Georgia Institute of Technology College of Sciences

We will present a broad overview of UTRC’s research initiative in Autonomous and Intelligent Systems (AIS) that was created to conceive, develop and mature a broad range of intelligent mobile robotic systems and capabilities to enhance and support the diverse array of businesses that comprise the United Technologies Corporation. While initial efforts have been focused on Sikorsky Aircraft unmanned rotorcraft, the initiative is now expanding to include other aerospace and commercial applications, as well. The research, conducted by a diverse team of researchers in robotics, dynamical systems, control, applied mathematics, computer vision, and computer science (in partnership with several leading universities including CMU, MIT, UPenn, and UCB) includes: • Real-time algorithms for dynamic collision avoidance in an obstacle-rich environment using probabilistic roadmaps. • Navigation with imperfect and intermittent sensors in GPS degraded environments. • Multi-vehicle missions including efficient robotic search algorithms based on ergodic theory methods. • Collaborative motion planning for multiple aerial and ground robots in large, cluttered environments, trading off mission objectives while satisfying logical/spatial/temporal constraints. • Intelligent system design methodology including architectures for autonomy, human-machine systems, and formal verification. We will conclude with research problems of interest to UTRC and discuss existing and future career and internship opportunities in the broad area of autonomy and robotics.

Existence of a tight contact structure on a closed oriented three manifold is still widely open problem. In this talk we will present some work in progress to answer this problem for manifolds that are obtained by Dehn surgery on a knot in three sphere. Our method involves on one side generalizing certain geometric methods due to Baldwin, on the other unfolds certain homological algebra methods due to Ozsvath and Szabo.

Primary decomposition is a fundamental operation in commutative algebra. Although there are several algorithms to perform it, this remains a very difficult undertaking in general. In cases with additional combinatorial structure, it may be possible to do primary decomposition "by hand". The goal of this talk is to explain in detail one such example. This is joint work with Zekiye Eser; no prerequisites are assumed beyond knowing the definitions of "polynomial ring" and "ideal".

We consider several possibilities on how to select a Filippov sliding vector field on a co-dimension 2 singularity manifold, intersection of two co-dimension 1 manifolds, under the assumption of general attractivity. Of specific interest is the selection of a smoothly varying Filippov sliding vector field. As a result of our analysis and experiments, the best candidates of the many possibilities explored are based on so-called barycentric coordinates: in particular, we choose what we call the moments solution. We then examine the behavior of the moments vector field at the first order exit points, and show that it aligns smoothly with the exit vector field. Numerical experiments illustrate our results and contrast the present method with other choices of Filippov sliding vector field. We further generalize this construction to co-dimension 3 and higher.