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

2026-02-10

AI Summary

This work addresses the challenge that hybrid contact dynamics in contact-intensive manipulation induce gradient discontinuities or vanishing gradients, thereby hindering gradient-based controllers from guaranteeing safety and reachability on real systems. The paper proposes the first certifiable gradient-based optimization framework that plans with smoothed contact dynamics, explicitly quantifies and compensates for smoothing-induced errors, and constrains time-varying affine feedback policies via reachability analysis to ensure state constraints are satisfied and goals are achieved under the true hybrid dynamics. By integrating differentiable physics simulation, geometric smoothing, a convex optimization–driven differentiable simulator, and set-valued robust control, the method significantly reduces safety violations and goal-reaching errors in tasks such as object pushing, rotation, and dexterous hand manipulation, establishing the first formal safety and performance guarantees for contact-intensive policies.

Technology Category

• Intelligent Robots: Manipulation
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Gradient-based methods can efficiently optimize controllers using physical priors and differentiable simulators, but contact-rich manipulation remains challenging due to discontinuous or vanishing gradients from hybrid contact dynamics. Smoothing the dynamics yields continuous gradients, but the resulting model mismatch can cause controller failures when executed on real systems. We address this trade-off by planning with smoothed dynamics while explicitly quantifying and compensating for the induced errors, providing formal guarantees of constraint satisfaction and goal reachability on the true hybrid dynamics. Our method smooths both contact dynamics and geometry via a novel differentiable simulator based on convex optimization, which enables us to characterize the discrepancy from the true dynamics as a set-valued deviation. This deviation constrains the optimization of time-varying affine feedback policies through analytical bounds on the system's reachable set, enabling robust constraint satisfaction guarantees for the true closed-loop hybrid dynamics, while relying solely on informative gradients from the smoothed dynamics. We evaluate our method on several contact-rich tasks, including planar pushing, object rotation, and in-hand dexterous manipulation, achieving guaranteed constraint satisfaction with lower safety violation and goal error than baselines. By bridging differentiable physics with set-valued robust control, our method is the first certifiable gradient-based policy synthesis method for contact-rich manipulation.

Problem

• contact-rich manipulation
• gradient-based control
• model mismatch
• hybrid dynamics
• constraint satisfaction

Innovation

• differentiable simulation
• contact-rich manipulation
• reachable set
• robust control
• gradient-based policy synthesis