发表机构
Illinois Institute of Technology（伊利诺伊理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出带记忆的备用控制障碍函数，通过存储并连接认证球扩展终端集，在固定预测时域下实现更短时域的安全控制，并在四旋翼仿真中验证有效性。
AI 中文摘要
备用控制障碍函数（bCBFs）利用备用控制器下的有限时域预测，为具有有界输入的非线性系统构造隐式安全集合。与模型预测控制类似，不变备用集作为终端集，保证预测时域之外的安全延续。然而，到达小的终端集可能需要较长的预测时域，从而增加在线预测的成本。本文提出一种在线构造方法，在保持预测时域固定的同时，利用沿备用轨迹存储的集合构建认证区域。该方法存储有限集合的球，并将每个新认证的集合连接到备用集或先前存储的球。我们推导出保证这些球与备用集在固定备用控制器下并集前向不变的条件。这些条件还确保每个存储状态在有限时间内到达备用集。由此产生的并集作为扩大的终端集，允许以更短的预测时域认证安全性。我们为安全控制制定了一个可行的二次规划，并证明在在线存储额外认证集合时安全性得以保持。四旋翼仿真表明，与标准bCBF相比，该方法能以更短的预测时域完成安全任务。
英文摘要
Backup control barrier functions (bCBFs) construct implicit safe sets for nonlinear systems with bounded inputs using finite-horizon predictions under a backup controller. As in model predictive control, an invariant backup set serves as a terminal set that guarantees safe continuation beyond the prediction horizon. However, reaching a small terminal set may require long prediction horizons, increasing the cost of online prediction. In this paper, we introduce an online construction that builds a certified region from sets stored along backup trajectories while keeping the prediction horizon fixed. The method stores finite collections of balls and connects each newly certified collection to the backup set or to previously stored balls. We derive conditions that guarantee forward invariance of the union of these balls and the backup set under a fixed backup controller. These conditions also ensure that every stored state reaches the backup set in finite time. The resulting union serves as an enlarged terminal set, allowing safety to be certified with shorter prediction horizons. We formulate a feasible quadratic program for safe control and prove that safety is preserved as additional certified collections are stored online. Simulations on a quadrotor demonstrate safe task completion with a shorter prediction horizon than the standard bCBF.
