1. Competition registration and thinking analysis (continuous update 750967193)
2. Competition time: from 18:00 on September 15, 2022 to 20:00 on September 18, 2022
The idea of problem B is as follows:
Paste the topic first:
The following is a preliminary analysis:
The problem of drones is a hot issue in recent years. In the past, it was mostly a scheduling problem. This time it is related to the positioning of drones. On the basis of the establishment of a simple positioning model, the deviation of drones should be considered. How the bias can be optimized. The overall analysis of Question B is as follows:
Question (1) of Question 1 is equivalent to having determined the position of one UAV, and the positions of the other two UAVs. The combination of different UAV positions should be considered to establish a basic mathematical model; Question (2) is equivalent to knowing the positions of the two drones. How many drones need to transmit signals to realize the effective positioning of the drones. This is an optimization problem. It is still recommended to consider different situations. For Model building in different situations; question (3) of question 1 is similar to the scheduling problem. This small question is another deepening on the basis of question 1 and question 2. It will be one of the core questions of question B. Strictly It is said that it is also a scheduling problem. Question 2 is an expansion on the basis of Question 1, which needs to be adjusted for different formations. If you have students with related majors who can carry out simulations, the effect will be the best, but it doesn't matter, and you can do it.
For specific problems, the analysis is as follows:
Question 1:
(1) As shown in Figure 1, the determination of the position of the UAV is mainly based on the angle. There are 9 UAVs on the periphery of the trajectory. According to the positioning of FY00 and the other 2 UAVs, it is first necessary to clarify how many situations there are. As shown in Figure 2, there are 4 situations in total, and then combine the relative positions of the UAVs , the change of the relative position also needs to be considered. After that, the model should be established and solved for each situation. The principle of positioning is to have a fixed angle. It is also possible to build a measurement model first, and then change the parameters for analysis.
Figure 1 Schematic diagram of UAV position determination
Figure 2 Schematic diagram of UAV position determination
(2) Problem (2) is a deepening on the basis of problem (1), and should be optimized on the basis of problem (1). Undoubtedly, two planes will definitely not work, and in some specific positions, three planes will not be seen. It's okay. This question must bear in mind the background of the problem - it is required to send as few electromagnetic wave signals as possible, so it is similar to an optimization problem and can be optimized on the basis of the problem-model. In addition, for this question, you can combine the connection between the topics and respond flexibly. The following is the derivation of the self-adaptive variable dimension algorithm, you can refer to it, combine the actual problem, establish a basic model, and then improve on this basis, analyze the results, and make improvements.
Here are some other ideas and ideas: Question B is the correction of the position offset of the drone. Assuming the same height, only two drones are needed for correction. The correction can be adjusted by angle and distance, and the model can be The solution is established by passing the Pythagorean theorem. Use the data in Table 1 to first fit a standard circle for position deviation calculation (deviation distance, deviation angle). Once the radius R is known, the distance can be adjusted.
As for the effective adjustment, as long as there are two drones, it can be adjusted effectively, but if the two drones responsible for transmitting signals are in line with one drone receiving signals, although it can be adjusted, but from a practical point of view The effect is relatively poor. You can set a certain penalty. For example, the smaller the angle, the greater the penalty value. The drones that have been corrected are included in the set of drones that can be used to transmit signals. How to pursue the smallest overall penalty value, then the correction priority is also particular. , then it can also be used as an optimization point.