for i in range(traj_count): plt.plot(wp_area_traj_3[i][:,0],wp_area_traj_3[i][:,1], linewidth = 3, c = colors_2[labels[i]]) ax1.grid()表示什么意思
时间: 2024-06-02 15:01:10 浏览: 15
这段代码是用来画多条轨迹的,具体的解释如下:
1. for i in range(traj_count): 表示一个循环,从0到traj_count-1,每次循环i的值都会递增1。
2. plt.plot(wp_area_traj_3[i][:,0],wp_area_traj_3[i][:,1], linewidth = 3, c = colors_2[labels[i]]) 表示用matplotlib库中的plot函数画出一条轨迹,其中wp_area_traj_3[i][:,0]表示第i条轨迹的横坐标数据,wp_area_traj_3[i][:,1]表示第i条轨迹的纵坐标数据;linewidth = 3表示轨迹的线宽为3个像素;c = colors_2[labels[i]]表示轨迹的颜色,颜色是根据标签labels[i]来确定的,每个标签对应一个颜色。
3. ax1.grid()表示给画布添加网格线。
总体来说,这段代码是用来画多条轨迹,并加入网格线以便于观察。
相关问题
Write a code to calculate the trajectory that is traced out between time t=0 and t=20 by an air parcel in the flow: F(x, y)=-(y^2)/2+cos(x). Use the explicit (Euler forward) scheme for the first step, and the leapfrog scheme for all subsequent steps. Use △t = 0.01 and include a Robert-Asselin filter applied to both x and y with a coefficient of 0.01. You will need to import math to use the Python function math.sin(). Run your program for the following two starting positions, which are marked with crosses in the above figure:(x0.y0)=(1.0,1.0) (in the eddy region) ,(x0,y0)=(1.0,2.0) (in the stream region) For each of these starting positions, plot the trajectory in the (x ,y) plane. Use the trajectory in the eddy region to verify the stability of the numerical method and explain your reasoning
Sure, here's a Python code that solves the problem you presented:
```python
import math
import matplotlib.pyplot as plt
# Define the flow field function F(x, y)
def F(x, y):
return -(y**2)/2 + math.cos(x)
# Define initial positions
x0, y0 = 1.0, 1.0 # starting position in the eddy region
x1, y1 = 1.0, 2.0 # starting position in the stream region
# Define time step and total time
dt = 0.01
T = 20
# Define Robert-Asselin filter coefficient
alpha = 0.01
# Define arrays to store positions
x_traj = [x0]
y_traj = [y0]
# Solve for starting position (x0, y0)
x, y = x0, y0
for t in range(1, int(T/dt)+1):
# Explicit Euler forward scheme for the first step
if t == 1:
x += dt * F(x, y)
y += dt * F(x0+dt, y)
# Leapfrog scheme for all subsequent steps
else:
x += 2*dt * F(x, y)
y += 2*dt * F(x, y0+dt)
# Apply Robert-Asselin filter
x = x + alpha * (x - x0)
y = y + alpha * (y - y0)
# Store positions
x_traj.append(x)
y_traj.append(y)
# Plot trajectory for starting position (x0, y0)
plt.plot(x_traj, y_traj, label='Starting position: (1.0, 1.0)')
# Repeat for starting position (x1, y1)
x_traj = [x1]
y_traj = [y1]
x, y = x1, y1
for t in range(1, int(T/dt)+1):
if t == 1:
x += dt * F(x, y)
y += dt * F(x1+dt, y)
else:
x += 2*dt * F(x, y)
y += 2*dt * F(x, y1+dt)
x = x + alpha * (x - x1)
y = y + alpha * (y - y1)
x_traj.append(x)
y_traj.append(y)
# Plot trajectory for starting position (x1, y1)
plt.plot(x_traj, y_traj, label='Starting position: (1.0, 2.0)')
# Customize plot
plt.title('Trajectory of an Air Parcel')
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()
```
The code defines the flow field function F(x, y), the initial positions (x0, y0) and (x1, y1), the time step dt, the total time T, and the Robert-Asselin filter coefficient alpha. It then solves for the trajectory of the air parcel using an explicit Euler forward scheme for the first step, and a leapfrog scheme for all subsequent steps. The Robert-Asselin filter is applied at each time step to reduce numerical noise. Finally, the code plots the trajectories for both starting positions.
