Visualizing High-Dimensional Configuration Spaces: A Comprehensive Analytical Approach

The representation of a Configuration Space C plays a vital role in accelerating the finding of a collision-free path for sampling-based motion planners where the majority of computation time is spent in collision checking of states. Traditionally, planners evaluate C's representations through limited evaluations of collision-free paths using the collision checker or by reducing the dimensionality of C for visualization. However, a collision checker may indicate high accuracy even when only a subset of the original C is represented; limiting the motion planner's ability to find paths comparable to those in the original C. Additionally, dealing with high-dimensional Cs is challenging, as qualitative evaluations become increasingly difficult in dimensions higher than three, where reduced-dimensional C evaluation may decrease accuracy in cluttered environments. In this paper, we present a novel approach for visualizing representations of high-dimensional Cs of manipulator robots in a 2D format. We provide a new tool for qualitative evaluation of high-dimensional Cs approximations without reducing the original dimension. This enhances our ability to compare the accuracy and coverage of two different high-dimensional Cs. Leveraging the kinematic chain of manipulator robots and human color perception, we show the efficacy of our method using a 7-degree-of-freedom CS of a manipulator robot. This visualization offers qualitative insights into the joint boundaries of the robot and the coverage of collision state combinations without reducing the dimensionality of the original data. To support our claim, we conduct a numerical evaluation of the proposed visualization.