python示例找到dubins曲线切点
时间: 2023-10-14 16:19:22 浏览: 47
抱歉,我是语言模型,无法提供图形化示例。在找到Dubins曲线切点方面,以下是Python代码示例:
```python
import numpy as np
from math import cos, sin, tan, atan2, sqrt
# Define a function to calculate the intersection point of two circles
def circle_intersection(x1, y1, r1, x2, y2, r2):
d = sqrt((x2 - x1)**2 + (y2 - y1)**2)
a = (r1**2 - r2**2 + d**2) / (2*d)
h = sqrt(r1**2 - a**2)
x3 = x1 + a*(x2 - x1)/d
y3 = y1 + a*(y2 - y1)/d
x4_1 = x3 + h*(y2 - y1)/d
y4_1 = y3 - h*(x2 - x1)/d
x4_2 = x3 - h*(y2 - y1)/d
y4_2 = y3 + h*(x2 - x1)/d
return (x4_1, y4_1), (x4_2, y4_2)
# Define a function to calculate the Dubins curve tangent points
def dubins_tangent_points(q1, q2, R):
dx = q2[0] - q1[0]
dy = q2[1] - q1[1]
d = sqrt(dx**2 + dy**2)
theta = atan2(dy, dx)
alpha = atan2(2*R, d)
t1 = (q1[0] + R*cos(theta + alpha), q1[1] + R*sin(theta + alpha))
t2 = (q1[0] + R*cos(theta - alpha), q1[1] + R*sin(theta - alpha))
t3 = (q2[0] + R*cos(theta + alpha - np.pi), q2[1] + R*sin(theta + alpha - np.pi))
t4 = (q2[0] + R*cos(theta - alpha - np.pi), q2[1] + R*sin(theta - alpha - np.pi))
return t1, t2, t3, t4
# Define a function to calculate the Dubins curve length
def dubins_curve_length(q1, q2, R):
t1, t2, t3, t4 = dubins_tangent_points(q1, q2, R)
lengths = []
lengths.append(sqrt((t1[0] - q1[0])**2 + (t1[1] - q1[1])**2))
lengths.append(sqrt((t2[0] - q1[0])**2 + (t2[1] - q1[1])**2))
lengths.append(sqrt((t3[0] - q2[0])**2 + (t3[1] - q2[1])**2))
lengths.append(sqrt((t4[0] - q2[0])**2 + (t4[1] - q2[1])**2))
lengths.append(sqrt((t1[0] - t3[0])**2 + (t1[1] - t3[1])**2))
lengths.append(sqrt((t1[0] - t4[0])**2 + (t1[1] - t4[1])**2))
lengths.append(sqrt((t2[0] - t3[0])**2 + (t2[1] - t3[1])**2))
lengths.append(sqrt((t2[0] - t4[0])**2 + (t2[1] - t4[1])**2))
return min(lengths)
# Define a function to calculate the Dubins curve path
def dubins_curve(q1, q2, R):
t1, t2, t3, t4 = dubins_tangent_points(q1, q2, R)
lengths = []
lengths.append(sqrt((t1[0] - q1[0])**2 + (t1[1] - q1[1])**2))
lengths.append(sqrt((t2[0] - q1[0])**2 + (t2[1] - q1[1])**2))
lengths.append(sqrt((t3[0] - q2[0])**2 + (t3[1] - q2[1])**2))
lengths.append(sqrt((t4[0] - q2[0])**2 + (t4[1] - q2[1])**2))
lengths.append(sqrt((t1[0] - t3[0])**2 + (t1[1] - t3[1])**2))
lengths.append(sqrt((t1[0] - t4[0])**2 + (t1[1] - t4[1])**2))
lengths.append(sqrt((t2[0] - t3[0])**2 + (t2[1] - t3[1])**2))
lengths.append(sqrt((t2[0] - t4[0])**2 + (t2[1] - t4[1])**2))
min_length_index = np.argmin(lengths)
if min_length_index == 0:
return [q1, t1]
elif min_length_index == 1:
return [q1, t2]
elif min_length_index == 2:
return [t3, q2]
elif min_length_index == 3:
return [t4, q2]
elif min_length_index == 4:
return [t1, t3, q2]
elif min_length_index == 5:
return [t1, t4, q2]
elif min_length_index == 6:
return [t2, t3, q2]
elif min_length_index == 7:
return [t2, t4, q2]
# Define the inputs
q1 = (0, 0, 0)
q2 = (5, 5, np.pi/2)
R = 1
# Calculate the Dubins curve path
path = dubins_curve(q1, q2, R)
# Calculate the Dubins curve length
length = dubins_curve_length(q1, q2, R)
# Print the results
print("Dubins curve path:", path)
print("Dubins curve length:", length)
```
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