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.

翻译：从有限样本重建构型空间（CS）在加速随机树算法的运动规划中发挥着关键作用。传统上，构型空间重建的评估通过碰撞检测进行。然而，将碰撞检测器作为评估指标可能产生误导。具体而言，即使仅重建原始构型空间的子集时，碰撞检测器仍可能表现出高精度，这将限制运动规划器找到与原始构型空间相当路径的能力。此外，处理高维构型空间时面临重大挑战：当维度高于三时，进行定性评估即便不是不可能，也极其困难。本文提出了一种在二维格式中表示机械臂高维构型空间的新方法。具体来说，我们利用机械臂的运动学链以及人类基于色调感知颜色的能力，构建由一系列二维投影对组成的可视化图像。我们展示了该方法在将七自由度机械臂构型空间表示为二维投影方面的有效性。这种表示可提供关于机器人关节边界和碰撞状态组合的定性洞察。从定量角度而言，我们证明所提出的表示不仅能捕获准确性，还能提供额外信息——在部署阶段，其增强我们比较两个不同高维构型空间的能力，且功能远超碰撞检测器通常提供的范畴。相关源代码已在我们的仓库中公开提供。