提出新表示方法，让运动与力轨迹跨坐标系识别更稳定可靠。
A Coordinate-Invariant Local Representation of Motion and Force Trajectories for Identification and Generalization Across Coordinate Systems
- 基于双上三角结构构建坐标不变表示，提升鲁棒性。
- 可同时处理刚体运动与交互力轨迹，适用范围广。
- 适合机器人、生物力学中需跨坐标系分析的场景。
识别刚体轨迹和相互作用力轨迹在机器人学、生物力学等众多领域至关重要，涉及轨迹分割、识别与预测等任务。其核心挑战在于不同坐标系下结果的一致性。本文提出一种新型双上三角不变表示（DUTIR），通过抽象层级统一建模刚体轨迹与力轨迹，有效缓解传统坐标不变表示对测量噪声敏感及奇异点导致定义不唯一的问题。该方法具备更强的抗噪能力和奇异性鲁棒性，并配有配套计算算法，为多领域轨迹分析提供通用工具。
原文摘要 · Abstract (English)
Identifying the trajectories of rigid bodies and of interaction forces is essential for a wide range of tasks in robotics, biomechanics, and related domains. These tasks include trajectory segmentation, recognition, and prediction. For these tasks, a key challenge lies in achieving consistent results when the trajectory is expressed in different coordinate systems. A way to address this challenge is to utilize trajectory models that can generalize across coordinate systems. The focus of this paper is on such trajectory models obtained by transforming the trajectory into a coordinate-invariant representation. However, coordinate-invariant representations often suffer from sensitivity to measurement noise and the manifestation of singularities in the representation, where the representation is not uniquely defined. This paper aims to address this limitation by introducing the novel Dual-Upper-Triangular Invariant Representation (DUTIR), with improved robustness to singularities, along with its computational algorithm. The proposed representation is formulated at a level of abstraction that makes it applicable to both rigid-body trajectories and interaction-force trajectories, hence making it a versatile tool for robotics, biomechanics, and related domains.
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