The math and computer science behind the Super Bowl half time show

Cor Hurkens & Jan Friso Groote | Department of Mathematics and Computer Science @ Eindhoven University of Technology

During the half time show of the Super Bowl, the many millions of viewers were surprised with something they had never seen before. At the beginning of the show by Lady Gaga 300 drones lit up the sky. A spectacular light show followed, in which an animated starry sky, the US flag, and logos of Intel and Pepsi were formed.

This technological masterpiece in which multiple drones were flying in formation, was made possible by technology company Intel. They built the quadcopters, software and were accountable for programming the algorithms behind the show. Because without mathematics the light show could never have happened. “That’s simply impossible without good and fast heuristics, geometry, control theory and excellent data structures,” said assistant professor operational research Cor Hurkens of TU Eindhoven.

Kaleidoscope
The drones are controlled by a single computer. Based on the input of a reference pattern of the desired figure, the software automatically determine how many drones are needed to create the figure, where the drones should fly, which color they should show and what the most efficient route is to create the formation. And because the drones lack detection sensors, this needs to be done in such a way that the drones avoid each other.

“A kaleidoscope of mathematical problems,” according to Hurkens. “A drone must know its own location, make sure it stays in position, know what position it holds in the following figure, and fly the safest route.” Mathematics helps determining and controlling these situations. The transformation of one figure into another is the most critical part of the choreography. “The navigation of 300 drones must be determined, of course without collisions. Calculating this properly without software could take up to weeks,” concludes Hurkens.

Safety
According to Intel the light show was only the beginning and another step towards flying in formations of 10,000 drones. And although the drones have been developed primarily for entertainment, the technique can also be used for practical purposes. For example agriculture, or rescue operations. As long as the software is programmed correctly.

Concerns about safety of the crowd could be one of the reasons why the half time drone show was prerecorded and was not performed live. An incident a few days after the Super Bowl illustrates why: drones produced by Japanese manufacturer DJI fell out of the sky out of nowhere after an automatic software update. Another example of software errors causing dangerous situations. Especially when drones are going to fly above large crowds.

Nevertheless the consequences of software errors remain underexposed. “Organizers of major events invest lots of money in equipment to prevent lightning strikes. But no one is concerned about software failures that cause problems for many people every day,” according to Jan Friso Groote who is full professor computer science at TU Eindhoven. “Even though the likelihood of software errors is substantially higher than the probability of a lightning strike.” Groote therefore calls for fundamental changes in the approach of software development. “In order to reduce future error rates in software substantially, software must be constructed fundamentally different. We are increasingly dependent on software in the future. If we keep continuing in the same manner, we will face the increasing burden of software failures which additionally are more difficult to control. With all its consequences.”