Don’t Break the Egg: Branch-Rejoining Trajectory Optimization under Contact Timing Uncertainties

Zhuocheng Zhang, Haizhou Zhao, Xudong Sun, Aaron M. Johnson, Majid Khadiv

Keywords: Trajectory Optimization, Planning under Uncertainty, Contact-rich Manipulation

TL;DR: A robust trajectory optimization framework that explicitly handles contact-timing uncertainty via branching trajectories, improving safety and reliability in real robot interactions.

Abstract: Robotic systems involving intermittent contact present major challenges for trajectory optimization due to discontinuous dynamics and uncertain contact timing. Conventional formulations assume deterministic contact times, limiting robustness and adaptability to real-world uncertainties. In this work, we propose SURE, a robust approach to trajectory optimization that explicitly accounts for contact timing uncertainty. By allowing multiple trajectories to branch from possible pre-impact states and rejoin a shared post-impact trajectory, this method achieves both robustness and computational efficiency within a single optimization framework. We evaluate SURE on two representative tasks with unknown impact times. In a cart–pole balancing task with wall contact, SURE achieves an average improvement of 21.6\% in success rate when branch switching is enabled during control. In an egg-catching experiment using a robotic manipulator, SURE improves the success rate by 40\%. These results demonstrate that SURE substantially enhances robustness over conventional nominal formulations.

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Submission Number: 7