Characterizations of the plenary hull of the generalized Jacobian matrix

1982 ◽  
pp. 1-12 ◽  
Author(s):  
J.-B. Hiriart-Urruty
Keyword(s):  
Jacobian Matrix ◽  
Generalized Jacobian ◽  
Generalized Jacobian Matrix

The Generalized Jacobian Matrix and the Manipulators Kinetostatic Properties

2010 ◽  
Author(s):  
Simone Cinquemani ◽  
Hermes Giberti ◽  
Giovanni Legnani
Keyword(s):  
Theoretical Analysis ◽  
Geometrical Structure ◽  
Jacobian Matrix ◽  
Drive System ◽  
Transmission Ratio ◽  
Generalized Jacobian ◽  
Generalized Jacobian Matrix

Manipulator kinetostatic performances are usually investigated considering only the geometrical structure of the robot, neglecting the effect of the drive system. In some circumstances this approach may leads to errors and mistakes. This may happen if the actuators are not identical to each other or when the employed transmission ratio are not identical and/or not constant. The paper introduces the so called “Generalized Jacobian Matrix” obtained identifying an appropriate matrix, generally diagonal, defined in order to: 1. properly weigh the different contributions of speed and force of each actuator. 2. describe the possible non-homogeneous behaviour of the drive system that depends on the configuration achieved by the robot. Theoretical analysis is supported by examples highlighting some of the most common mistakes done in the evaluation of a manipulator kinetostatic properties and how they can be avoided using the generalized jacobian matrix.

The relationship between controlled joint torque and end-effector force in underactuated robotic systems

Robotica ◽  
2010 ◽  
Vol 29 (4) ◽  
pp. 581-584 ◽  
Author(s):  
Jaeheung Park
Keyword(s):  
Jacobian Matrix ◽  
Joint Torque ◽  
Generalized Jacobian ◽  
End Effector ◽  
Joint Torques ◽  
Floating Base ◽  
Force Moment ◽  
Generalized Jacobian Matrix ◽  
The Relationship ◽  
Jacobian Inverse

SUMMARYThe generalized Jacobian matrix was introduced for dealing with end-effector control in space robots. One of the applications of this Jacobian is to be used in Jacobian transpose control to generate joint torques given end-effector position error. It would be misleading, however, to consider the transpose of this Jacobian as a mapping from end-effector force/moment to controlled joint torques for underactuated systems or floating base robots. This paper explains why it does not represent the mapping and provides a simple example. Later, the correct mapping is provided using the dynamically consistent Jacobian inverse and then a method to compute the actuated-joint torques is explained given the desired end-effector force. Finally, the effect of using the generalized Jacobian in the Jacobian transpose control is analyzed.

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