用四次超环面建模带孔物体，提升机器人抓取与场景生成的几何精度
Supertoroid fitting of objects with holes for robotic grasping and scene generation
- 提出四次超环面拟合方法，解决传统几何模型无法处理带孔物体的问题
- 通过径向距离公式实现内外参数联合优化，提升对称物体建模精度
- 适用于含手柄等单孔结构物体，适合机器人抓取与三维场景生成任务
检测未知物体姿态与形状的一种策略是其几何建模，即拟合已知几何体。经典建模仅限于球体、圆柱等简单形状，难以覆盖复杂形态。超二次曲面可适应更广范围形状，但无法建模带孔物体（如带把手的容器）。本文针对单孔物体，提出四次超表面——超环面的拟合方法。基于超二次曲面的研究成果，推导出主径向与次径向距离的简洁表达式，进而实现超环面内在与外在参数的拟合。同时研究了曲面微分几何随参数的变化规律。结果表明，该方法可统一建模有孔与无孔对称物体，采用简单距离函数完成拟合，显著扩展了可用于几何建模的形状范围。
原文摘要 · Abstract (English)
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those don't cover the variety of shapes that can be encountered. For those situations, one solution is the use of superquadrics, which can adapt to a wider variety of shapes. One of the limitations of superquadrics is that they cannot model objects with holes, such as those with handles. This work aims to fit supersurfaces of degree four, in particular supertoroids, to objects with a single hole. Following the results of superquadrics, simple expressions for the major and minor radial distances are derived, which lead to the fitting of the intrinsic and extrinsic parameters of the supertoroid. The differential geometry of the surface is also studied as a function of these parameters. The result is a supergeometric modeling that can be used for symmetric objects with and without holes with a simple distance function for the fitting. The proposed algorithm expands considerably the amount of shapes that can be targeted for geometric modeling.
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