mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
synced 2026-02-16 10:55:07 -05:00
140 lines
5.2 KiB
Python
140 lines
5.2 KiB
Python
import numpy as np
|
|
import math
|
|
from mpl_toolkits.mplot3d import Axes3D
|
|
import matplotlib.pyplot as plt
|
|
|
|
class Link:
|
|
def __init__(self, dh_params):
|
|
self.dh_params_ = dh_params
|
|
|
|
def transformation_matrix(self):
|
|
theta = self.dh_params_[0]
|
|
alpha = self.dh_params_[1]
|
|
a = self.dh_params_[2]
|
|
d = self.dh_params_[3]
|
|
|
|
trans = np.array(
|
|
[[math.cos(theta), -math.sin(theta), 0, a],
|
|
[math.cos(alpha) * math.sin(theta), math.cos(alpha) * math.cos(theta), -math.sin(alpha), -d * math.sin(alpha)],
|
|
[math.sin(alpha) * math.sin(theta), math.sin(alpha) * math.cos(theta), math.cos(alpha), d * math.cos(alpha)],
|
|
[0, 0, 0, 1]])
|
|
|
|
return trans
|
|
|
|
def basic_jacobian(self, trans_prev, ee_pose):
|
|
pos_prev = np.array([trans_prev[0, 3], trans_prev[1, 3], trans_prev[2, 3]])
|
|
z_axis_prev = np.array([trans_prev[0, 2], trans_prev[1, 2], trans_prev[2, 2]])
|
|
|
|
basic_jacobian = np.hstack((np.cross(z_axis_prev, ee_pose - pos_prev), z_axis_prev))
|
|
return basic_jacobian
|
|
|
|
|
|
class NLinkArm:
|
|
def __init__(self, dh_params_list):
|
|
self.link_list = []
|
|
for i in range(len(dh_params_list)):
|
|
self.link_list.append(Link(dh_params_list[i]))
|
|
|
|
self.fig = plt.figure()
|
|
self.ax = Axes3D(self.fig)
|
|
|
|
def transformation_matrix(self):
|
|
trans = np.identity(4)
|
|
for i in range(len(self.link_list)):
|
|
trans = np.dot(trans, self.link_list[i].transformation_matrix())
|
|
return trans
|
|
|
|
def forward_kinematics(self):
|
|
trans = self.transformation_matrix()
|
|
|
|
x = trans[0, 3]
|
|
y = trans[1, 3]
|
|
z = trans[2, 3]
|
|
alpha = math.atan2(trans[1, 2], trans[1, 3])
|
|
beta = math.atan2(trans[0, 2] * math.cos(alpha) + trans[1, 2] * math.sin(alpha), trans[2, 2])
|
|
gamma = math.atan2(-trans[0, 0] * math.sin(alpha) + trans[1, 0] * math.cos(alpha), -trans[0, 1] * math.sin(alpha) + trans[1, 1] * math.cos(alpha))
|
|
|
|
return [x, y, z, alpha, beta, gamma]
|
|
|
|
def basic_jacobian(self, ref_ee_pose):
|
|
basic_jacobian_mat = []
|
|
|
|
trans = np.identity(4)
|
|
for i in range(len(self.link_list)):
|
|
trans = np.dot(trans, self.link_list[i].transformation_matrix())
|
|
basic_jacobian_mat.append(self.link_list[i].basic_jacobian(trans, ref_ee_pose[0:3]))
|
|
|
|
#print(np.array(basic_jacobian_mat).T)
|
|
return np.array(basic_jacobian_mat).T
|
|
|
|
def inverse_kinematics(self, ref_ee_pose):
|
|
ee_pose = self.forward_kinematics()
|
|
diff_pose = ee_pose - np.array(ref_ee_pose)
|
|
|
|
for cnt in range(1000):
|
|
basic_jacobian_mat = self.basic_jacobian(ref_ee_pose)
|
|
alpha, beta, gamma = self.calc_euler_angle()
|
|
|
|
K_zyz = np.array([[0, -math.sin(alpha), math.cos(alpha) * math.sin(beta)],
|
|
[0, math.cos(alpha), math.sin(alpha) * math.sin(beta)],
|
|
[1, 0, math.cos(beta)]])
|
|
K_alpha = np.identity(6)
|
|
K_alpha[3:, 3:] = K_zyz
|
|
|
|
theta_dot = np.dot(np.dot(np.linalg.pinv(basic_jacobian_mat), K_alpha), np.array(diff_pose))
|
|
self.update_joint_angles(theta_dot)
|
|
|
|
def calc_euler_angle(self):
|
|
trans = self.transformation_matrix()
|
|
|
|
alpha = math.atan2(trans[1][2], trans[0][2])
|
|
beta = math.atan2(trans[0][2] * math.cos(alpha) + trans[1][2] * math.sin(alpha), trans[2][2])
|
|
gamma = math.atan2(-trans[0][0] * math.sin(alpha) + trans[1][0] * math.cos(alpha), -trans[0][1] * math.sin(alpha) + trans[1][1] * math.cos(alpha))
|
|
|
|
return alpha, beta, gamma
|
|
|
|
def set_joint_angles(self, joint_angle_list):
|
|
for i in range(len(self.link_list)):
|
|
self.link_list[i].dh_params_[0] = joint_angle_list[i]
|
|
|
|
def update_joint_angles(self, diff_joint_angle_list):
|
|
for i in range(len(self.link_list)):
|
|
self.link_list[i].dh_params_[0] += diff_joint_angle_list[i]
|
|
|
|
def plot(self):
|
|
x_list = []
|
|
y_list = []
|
|
z_list = []
|
|
|
|
trans = np.identity(4)
|
|
|
|
x_list.append(trans[0, 3])
|
|
y_list.append(trans[1, 3])
|
|
z_list.append(trans[2, 3])
|
|
for i in range(len(self.link_list)):
|
|
trans = np.dot(trans, self.link_list[i].transformation_matrix())
|
|
x_list.append(trans[0, 3])
|
|
y_list.append(trans[1, 3])
|
|
z_list.append(trans[2, 3])
|
|
|
|
self.ax.plot(x_list, y_list, z_list, "o-", color="#00aa00", ms=4, mew=0.5)
|
|
self.ax.plot([0], [0], [0], "o")
|
|
|
|
self.ax.set_xlim(-1, 1)
|
|
self.ax.set_ylim(-1, 1)
|
|
self.ax.set_zlim(-1, 1)
|
|
plt.show()
|
|
|
|
if __name__ == "__main__":
|
|
n_link_arm = NLinkArm([[0., -math.pi/2, .1, 0.],
|
|
[math.pi/2, math.pi/2, 0., 0.],
|
|
[0., -math.pi/2, 0., .4],
|
|
[0., math.pi/2, 0., 0.],
|
|
[0., -math.pi/2, 0., .321],
|
|
[0., math.pi/2, 0., 0.],
|
|
[0., 0., 0., 0.]])
|
|
|
|
print(n_link_arm.forward_kinematics())
|
|
n_link_arm.set_joint_angles([1, 1, 1, 1, 1, 1, 1])
|
|
n_link_arm.plot()
|