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

2026-02-04

AI Summary

Existing robotic planning methods struggle to accurately model the coupling and mode transitions between free motion and frictional contact in unstructured environments, limiting real-time robust execution of contact-intensive tasks. This work proposes Unicomp, a unified discrete-time framework grounded in complementarity theory that seamlessly integrates free motion and frictional contact into coupled linear and nonlinear complementarity problems, enabling natural mode switching without pre-specified contact assumptions. A novel ellipsoidal limit surface contact model—agnostic to pressure distribution—is introduced in conjunction with the principle of maximum dissipation to effectively capture force-moment coupling, including torsional friction. Experiments demonstrate that the approach achieves physically consistent, stable, and computationally efficient real-time interaction in tasks such as pushing objects into full-body contact.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• rigid-body manipulation
• frictional contact
• contact-rich planning
• complementarity-based dynamics
• motion prediction

Innovation

• complementarity-based dynamics
• unified contact modeling
• ellipsoidal friction model
• real-time motion planning
• rigid-body manipulation