Solvability theory for a class of hemivariational inequalities involving copositive plus matrices. Applications in robotics
The purpose of this very important paper is to study the solvability of the following hemivariational inequality: Problem P. Find \(u\in C\) such that \[ \langle Mu-q,v \rangle\geq 0 \quad \forall v\in T_C (u) \] where \(C\) is a nonempty closed subset of \(\mathbb{R}^n_+ \), \(M\) is a copositive plus matrix of order \(N\) and \(q\) is fixed in \(\mathbb{R}^N\). The robot hand grasping problem can be formulated as Problem P. This means that the theory presented here is devoted to the study of the corresponding equilibrium problem of a system composed of an object and a robotic hand with nonmonotone adhesive effects and nonclassical friction effects. The main result is the following: The authors present a new inequality method in robotics and provide a corresponding suitable mathematical theory for the solvability of the hemivariational inequality with nonsymmetric matrix.
scientific article; zbMATH DE number 1046464
scientific article