Safety-Critical Control for Smoothed Implicit Contact Dynamics

2026-05-20

AI Summary

This work addresses the issue of underestimated contact forces in gradient-based optimization using smooth implicit contact dynamics, where relaxed complementarity constraints can compromise safety-critical control. The study reveals a non-monotonic relationship between the smoothing parameter κ and system safety performance, and proposes a boundary-focused trajectory replay mechanism to select an optimal κ. Building upon this, a robust discrete-time Control Barrier Function (CBF) is constructed using a first-order Taylor expansion, incorporating a fixed safety margin to compensate for uncertainties in contact force prediction. Evaluated on four contact-intensive dynamical systems, the proposed approach effectively eliminates contact force violations observed with standard CBFs and significantly enhances safety.

Abstract

Smoothed implicit contact dynamics enables gradient-based planning and control for contact-rich tasks without predefined mode sequences. However, safety-critical control remains challenging because implicit contact dynamics makes safety-filter design nontrivial. The smoothing parameter $κ$ relaxes contact complementarity constraints, which makes the dynamics smooth but affects the contact force. This paper provides a method for bounding the actual contact force despite the use of relaxed complementarity constraints. We show that constraint violations can be non-monotonic in $κ$. Smaller $κ$ reduces force-approximation error, but it does not necessarily improve safety performance. To address this issue, we introduce boundary-focused rollouts to screen $κ$ by comparing the safety margin with the approximation error. We then develop a discrete-time control barrier function (CBF) framework based on a first-order Taylor approximation of the implicitly defined contact force. To account for possible force under-prediction, we augment the resulting safety constraint with a fixed robust margin. Simulations on four contact-rich systems show that the proposed method eliminates force violations observed under a standard CBF.

Problem

• safety-critical control
• implicit contact dynamics
• contact force
• complementarity constraints
• smoothing parameter

Innovation

• smoothed implicit contact dynamics
• control barrier function
• safety-critical control
• contact force approximation
• robust margin