通过平滑误差可达管实现认证的基于梯度的接触密集 manipulation
Certified Gradient-Based Contact-Rich Manipulation via Smoothing-Error Reachable Tubes
AI总结：
本文提出通过平滑动力学并量化补偿误差，实现接触密集 manipulation 的安全性和任务完成的认证，采用凸优化生成鲁棒反馈策略。
摘要：
基于梯度的方法通过可微模拟和物理先验高效优化控制器。然而，接触密集 manipulation 因混合接触动力学产生不连续或消失的梯度而具有挑战性。尽管平滑动力学可恢复信息梯度，但由此导致的模型不匹配可能在真实系统中导致控制器失效。我们通过规划平滑动力学并显式量化和补偿诱导误差，提供对原始非光滑动力学的安全性和任务完成的正式保证。我们的方法在可微模拟器中基于凸优化对接触动力学和接触几何进行平滑，将偏离非光滑动力学的特性表示为集合值偏差。通过分析可达集将此偏差纳入时间变化仿射反馈策略的优化中，从而在闭环混合系统中实现鲁棒约束满足，仅依赖于平滑模型的信息梯度。通过可微模拟与集合值鲁棒控制的结合，我们的方法生成尊重接触单向性的仿射反馈策略。我们在多个接触密集任务上评估了我们的方法，包括平面推动、物体旋转和手部灵巧 manipulation，实现了比基线方法更小的安全违规和目标误差的认证约束满足。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
