Robot Kinematics

Initialize Robot Model

A robot model, at a very minimum, is a kinematic chain
The kinematic chain is defined by a series of parameters
- See Modified DH parameters for more info



In [1]:

    
from pybotics.robot import Robot
from pybotics.predefined_models import ur10

robot = Robot.from_parameters(ur10())

Forward Kinematics

The forward kinematics (FK) refer to the use of the kinematic equations of a robot to compute the pose of the end-effector (i.e., 4x4 transform matrix) from specified values for the joint parameters (i.e., joint angles)
ELI5: Where am I with the given joint angles?



In [2]:

    
import numpy as np
np.set_printoptions(suppress=True)

joints = np.deg2rad([5,5,5,5,5,5])
pose = robot.fk(joints)
display(pose)









    





array([[    0.94003631,    -0.34106157,     0.00295846, -1124.43089247],
       [   -0.00491322,    -0.02221388,    -0.99974117,  -355.10102738],
       [    0.34103901,     0.93977846,    -0.02255757,  -148.49504763],
       [    0.        ,     0.        ,     0.        ,     1.        ]])

Inverse Kinematics

The inverse kinematics (IK) makes use of the kinematics equations to determine the joint parameters that provide a desired position for the robot's end-effector
The default internal IK implementation uses scipy.optimize.least_squares with joint limit bounds
ELI5: What joint angles do I need to have this position?



In [3]:

    
solved_joints = robot.ik(pose)
display(np.rad2deg(solved_joints))









    





array([5.00000032, 4.97126286, 5.05937406, 4.95609777, 5.00005964,
       5.01321487])