Document Type

Paper

Publication Date

11-2017

Advisor(s)

Julie Dowling; Illinois Mathematics and Science Academy

Description

Drone technology is beginning to permeate many aspects of life in the modern world, and for good reason. Delivery drones can efficiently deliver packages better than any existing methods. Medical drones can reach emergency patients faster than any ambulance. Security drones can surveil areas more quickly and more thoroughly than a team of human guards. The advent of commercial and industrial uses for drones, however, begets the vital question of how can drones be used outside the workplace. Intel's answer? Entertainment.

Thus, the Intel Shooting StarTM drone was born, a quadcopter explicitly built for producing breathtaking aerial light shows similar in appearance to fireworks displays (Intel, n.d.). On October 7, 2016, 500 drones were used by Intel to set a Guinness World Record for the most Unmanned Aerial Vehicles (UAVs) airborne simultaneously. More impressively, however, is that only one pilot and one laptop were used to guide the show (Cheung, 2017). This master computer" uses Intel's proprietary drone-piloting algorithm to marshall each drone to its designated place in an aerial image, and once the show is complete, to bring each safely back to earth.

Our task is to develop a model to choreograph a drone light show with modeled flight paths for each drone that a similar \master computer" would control. We, however, must tackle issues Intel did not need to consider during their drone displays: those of economy and efficiency, by optimizing both the number and the placement of drones. We wish to perform a drone show optimized for both resource and time efficiency, and thus, the number of drones used in the show will be kept to a minimum to lower cost. The travel time for each drone (from liftoff to formation, and from one formation to each subsequent formation) during the show will be minimized as well { the Shooting Star's battery lasts for approximately twenty minutes, and hence the drone show must run safely inside of that time frame. And of course, the less time spent positioning drones, the more viewing time will be available for the show!

During our light show, we will project the images of a dragon, a Ferris wheel, and our team number in the sky by creating corresponding sets of drone positions. However, the use of the model will not be limited to one show; in order to be of utility for future drone-show organizers, our model must be able to accept any image (given that there are enough drones available to properly display the image's complexity) and convert it into a drone pattern. Our model must also take into account how wind affects drone flight performance. Based on our model's optimized output, we can determine the number of drones our city must acquire to host our light show, and therefore the cost of staging the performance. We can also calculate the timing of the show, and any flight path adjustments necessitated by the wind. Using this information, we can then give the Mayor of our city an informed perspective of whether or not to pursue the option of a drone light show for our city's annual festival this year.

However, our model will not be limited for use on merely one occasion, in one city, and for one holiday. Quite the contrary, our model will be be implementable not only in our city, but cities around the globe to help establish drone shows as traditional holiday events, and to demonstrate that drones can be just as valuable for entertainment as they are for business.

Included in

Mathematics Commons

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