Learning and exploiting low-dimensional structure for efficient holonomic motion planning in high-dimensional spaces

We present a class of methods for optimal holonomic planning in high-dimensional spaces that automatically learns and leverages low-dimensional structure to efficiently find high-quality solutions. These methods are founded on the principle that problems possessing such structure are inherently simple to solve. This is demonstrated by presenting algorithms to solve these problems in time that scales with the dimension of a salient subspace, as opposed to the scaling with configuration-space dimension that would result from a naive approach. For generic problems possessing only approximate low-dimensional structure, we give iterative algorithms that are guaranteed convergence to local optima while making non-local path adjustments to escape poor local minima. We detail the theoretical underpinnings of these methods as well as give simulation and experimental results demonstrating the ability of our approach to efficiently find solutions of a quality exceeding that of known methods, and in problems of high dimensionality.