Models of Noise and Robust Estimates

Given n noisy observations g; of the same quantity f, it is common use to give an estimate of f by minimizing the function Eni=1(gi-f)2. From a statistical point of view this corresponds to computing the Maximum likelihood estimate, under the assumption of Gaussian noise. However, it is well known that this choice leads to results that are very sensitive to the presence of outliers in the data. For this reason it has been proposed to minimize the functions of the form Eni=1V(gi-f), where V is a function that increases less rapidly than the square. Several choices for V have been proposed and successfully used to obtain "robust" estimates. In this paper we show that, for a class of functions V, using these robust estimators corresponds to assuming that data are corrupted by Gaussian noise whose variance fluctuates according to some given probability distribution, that uniquely determines the shape of V.

Generalized Low-Rank Approximations

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering).

Roles of Knowledge in Motor Learning

The goal of this thesis is to apply the computational approach to motor learning, i.e., describe the constraints that enable performance improvement with experience and also the constraints that must be satisfied by a motor learning system, describe what is being computed in order to achieve learning, and why it is being computed. The particular tasks used to assess motor learning are loaded and unloaded free arm movement, and the thesis includes work on rigid body load estimation, arm model estimation, optimal filtering for model parameter estimation, and trajectory learning from practice. Learning algorithms have been developed and implemented in the context of robot arm control. The thesis demonstrates some of the roles of knowledge in learning. Powerful generalizations can be made on the basis of knowledge of system structure, as is demonstrated in the load and arm model estimation algorithms. Improving the performance of parameter estimation algorithms used in learning involves knowledge of the measurement noise characteristics, as is shown in the derivation of optimal filters. Using trajectory errors to correct commands requires knowledge of how command errors are transformed into performance errors, i.e., an accurate model of the dynamics of the controlled system, as is demonstrated in the trajectory learning work. The performance demonstrated by the algorithms developed in this thesis should be compared with algorithms that use less knowledge, such as table based schemes to learn arm dynamics, previous single trajectory learning algorithms, and much of traditional adaptive control.

Automated Assembly Using Feature Localization

Automated assembly of mechanical devices is studies by researching methods of operating assembly equipment in a variable manner; that is, systems which may be configured to perform many different assembly operations are studied. The general parts assembly operation involves the removal of alignment errors within some tolerance and without damaging the parts. Two methods for eliminating alignment errors are discussed: a priori suppression and measurement and removal. Both methods are studied with the more novel measurement and removal technique being studied in greater detail. During the study of this technique, a fast and accurate six degree-of-freedom position sensor based on a light-stripe vision technique was developed. Specifications for the sensor were derived from an assembly-system error analysis. Studies on extracting accurate information from the sensor by optimally reducing redundant information, filtering quantization noise, and careful calibration procedures were performed. Prototype assembly systems for both error elimination techniques were implemented and used to assemble several products. The assembly system based on the a priori suppression technique uses a number of mechanical assembly tools and software systems which extend the capabilities of industrial robots. The need for the tools was determined through an assembly task analysis of several consumer and automotive products. The assembly system based on the measurement and removal technique used the six degree-of-freedom position sensor to measure part misalignments. Robot commands for aligning the parts were automatically calculated based on the sensor data and executed.