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arXiv 2602.04522cs.RO
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一种基于互补性的统一方法用于刚体操作和运动预测

A Unified Complementarity-based Approach for Rigid-Body Manipulation and Motion Prediction

Technical University of Munich(慕尼黑技术大学);Stony Brook University(石溪大学);Northeastern University(东北大学)

Bingkun Huang, Xin Ma, Nilanjan Chakraborty, Riddhiman Laha

AI总结:

本文提出了一种统一的互补性方法,用于机器人刚体操作和运动预测,通过耦合线性和非线性互补问题实现接触模式的原理性转换,提升实时规划的鲁棒性。

摘要:

在无结构环境中进行机器人操作需要规划者同时考虑自由空间运动和持续的摩擦接触。现有(局部)规划和仿真框架通常将这些领域分开或依赖于简化的接触表示,特别是在建模非凸或分布式接触区域时。此类近似限制了接触模式转换的精度,并阻碍了在实时中执行丰富的接触行为的鲁棒性。本文提出了一种统一的离散时间建模框架,用于机器人操作,该框架在单一数学形式化(Unicomp)中一致地捕捉了自由运动和摩擦接触。基于互补性刚体动力学,我们将自由空间运动和接触相互作用作为耦合的线性和非线性互补问题进行公式化,从而在不强制固定接触假设的情况下实现接触模式的原理性转换。对于平面斑点接触,我们从最大功率耗散原理中推导出摩擦接触模型,其中允许的接触力矩集由一个椭球体极限表面表示。这种表示捕捉了耦合的力矩效应,包括扭转摩擦,同时不依赖于接触斑点下压力分布的底层情况。所得到的公式化产生了一个离散时间预测模型,通过二次约束将广义速度和接触力矩联系起来,并适用于基于优化的实时规划。实验结果表明,所提出的方法在交互速度下能够实现稳定且物理一致的行为,涵盖从平面推动到接触丰富的全身操作任务。

英文摘要:

Robotic manipulation in unstructured environments requires planners to reason jointly about free-space motion and sustained, frictional contact with the environment. Existing (local) planning and simulation frameworks typically separate these regimes or rely on simplified contact representations, particularly when modeling non-convex or distributed contact patches. Such approximations limit the fidelity of contact-mode transitions and hinder the robust execution of contact-rich behaviors in real time. This paper presents a unified discrete-time modeling framework for robotic manipulation that consistently captures both free motion and frictional contact within a single mathematical formalism (Unicomp). Building on complementarity-based rigid-body dynamics, we formulate free-space motion and contact interactions as coupled linear and nonlinear complementarity problems, enabling principled transitions between contact modes without enforcing fixed-contact assumptions. For planar patch contact, we derive a frictional contact model from the maximum power dissipation principle in which the set of admissible contact wrenches is represented by an ellipsoidal limit surface. This representation captures coupled force-moment effects, including torsional friction, while remaining agnostic to the underlying pressure distribution across the contact patch. The resulting formulation yields a discrete-time predictive model that relates generalized velocities and contact wrenches through quadratic constraints and is suitable for real-time optimization-based planning. Experimental results show that the proposed approach enables stable, physically consistent behavior at interactive speeds across tasks, from planar pushing to contact-rich whole-body maneuvers.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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