2019/05/09 by Sang-ik An, An, Sang-ik, Dongheui Lee +1 · 1 citation
Engineering · #Dynamics and Control of Mechanical Systems #FOS: Computer and information sciences #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Robot Manipulation and Learning #Robotic Mechanisms and Dynamics #Robotics (cs.RO) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1905.03416
openalex publication_date 2019/05/09 · openalex created_date 2019/05/16 · openalex updated_date 2026/07/28
In this paper, we study various theoretical properties of a class of prioritized inverse kinematics (PIK) solutions that can be considered as a class of (output regulation or tracking) control laws of a dynamical system with prioritized multiple outputs. We first develop tools to investigate nonsmoothness of PIK solutions and find a sufficient condition for nonsmoothness. It implies that existence and uniqueness of a joint trajectory satisfying a PIK solution cannot be guaranteed by the classical theorems. So, we construct an alternative existence and uniqueness theorem that uses structural information of PIK solutions. Then, we narrow the class of PIK solutions down to the case that all tasks are designed to follow some desired task trajectories and discover a few properties related to task convergence. The study goes further to analyze stability of equilibrium points of the differential equation whose right hand side is a PIK solution when all tasks are designed to reach some desired task positions. Finally, we furnish an example with a two-link manipulator that shows how our findings can be used to analyze the behavior of a joint trajectory generated from a PIK solution.