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.

翻译：非结构化环境中的机器人操作要求规划器同时考虑自由空间运动与环境中持续、有摩擦的接触。现有的（局部）规划与仿真框架通常将这些状态分离，或依赖简化的接触表示，特别是在建模非凸或分布式接触面时。此类近似限制了接触模式转换的保真度，并阻碍了实时鲁棒执行富含接触的行为。本文提出了一种用于机器人操作的统一离散时间建模框架（Unicomp），其在单一数学形式中一致地捕捉自由运动与摩擦接触。基于互补性刚体动力学，我们将自由空间运动与接触交互表述为耦合的线性和非线性互补问题，从而实现在不强制固定接触假设的情况下，在接触模式之间进行有原则的转换。对于平面面接触，我们从最大功率耗散原理推导出一个摩擦接触模型，其中允许的接触力旋量集合由椭球极限曲面表示。该表示捕捉了耦合的力-力矩效应（包括扭转摩擦），同时独立于接触面底层的压力分布。所得公式产生了一个离散时间预测模型，该模型通过二次约束关联广义速度与接触力旋量，适用于基于优化的实时规划。实验结果表明，所提方法能够在交互速度下，在从平面推送到富含接触的全身操作等多种任务中，实现稳定且物理一致的行为。