In robotics and human biomechanics, the tension between energy economy and kinematic readiness is well recognized; this work brings that fundamental principle to aerial multirotors. We show that the limited torque of the motors and the nonlinear aerodynamic map from rotor speed to thrust naturally give rise to the novel concept of promptness-a metric akin to dynamic aerodynamic manipulability. By treating energy consumption as a competing objective and introducing a geometric fiber-bundle formulation, we turn redundancy resolution into a principled multi-objective program on affine fibers. The use of the diffeomorphic transformation linearizing the signed-quadratic propulsion model allows us to lay the foundations for a rigorous study of the interplay between these costs. Through an illustrative case study on 4-DoF allocation on the hexarotor, we reveal that this interplay is fiber-dependent and physically shaped by hardware inequalities. For unidirectional thrusters, the feasible fibers are compact, yielding interior allocations and a short Pareto arc, while torque demands break symmetry and separate the optima. Conversely, with reversible propellers, the null space enables antagonistic rotor co-contraction that drives promptness to hardware limits, making optimal endurance and agility fundamentally incompatible in those regimes. Ultimately, rather than relying on heuristic tuning or black box algorithms to empirically improve task execution, this framework provides a foundational understanding of why and how to achieve agility through geometry-aware control allocation, offering possible guidance for vehicle design, certification metrics, and threat-aware flight operation.

翻译：在机器人学与人体生物力学中，能量经济性与运动响应性之间的张力已得到充分认识；本研究将这一基本原理引入空中多旋翼系统。我们证明，电机有限的扭矩以及从旋翼转速到推力的非线性空气动力学映射，自然催生了响应性这一新概念——这是一种类似于动态空气动力学可操作性的度量指标。通过将能量消耗视为竞争目标，并引入几何纤维丛表述，我们将冗余解析转化为仿射纤维上的原则性多目标规划。利用可微分同胚变换对符号二次推进模型进行线性化，使我们能够为严格研究这些成本之间的相互作用奠定基础。通过对六旋翼飞行器四自由度分配进行的示例性案例研究，我们揭示了这种相互作用具有纤维依赖性，并受到硬件不等式的物理塑造。对于单向推进器，可行纤维是紧致的，产生内部分配和较短的帕累托弧，而扭矩需求则打破对称性并使最优解分离。相反，对于可逆推进器，零空间使得对抗性旋翼协同收缩成为可能，从而将响应性推向硬件极限，使得在这些状态下最优续航能力与敏捷性从根本上无法兼容。最终，该框架并非依赖启发式调参或黑箱算法来经验性地改进任务执行，而是通过几何感知的控制分配，为理解为何及如何实现敏捷性提供了基础性见解，为飞行器设计、认证指标以及威胁感知的飞行操作提供了可能的指导。