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Learning from Demonstration (LfD) enables novice users to teach robots new skills. However, many LfD methods do not facilitate skill maintenance and adaptation. Changes in task requirements or in the environment often reveal the lack of resiliency and adaptability in the skill model. To overcome these limitations, we introduce ARC-LfD: an Augmented Reality (AR) interface for constrained Learning from Demonstration that allows users to maintain, update, and adapt learned skills. This is accomplished through insitu visualizations of learned skills and constraint-based editing of existing skills without requiring further demonstration. We describe the existing algorithmic basis for this system as well as our Augmented Reality interface and the novel capabilities it provides. Finally, we provide three case studies that demonstrate how ARC-LfD enables users to adapt to changes in the environment or task which require a skill to be altered after initial teaching has taken place. 

This thesis summary presents research focused on incorporating high-level abstract behavioral requirements, called 'conceptual constraints', into the modeling processes of robot Learning from Demonstration (LfD) techniques. This idea is realized via an LfD algorithm called Concept Constrained Learning from Demonstration. This algorithm encodes motion planning constraints as temporally associated logical formulae of Boolean operators that enforce high-level constraints over portions of the robot's motion plan during learned skill execution. This results in more easily trained, more robust, and safer learned skills. Current work focuses on automating constraint discovery, introducing conceptual constraints into human-aware motion planning algorithms, and expanding upon trajectory alignment techniques for LfD. Future work will focus on how concept constrained algorithms and models are best incorporated into effective interfaces for end-users. 

The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and study the other part of intermittency, i.e., the part of the probability space on which the solution is close to zero. This set has probability very close to one, and we show that on this set, the supremum of the solution over space is close to 0. As a consequence, we find that almost surely the spatial supremum of the solution tends to zero exponentially fast as time increases. We also show that if the noise term is very large, then the probability of the set on which the supremum of the solution is very small has a very high probability.