Toward smooth analysis of robotic contact tasks problem

In robotic tasks where the manipulator has to make transition from free space motion to constrained motion, there always exists an inevitable phase transition. A number of controllers have been proposed in the literature with various discussions on their practical implications. In this paper first a discussion on the nature of the structure of a practical contact transition controller is presented. Then a framework which can be used toward studying and analysis of such controllers for the robotic contact tasks problem is proposed. This framework presents a natural set-up to study the performance of the controller. The framework is based on the Flippov´s (1964) notion of differential inclusion and a definition of the smooth Lyapunov function