Sampling-Based Path Planning in Heterogeneous Dimensionality-Reduced Spaces∗

Many sampling strategies often consider the goal and obstacle population to bias/restrict the search area, and they however become less effective when the robot has many degrees of freedom. This paper explores the nonhomogeneous restriction imposed by the obstacles and presents an improved SBP approach enhanced by heterogeneous dimensionality reduction of the full configuration space. Based on the projection residual, a new Dirichlet process (DP) mixture model is proposed to capture a number of Dimensionality-Reduced Spaces (DRSs), which offer the planning spaces with fewer dimensions than its single-DRS counterpart. Then, the sampling and planning procedures are unified with a proposed transversality condition, connecting sampled nodes across DRSs. At last, a quadratic programming is formulated and quickly solved to map the found path in DRSs to an output path in the full configuration space. Numerical simulations on path planning problems of a high-dimensional Intervention Autonomous Underwater Vehicle (I-AUV) have been conducted, showing the feasibility and efficiency of the proposed method.