An Extended Jacobian Inverse Kinematics Algorithm for Doubly Nonholonomic Mobile Manipulators

2006 ◽  
Author(s):  
K. Tchon ◽  
J. Jakubiak
Keyword(s):  
Inverse Kinematics ◽  
Mobile Manipulators ◽  
Jacobian Inverse

Extended Jacobian inverse kinematics algorithms for mobile manipulators

2002 ◽  
Vol 19 (9) ◽  
pp. 443-454 ◽  
Author(s):  
Krzysztof Tcho? ◽  
Janusz Jakubiak
Keyword(s):  
Inverse Kinematics ◽  
Mobile Manipulators ◽  
Jacobian Inverse

Performance-Oriented Design of Inverse Kinematics Algorithms: Extended Jacobian Approximation of the Jacobian Pseudo-Inverse

2012 ◽  
Vol 4 (2) ◽  
Author(s):  
Joanna Karpińska ◽  
Krzysztof Tchoń
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Ritz Method ◽  
Approximation Error ◽  
Robotic Manipulators ◽  
Error Functional ◽  
Free Representation ◽  
Pseudo Inverse ◽  
Jacobian Inverse ◽  
Jacobian Algorithm

For redundant robotic manipulators, we study the design problem of Jacobian inverse kinematics algorithms of desired performance. A specific instance of the problem is addressed, namely the optimal approximation of the Jacobian pseudo-inverse algorithm by the extended Jacobian algorithm. The approximation error functional is derived for the coordinate-free representation of the manipulator’s kinematics. A variational formulation of the problem is employed, and the approximation error is minimized by means of the Ritz method. The optimal extended Jacobian algorithm is designed for the 7 degrees of freedom (dof) POLYCRANK manipulator. It is concluded that the coordinate-free kinematics representation results in more accurate approximation than the coordinate expression of the kinematics.

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