Low-dimensional projections for SyCLoP

This paper presents an extension to SyCLoP, a multilayered motion planning framework that has been shown to successfully solve high-dimensional problems with differential constraints. SyCLoP combines traditional sampling-based planning with a high-level decomposition of the workspace through which it attempts to guide a low-level tree of motions. We investigate a generalization of SyCLoP in which the high-level decomposition is defined over a given low-dimensional projected subspace of the state space. We begin with a manually-chosen projection to demonstrate that projections other than the workspace can potentially work well. We then evaluate SyCLoP's performance with random projections and projections determined from linear dimensionality reduction over elements of the state space, for which the results are mixed. As we will see, finding a useful projection is a difficult problem, and we conclude this paper by discussing the merits and drawbacks of various types of projections.