Visualizing High-Dimensional Configuration Spaces For Robots: A Comprehensive Approach for Quantitative and Qualitative Analysis

The reconstruction of Configuration Space (CS) from a limited number of samples plays a vital role in expediting motion planning for random tree algorithms. Traditionally, the evaluation of CS reconstruction is performed through collision checking. However, employing the collision checker as an evaluation measure can be misleading. In particular, a collision checker may exhibit high accuracy even when only a subset of the original CS is reconstructed, limiting the motion planner's ability to find paths comparable to those in the original CS. Additionally, a significant challenge arises when dealing with high-dimensional CSs, as it becomes increasingly difficult, if not impossible, to perform qualitative evaluations when working in dimensions higher than three. In this paper, we introduce a novel approach for representing high-dimensional CSs of manipulator robots in a 2D format. Specifically, we leverage the kinematic chain of manipulator robots and the human ability to perceive colors based on hue. This allows us to construct a visualization comprising a series of pairs of 2D projections. We showcase the efficacy of our method in representing a 7-degree-of-freedom CS of a manipulator robot in a 2D projection. This representation provides qualitative insights into the joint boundaries of the robot and the collision state combinations. From a quantitative perspective, we show that the proposed representation not only captures accuracy but also furnishes additional information, enhancing our ability to compare two different high-dimensional CSs during the deployment phase, beyond what is usually offered by the collision checker. The source code is publicly available on our repository.