Configuration space learning for constrained manipulation tasks using Gaussian processes

We 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.