Gaussian Process Manifold Learning
Adams, Larin Cole
Gaussian Process Manifold Learning is a novel model based machine learning method that uses a probabilistic approach to represent a set of data as a manifold. The manifold structure contains information about the constraints and features, allowing for simplifications when working with the data through dimensionality reduction. This dissertation used Gaussian Process Manifolds for constrained motion planning of robotic manipulators. Motion planning for robotic manipulators took place by solving for geodesics on the manifold, reducing the complexity needed by making use of the manifold geometry. Gaussian Process Manifolds showed improvements over earlier versions of motion planning on manifolds due to the probabilistic nature of the manifold. The framework needed to use Gaussian Process Manifolds was developed, and several adaptations to classical differential geometry were made. A novel metric tensor that includes a notion of uncertainty when measuring distance was developed and several derived properties such as the Christoffel symbols and the curvature tensor were derived from the new metric tensor. Geodesics solved using these new adaptations were shown to give more accurate results when compared to previous work using geodesics for constrained motion planning.