arXiv:2608.16335cs.ROcs.SY2026-08

提出新型控制屏障函数,确保多旋翼在过驱动时的力矩权威始终达标且连续。

Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation

  • 用对数行列式构造前向不变的权威屏障,通过二次规划保持控制连续性。
  • 在六旋翼和八旋翼上验证,权威不足时传统方法误差可达80倍,本方法误差极小。
  • 适合对飞行器控制可靠性要求高的场景,如高动态任务或电机参数不确定环境。

过度驱动多旋翼的分配策略中,贪婪最大化就绪度指标会导致指令在不连通的最优层间跳跃,要求的电机速率超出实际承载能力;而努力最小化方案虽连续,却无法保证力矩率权威不低于某一认证水平。本文通过将权威视为前向不变量,构建基于阻力感知的执行器权威共度量对数行列式的控制屏障函数,并在分配零空间中以二次规划在扭矩层级施加约束。单一设计不等式使认证集紧凑且严格位于执行器盒内部,对称设计下任一旋翼停用的就绪代价可闭式表达为 $\ln(n/(n{-}m))$。跟踪性能仅因显式对齐比下降,力矩误差被限定在 $\mathcal{O}(ρ^{-1/2})$,鲁棒变体在电机参数不确定下仍具闭式下界偏移,与机架矩阵无关。在六旋翼和全驱动八旋翼上,闭式间隙与仿真结果达到机器精度一致;在权威稀缺情况下,贪婪最大化违反认证下界,力矩误差达所提滤波器的八十倍,而该方法在极低跟踪成本下维持认证集不变性。

原文摘要 · Abstract (English)

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.

多旋翼控制屏障函数过驱动分配飞行安全

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