发表机构
Hanyang University; Hanyang University ERICA（汉阳大学; 汉阳大学ERICA校区）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出类型化语义到几何接口，通过编译器将自然语言指令的定性关系映射为保留自由度的连续任务目标，实验验证其有效性和可靠性。
AI 中文摘要
自然语言操作指令指定定性关系，而连续控制器需要可评估状态的任务量、微分和完成条件。由于定性关系通常留下部分相对配置未指定，将其扩展为完整位姿可能引入意外约束。我们提出一种类型化的语义到几何接口，其中语言指定实体、关系和阶段，而每个关系索引其任务相关区别和保留自由度的注册规范。机器人端编译器对这些规范进行落地，使用共形几何代数构建关系特定的任务映射和一致的微分，并通过RMPflow组合所得策略。为评估语言模型与编译器之间的职责划分，我们比较了语义拓扑接口与另一种额外要求关系特定几何规范的接口，共60条指令。两者在41/60案例中产生正确的共享语义内容，但在各自接口要求下的关键错误分别出现在19/60和58/60案例中。在跨越八种几何关系形式的64次落地评估中，任务映射保留了注册的零方向并响应关系相关扰动；解析方向导数与有限差分一致，雅可比秩与注册维度匹配。在MuJoCo中使用模拟Franka Emika Panda进行的三次闭环消融实验中，固定关系保留坐标使中位终端进度误差增加20.24–71.00毫米，而保留的关系误差保持在评估界限内。这些结果支持将关系可见几何和保留自由度一起编译为可组合的连续目标。
英文摘要
Natural-language manipulation instructions specify qualitative relations, whereas continuous controllers require state-evaluable task quantities, differentials, and completion conditions. Because a qualitative relation generally leaves part of the relative configuration unspecified, expanding it into a complete pose can introduce unintended constraints. We present a typed semantic-to-geometric interface in which language specifies entities, relations, and phases, while each relation indexes a registered specification of its task-relevant distinctions and preserved freedoms. A robot-side compiler grounds these specifications, constructs relation-specific task maps and consistent differentials using conformal geometric algebra, and composes the resulting policies through RMPflow. To evaluate the division of responsibility between the language model and the compiler, we compared a Semantic Topology interface with one that additionally requires relation-specific geometric specifications over 60 instructions. Both produced correct shared semantic content in 41/60 cases, but critical errors under their respective interface requirements occurred in 19/60 and 58/60 cases. Across 64 grounded evaluations spanning eight geometric relation forms, the task maps preserved registered null directions and responded to relation-relevant perturbations; analytic directional derivatives agreed with finite differences, and Jacobian ranks matched the registered dimensions. In three closed-loop ablations using a simulated Franka Emika Panda in MuJoCo, fixing a relation-preserved coordinate increased median terminal progress error by 20.24--71.00~mm while the retained relation errors remained within their evaluation bounds. These results support compiling relation-visible geometry and preserved freedom together into composable continuous objectives.
