2017 HiMCM A题特等奖学生论文下载8028

2017 HiMCM A题特等奖学生论文下载8028

 

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论文摘要如下：

20th Annual High School Mathematical Contest in Modeling (HiMCM) Summary Sheet (Please make this the first page of your electronic Solution Paper.)

 

Team Control Number: 8028 Problem Chosen: A

 

Please paste or type a summary of your results on this page.

 

Please remember not to include the name of your school, advisor, or team members on this page. We were very excited to be assigned the task of researching the feasibility and the requirements for an air light show using hundreds of drones for our city to celebrate the 40th anniversary. We have made our best to study the mathematical principles of the design, includingtherepresentationofdrones, thedesignofstaticimagedisplays, andespeciallythe implementation of animations of images. We have enjoyed a few intensive working hours to make our research valuable and more over, feasible for the actual realization of the air light show within two years, before the actual 40th anniversary air light show to come true.

 

In this paper, we did not talk about too much about the principle of the drone’s fly, instead, we assume that the drone can be controlled almost accurately to any position at our will, which made us focus on the positioning for the static images to display, and the route planning for images to animate.

 

In the modeling of the drones, we used 3D coordinates for each drone. The control of the drones was simplified to a sequence of positions that each drone should appear at predetermined time points in 3D space. In order to design and implement the show, we need to implement some basic actions for the set of drones, including launching, launching to form staticimages,translation of the static images without reshaping,rotation of the static images about arbitrary axis, transition between different static images, etc. With these basic action being implemented, we were able to make a sequence of combinations of multiple actions into a complicated action to make the show much more attractive. For example, we can see a static ferris wheel in the sky, and a static dragon in the sky, and a transition from the ferriswheeltoadragoninplace, butwiththecombination, wecaneasilyrealizeatransition from the ferris wheel to the dragon while the drone as a whole, were flying to some where. We can definitely implement many more very attractive effects for the air show to make the whole air show a unforgettable experience to anyone who would be an audience of the show.

 

In the implementing of the show, we found out that matrix is such a powerful tool in this task. We have seen the simple but elegant way to writing complicated formulas, and especially, that easiness of using matrices in MATLAB to make a simple emulations to test our ideas. We used matrices to implemented the representation of positions of drones in 3D space, and implemented the translation of image as a whole, and rotation of image as a whole about arbitrary axis in a few matrix operations, and the most exciting part, the implementation of the transition from one image to another with the help of matrices. The math part looks so elegant and makes us very excited.

 

 

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