Eigenvalues Assignment for a Special Class of Singular Systems in Constrained Robotics

 

Ivan Buzurović

 

Robotic systems in contact with environment are typical examples where external contact forces play an important role to the system dynamics. Mathematical modeling of these systems is challenging due to a variety of reasons. Mathematical models for the described class of systems contain differential equations with an associate algebraic equation, which outlines constrained system dynamics. Such a system is considered to be a singular system of differential equations (semi-state or descriptor systems). In this article, the geometric approach to the solution of singular systems with contact problem has been introduced. The mutual eigenvalues and corresponding eigenvectors assignment for the robotic systems have been investigated. In order to achieve desired dynamical system behavior the controllability conditions have been investigated as well.

Key words: singular system, controllability, geometric approach, pole adjustment, system dynamics, mathematical model, robotics.