Ensuring safe robot operation in cluttered and dynamic environments remains a fundamental challenge. While control barrier functions provide an effective framework for real-time safety filtering, their performance critically depends on the underlying geometric representation, which is often simplified, leading to either overly conservative behavior or insufficient collision coverage. Superquadrics offer an expressive way to model complex shapes using a few primitives and are increasingly used for robot safety. To integrate this representation into collision avoidance, most existing approaches directly use their implicit functions as barrier candidates. However, we identify a critical but overlooked issue in this practice: the gradients of the implicit SQ function can become severely ill-conditioned, potentially rendering the optimization infeasible and undermining reliable real-time safety filtering. To address this issue, we formulate an SQ-based safety filtering framework that uses signed distance functions as barrier candidates. Since analytical SDFs are unavailable for general SQs, we compute distances using the efficient Gilbert-Johnson-Keerthi algorithm and obtain gradients via randomized smoothing. Extensive simulation and real-world experiments demonstrate consistent collision-free manipulation in cluttered and unstructured scenes, showing robustness to challenging geometries, sensing noise, and dynamic disturbances, while improving task efficiency in teleoperation tasks. These results highlight a pathway toward safety filters that remain precise and reliable under the geometric complexity of real-world environments.

翻译：确保机器人在杂乱动态环境中的安全运行仍是一项根本性挑战。尽管控制屏障函数为实时安全滤波提供了有效框架，但其性能关键依赖于底层的几何表示，而后者常被简化，导致行为过于保守或碰撞覆盖不足。超二次曲面提供了一种使用少量基元对复杂形状进行建模的表达方式，并越来越多地用于机器人安全领域。为了将此表示集成到避碰中，现有方法大多直接将其隐函数用作屏障候选函数。然而，我们发现了这一实践中一个关键但被忽视的问题：超二次曲面隐函数的梯度可能变得严重病态，可能导致优化不可行，并破坏可靠的实时安全滤波。为解决此问题，我们构建了一个基于超二次曲面的安全滤波框架，该框架使用符号距离函数作为屏障候选函数。由于一般超二次曲面无法获得解析的符号距离函数，我们使用高效的Gilbert-Johnson-Keerthi算法计算距离，并通过随机平滑方法获取梯度。大量的仿真和真实世界实验证明，该方法能在杂乱和非结构化场景中实现一致的免碰撞操作，对挑战性几何形状、感知噪声和动态干扰表现出鲁棒性，同时提高了遥操作任务的任务效率。这些结果指明了一条实现安全滤波器的路径，使其能够在真实世界环境的几何复杂性下保持精确性和可靠性。