On Probabilistic Strategies for Robot Tasks

Robots must act purposefully and successfully in an uncertain world. Sensory information is inaccurate or noisy, actions may have a range of effects, and the robot's environment is only partially and imprecisely modeled. This thesis introduces active randomization by a robot, both in selecting actions to execute and in focusing on sensory information to interpret, as a basic tool for overcoming uncertainty. An example of randomization is given by the strategy of shaking a bin containing a part in order to orient the part in a desired stable state with some high probability. Another example consists of first using reliable sensory information to bring two parts close together, then relying on short random motions to actually mate the two parts, once the part motions lie below the available sensing resolution. Further examples include tapping parts that are tightly wedged, twirling gears before trying to mesh them, and vibrating parts to facilitate a mating operation.

An Analysis of the Effect of Gaussian Error in Object Recognition

Object recognition is complicated by clutter, occlusion, and sensor error. Since pose hypotheses are based on image feature locations, these effects can lead to false negatives and positives. In a typical recognition algorithm, pose hypotheses are tested against the image, and a score is assigned to each hypothesis. We use a statistical model to determine the score distribution associated with correct and incorrect pose hypotheses, and use binary hypothesis testing techniques to distinguish between them. Using this approach we can compare algorithms and noise models, and automatically choose values for internal system thresholds to minimize the probability of making a mistake.

Probabilistic Independence Networks for Hidden Markov Probability Models

Graphical techniques for modeling the dependencies of randomvariables have been explored in a variety of different areas includingstatistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics.Formalisms for manipulating these models have been developedrelatively independently in these research communities. In this paper weexplore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independencenetworks (PINs). The paper contains a self-contained review of the basic principles of PINs.It is shown that the well-known forward-backward (F-B) and Viterbialgorithms for HMMs are special cases of more general inference algorithms forarbitrary PINs. Furthermore, the existence of inference and estimationalgorithms for more general graphical models provides a set of analysistools for HMM practitioners who wish to explore a richer class of HMMstructures.Examples of relatively complex models to handle sensorfusion and coarticulationin speech recognitionare introduced and treated within the graphical model framework toillustrate the advantages of the general approach.

Certified Rapid Solution of Parametrized Linear Elliptic Equations: Application to Parameter Estimation

We present a technique for the rapid and reliable evaluation of linear-functional output of elliptic partial differential equations with affine parameter dependence. The essential components are (i) rapidly uniformly convergent reduced-basis approximations — Galerkin projection onto a space WN spanned by solutions of the governing partial differential equation at N (optimally) selected points in parameter space; (ii) a posteriori error estimation — relaxations of the residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs; and (iii) offline/online computational procedures — stratagems that exploit affine parameter dependence to de-couple the generation and projection stages of the approximation process. The operation count for the online stage — in which, given a new parameter value, we calculate the output and associated error bound — depends only on N (typically small) and the parametric complexity of the problem. The method is thus ideally suited to the many-query and real-time contexts. In this paper, based on the technique we develop a robust inverse computational method for very fast solution of inverse problems characterized by parametrized partial differential equations. The essential ideas are in three-fold: first, we apply the technique to the forward problem for the rapid certified evaluation of PDE input-output relations and associated rigorous error bounds; second, we incorporate the reduced-basis approximation and error bounds into the inverse problem formulation; and third, rather than regularize the goodness-of-fit objective, we may instead identify all (or almost all, in the probabilistic sense) system configurations consistent with the available experimental data — well-posedness is reflected in a bounded "possibility region" that furthermore shrinks as the experimental error is decreased.