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

TL;DR

This paper introduces a unified modeling framework for robotic manipulation that seamlessly integrates free-space motion and frictional contact, improving the fidelity and robustness of contact-rich behavior execution in real time.

Contribution

It presents Unicomp, a novel complementarity-based discrete-time model that captures both free motion and contact interactions within a single formalism, enabling principled contact mode transitions.

Findings

Enables stable, physically consistent manipulation at interactive speeds

Supports a wide range of contact-rich tasks including pushing and whole-body maneuvers

Provides a real-time optimization framework for manipulation planning

Abstract

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.