Gradient-based methods can efficiently optimize controllers by leveraging differentiable simulation and physical priors. However, contact-rich manipulation remains challenging because hybrid contact dynamics often produce discontinuous or vanishing gradients. Although smoothing the dynamics can restore informative gradients, the resulting model mismatch can cause controller failures when deployed on real systems. We address this trade-off by planning with smoothed dynamics while explicitly quantifying and compensating for the induced error, providing formal guarantees on safety and task completion under the original nonsmooth dynamics. Our approach applies smoothing to both contact dynamics and contact geometry within a differentiable simulator based on convex optimization, allowing us to characterize the deviation from the nonsmooth dynamics as a set-valued discrepancy. We incorporate this discrepancy into the optimization of time-varying affine feedback policies through analytical reachable sets, enabling robust constraint satisfaction for the closed-loop hybrid system while relying solely on the informative gradients of the smoothed model. By bridging differentiable simulation with set-valued robust control, our method produces affine feedback policies that respect the unilateral nature of contact. We evaluate our method on several contact-rich tasks, including planar pushing, object rotation, and in-hand dexterous manipulation, achieving certified constraint satisfaction with lower safety violations and smaller goal errors than baseline approaches.

翻译：基于梯度的方法通过利用可微仿真和物理先验知识，能够高效优化控制器。然而，接触丰富的操控仍具挑战性，因为混合接触动力学常产生不连续或消失的梯度。尽管平滑动力学可恢复信息性梯度，但由此产生的模型失配可能导致控制器在实际系统中部署时失效。我们通过采用平滑动力学规划并显式量化与补偿引入误差的方法来应对这一权衡，从而在原始非光滑动力学下为安全性和任务完成提供形式化保障。本方法在基于凸优化的可微仿真器中同时平滑接触动力学与接触几何，使我们能够将非光滑动力学的偏差表征为集值差异。通过分析可达集，我们将这一差异融入时变仿射反馈策略的优化中，使得闭环混合系统能够在仅依赖平滑模型信息性梯度的同时实现鲁棒约束满足。通过桥接可微仿真与集值鲁棒控制，我们的方法生成的仿射反馈策略尊重接触的单向性。我们在平面推搡、物体旋转及手内灵巧操控等多项接触丰富任务上评估本方法，在认证约束满足方面实现了比基线方法更少的安全违规次数和更小的目标误差。