发表机构
University of Twente; Sapienza University of Rome（特文特大学; 罗马大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，在全驱动多旋翼仅跟踪位置轨迹时，最小化齐次分配代价会自然涌现类似欠驱动的行为，同时保留全驱动在扰动抑制和瞬态力生成方面的优势。
AI 中文摘要
全驱动通常因其能够独立进行位置和姿态跟踪而受到重视。本研究确立了一个互补性原则：当仅给定位置轨迹时，最小化正齐次分配代价会在全驱动多旋翼上选择类似欠驱动的行为。该代价类别包括范数和幂律，包括标准的最小范数伪逆分配。我们利用纤维逐点下确界将执行器输出代价传递到 wrench 空间，得到齐次下确界分配代价。限制在单位零力矩力上定义了一个方向景观，其最小化方向与力的大小无关。我们证明，将任何固定的最小化方向与所需的世界坐标系力对齐，可以最小化瞬时和积分的零力矩分配代价。由此产生的机体力保持在固定的一维子空间中，没有横向分量。我们推导出一个精确的最优性间隙分解，量化了每个其他姿态轨迹的额外代价，并刻画了最小代价类别。当扰动或规定运动变化改变所需力的方向时，全驱动平台可以立即利用横向权限生成修改后的力，并重新定向到新的最小代价族。结构欠驱动平台必须在生成该力之前重新定向。因此，齐次分配代价最小化解释了为什么最优标称运动可以是类似欠驱动的，而全驱动对于扰动抑制和瞬态力生成仍然有价值。
英文摘要
Full actuation is commonly valued for independent position and attitude tracking. This work establishes a complementary principle: when only a position trajectory is prescribed, minimizing a positively homogeneous allocation cost selects underactuated-like behavior on a fully actuated multirotor. This cost class includes norms and power laws, including standard minimum-norm pseudoinverse allocation. We use fiberwise infimization to transport the actuator-output cost to wrench space, yielding a homogeneous infimal allocation cost. Restriction to unit zero-moment forces defines a directional landscape whose minimizing directions are independent of force magnitude. We show that aligning any fixed minimizing direction with the required world-frame force minimizes instantaneous and integrated zero-moment allocation costs. The resulting body force remains in a fixed one-dimensional subspace without transverse components. We derive an exact optimality-gap decomposition quantifying the additional cost of every other attitude trajectory and characterizing the minimum-cost class. When a disturbance or prescribed-motion change modifies the required-force direction, a fully actuated platform can immediately generate the modified force using transverse authority and reorient toward the new minimum-cost family. A structurally underactuated platform must reorient before generating that force. Thus, homogeneous allocation-cost minimization explains why optimal nominal motion can be underactuated-like, while full actuation remains valuable for disturbance rejection and transient force generation.
