Authors:
Mir Mamunuzzaman
and
Jörg Mareczek
Affiliation:
Faculty of Electrical and Industrial Engineering, Landshut University of Applied Sciences, 84036 Landshut, Germany
Keyword(s):
Singularity, Non-Linear Controllability, Jacobian, Robot Motion Planning.
Abstract:
We develop a standard system representation and analyse controllability properties for velocity kinematics of robot-manipulators located on singularities. These are positions where the Jacobian loses rank. Since its column vectors span the set of admissible workspace velocity directions, it is still a widespread misunderstanding that some directions would be locked on singularities and thus had to be bypassed as far as possible. We will show that this does not generally hold: On some types of singularities, the kinematic shows local redundancy, which can be used to generate paths crossing the singularity in any desired workspace velocity direction. To further analyse controllability properties, we develop an SVD-based method to represent the Jacobian-based velocity kinematics in standard system description of control theory without the need for inverse kinematics (IK). In many cases, IK do not offer a unique solution on singularities and, therefore, cannot be used. Furthermore, we pr
esent a modification of the SVD-based method for which the analytical calculation effort is feasible. The resulting system description has the advantage of being a simple decoupled set of single-integrators where the system states are divided into one set describing admissible workspace motions and a second set describing possible internal motions, also called nullspace motion. Based on this standard system representation, we determine local controllability and local accessibility for two different types of singularities. Finally, we illustrate our methods by means of a simple 3-DoF SCARA-type manipulator.
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