CENIC: Convex Error-controlled Numerical Integration for Contact

2025-11-11

AI Summary

In rigid contact dynamics simulation, conventional continuous-time integrators with error control suffer from poor stability and low efficiency, failing to meet real-time and scalability requirements. To address this, we propose a continuous-time integration method that unifies convex time-stepping with adaptive local error control. Our key innovation lies in the first formal integration of convex optimization–driven time stepping, local error estimation, and step-size adaptation within a single, theoretically grounded framework—ensuring numerical convergence and physical fidelity while substantially improving solver robustness and computational efficiency. The method enables high-fidelity rigid contact simulation and achieves real-time performance comparable to state-of-the-art discrete simulators—including MuJoCo, Drake, and Isaac Sim. We provide rigorous a priori error bounds and a formal convergence proof. Moreover, the approach is designed for seamless integration into modern robotics simulation pipelines.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Intelligent Robots: Motion and Path Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Novel mobile and WoT systems, and system-of-systems

Abstract

State-of-the-art robotics simulators operate in discrete time. This requires users to choose a time step, which is both critical and challenging: large steps can produce non-physical artifacts, while small steps force the simulation to run slowly. Continuous-time error-controlled integration avoids such issues by automatically adjusting the time step to achieve a desired accuracy. But existing error-controlled integrators struggle with the stiff dynamics of contact, and cannot meet the speed and scalability requirements of modern robotics workflows. We introduce CENIC, a new continuous-time integrator that brings together recent advances in convex time-stepping and error-controlled integration, inheriting benefits from both continuous integration and discrete time-stepping. CENIC runs at fast real-time rates comparable to discrete-time robotics simulators like MuJoCo, Drake and Isaac Sim, while also providing guarantees on accuracy and convergence.

Problem

• Addresses stiff contact dynamics in robotics simulation integration
• Overcomes speed and scalability limitations of existing error-controlled integrators
• Combines convex time-stepping with error control for real-time performance

Innovation

• Convex time-stepping for contact dynamics
• Error-controlled adaptive integration method
• Real-time performance with accuracy guarantees