提出无需优化的平滑碰撞避让方法，高效且不保守。
Optimization-free Smooth Control Barrier Function for Polygonal Collision Avoidance
- 用布尔逻辑表达SDF下界，再通过log-sum-exp光滑化
- 计算效率高，理论证明不保守，避免冗余约束
- 适用于非完整车辆和集装箱起重机避障，适合实时系统
多边形碰撞避让（PCA）指两个具有动力学方程的多边形（平面多面体）之间的避障问题。该问题因非光滑边界而困难，近期研究采用有符号距离场（SDF）及其变体作为控制屏障函数（CBF）来应对。本文提出一种无优化的平滑CBF方法，计算高效且被证明不保守。核心步骤包括：首先将SDF下界表示为嵌套布尔逻辑组合，然后利用最新的log-sum-exp方法建立其光滑近似，最后设计特定的基于CBF的安全滤波器解决此类问题。为展示广泛应用性，该方法分别拓展至两辆欠驱动非完整车辆的分布式避障与欠驱动集装箱起重机避让移动障碍的场景，并进行了数值仿真。
原文摘要 · Abstract (English)
Polygonal collision avoidance (PCA) is short for the problem of collision avoidance between two polygons (i.e., polytopes in planar) that own their dynamic equations. This problem suffers the inherent difficulty in dealing with non-smooth boundaries and recently optimization-defined metrics, such as signed distance field (SDF) and its variants, have been proposed as control barrier functions (CBFs) to tackle PCA problems. In contrast, we propose an optimization-free smooth CBF method in this paper, which is computationally efficient and proved to be nonconservative. It is achieved by three main steps: a lower bound of SDF is expressed as a nested Boolean logic composition first, then its smooth approximation is established by applying the latest log-sum-exp method, after which a specified CBF-based safety filter is proposed to address this class of problems. To illustrate its wide applications, the optimization-free smooth CBF method is extended to solve distributed collision avoidance of two underactuated nonholonomic vehicles and drive an underactuated container crane to avoid a moving obstacle respectively, for which numerical simulations are also performed.
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