Safety-Critical Control for Smoothed Implicit Contact Dynamics
For roboticists working on contact-rich manipulation, this method enables safety guarantees despite the relaxation of contact complementarity constraints, addressing a key limitation in prior work.
The paper addresses safety-critical control for contact-rich tasks using smoothed implicit contact dynamics. It introduces a discrete-time control barrier function framework with a robust margin that eliminates force violations observed under standard CBFs, as demonstrated in simulations on four contact-rich systems.
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.