Safety-Critical Control for Smoothed Implicit Contact Dynamics

TL;DR

This paper develops a safety-critical control framework for contact-rich systems using smoothed implicit contact dynamics, ensuring safety despite approximation errors in contact force estimation.

Contribution

It introduces a boundary-focused rollout method and a robust control barrier function framework to guarantee safety with smoothed contact models.

Findings

The method eliminates force violations in simulations.

Constraint violations can be non-monotonic in the smoothing parameter.

Smoothed models can be safely used with proper margin adjustments.

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 method for bounding the actual contact force despite the use of relaxed complementarity constraints. We show that constraint violations can be non-monotonic in $\kappa$. Smaller $\kappa$ reduces force-approximation error, but it does not necessarily improve safety performance. To address this issue, we introduce boundary-focused rollouts to screen $\kappa$ 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.