manipulator jacobian for robotics in lie group formuation
TRANSCRIPT
1Terry Taewoong Um ([email protected])
University of Waterloo
Department of Electrical & Computer Engineering
Terry Taewoong Um
MANIPULATOR JACOBIAN IN LIE GROUP FORMULATION
Jacobian in Lie Group
space Jacobian
from {0} to {tool}
space vel.(There exist body vel. & body Jacobian as well)
[6x1] [6x6] [6x1]
[4x4]
• Space Jacobian
• Space Velocity
[4x4] [4x4]
(Note that velocity of a point on the body is as follows due to coordinate transformation)
Jacobian in Lie Group
From the chain rule,
Note that is forward kinematics solution
Jacobian in Lie Group
The Lie algebra vector seen from {0} at (The Jacobian changes over time(pose))
Example 1
The Lie algebra vector seen from {0} at (The Jacobian changes over time(pose))
[SCARA robot]
Example 2
[Stanford arm]
prismatic
Body Jacobian
• In robotics, body Jacobian is preferred because the body Jacobian is independent of the choice of base frame
coordinate change
Reference
• R. Murray, A Mathematical Introduction to Robotics (pp 115-123), CRC press, 1994.