The problem with overtaking collisions begins with the mathematics of closure. The Traffic Collision Avoidance System, or TCAS, that protects passenger aircraft works by calculating time-to-impact thresholds and sizing protective airspace volumes around each plane. When closure rates are high, as in head-on encounters, time-to-impact shrinks rapidly and triggers escalating alerts. But overtaking collisions are fundamentally different. An intruder approaching from behind often has a closure rate close to zero, and as closure approaches zero, time-to-impact approaches infinity, rendering the detection parameter nearly useless. TCAS attempts to compensate with a distance modifier called DMOD, but sizing DMOD is a delicate trade-off: too large and the system floods pilots with false alerts, too small and there is insufficient time to react once a genuine threat is detected.

For autonomous drones, the situation is even more constrained. Current uncrewed aircraft collision avoidance systems typically require a remote pilot to execute avoidance maneuvers or provide generic guidance that autonomous vehicles cannot reliably follow. The International Civil Aviation Organization defines three main categories of aerial collisions: head-on, where the intruder approaches directly; converging, where it approaches from the side; and overtaking, where it approaches from behind at an angle of less than 70 degrees with the mission aircraft’s plane of symmetry. Regulations typically place responsibility for avoidance on the faster aircraft in overtaking scenarios, but drones are required to give way to all other aircraft, and specific right-of-way laws for uncrewed systems remain undefined. Since the majority of aerial collisions are overtaking collisions, any autonomous collision avoidance system must be able to identify and resolve them.

Enter PRACAS, the Path Recovery Automated Collision Avoidance System developed at Ohio University. PRACAS takes the deterministic detection volumes of TCAS and simplifies them into two-dimensional probability cones projected in front of each aircraft. These cones are constructed from the vehicle’s velocity, its maximum turn rate, and a specified look-ahead time, representing all the states the aircraft could reach within that time window. When the probability cones of a mission drone and an intruder overlap, PRACAS converts the intruder’s cone into a keep-out zone, or KOZ, and then employs the A* path planner to find the shortest avoidance path around it, delivering clearly defined waypoints that an autonomous autopilot can follow. The system has proven effective in head-on and perpendicular converging scenarios, but until now it could not detect overtaking collisions at all.

The overtaking scenario poses a unique geometric puzzle. When an intruder’s probability cone envelops the mission drone, the keep-out zone generated from that cone surrounds the drone’s own starting position. Any action the A* planner could take would cause the drone to enter a keep-out zone, so the planner simply fails to produce a solution. The researchers solved this detection problem by shrinking or removing the intruder cone’s keep-out zone, which is handled in a separate process from the probability cone itself, and by classifying the encounter: if the intruder was approaching from behind at between 110 and 250 degrees of the mission drone’s heading, the scenario was treated as overtaking and handled with special logic.

Dimensioning the new keep-out zones required relating the relative velocities and turn rates of the two aircraft. The width of each zone was defined by summing the widths of both aircraft’s collision cones, which depend on velocity, look-ahead time, and maximum turn rate. The length was determined by calculating how much time the intruder needs to pass well clear of the mission drone, then multiplying the mission drone’s velocity by that time-to-pass. Placement was equally critical: the zone was fixed at the end of the mission drone’s probability cone to prompt immediate avoidance action while ensuring that turn-rate constraints are not violated. The two vertexes nearest the mission drone were referenced to the mission heading, while the furthest vertexes shifted with the intruder heading so the zone accurately reflected the intruder’s trajectory without keeping the drone off its planned path longer than necessary.

One subtle failure mode emerged during testing: crossing maneuvers. As approach angles grew further from directly behind, the mission drone sometimes passed in front of the intruder, because the A* planner optimizes only for the shortest path without directional preference. The researchers discouraged these dangerous crossings by extending the keep-out zone to one side or another based on both the intruder’s position and its heading, making non-crossing avoidance paths shorter and therefore preferred by the planner.

The simulation campaign was exhaustive. Using Dubins turn-rate constraints, where aircraft move in ideal circles while turning and straight lines otherwise, the team simulated one mission drone flying at 10 meters per second against an uncooperative intruder across relative velocities from 1 to 20, look-ahead times from 1 to 25 seconds, and approach angles from 110 to 250 degrees in one-degree increments. Positions were updated at 100 hertz, and separation distance was measured at every update. The goal was to maintain at least one standard wingspan, 7.5 meters, of separation, with anything below considered a mid-air collision and anything below 15 meters a near mid-air collision. The upper bound of relative velocity represented the extreme scenario of a commercial airliner overtaking a small drone.

The results were striking. Look-ahead times between 5 and 12 seconds maintained minimum separation for relative velocities from 2 to 20 across all approach angles, and encounters at look-ahead times of 5 to 8 seconds were handled with more than twice the separation required for success. Intruders approaching from directly behind, the worst-case scenario, actually produced the highest minimum separation distances of all approach angles when the overtaking keep-out zones were active. For slow rate-of-approach encounters with relative velocities between 1.1 and 2.0, minimum separation was maintained for look-ahead times between 2 and 8 seconds at all approach angles. Separation distance proved primarily determined by look-ahead time rather than relative velocity, since higher look-ahead times give the mission drone more time to maneuver.

The limits of the approach were equally informative. At high relative velocities combined with look-ahead times above 12 seconds, the keep-out zone grew too wide to fit inside the A* search grid, a 1,000 by 1,000 meter grid with 10-meter steps, causing the planner to take no avoidance action at all. At very low relative velocities approaching 1, the zone grew too long for the same reason, since the intruder requires more time to pass the mission drone once the latter has given way. Tuning the search grid size to mission requirements would eliminate these failure zones, but even without tuning, the keep-out zones maintained separation above one wingspan across the full tested range of relative velocities and approach angles using look-ahead times between 5 and 8 seconds. The researchers note that future work will increase simulation fidelity to capture bank angle and speed-loss effects, followed by flight tests to identify hardware integration issues. For now, the message is clear: a set of simple geometric shapes, derived from nothing more exotic than velocity, turn rate, and time, may be what finally lets autonomous drones handle the most common collision threat in the sky.

Subject of Research: Aerospace Engineering

Article Title: Overtaking collision avoidance for small autonomous uncrewed aircraft using geometric keep-out zones

Article References: Hawes, N. C., & Wilhelm, J. P. (2023). Overtaking collision avoidance for small autonomous uncrewed aircraft using geometric keep-out zones. Frontiers in Aerospace Engineering, 2, Article 1334291. https://doi.org/10.3389/fpace.2023.1334291

Image Credits: AI Generated

DOI: 10.3389/fpace.2023.1334291

Keywords: drones, autonomy, collision avoidance, UAS, aerospace, air traffic, Overtaking, collision, avoidance, small, autonomous, uncrewed