提出新方法在输入受限下最大化动态系统的安全区域。
Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints
- 用帕累托多任务学习平衡安全与安全区大小。
- 在倒立摆和12维四旋翼系统上显著扩大安全集。
- 适合需要高维系统安全控制的研究者使用。
本文提出帕累托控制屏障函数（PCBF）算法，旨在输入受限条件下最大化动态系统的内安全集。传统控制屏障函数（CBF）虽能保证轨迹在安全集内，但常忽略实际输入约束。为此，我们采用帕累托多任务学习框架，权衡安全与安全集体积的冲突目标。PCBF适用于高维系统且计算高效。通过与哈密顿-雅可比可达性方法对比验证倒立摆系统，并在12维四旋翼系统上进行仿真。结果表明，PCBF持续优于现有方法，在满足输入约束的同时获得更大安全集。
原文摘要 · Abstract (English)
This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system trajectories within a safe set but often fail to account for realistic input constraints. To address this problem, we leverage the Pareto multi-task learning framework to balance competing objectives of safety and safe set volume. The PCBF algorithm is applicable to high-dimensional systems and is computationally efficient. We validate its effectiveness through comparison with Hamilton-Jacobi reachability for an inverted pendulum and through simulations on a 12-dimensional quadrotor system. Results show that the PCBF consistently outperforms existing methods, yielding larger safe sets and ensuring safety under input constraints.
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