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rtp_bezier.py
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rtp_bezier.py
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#! /usr/binenv python3
from logging import exception
from math import atan2, sin, sqrt
import math
from numpy.lib.polynomial import poly1d
from numpy.matrixlib.defmatrix import matrix
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as mpl
mpl.rcParams['font.size'] = 30
o=np.matrix([[0,0,0,1]])
class FK:
def __init__(self, theta1, theta2,theta3):
self.theta1=theta1
self.theta2=theta2
self.theta3=theta3
def point(self,x):
#ax.scatter(df.item(0),df.item(1),df.item(2),cmap='Greens')
return df
def lin_plot(self,x,y):
a=x
b=y
plt.plot([a.item(0),b.item(0)],[a.item(1),b.item(1)],[a.item(2),b.item(2)],linewidth=0.5)
def dh(self,q, a, d, t):
z = np.matrix([[np.cos(math.radians(t)), -np.sin(math.radians(t)), 0, q],
[np.sin(math.radians(t)) * np.cos(math.radians(a)), np.cos(math.radians(t)) * np.cos(math.radians(a)),
-np.sin(math.radians(a)), -d * np.sin(math.radians(a))],
[np.sin(math.radians(t)) * np.sin(math.radians(a)), np.cos(math.radians(t)) * np.sin(math.radians(a)),
np.cos(math.radians(a)), d * np.cos(math.radians(a))],
[0, 0, 0, 1]])
return z
def fk(self,theta1, theta2, theta3):
fg = self.dh(0, theta1, 0, 0)
a = self.dh(0, -90, 2, theta2)
b = self.dh(l2, 0, 0, theta3)
c = self.dh(l3, 0, 0, 45)
self.lin_plot(o, self.point(fg))
self.lin_plot(self.point(fg), self.point(fg @ a))
self.lin_plot(self.point(fg @ a), self.point(fg @ a @ b))
self.lin_plot(self.point(fg @ a @ b), self.point(fg @ a @ b @ c))
#print(fg @ a @ b @ c @np.transpose(o))
q=fg @ a @ b @ c @np.transpose(o)
x1=q.item(0)
y1=q.item(1)
z1=q.item(2)
return x1,y1,z1
def point(x):
df=x@o
#print(df)
ax.scatter(df.item(0),df.item(1),df.item(2),cmap='Greens')
#print(df.item(0),"------",df.item(1),"------",df.item(2))
return df
def dh(q, a, d, t):
z = np.matrix([[np.cos(math.radians(t)), -np.sin(math.radians(t)), 0, q],
[np.sin(math.radians(t)) * np.cos(math.radians(a)), np.cos(math.radians(t)) * np.cos(math.radians(a)),
-np.sin(math.radians(a)), -d * np.sin(math.radians(a))],
[np.sin(math.radians(t)) * np.sin(math.radians(a)), np.cos(math.radians(t)) * np.sin(math.radians(a)),
np.cos(math.radians(a)), d * np.cos(math.radians(a))],
[0, 0, 0, 1]])
return z
def ik(x, y, z):
p=math.sqrt(z**2+y**2)
phi=math.degrees(math.atan2(y,z))
q=math.sqrt(p**2-l1**2)
D=(z**2+q**2-l2**2-l3**2)/(2*l2*l3)
theta1=phi+math.degrees(atan2(q,l1))-90
theta3=math.degrees(math.atan2(math.sqrt(1-D**2),D))
theta2=math.degrees(math.atan2(l3*math.sin(math.radians(theta3)),l2+l3*math.cos(math.radians(theta3)))) - math.degrees(math.atan2(x,q))
return theta1,theta2,theta3
l1=2
l2=4
l3=4
limit=10
fig = plt.figure()
ax=fig.add_subplot(111,projection='3d')
ax.set_xlim(-limit,limit)
ax.set_ylim(-limit,limit)
ax.set_zlim(-limit,limit)
ax.set_xlabel('X')
ax.set_ylabel("Y")
ax.set_zlabel("Z")
ax.quiver(0, 0, 0, 0, -3, 0,
arrow_length_ratio=0.1)
ax.quiver(0, 0, 0, 3, 0, 0,
arrow_length_ratio=0.1)
ax.quiver(0, 0, 0, 0, 0, 3,
arrow_length_ratio=0.1)
h=2.5
s=8
def rotz(gamma):
rz = np.matrix([[np.cos(gamma), -np.sin(gamma), 0,gp[0]],
[np.sin(gamma), np.cos(gamma), 0,gp[1]],
[0, 0, 1,gp[2]],
[0,0,0,1]])
return rz
mat = np.matrix([[1, -6, 15, -20, 15, -6, 1],
[-6, 30, -60, 60, -30, 6, 0],
[15, -60, 90, -60, 15, 0, 0],
[-20, 60, -60, 20, 0, 0, 0],
[15, -30, 15, 0, 0, 0, 0],
[-6, 6, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0]])
#ang=45
z=FK(0,45,90)
gp=z.fk(0,45,90)
gp=np.round(gp,3)
"""
print(type(hp))
print(ik(hp[0],hp[1],hp[2]))
plt.scatter(hp[0],hp[1],hp[2],linewidths=5, c='b')"""
print("-----------------------------")
#/////////////// ANGLE ///////////////////////
hp=[0,0,0]
r_z=rotz(np.radians(22.5))
print("r_z : ",r_z)
p1=np.matrix([[hp[0],hp[1],hp[2],1],
[hp[0]-s/2,hp[1],hp[2],1],
[hp[0]-s/2,hp[1],hp[2]+3*h/4,1],
[hp[0],hp[1],hp[2]+h,1],
[hp[0]+(s/2)+1,hp[1],hp[2]+h+1,1],
[hp[0]+s/2,hp[1],hp[2],1],
[hp[0],hp[1],hp[2],1]])
T=np.matrix([[1,0,0,gp[0]],
[0,1,0,gp[1],
[0,0,1,gp[2]],
[0,0,0,1]]])
print(np.transpose(p1))
print("/////////////////////////////////")
print(point_matrix)
for t in np.arange(0,1,0.05):
p = np.matrix([t ** 6, t ** 5, t ** 4, t ** 3, t ** 2, t, 1])
x1=p@[email protected](point_matrix[0,:])
y1=p@[email protected](point_matrix[1,:])
z1=p@[email protected](point_matrix[2,:])
#print("x1: ",x1," ","y1: ",y1,"z1 ",z1)
ax.scatter(np.asscalar(x1),np.asscalar(y1),np.asscalar(z1),cmap='Greens')
theta1,theta2,theta3=ik(np.asscalar(x1),np.asscalar(y1),np.asscalar(z1))
#print("x:",np.asscalar(x1),"y: ",np.asscalar(y1),"z: ",np.asscalar(z1))
g = FK(round(theta1,0),round(theta2,0),round(theta3,0))
g.fk(theta1, theta2,theta3)
ax.scatter(5,5,5,cmap='Greens')
plt.tight_layout()
plt.show()