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Joseph Quinn

Publications and source records attributed to Joseph Quinn.

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Feedback Motion Planning for Long-Range Autonomous Underwater Vehicles

Ocean ecosystems have spatiotemporal variability and dynamic complexity that require a long-term deployment of an autonomous underwater vehicle for data collection. A new long-range autonomous underwater vehicle called Tethys is adapted to study different oceanic phenomena. Additionally, an ocean environment has external forces and moments along with changing water currents which are generally not considered in a vehicle kinematic model. In this scenario, it is not enough to generate a simple trajectory from an initial location to a goal location in an uncertain ocean as the vehicle can deviate from its intended trajectory. As such, we propose to compute a feedback plan that adapts the vehicle trajectory in the presence of any modeled or unmodeled uncertainties. In this work, we present a feedback motion planning method for the Tethys vehicle by combining a predictive ocean model and its kinematic modeling. Given a goal location, the Tethys kinematic model, and the water flow pattern, our method computes a feedback plan for the vehicle in a dynamic ocean environment that reduces its energy consumption. The computed feedback plan provides the optimal action for the Tethys vehicle to take from any location of the environment to reach the goal location considering its orientation. Our results based on actual ocean model prediction data demonstrate the applicability of our method.

cs.RO

Cusp shapes of Hilbert-Blumenthal surfaces

We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n). This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a foliation of the biplane. The region is the Cartesian product of the positive reals with a 3-dimensional tower formed by deformations of lattices in the ring of integers of K, and makes explicit the cusp cross section's Sol 3-manifold structure and Anosov diffeomorphism. We include computer generated images and data illustrating various examples.

math.GT