Singularity-Consistent Parameterization of Robot Motion and Control

The inverse kinematics problem is formulated as a parameterized autonomous dynamical system problem, and respective analysis is carried out. It is shown that a singular point of work space can be mapped either as a critical or a noncritical point of the autonomous system, depending on the direction of approach to the singular point. Making use of the noncritical mapping, a closed-loop kinematic controller with asymptotic stability and velocity limits along degenerate singular or near-singular paths is designed. The authors introduce a specific type of motion along the reference path, the so-called natural motion. This type of motion is obtained in a straightforward manner from the autonomous dynamical system and always satisfies the motion constraint at a singular point. In the vicinity of the singular point, natural motion slows down the end-effector speed and keeps the joint velocity bounded. Thus, no special trajectory replanning will be required. In addition, the singular manifold...

• Type: Journal
• Year: 2000
• Where: IJRR
• Authors: Dragomir N. Nenchev, Yuichi Tsumaki, Masaru Uchiyama
• Keywords: Dynamical System, IJRR 2000, Natural Motion, Singular Point