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http://dx.doi.org/10.7746/jkros.2015.10.4.230

Solution Space of Inverse Differential Kinematics  

Kang, Chul-Goo (Mechanical Engineering, Konkuk University)
Publication Information
The Journal of Korea Robotics Society / v.10, no.4, 2015 , pp. 230-244 More about this Journal
Abstract
Continuous-path motion control such as resolved motion rate control requires online solving of the inverse differential kinematics for a robot. However, the solution space of the inverse differential kinematics related to Jacobian J is not well-established. In this paper, the solution space of inverse differential kinematics is analyzed through categorization of mapping conditions between joint velocities and end-effector velocity of a robot. If end-effector velocity is within the column space of J, the solution or the minimum norm solution is obtained. If it is not within the column space of J, an approximate solution by least-squares is obtained. Moreover, this paper introduces an improved mapping diagram showing orthogonality and mapping clearly between subspaces, and concrete examples numerically showing the concept of several subspaces. Finally, a solver and graphics user interface (GUI) for inverse differential kinematics are developed using MATLAB, and the solution of inverse differential kinematics using the GUI is demonstrated for a vertically articulated robot.
Keywords
Differential kinematics; Robot manipulator; Jacobian; Range; Nullspace; Moore-Penrose pseudoinverse;
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Times Cited By KSCI : 4  (Citation Analysis)
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