Performance Evaluation of Robot Arms from the Viewpoint of Controllability and Observability

This paper proposes performance indeces of robot arms from a new viewpoint of the degrees of controllability and observability. The definitions of the controllability, observability and output-controllability Gramians of linear systems are given to show these degrees, and the physical meanings of these Gramians are explained. Using the products of the eigenvalues of these Gramians, the controllability, observability and output-controllability gains are proposed as the measures of performance evaluation of robot arms. Furthermore, it is shown that manipulability and dynamic manipulability can be obtained as the degrees of observability and output-controllability. As a numerical example, a two link arm is evaluated using the controllability, observability and output-controllability measures.