考虑机体角速度限制的四旋翼安全性的逃逸感知控制障碍函数

中文摘要 AI 辅助

针对输入受限系统的控制障碍函数将可容许输入集置于安全集定义之内，然而由此产生的障碍函数几乎总是仅依赖于状态本身；在四旋翼上，这一点并非无关紧要：因为推力矢量必须先重新定向才能减速接近，而重新定向受到可达机体角速度的限制，仅基于状态的障碍函数所认证的状态中，有些状态无法及时实现逃逸；我们以闭式形式刻画了这一认证差距，并证明其宽度与接近速度成正比，与机体角速度限制成反比；随后，我们在状态与先前施加输入的增广对上定义了逃逸障碍函数，其中逃逸能力通过单步可达推力上限来衡量；该函数具有闭式形式，并给出了最大可认证接近速度的解析逆函数，且嵌入预测控制器时无需额外状态代价；在13状态四旋翼的550次配对闭环实验中，所提出的控制器完成了所有测试场景，而在相同预测时域上施加的停车距离障碍函数在恰好进入预测差距的两个场景中分别有15%和25%的回合失败；与在到达状态施加相同逃逸条件的在线备份CBF基线相比，该方法保持了29-74度更大的方向裕度和3-18倍的间隙，且独立的保守滚动裁判未发现任何认证状态存在逃逸失败。

英文摘要

Control barrier functions for input-constrained systems place the admissible input set inside the definition of the safe set, yet the resulting barrier is almost always a function of the state alone; On a quadrotor this is not cosmetic: because the thrust vector must be reoriented before it can decelerate an approach, and reorientation is limited by the attainable body rate, a state-only barrier certifies states from which no escape is reachable in time; We characterize the certification gap in closed form and show its width is proportional to closing speed and inversely proportional to the body-rate limit; We then define an escape barrier on the augmented pair of state and previously applied input, with escape authority measured over the one-step reachable thrust cap; It admits a closed form and an analytic inverse for the maximum certifiable closing speed, and embeds in a predictive controller at no additional state cost; Across 550 paired closed-loop episodes on a 13-state quadrotor, the proposed controller completes every tested scenario, whereas the stopping-distance barrier enforced over the same horizon fails 15% and 25% of episodes in exactly the two scenarios that enter the predicted gap; Against an online backup-CBF baseline enforcing the same escape condition at the reached state, it holds a 29-74 degree larger directional margin and 3-18 times the clearance, and an independent conservative rollout referee finds no certified state from which escape fails.

发表机构

• University of Wisconsin–Madison（威斯康星大学麦迪逊分校）
• Southeast University（东南大学）
• The Hong Kong Polytechnic University（香港理工大学）

机构由 AI 辅助整理，请以论文原文为准。