基于局部占位图在线生成安全屏障函数，实现实时避障。
Online Synthesis of Control Barrier Functions with Local Occupancy Grid Maps for Safe Navigation in Unknown Environments
- 将占位图转为热传导方程求解，快速生成安全值。
- 200×200网格下平均毫秒级计算，满足实时性要求。
- 适合需要动态避障的无人系统部署应用。
控制屏障函数（CBFs）已成为在动态环境中确保自主系统安全的有效且非侵入性安全过滤器，并提供形式化保障。然而，现有大多数CBF合成方法集中于已知环境。在未知环境中基于感知数据在线合成CBF面临特殊挑战，尤其需要从高维数据中高效实时地构建CBF。本文提出一种直接从局部占位图（OGMs）在线合成CBF的新方法。受稳态热场启发，我们证明了CBF的平滑性要求对应于在适当边界条件下求解稳态热传导方程。通过利用拉普拉斯方程系数矩阵的稀疏性，该方法可高效计算地图中每个栅格单元的安全值。仿真与真实世界实验表明，本方法可在200×200网格地图上以平均毫秒级速度合成CBF，凸显其实时适用性。
原文摘要 · Abstract (English)
Control Barrier Functions (CBFs) have emerged as an effective and non-invasive safety filter for ensuring the safety of autonomous systems in dynamic environments with formal guarantees. However, most existing works on CBF synthesis focus on fully known settings. Synthesizing CBFs online based on perception data in unknown environments poses particular challenges. Specifically, this requires the construction of CBFs from high-dimensional data efficiently in real time. This paper proposes a new approach for online synthesis of CBFs directly from local Occupancy Grid Maps (OGMs). Inspired by steady-state thermal fields, we show that the smoothness requirement of CBFs corresponds to the solution of the steady-state heat conduction equation with suitably chosen boundary conditions. By leveraging the sparsity of the coefficient matrix in Laplace's equation, our approach allows for efficient computation of safety values for each grid cell in the map. Simulation and real-world experiments demonstrate the effectiveness of our approach. Specifically, the results show that our CBFs can be synthesized in an average of milliseconds on a 200 * 200 grid map, highlighting its real-time applicability.
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