统一建模刚体运动与摩擦接触，实现真实物理交互的实时规划。
A Unified Complementarity-based Approach for Rigid-Body Manipulation and Motion Prediction
- 用互补约束统一描述自由运动与摩擦接触，无需预设固定接触点。
- 基于最大耗散原理构建椭球形力矩约束，支持扭转摩擦等复杂耦合效应。
- 适用于从推移物到全身接触的复杂任务，可在交互速度下稳定运行。
在非结构化环境中进行机器人操作，要求规划器同时考虑自由空间运动与与环境的持续摩擦接触。现有（局部）规划与仿真框架通常将这两种状态分开处理，或依赖简化的接触表示，尤其在处理非凸或分布接触时。此类近似限制了接触模式转换的保真度，阻碍了实时执行高接触行为。本文提出一种统一的离散时间建模框架（Unicomp），将自由运动与摩擦接触统一于单一数学形式中。基于互补型刚体动力学，将自由空间运动与接触交互建模为耦合的线性与非线性互补问题，实现接触模式间的合理转换，无需固定接触假设。针对平面接触区域，从最大功率耗散原理推导出摩擦接触模型，其可允许的接触力偶由椭球形极限曲面表示，能捕捉力-力矩耦合效应（如扭转摩擦），且对接触区域的压力分布不敏感。该公式生成的离散时间预测模型通过二次约束关联广义速度与接触力偶，适用于实时优化规划。实验表明，该方法在从平面推移至全身接触操作的任务中均实现了稳定、物理一致的行为，且能在交互速度下运行。
原文摘要 · Abstract (English)
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.
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