Mixed-Integer Linear Programming Model for Collision Avoidance Planning in Commercial Aircraft Formations

TL;DR

This paper addresses collision avoidance planning for commercial aircraft formations facing intruders by developing a MILP formulation in a 3D near-inertial reference frame that minimizes $J_{ ext{maneuver}}(x,v,u) + J_{ ext{avoidance}}(x) + J_{ ext{drag}}(x) + J_{ ext{smoothness}}(x)$ under dynamics $x_{(i+1)pd} = x_{ipd} + (v_{ipd} + W_d)\Delta t$ and $v_{(i+1)pd} = v_{ipd} + u_{ipd}\Delta t$, with wind neglected ($W_d=0$) and $\Delta t \in [0.8,1.2]$. It enforces inter-aircraft, wake-turbulence, and intruder safety through $\mathcal{S}_q$, $\mathcal{W}_q$, and $R_s$ constraints, and uses a binary indicator $a_{iprds}$ to model intruder avoidance. Demonstrations on 2-, 3-, and 5-aircraft formations show that two-aircraft cases can avoid intruders with lateral maneuvers alone, while larger formations require vertical components and, in some cases, swapping of side positions after avoidance. The results provide theoretical support and practical guidance for implementing commercial formation flying with contingency planning under ATC and wake-turbulence safety considerations.

Abstract

With advancements in technology, commercial aircraft formation flying is becoming increasingly feasible as an efficient and environmentally friendly flight method. However, gaps remain in practical implementation, particularly in collision avoidance for aircraft formations. Existing avoidance algorithms mainly focus on single aircraft or UAV swarms, lacking comprehensive studies on the complex interactions within commercial aircraft formations. To address this, this paper proposes an optimization model designed to generate safe and effective collision avoidance solutions for commercial aircraft formations. This model demonstrates avoidance paths for formations facing intruders and offers insights for developing formation flight strategies. This study explores response strategies for commercial aircraft formations encountering intruders, considering the difficulty of pilot maneuvers. The findings provide theoretical support for the practical implementation of commercial formation flying and may advance the adoption of this technology.

Figures (8)

• Figure 1: Illustration of possible intruders: scenario A: Head-on Intruder, scenario B: Side Intruder
• Figure 2: Illustration of the initial formation setting.
• Figure 3: 2-aircraft avoidance solution of side intruder.
• Figure 4: 3D View of 2-aircraft avoidance solution of side intruder.
• Figure 5: 3-aircraft avoidance solution of side intruder.