Gaussian Model-Based Methods for Task Constraint Learning and Optimal Motion Generation of High-Dimensional Robot Systems

Abstract

This thesis is concerned with motion learning for complex, high-dimensional robot systems operating in unstructured environments, and subject to various task constraints whose analytical characterization may not be a priori available. We first present a Gaussian process algorithm for learning the configuration space of a robot subject to holonomic task constraints. Given an observed data set of points that lie on this task constrained configuration space, or constraint manifold, a point-to- manifold distance function is constructed that measures the distance of any given point from the constraint manifold. The observed data are first encoded using a Gaussian mixture model, and the distance function is learned via Gaussian process regression. The constructed distance function admits an explicit representation that can be differentiated to obtain analytic gradients. We apply this distance function and its gradient to a sampling-based path planning problem for a robot performing a constrained task. We also propose an efficient method for generating suboptimal motions for multibody systems using Gaussian process dynamical models. Given a dynamical model for a multibody system, and a trial motion, a lower-dimensional Gaussian process dynamical model is fitted to the trial motion. New motions are then generated by performing a dynamic optimization in the lower-dimensional space. We introduce the notion of variance tubes as an intuitive and efficient means of restricting the optimization search space. The performance of our algorithm is evaluated through detailed case studies of raising motions for an arm, swing, pitching and jumping motions for a humanoid and lifting motions for a mobile manipulator.