Robotic tasks involving contact interactions pose significant challenges for trajectory optimization due to discontinuous dynamics. Conventional formulations typically assume deterministic contact events, which limit robustness and adaptability in real-world settings. In this work, we propose SURE, a robust trajectory optimization framework that explicitly accounts for contact timing uncertainty. By allowing multiple trajectories to branch from possible pre-impact states and later rejoin a shared trajectory, SURE achieves both robustness and computational efficiency within a unified optimization framework. We evaluate SURE on two representative tasks with unknown impact times. In a cart-pole balancing task involving uncertain wall location, 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 compared to conventional nominal formulations.

翻译：涉及接触交互的机器人任务因动力学不连续性而对轨迹优化提出了重大挑战。传统方法通常假设确定性接触事件，这限制了实际应用中的鲁棒性和适应性。本文提出SURE，一种显式考虑接触时序不确定性的鲁棒轨迹优化框架。通过允许多条轨迹从可能的碰撞前状态分支出发，随后重新汇合至共享轨迹，SURE在统一优化框架内同时实现了鲁棒性与计算效率。我们在两个具有未知碰撞时间的代表性任务上评估SURE。在涉及墙面位置不确定的倒立摆平衡任务中，当在控制过程中启用分支切换时，SURE实现了成功率平均21.6%的提升。在使用机械臂的接蛋实验中，SURE将成功率提高了40%。这些结果表明，与传统标称优化方法相比，SURE显著增强了系统的鲁棒性。