Title: Certified Gradient-Based Contact-Rich Manipulation via Smoothing-Error Reachable Tubes
Authors: Wei-Chen Li, Glen Chou
arXiv: https://arxiv.org/abs/2602.09368
This work targets a painful contradiction in differentiable manipulation: we smooth contact dynamics to get useful gradients, but that smoothing perturbs the true hybrid system enough to break constraints at execution. The paper’s key idea is to keep smoothing for optimization while explicitly certifying the mismatch through reachable-set analysis.
The simulator side introduces differentiable smoothing over both contact dynamics and geometry via convex-optimization-based modeling. Then, instead of pretending the smoothed system is exact, they characterize true-minus-smoothed dynamics as a set-valued disturbance and propagate this into tube-style bounds for closed-loop trajectories.
The feedback policy is optimized on , while robust guarantees are checked over the uncertainty tube induced by . They use time-varying affine feedback to maintain tractability and derive analytical reachable bounds that certify constraint satisfaction and goal reachability on the original hybrid dynamics.
Experiments on planar pushing, object rotation, and in-hand dexterous manipulation report lower safety violations and smaller goal error than prior methods, with the noteworthy claim that this is the first certifiable gradient-based synthesis pipeline for contact-rich manipulation.
The bigger lesson is methodological: do not choose between gradient quality and safety guarantees; separate them into two linked layers (smooth optimization model + formal error envelope). This pattern can transfer to many robotics settings where training-time surrogates are unavoidable.
Graph: Paper Node 2602.09368