CENIC: Convex Error-controlled Numerical Integration for Contact

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 variable-step 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.

20 pages with 20 figures. Submitted to IEEE Transactions on Robotics (T-RO). The supplemental video is available publicly at this https URL

Robotics (cs.RO); Computational Engineering, Finance, and Science (cs.CE); Computational Physics (physics.comp-ph)

arXiv:2511.08771 [cs.RO]

(or arXiv:2511.08771v2 [cs.RO] for this version)

https://doi.org/10.48550/arXiv.2511.08771 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.