发表机构
University of Cincinnati; Indian Institute of Technology Bombay（辛辛那提大学; 印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个任务相对框架，利用凸几何为多旋翼在悬停和接触后认证残余扳手裕度，并通过指令投影和增益综合保持储备，模拟验证八旋翼裕度优于六旋翼。
AI 中文摘要
我们开发了一个任务相对框架，用于在具有有界执行器的多旋翼中，在悬停和接触载荷后认证残余扳手能力。利用凸几何，我们为规定的凸储备（包括欧几里得球和加权椭球）推导了有符号裕度。我们从执行器内部性界限获得可计算的储备证书，以支持最大化松弛度的分配。为了保持所需的储备，我们提出将指令投影到收紧的可行集上。然后，我们将可用储备与结构化增益综合联系起来，并认证一个尊重执行器限制的局部跟踪区域。在该区域内，我们建立了名义指数收敛和鲁棒最终有界性。对于规定的任务和形态族，我们展示了优化后的八旋翼在相同总推力下比优化后的六旋翼获得更大的裕度。我们在使用固定几何八旋翼和具有匹配安装推力的可变倾转四旋翼的持续刚性墙接触的闭环模拟中评估了所提出的框架。四旋翼的局部证书为规定的任务族允许更高的归一化推力极限。在超出可实现性边界的测试中，我们观察到八旋翼通过旋翼推力极限和四旋翼通过倾转伺服极限预测的能力丧失。
英文摘要
We develop a task-relative framework for certifying residual wrench authority after hover and contact loading in multirotors with bounded actuators. Using convex geometry, we derive signed margins for prescribed convex reserves, including Euclidean balls and weighted ellipsoids. We obtain computable reserve certificates from actuator-interiority bounds to support slack-maximizing allocation. To preserve the required reserve, we propose command projection onto a tightened feasible set. We then connect the available reserve to structured gain synthesis and certify a local tracking region that respects actuator limits. Within this region, we establish nominal exponential convergence and robust ultimate boundedness. For the prescribed task and morphology family, we show that the optimized octarotor attains a larger margin than the optimized hexarotor at equal total thrust. We evaluate the proposed framework in closed-loop simulations of sustained rigid-wall contact using a fixed-geometry octarotor and a variable-tilt quadrotor with matched installed thrust. The quadrotor's local certificate admits a higher normalized push limit for the prescribed task family. In tests beyond the realizability boundaries, we observe the predicted loss of authority through rotor-thrust limits for the octarotor and tilt-servo limits for the quadrotor.
