# Mathmatical-model-to-IROS_2020
In this task, there are three ODE solvers for mathematical model of MallARD. The first solver is named 'ode-45', which is a built-in solver in MATLAB. The rests are built in addition using Runge-Kutta method and euler's method. These models plot some figures out, including surge velocity(u), sway velocity(v) and yaw rate(r). The result is compared with the Figure.8 in 'Model Identification of a Small Fully-Actuated Aquatic Surface Vehicle Using a Long Short-Term Memory Neural Network'.
All of the three models are tested using the datasets form Marin and Keir. Dataset "X" is predominantly excited in X_b by control inputs in F_u. Dataset "Y" and "PSI" excitation is focused on Y_b and by F_v and F_r, respectively. In the datasets "XTPSI", MallARD was excited in all degrees of freedom and was driven in squares, circles and figures of eight, which are motions that could be expected in practice.
## Clone the repository
git clone https://github.com/Xue1iang/Mathmatical-model-to-IROS_2020.git
This repo contains a package of datasets, and three MATLAB codes of ODE solver.
## Explanation of the code
There are three MATLAB files. The firt one is a built-in solver in matlab, namd ODE45. Second one is Runge-kutta and third on is Euler's solver. Three files that all do he same thing using different methods.
First, pre-processing the data to setup the time. And then, using the solver to solve the ordinary differential equation. Calculate the yaw angle via integrating the yaw rate. Mutiply the rotation matrix to transfer to global frame.
The code uses experimental data from MallARD. Joypad input and MallARD position are recorded in the experiments. The mathematical model predicts velocities and position using the joypad inputs and identified model coefficients. Model and coefficients were taken from 'Model Identification of a Small Omnidirectional Aquatic Surface Vehicle: a Practical Implementation'.
## To run the MallARD simulation
Before your running, do not forget to change the address in xlsread('') for choosing the different datasets. After that, run the code and a 6-pack plot and a quiverplot will come out.
## Explanation about plots
### OED45
1. Plots show the measured velocity v in Yb taken from dataset '\XYPSI\XYPSI_1\' against the estimated velocity in Yb for the classical parametric model. Fv is the control input. Yb is the y axis in body-fixed frame.
![OED_45](https://user-images.githubusercontent.com/77399327/114861698-2f9ea400-9e20-11eb-96ad-68707e82ad66.jpg)
### Runge-Kutta Method
This method is mainly applied when the derivative and initial value information of the equation are known and the computer simulation is used to save the complicated process of solving differential equations. The accuracy of this solver can be changed via changing the step.
![Runge-kutta](https://user-images.githubusercontent.com/77399327/114861777-4ba24580-9e20-11eb-8223-89e2758a762b.jpg)
### Euler's Method
Euler's method is an important type of numerical solution. This type of method avoids solving the function expression, but seeks its approximate value on a series of discrete nodes. The distance between two adjacent nodes is called the step. The accuracy of this solver can be changed via changing the step.
![Euler's method](https://user-images.githubusercontent.com/77399327/114861788-4f35cc80-9e20-11eb-9fee-735ae23f09ba.jpg)
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离散控制Matlab代码-Mathmatical-model-to-IROS_2020数学模型到IROS_2020 1.zip
共42个文件
csv:36个
m:3个
txt:1个
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离散控制Matlab代码数学模型到IROS_2020 在此任务中,存在用于MallARD数学模型的三个ODE求解器。 第一个求解器名为“ ode-45”,它是MATLAB中的内置求解器。 其余部分是使用Runge-Kutta方法和euler方法另外构建的。 这些模型列出了一些数字,包括喘振速度(u),摇摆速度(v)和偏航率(r)。 将结果与“使用长短期记忆神经网络的小型全驱动水上水面车辆的模型识别”中的图8进行了比较。 使用Marin和Keir的数据集对所有三个模型进行了测试。 数据集“ X”主要由F_u中的控制输入在X_b中激发。 数据集“ Y”和“ PSI”激励分别集中在Y_b和F_v和F_r上。 在数据集“ XTPSI”中,MallARD在所有自由度上都感到兴奋,并以正方形,圆形和八个数字驱动,这在实践中是可以预期的。 克隆存储库 git clone https://github.com/Xue1iang/Mathmatical-model-to-IROS_2020.git 此仓库包含一组数据集,以及三个ODE求解器的MATLAB代码。 代码说明 有三个MATLAB文件。 第一个
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离散控制Matlab代码-Mathmatical-model-to-IROS_2020数学模型到IROS_2020 1.zip (42个子文件)
Mathmatical-model-to-IROS_2020-main
.gitattributes 42B
Euler's method.m 8KB
Runge-kutta.m 8KB
README.md 3KB
Data
XYPSI
XYPSI_3
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
XYPSI_1
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
XYPSI_2
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
PSI
PSI_2
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
PSI_1
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
PSI_3
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
X
X_2
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
X_1
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
X_3
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
Y
Y_1
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
Y_3
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
Y_2
joystick.csv 131B
pwm.csv 131B
pose_slam.csv 131B
ODE45.m 8KB
a.txt 19B
共 42 条
- 1
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