就绪屏障函数：过驱动多旋翼分配的前向不变控制权限
Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation
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中文总结 AI 辅助
该研究针对过驱动多旋翼分配问题，提出就绪屏障函数方法，通过前向不变控制权限调和贪心方案与最小 effort 方案的缺陷，在六旋翼、八旋翼仿真中验证其能保持认证集合不变性且跟踪代价低。
中文摘要 AI 辅助
过驱动多旋翼的执行器纤维丛上，贪心最大化就绪度指标的分配方案会生成在不连通最优层之间跳变的指令，要求的执行器速率超出任何电机的能力；最小化 effort 的方案是连续的，但无法保证力旋量速率权限保持在任何认证水平之上。我们通过将权限视为前向不变量来调和两者：基于阻力感知的执行器权限共矩阵对数行列式的控制屏障函数，通过分配零空间中的二次规划在转矩级别强制执行。单一设计不等式使认证集合紧致且严格位于执行器框内部，对称设计下，任何旋翼弃权（不执行）的就绪度代价以闭式形式给出为 ln(n/(n−m))。跟踪仅通过显式对齐比被牺牲，力旋量误差界为 O(ρ^−1/2)，鲁棒变体通过与机身矩阵无关的闭式 floor 偏移处理电机参数不确定性。在六旋翼和全驱动八旋翼上，闭式间隙与仿真匹配至机器精度；在权限稀缺区域，贪心最大化违反认证 floor，产生的力旋量误差比所提滤波器大80倍，该滤波器以可忽略的跟踪代价保持认证集合的不变性。
英文摘要
Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. Tracking is sacrificed only through an explicit alignment ratio, with wrench error bounded by $\mathcal{O}(ρ^{-1/2})$ and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision; in the authority-scarce regime greedy maximization violates the certified floor and commits wrench errors up to eighty times larger than the proposed filter, which holds invariance of the certified set at negligible tracking cost.
发表机构
- Ricerca sul Sistema Energetico（能源系统研究机构）
- Czech Technical University（捷克技术大学）
机构由 AI 辅助整理，请以论文原文为准。
