Heterogeneous Dimensionality Reduction for Efficient Motion Planning in High-Dimensional Spaces

Increasing the dimensionality of the configuration space quickly makes trajectory planning computationally intractable. This paper presents an efficient motion planning approach that exploits the heterogeneous low-dimensional structures of a given planning problem. These heterogeneous structures are obtained via a Dirichlet process (DP) mixture model and together cover the entire configuration space, resulting in more dimensionality reduction than single-structure approaches from the existing literature. Then, a unified low-dimensional trajectory optimization problem is formulated based on the obtained heterogeneous structures and a proposed transversality condition which is further solved via SQP in our implementation. The positive results demonstrate the feasibility and efficiency of our trajectory planning approach on an autonomous underwater vehicle (AUV) and a high-dimensional intervention autonomous underwater vehicle (I-AUV) in cluttered 3D environments.