Safety-Critical Control for Smoothed Implicit Contact Dynamics

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 $\kappa$ relaxes contact complementarity constraints, which makes the dynamics smooth but affects the contact force. This paper provides a safety-filtering framework for smoothed implicit contact dynamics. We first derive a discrete-time control barrier function (CBF) constraint using a first-order Taylor approximation of the implicitly defined contact force. We show that, although reducing $\kappa$ can improve local force-approximation accuracy, the resulting closed-loop force-constraint violations can vary non-monotonically with $\kappa$. Motivated by this observation, we introduce boundary-focused rollouts that screen candidate $\kappa$ values by comparing the predicted safety margin with the observed one-step under-prediction. We then robustly tighten the predicted CBF constraint with a fixed margin to account for residual force under-prediction. Simulations on four contact-rich systems show that the proposed method eliminates force violations observed under a standard CBF. Project website https://contact-cbf.github.io/

arXiv commentAccepted to Robotics and Automation Letters (RA-L)