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.

翻译：配置空间C的表示对于加速基于采样的运动规划器寻找无碰撞路径至关重要，其中大部分计算时间消耗在状态碰撞检测上。传统规划器通过碰撞检测器评估有限无碰撞路径，或通过降维可视化来评估C的表示。然而，碰撞检测器可能仅在表示原始C的子集时显示高精度，从而限制运动规划器找到与原始C中路径可比路径的能力。此外，处理高维C具有挑战性——当维度超过三维时，定性评估愈发困难，而在杂乱环境中降维评估可能降低精度。本文提出一种新颖方法，将高维机械臂配置空间的表示以二维格式可视化。我们提供了一种无需降维即可定性评估高维C近似的全新工具，增强了比较两个不同高维C精度与覆盖范围的能力。通过利用机械臂运动学链与人类颜色感知，我们以七自由度机械臂的配置空间验证了该方法有效性。该可视化在不降低原始数据维度的情况下，提供了关于机械臂关节边界及碰撞状态组合覆盖范围的定性洞察。为支持论点，我们对该可视化方法进行了数值评估。