2017 HiMCM A题特等奖学生论文下载8206

2017 HiMCM A题特等奖学生论文下载8206

 

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论文摘要如下：

HiMCM Summary Sheet

Step aside, fireworks - traditional pyrotechnics now have a new competitor for lighting up the night sky! Intel recently performed a 3D light show using 500 LED-carrying drones and captivated the world’s attention. The Mayor of our city asked our team to analyze the viability of a potential light show for our annual city festival, which would contain three separate displays: a Ferris wheel, a dragon, and a third display of our choosing, which we elected to be an expanding balloon.

 

Intel’s Shooting Star drones are not commercially available, so we chose the DJI Phantom 3, a mid-priced drone with a long battery life and a pre-programmable GPS control system. The DJI Phantom 3s will be placed in a rectangular grid on the ground before the show for easy set up. We mathematically modeled the paths that each of these drones would take in performing a display demonstration using both MATLAB and Python algorithms. Our drone’s paths were split up into three major phases: Transition from Grid to Display, Animation, and Transition from Display to Grid. The model we developed computed the position and velocity of the drones in each of these phases and generated an animation of drone movement for each display.

 

During the first phase (Transition from Grid to Display), a Python script uses the Hungarian Algorithm to compute the shortest set of paths between the grid location and the initial points of the display. Our model also implements a collision avoidance protocol, which uses the predicted flight paths of the drones to fine-tune their velocities such that no drones collide.

 

Once the initial display image was formed during the first phase, we made the image dynamic by moving it around the aerial space in the Animation phase. The Ferris wheel’s spokes and wheel spin around its center while the entire Ferris wheel rotates around its vertical axis so that the entire crowd can view it. The dragon follows a helical toroid curve, mimicking the traditionally portrayed movement of dragons. The balloon gradually expands as if it is being inflated by using a center of homothety at the bottom of the balloon to scale it up over time. At the end of each animation phase, the drones return to the grid pattern before transforming into the next animation (Transition from Display to Grid).

 

Our model indicates that this 3-display light show requires 196 drones (worth $97,804) and an airspace the size of a right cylinder whose base has a radius of 250 meters and whose height ranges from 10 meters to 115 meters above the ground. The show lasts 9.7 minutes. We recommend that all viewers stand at least 15 meters away in the all directions from the drone-occupied airspace and that drones are only flown when wind speed is less than 11.72 m/s for safety reasons.

 

Overall, our planned light show uses a variety of mathematical models to create a fluid and dynamic light display without any collisions, and is protected by enough regulations to ensure viewer safety. We’ve demonstrated that a drone light show is a viable and exciting prospect for our city’s festival.

 

 

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