Visualizing High-Dimensional Configuration Spaces: A Comprehensive Analytical Approach

The representation of a Configuration Space \mathcal {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 \mathcal {C}'s representations through limited evaluations of collision-free paths using the collision checker or by reducing the dimensionality of \mathcal {C} for visualization. However, a collision checker may indicate high accuracy even when only a subset of the original \mathcal {C} is represented; limiting the motion planner's ability to find paths comparable to those in the original \mathcal {C}. Additionally, dealing with high-dimensional \mathcal {C}s is challenging, as qualitative evaluations become increasingly difficult in dimensions higher than three, where reduced-dimensional \mathcal {C} evaluation may decrease accuracy in cluttered environments. In this letter, we present a novel approach for visualizing representations of high-dimensional \mathcal {C}s of manipulator robots in a 2D format. We provide a new tool for qualitative evaluation of high-dimensional \mathcal {C}s approximations without reducing the original dimension. This enhances our ability to compare the accuracy and coverage of two different high-dimensional \mathcal {C}s. Leveraging the kinematic chain of manipulator robots and human color perception, we show the efficacy of our method using a 7-degree-of-freedom \mathcal {C} 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