发表机构
Indian Institute of Science（印度科学理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多机器人CBF安全滤波器不可行问题，提出精确可行性证书量化储备并识别冲突来源，通过最优分配共享约束，将不可行步骤从50%降至6.2%，安全违规运行大幅减少。
AI 中文摘要
多机器人控制屏障函数（CBF）安全滤波器可能变得不可行，但失败的二次规划（QP）并不能表明冲突发生的原因或如何解决。为此，我们为具有异构控制仿射动力学和凸输入集的多智能体CBF滤波器开发了一种精确的可行性证书。该证书通过将安全约束施加的需求与可用的执行器供应分离来量化可行性储备。这种分解表明CBF增益调整或增加执行能力何时能解决不可行性以及何时不能，并识别出导致冲突的智能体和交互。我们进一步提出一种算法，通过最大化最差局部可行性裕度来最优分配共享安全约束，对于多面体输入集，该算法产生一个线性规划。在320次配对闭环仿真中，所提出的分配将不可行控制步骤从约50%降低到6.2%，并将违反安全的运行从118/160降低到24/160。此外，在52次不可行事件中，该证书识别出一种交互，其松弛在94%的情况下恢复了可行性。
英文摘要
Multi-robot Control Barrier Function (CBF) safety filters can become infeasible, but a failed quadratic program (QP) does not indicate why the conflict occurred or how to resolve it. To address this, we develop an exact feasibility certificate for multi-agent CBF filters with heterogeneous control-affine dynamics and convex input sets. The certificate quantifies a feasibility reserve by separating the demand imposed by safety constraints from the available actuator supply. This decomposition shows when CBF gain tuning or increased actuation can and cannot resolve infeasibility, and identifies the agents and interactions responsible for the conflict. We further propose an algorithm to optimally allocate shared safety constraints by maximizing the worst local feasibility margin, yielding a linear program for polyhedral input sets. In $320$ paired closed-loop simulations, the proposed allocation reduces infeasible control steps from roughly $50\%$ to $6.2\%$, and reduces safety-violating runs from $118/160$ to $24/160$. In addition, across $52$ infeasibility events, the certificate identifies an interaction whose relaxation restores feasibility in $94\%$ of cases.
