多无人机分布式模型预测控制中的冲突预测可变时域
Conflict-Predictive Variable Horizons in Multi-Drone Distributed Model Predictive Control
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中文总结 AI 辅助
针对多无人机分布式模型预测控制中固定时域的折中问题，提出冲突预测的可变时域，由各无人机本地设定，在保持稳定性保证的同时降低计算成本并维持避碰性能。
中文摘要 AI 辅助
在多无人机避碰的分布式模型预测控制中，固定的预测时域迫使人们做出妥协：短时域成本低，但对接近的邻居反应迟缓，而长时域能预判冲突，但其每步成本随长度超线性增长。我们提出一种冲突预测的可变时域，由每架无人机本地设定，而分布式模型预测控制本身保持不变。根据观测位置的短历史，无人机外推其邻居的飞行线，并使用随预测范围收窄的置信漏斗将其与自身飞行线进行检验，以闭式获得每次冲突时间。随后，时域取为最小的可行值，其规划窗口覆盖最远的预测冲突。在空旷空域中，它收缩至最小值，仅当前方存在冲突时才增长。只要该最小值满足一个可计算的可行性界，我们证明递归可行性和渐近稳定性对于策略可选择的每个时域均得以保持。这些保证适用于线性模型，且级联内环将每架四旋翼的平动动力学简化为受扰动的双积分器，因此它们可推广至线性化的四旋翼模型，并作为实际稳定性推广至完全非线性模型。在密集对向交换基准的仿真中，可变时域将每步求解器成本和总计算量均降至远低于长固定时域的水平，并在每次运行中保持间距，而具有相当每步成本的短固定时域则无法做到。
英文摘要
In distributed model predictive control for multi-drone collision avoidance, a fixed prediction horizon forces a compromise: a short horizon is inexpensive but reacts late to approaching neighbors, whereas a long one anticipates conflicts at a per-step cost that grows superlinearly with its length. We propose a conflict-predictive variable horizon that each drone sets locally, leaving the distributed model predictive control itself unchanged. From a short history of observed positions, a drone extrapolates the flight lines of its neighbors, tests each against its own using confidence funnels that narrow with prediction range, and obtains each time to conflict in closed form. The horizon is then the smallest admissible value whose planning window covers the farthest predicted conflict. It collapses to its minimum in clear airspace and grows only when a conflict lies ahead. Provided this minimum meets a single computable feasibility bound, we prove that recursive feasibility and asymptotic stability are preserved for every horizon the policy can select. These guarantees hold for a linear model, and a cascaded inner loop reduces each quadrotor's translational dynamics to a perturbed double integrator, so they carry over to the linearized quadrotor model and, as practical stability, to the full nonlinear one. In simulation on dense antipodal-swap benchmarks, the variable horizon reduces both per-step solver cost and total computation well below those of a long fixed horizon, and it maintains separation in every run, which a short fixed horizon of comparable per-step cost does not.
发表机构
- South Westphalia University of Applied Sciences（南威斯特法伦应用科学大学）
- Ruhr University Bochum（波鸿鲁尔大学）
机构由 AI 辅助整理，请以论文原文为准。
