用动态软最大函数融合感知数据，实现未知动态环境下的安全导航。
Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments
- 通过周期性感知构建局部安全屏障函数，再用时变软最大值融合
- 在闭式解优化中保证控制安全且接近最优，支持动态环境
- 适用于带惯性的地面机器人和四旋翼无人机，无需预先建图
本文提出一种闭式最优反馈控制方法，确保在事先未知且可能动态变化的环境中安全运行。该方法基于周期性获取的局部感知数据（如激光雷达），构建局部控制屏障函数（CBF），用于描述未来一段时间内的安全区域。随后，利用平滑的时间变软最大函数将最近获得的N个局部CBF组合成一个复合屏障函数，近似表示这些局部安全集的并集。该复合屏障函数被用于约束二次优化问题，并以闭式解求得安全且最优的反馈控制律。研究还将其应用于两种机器人系统：具有不可忽略惯性的非完整地面机器人和四旋翼无人机，目标是在未知环境中安全导航至指定位置。文中提出了从周期性感知数据生成局部CBF的简单方法。
原文摘要 · Abstract (English)
We present a closed-form optimal feedback control method that ensures safety in an a prior unknown and potentially dynamic environment. This article considers the scenario where local perception data (e.g., LiDAR) is obtained periodically, and this data can be used to construct a local control barrier function (CBF) that models a local set that is safe for a period of time into the future. Then, we use a smooth time-varying soft-maximum function to compose the N most recently obtained local CBFs into a single barrier function that models an approximate union of the N most recently obtained local sets. This composite barrier function is used in a constrained quadratic optimization, which is solved in closed form to obtain a safe-and-optimal feedback control. We also apply the time-varying soft-maximum barrier function control to 2 robotic systems (nonholonomic ground robot with nonnegligible inertia, and quadrotor robot), where the objective is to navigate an a priori unknown environment safely and reach a target destination. In these applications, we present a simple approach to generate local CBFs from periodically obtained perception data.
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