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
研究空中物理交互中全驱动问题，结合刚体模型与力映射定义相关集合，给出接触持续全驱动等价条件及相关证书，通过数值评估表明仅满行秩不能保证可行接触操作，中间倾斜角度在推动时保留剩余权限。
AI 中文摘要
全驱动无人机通常通过控制分配矩阵的秩条件或自由飞行跟踪性能来认证。对于空中物理交互，这种认证可能不完整。在持续接触期间，部分可用力被交互任务消耗，只有剩余力可用于稳定、抗干扰和机动。本文介绍了一种用于接触持续全驱动的控制理论框架。将$\R^{3}\times\SO\left(3\right)$上的刚体模型与形态相关的力映射相结合，该映射捕获固定倾斜、可变倾斜、同轴和过驱动多旋翼架构。定义了执行器限制下的可行力集、任务负载下的剩余力集和剩余权限余量。主要结果表明，接触持续全驱动等同于任务力在约束可行力多面体中的内部性，剩余权限半径恰好是到多面体边界的距离。还介绍了不可行和边界情况的有符号剩余余量证书、松弛最大化分配证书和可作为余量感知安全过滤器的鲁棒可实现性条件。对抽象倾斜六旋翼的数值评估表明，仅满行秩并不意味着可行的接触操作。中间倾斜角度在推动过程中保留剩余权限，而小倾斜或过大倾斜因横向力不足或悬停余量损失而失败。
英文摘要
Fully actuated unmanned aerial vehicles (UAVs) are usually certified through rank conditions on a control-allocation matrix or through free-flight tracking performance. For aerial physical interaction, this certification may be incomplete. During sustained contact, part of the available wrench is consumed by the interaction task, and only the residual wrench remains available for stabilization, disturbance rejection, and maneuvering. This paper introduces a control-theoretic framework for \emph{contact-persistent full actuation}. A rigid-body model on $\R^{3}\times\SO\left(3\right)$ is combined with a morphology-dependent wrench map that captures fixed-tilt, variable-tilt, coaxial, and overactuated multirotor architectures. We define feasible wrench sets under actuator limits, residual wrench sets under task loading, and residual authority margins that strengthen the usual rank-based notion of full actuation. The main result shows that contact-persistent full actuation is equivalent to interiority of the task wrench in the constrained feasible wrench polytope, and that the residual authority radius is exactly the distance to the polytope boundary. We further introduce a signed residual-margin certificate for infeasible and boundary cases, a slack-maximizing allocation certificate, and a robust implementability condition that can be used as a margin-aware safety filter. Numerical evaluation on an abstract tilted hexarotor shows that full row rank alone does not imply feasible contact operation. Intermediate tilt angles preserve residual authority during pushing, whereas small or excessive tilts fail because of lateral-force deficiency or hover-margin loss.
