Navigation safety is critical for many autonomous systems such as self-driving vehicles in an urban environment. It requires an explicit consideration of boundary constraints that describe the borders of any infeasible, non-navigable, or unsafe regions. We propose a principled boundary-aware safe stochastic planning framework with promising results. Our method generates a value function that can strictly distinguish the state values between free (safe) and non-navigable (boundary) spaces in the continuous state, naturally leading to a safe boundary-aware policy. At the core of our solution lies a seamless integration of finite elements and kernel-based functions, where the finite elements allow us to characterize safety-critical states' borders accurately, and the kernel-based function speeds up computation for the non-safety-critical states. The proposed method was evaluated through extensive simulations and demonstrated safe navigation behaviors in mobile navigation tasks. Additionally, we demonstrate that our approach can maneuver safely and efficiently in cluttered real-world environments using a ground vehicle with strong external disturbances, such as navigating on a slippery floor and against external human intervention.

翻译：导航安全性对于城市环境中的自动驾驶等自主系统至关重要。这要求显式考虑描述任何不可行、不可导航或不安全区域边界的边界约束。我们提出了一种原理性边界感知的安全随机规划框架，取得了显著成果。该方法生成的价值函数能够严格区分连续状态空间中自由（安全）空间与不可导航（边界）空间的状态值，自然推导出安全边界感知策略。该解决方案的核心在于有限元方法与核函数的无缝融合：有限元可精确刻画安全关键状态的边界，而核函数则加速非安全关键状态的计算。通过大量仿真实验验证，该方法在移动导航任务中展现了安全导航行为。此外，我们证明该方法能够使地面车辆在强外部干扰的杂乱真实环境中（如湿滑地板行驶及抵抗人为干预）实现安全高效的机动导航。