interleukin-2 gene inducibility: developmental control and combinatorial action of transcription factors

Interleukin-2 is one of the lymphokines secreted by T helper type 1 cells upon activation mediated by T-cell receptor (TCR) and accessory molecules. The ability to express IL-2 is correlated with T-lineage commitment and is regulated during T cell development and differentiation. Understanding the molecular mechanism of how IL-2 gene inducibility is controlled at each transition and each differentiation process of T-cell development is to understand one aspect of T-cell development. In the present study, we first attempted to elucidate the molecular basis for the developmental changes of IL-2 gene inducibility. We showed that IL-2 gene inducibility is acquired early in immature CD4- CD8-TCR- thymocytes prior to TCR gene rearrangement. Similar to mature T cells, a complete set of transcription factors can be induced at this early stage to activate IL-2 gene expression. The progression of these cells to cortical CD4^+CD8^+TCR^(1o) cells is accompanied by the loss of IL-2 gene inducibility. We demonstrated that DNA binding activities of two transcription factors AP-1 and NF-AT are reduced in cells at this stage. Further, the loss of factor binding, especially AP-1, is attributable to the reduced ability to activate expression of three potential components of AP-1 and NF-AT, including c-Fos, FosB, and Fra-2. We next examined the interaction of transcription factors and the IL-2 promoter in vivo by using the EL4 T cell line and two non-T cell lines. We showed an all-or-none phenomenon regarding the factor-DNA interaction, i.e., in activated T cells, the IL-2 promoter is occupied by sequence-specific transcription factors when all the transcription factors are available; in resting T cells or non-T cells, no specific protein-DNA interaction is observed when only a subset of factors are present in the nuclei. Purposefully reducing a particular set of factor binding activities in stimulated T cells using pharmacological agents cyclosporin A or forskolin also abolished all interactions. The results suggest that a combinatorial and coordinated protein-DNA interaction is required for IL-2 gene activation. The thymocyte experiments clearly illustrated that multiple transcription factors are regulated during intrathymic T-cell development, and this regulation in tum controls the inducibility of the lineage-specific IL-2 gene. The in vivo study of protein-DNA interaction stressed the combinatorial action of transcription factors to stably occupy the IL-2 promoter and to initiate its transcription, and provided a molecular mechanism for changes in IL-2 gene inducibility in T cells undergoing integration of multiple environmental signals.

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.