Although air traffic is currently strongly restricted due to the coronavirus pandemic, the skies have grown increasingly busy in recent years. In 2019 the average number of aircraft in flight at any one time was 11,000, twice as many as ten years ago. This volume puts a lot of extra pressure on the central air traffic control, says Wouter Schaberg, who earned his Master's degree in Control and Operations from the Faculty of Aerospace Engineering this summer. “Every flight must be reported to air traffic control, which then guides the aircraft from A to B, often on fixed routes. But the flight routes are becoming increasingly full. It is an enormous puzzle to make sure everything runs smoothly.”

Carrying out manoeuvres independently

A possible solution to the pressure on air traffic control is to make flight control more decentralised. Wouter: “This means that rather than being guided by air traffic control, aircraft are free to determine their own flight path and carry out manoeuvres independently. Of course this must be done safely. Back in the early 1990s an American researcher – Martin Eby – conceived an algorithm that gives aircraft a signal when they fly too close to each other and then indicates which manoeuvre the pilots need to carry out to avert danger. As commercial aviation does not yet use this free flight concept, thus far the algorithm is only used in flight simulations. In 2000, Jacco Hoekstra, my thesis supervisor, made improvements to this algorithm.”

Spending days flying around the world

The algorithm that had been developed, called Modified Voltage Potential (MVP), was not entirely watertight, says Wouter. “In flight simulations the algorithm mainly did what it was supposed to do: aircraft that were detected too close together received a signal, after which the aircraft moved apart and the danger was averted. However, aircraft flying on near parallel paths that needed to cross each other somewhere along the route continued to re-conflict after the initial conflict situation was resolved. Sometimes this meant that aircraft in a simulation got so stuck that they spent days flying around the world in parallel, with the same recurring conflict. It was my task to find out the cause of this ‘repetitive conflict’ and maybe find a solution.”

Unsolved for 25 years

Before Wouter started on his thesis, he knew nothing about the problem with the MVP algorithm and the repetitive conflict. “My supervisor Jacco Hoekstra approached me with this issue, and it really appealed to me. Of course it's very special that he worked on this algorithm himself; that gave extra motivation to find a solution. At the same time, I knew that I was facing a considerable challenge; it was not without reason that this problem was still unresolved after 25 years. I started by reading all I could find on the subject and studied thousands of flight simulations to see the problem with my own eyes. Then I started to unravel the mathematics of the algorithm. I think I must have drawn more than a thousand triangles to see if there weren't any incorrect lines or calculations somewhere in the algorithm. But I was unable to discover any errors on the basis of this.” 

The great breakthrough

Just when Wouter was convinced he had come to a dead end, he experienced a ‘Eureka’ moment. “I went back to the literature to check whether I might have missed something. I suddenly noticed that the literature was mainly focused on conflict detection and the ways of solving this, but the phase following the conflict resolution, that of recovery, was hardly addressed at all, even though this is a problem that arises after a conflict situation has been resolved. For what should the aircraft do next? How and when can it return to its original route? I picked up the algorithm again, and then I saw where the problem was: in the mathematical elaboration of the recovery component.”

Algorithm modification

Once the problem had been identified, it was only a matter of time before a solution presented itself. Wouter: “Of course I was really happy to have discovered the problem but I wanted to get on with things right away. So I started tinkering with the algorithm and drawing even more triangles. In the end I removed an incorrect recovery component from the algorithm and added a new two-criteria method. This method starts by making a best guess for each aircraft of the desired route and velocity of the other, conflicting aircraft. Next, the method combines this best guess with the present route and velocity of the other aircraft, to determine whether reverting to the original route is possible without the aircraft getting dangerously close to each other. After this modification, I set the TU Delft computers to work testing the new algorithm on over a million flight simulations. This showed that the repetitive conflict now hardly occurred at all.”