To verify the stability of the numerical method, we can observe the trajectory of the air parcel starting at position (x0, y0) in the eddy region. If the trajectory remains within the eddy region and does not exhibit significant oscillations or diverge from the region, then the numerical method is considered stable. This is because the eddy region is known to have chaotic behavior, and if the method is stable in this region, it is likely to be stable in other regions as well.
L1 = Link('d', 0, 'a', 0, 'alpha', 0); L2 = Link('d', 0, 'a', 0.5, 'alpha', 0); L3 = Link('theta', 0, 'a', 1, 'alpha', pi); L4 = Link('d', 0.25, 'a', 0, 'alpha', 0); myrobot_199 = SerialLink([L1 L2 L3 L4], 'name', 'robot_199'); myrobot_199.display();设初始关节位姿qz=[0, 0, 0.01, 0],目标关节位姿为qr = [pi/3,pi/2,0.5, pi/5],运动时间为3s 1、使用jtraj()函数,在关节空间规划轨迹,插补间隔为0.05s; 2、利用正向运动学求解函数fkine(),求出末端执行器位姿矩阵T; 3、使用T.transl提取出末端执行器的坐标; 4、绘出末端执行器的x、y、z坐标随时间变化的曲线
好的,我知道了。以下是针对您的问题的代码和解答:
```python
import numpy as np
from math import pi
from robot import *
# 定义机器人的各个关节
L1 = Link('d', 0, 'a', 0, 'alpha', 0)
L2 = Link('d', 0, 'a', 0.5, 'alpha', 0)
L3 = Link('theta', 0, 'a', 1, 'alpha', pi)
L4 = Link('d', 0.25, 'a', 0, 'alpha', 0)
# 创建机器人对象
myrobot_199 = SerialLink([L1, L2, L3, L4], 'name', 'robot_199')
# 设定初始关节位姿和目标关节位姿
qz = np.array([0, 0, 0.01, 0])
qr = np.array([pi/3, pi/2, 0.5, pi/5])
# 使用jtraj()函数在关节空间规划轨迹
traj_q = jtraj(qz, qr, 50, 0.05)
# 将关节轨迹转化为末端执行器位姿矩阵轨迹
traj_T = myrobot_199.fkine(traj_q)
# 提取出末端执行器的坐标
traj_xyz = traj_T.transl
# 绘制末端执行器的x、y、z坐标随时间变化的曲线
import matplotlib.pyplot as plt
fig, axs = plt.subplots(3, 1, sharex=True)
axs[0].plot(traj_q[:, 0], traj_xyz[:, 0])
axs[0].set_ylabel('x (m)')
axs[1].plot(traj_q[:, 0], traj_xyz[:, 1])
axs[1].set_ylabel('y (m)')
axs[2].plot(traj_q[:, 0], traj_xyz[:, 2])
axs[2].set_ylabel('z (m)')
axs[2].set_xlabel('time (s)')
plt.show()
```
解释一下代码的每一部分:
- 第1-8行:定义机器人的各个关节,创建机器人对象。
- 第10-11行:设定初始关节位姿和目标关节位姿。
- 第14行:使用jtraj()函数在关节空间规划轨迹,插补间隔为0.05s。
- 第17行:将关节轨迹转化为末端执行器位姿矩阵轨迹。
- 第20行:提取出末端执行器的坐标。
- 第23-33行:绘制末端执行器的x、y、z坐标随时间变化的曲线。
注意,这里使用了一个叫做robot的Python库,用于处理机器人的运动学和动力学问题。如果您没有安装该库,可以通过以下命令安装:
```
pip install roboticstoolbox-python
```
希望这个代码能够帮到您,如果您还有其他问题,请随时提出,我会尽力解答。
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