[2023 May 1st Mathematical Modeling Contest Question A] Research on Fixed-point Delivery of UAVs-Complete Paper + Code

1. Question background and restatement

insert image description here

2. Analysis of problem-solving ideas

2.1 Analysis of Question 1

insert image description here

Question 1 Assuming that the UAV flies and drops materials parallel to the horizontal plane, the movement of the materials can be compared to a flat throwing movement. Because the weight of the materials is relatively large, it cannot be simply regarded as a mass point, and the weight of the materials must also be considered.
2.1.1 This question requires the impact of the drone's launch distance and its flight height, flight speed, and air resistance. The speed at which the materials are just dropped is the flight speed of the UAV. According to aerodynamics, this question distinguishes the air resistance of materials at different speeds. According to Newton’s second law F  ma , list the vertical and horizontal directions The differential equation of the resultant force on the material in the direction, the displacement of the material in the horizontal and vertical directions is solved by Matlab software, and finally the straight-line distance between the drop point and the designated position is obtained through the distance formula between two points.
2.1.2 This question gives the data of flight altitude and flight speed, and also adds the condition of wind speed parallel to the horizontal plane. According to the knowledge of relative speed, when the flying direction of the UAV is the same as the wind direction, the material running speed is The two are added; on the contrary, the velocity is the subtraction of the two; when the two are perpendicular, it is equivalent to an initial velocity in the vertical direction of the object. Through the above model, the specific values ​​are brought in, and Matlab is used to solve the result to obtain the result.

2.2 Analysis of Question 2

Question 2 Assuming that the UAV dives at an inclination angle and throws the explosives at this inclination angle, the movement of the explosives can be compared to a similar flat throwing motion. Add the angle  on the basis of problem 1, so that the explosive has a certain initial velocity in the parallel and vertical directions at the beginning. Since the flying speed of the drone is different from the launching speed of the explosive, it can be divided into two times and for consideration. 2.2.1 Since the flying speed of the aircraft is constant, only the launch speed is considered in this question. The influence of air resistance is also considered in this question, and the resultant force differential equations in the horizontal and vertical directions are listed separately to write the straight-line distance expression.
2.2.2 Since there is an extra movement of the UAV before launching explosives, the model of this question adds the movement displacement of the UAV in the horizontal and vertical directions. The wind speed given in the question does not indicate its direction, so this question discusses the initial velocity of the explosive in the horizontal and vertical directions under different wind directions, so as to list different displacement differential equations to find the time and dive angle. Finally, the launch strategy in different situations is obtained by software.

2.3 Analysis of Question 3

Question 3 requires describing the relationship between UAV stability and hit accuracy. By consulting the data, the stability of the UAV is related to its own factors and external factors.
2.3.1 In this question, by looking for the relationship expression between pitch angle, roll angle, yaw angle and aircraft stability, as well as the weight of different types of drones, and through the knowledge of fluid mechanics, find out the Reynolds number at different altitudes under the same weight. Analyze its impact on the stability of the aircraft, and then describe the relationship between the hit accuracy and flight altitude, flight speed, dive angle, etc. by writing the expression from the launch point to the target position, and change one of the parameters by controlling the variable method To compare the importance of these factors, and then assign weights, so as to write the expression that affects stability.

2.3.2 Calculate the optimal flight attitude of the UAV through the given wind speed, the constraint range of flight speed, and the dive angle. This question uses software to solve the optimal pitch angle, roll angle, and yaw angle to determine the optimal flight attitude to keep the drone stable.

3. Complete resource preview

Complete word version of the paper + all source code + data + paper
insert image description here

Guess you like

Origin blog.csdn.net/maligebilaowang/article/details/130584815