Certifiable Gradient-Based Contact-Rich Manipulation via Smoothing-Error Reachable Tubes

Venue: RSS 2026 (Sydney, Jul 13–17) · Session: Planning · paper #190 Authors: Wei-Chen Li, Glen Chou (Georgia Institute of Technology) arXiv: 2602.09368 · program page

Summary compiled from the arXiv paper (v2); all numbers quoted from the paper. The preprint is titled "Certified Gradient-Based Contact-Rich Manipulation…"; the RSS program lists it as "Certifiable…" — same paper. Trend context: RSS 2026 survey.

Figure 1. (a) Keyframes of the in-hand cube reorientation task executed by the method's affine feedback policy. (b) For every object degree of freedom (roll, pitch, yaw and x, y, z), the closed-loop rollout on the true nonsmooth dynamics (red) stays inside the predicted reachable tube (green) around the nominal trajectory (blue), certifying constraint satisfaction.

Problem

Gradient-based trajectory optimization is efficient but breaks on contact-rich manipulation, where hybrid contact dynamics give discontinuous or vanishing gradients. Smoothing the dynamics restores useful gradients but introduces model mismatch that makes controllers fail on the true system. The paper seeks the efficiency of smoothed planning with formal guarantees on the original nonsmooth dynamics.

Method

The method smooths both contact dynamics and contact geometry inside a convex-optimization-based differentiable simulator to get a well-conditioned optimization landscape, then characterizes the discrepancy from the true hybrid dynamics as a set-valued deviation (a smoothing-error bound). Propagating this bound through the dynamics yields reachable state and control tubes. It optimizes time-varying affine feedback policies (with an integral structure that rejects constant disturbances) that admit analytical reachable-set predictions of true closed-loop behavior while using only informative gradients from the smoothed model, and it respects the unilateral nature of contact. This gives certified goal reachability and constraint satisfaction without repeated MPC replanning.

Results

Evaluated on planar pushing (2-DOF), bimanual non-prehensile manipulation (9-DOF), and in-hand dexterous cube reorientation (22-DOF), including bimanual planar-bucket hardware with two Kuka iiwa 7 arms. The method certifies constraint satisfaction on the nonsmooth dynamics where the baseline TO-CTR (trajectory optimization with a contact trust region) and an exact-forward/smoothed-gradient variant both incur violations (robot collisions or the bucket falling off the table). On the bimanual bucket task (averaged over 1000 experiments), it achieves lower goal error than TO-CTR without replanning — goal position error 0.1447 vs 0.1522 m and goal angle error 0.0946 vs 0.1034 rad — at similar solve times, while also lowering nominal control and state cost.

Significance

By bridging differentiable physics with set-valued robust control, this is presented as the first certifiable gradient-based policy-synthesis method for contact-rich manipulation, giving formal safety/reachability guarantees on hybrid dynamics rather than heuristic trust regions. Related: Review-System-0-1-2.

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