arXiv:2509.14421cs.RO2025-09被引 3

用3D高斯点云构建可解析的碰撞锥,实现更早、更平滑的安全避障控制。

Perception-Integrated Safety Critical Control via Analytic Collision Cone Barrier Functions on 3D Gaussian Splatting

  • 将3D高斯点转换为解析碰撞锥,生成一阶控制屏障函数
  • 在17万点的场景中使规划时间减少3倍,轨迹抖动显著降低
  • 无需高阶屏障函数,适合带实体尺寸的机器人实时导航

我们提出一种感知驱动的安全过滤器,将每个3D高斯点(3DGS)转化为闭式前向碰撞锥,进而生成嵌入二次规划(QP)的一阶控制屏障函数(CBF)。通过利用点的解析几何特性,该方法提供连续、闭式的碰撞约束表示,兼具简洁性与计算高效性。不同于仅在障碍物临近时才激活的距离型CBF,本方法可主动提前预警,使机器人更早调整,从而实现更平滑、更安全的避障,且计算成本更低。我们在包含约17万3DGS点的大规模合成场景中验证,该方法使规划时间减少3倍,轨迹抖动显著下降,同时保持同等安全水平。方法完全解析,无需高阶控制屏障函数(HOCBFs),并通过点的闵可夫斯基和膨胀自然推广至具有物理尺寸的机器人。这些特性使其适用于复杂感知环境下的实时导航,如空间机器人与卫星系统。

原文摘要 · Abstract (English)

We present a perception-driven safety filter that converts each 3D Gaussian Splat (3DGS) into a closed-form forward collision cone, which in turn yields a first-order control barrier function (CBF) embedded within a quadratic program (QP). By exploiting the analytic geometry of splats, our formulation provides a continuous, closed-form representation of collision constraints that is both simple and computationally efficient. Unlike distance-based CBFs, which tend to activate reactively only when an obstacle is already close, our collision-cone CBF activates proactively, allowing the robot to adjust earlier and thereby produce smoother and safer avoidance maneuvers at lower computational cost. We validate the method on a large synthetic scene with approximately 170k splats, where our filter reduces planning time by a factor of 3 and significantly decreased trajectory jerk compared to a state-of-the-art 3DGS planner, while maintaining the same level of safety. The approach is entirely analytic, requires no high-order CBF extensions (HOCBFs), and generalizes naturally to robots with physical extent through a principled Minkowski-sum inflation of the splats. These properties make the method broadly applicable to real-time navigation in cluttered, perception-derived extreme environments, including space robotics and satellite systems.

3D高斯安全控制避障实时导航

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