# 平滑隐式接触动力学的安全关键控制

> 原文链接：https://robotics.hellobike.com/papers/2026-09-23-2605-21138
> 频道：papers | 更新日期：2026-09-23 | 标签：arxiv, cs.RO
> 核心摘要：针对平滑隐式接触动力学中安全滤波设计困难，提出基于离散时间CBF、κ筛选与鲁棒收紧的框架，并在四个富接触系统仿真验证。

# 平滑隐式接触动力学的安全关键控制

::: v-pre
> 原文链接：[Safety-Critical Control for Smoothed Implicit Contact Dynamics](https://arxiv.org/abs/2605.21138)（arXiv 2605.21138 · 发布日期：2026-09-23）

**Safety-Critical Control for Smoothed Implicit Contact Dynamics**

针对平滑隐式接触动力学中安全滤波设计困难，提出基于离散时间CBF、κ筛选与鲁棒收紧的框架，并在四个富接触系统仿真验证。

## 核心要点

- 平滑隐式接触动力学支持无预设模式序列的梯度规划控制，但安全滤波设计仍不直接。
- 方法用隐式接触力的一阶Taylor近似，推导离散时间控制障碍函数约束。
- 发现减小κ虽可提升局部力近似精度，闭环力约束违反却可能随κ非单调变化。
- 边界聚焦rollouts筛选κ并用固定裕度收紧约束，仿真中消除标准CBF下的力违反。

**验证范围与局限**：仅在四个富接触系统的仿真中验证。

## 英文摘要 (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 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 $κ$ can improve local force-approximation accuracy, the resulting closed-loop force-constraint violations can vary non-monotonically with $κ$. Motivated by this observation, we introduce boundary-focused rollouts that screen candidate $κ$ 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/

作者：H.Y. Lee, Yitaek Kim, Christoffer Sloth
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## 原始参考来源 (Sources)

- [arXiv 2605.21138：Safety-Critical Control for Smoothed Implicit Contact Dynamics](https://arxiv.org/abs/2605.21138)