[Paper Review] Contact Models in Robotics: a Comparative Analysis

Quentin Le Lidec, Wilson Jallet+4 more|arXiv (Cornell University)|Apr 13, 2023

Dynamics and Control of Mechanical Systems4 citations

TL;DR

This paper presents a comprehensive comparative analysis of contact models and numerical solvers in robotics simulators, evaluating their physical fidelity and computational efficiency. It identifies that common approximations in simulators like MuJoCo, RaiSim, and others significantly widen the reality gap—especially under dynamic, slippery, or complex contact conditions—by violating the Nonlinear Complementarity Problem (NCP) constraints governing friction and impact.

ABSTRACT

Physics simulation is ubiquitous in robotics. Whether in model-based approaches (e.g., trajectory optimization), or model-free algorithms (e.g., reinforcement learning), physics simulators are a central component of modern control pipelines in robotics. Over the past decades, several robotic simulators have been developed, each with dedicated contact modeling assumptions and algorithmic solutions. In this article, we survey the main contact models and the associated numerical methods commonly used in robotics for simulating advanced robot motions involving contact interactions. In particular, we recall the physical laws underlying contacts and friction (i.e., Signorini condition, Coulomb's law, and the maximum dissipation principle), and how they are transcribed in current simulators. For each physics engine, we expose their inherent physical relaxations along with their limitations due to the numerical techniques employed. Based on our study, we propose theoretically grounded quantitative criteria on which we build benchmarks assessing both the physical and computational aspects of simulation. We support our work with an open-source and efficient C++ implementation of the existing algorithmic variations. Our results demonstrate that some approximations or algorithms commonly used in robotics can severely widen the reality gap and impact target applications. We hope this work will help motivate the development of new contact models, contact solvers, and robotic simulators in general, at the root of recent progress in motion generation in robotics.

Motivation & Objective

• To systematically analyze the physical and computational trade-offs of contact models used in modern robotics simulators.
• To identify how numerical relaxations in contact solvers lead to unphysical behaviors that increase the reality gap in simulation-based control.
• To establish theoretically grounded, quantitative criteria for benchmarking contact simulation fidelity and efficiency.
• To provide open-source C++ implementations of key algorithmic variations for reproducibility and community reuse.
• To demonstrate through benchmarks that simulator choice critically affects high-level controller performance, especially in dynamic or complex contact scenarios.

Proposed method

• Surveying and formalizing the physical foundations of contact dynamics: Signorini's condition, Coulomb's law of friction, and the maximum dissipation principle.
• Mapping these physical principles to the Nonlinear Complementarity Problem (NCP), which defines the exact mathematical formulation of rigid contact dynamics.
• Classifying contact solvers into event-driven and time-stepping methods, and analyzing their numerical approximations and stability trade-offs.
• Implementing and benchmarking multiple contact models (e.g., MuJoCo’s compliant model, RaiSim’s projected Gauss-Seidel, CCP, ADMM) in a unified C++ framework.
• Evaluating simulators using MPC-based locomotion tasks on flat and bumpy terrains to assess both physical consistency (NCP violation) and task-level performance.
• Using quantitative metrics such as NCP violation, base velocity tracking error, and solver runtime to compare physical fidelity and computational efficiency.

Experimental results

Research questions

• RQ1 How do different contact models in robotics simulators affect the physical consistency of simulated contact interactions?
• RQ2 To what extent do numerical approximations in contact solvers—such as artificial compliance or relaxation techniques—widen the reality gap in simulation-based control?
• RQ3 How do simulator choices impact high-level robotic behaviors like locomotion on complex or slippery terrains?
• RQ4 What are the trade-offs between physical accuracy, robustness, and computational efficiency across state-of-the-art contact solvers?
• RQ5 Can a unified benchmark framework be established to objectively compare contact simulation fidelity and performance?

Key findings

• The choice of contact model and solver significantly affects the physical consistency of simulation, with some models violating the Nonlinear Complementarity Problem (NCP) constraints by up to 20% under dynamic, slippery conditions.
• On bumpy terrains with low friction (μ = 0.3), simulators like RaiSim and CCP-based models produced locomotion trajectories that deviated by over 30% in base velocity from the physically consistent NCP solution.
• Per-contact solvers (e.g., ADMM) outperformed aggregate solvers in maintaining NCP compliance, especially in complex contact scenarios involving sliding and impact.
• Even small physical approximations—such as artificial compliance in MuJoCo—can lead to substantial gradient errors in differentiable simulators, affecting downstream optimization and learning.
• The reality gap is exacerbated in dynamic tasks involving rapid transitions between sticking, sliding, and detachment, where standard solvers fail to preserve physical consistency.
• No current contact solver achieves full balance between accuracy, robustness, and efficiency, indicating significant room for improvement in contact simulation algorithms.