Designing transparent stabilizing haptic controllers

This paper addresses the design of controllers for haptic systems that are both stable and transparent. Stability refers to the property that the control system should not introduce oscillations felt in the haptic device by the human operator. Transparency refers to the property that the haptic system should faithfully reproduce the dynamics of the virtual environment. We propose a design methodology that converts the problem of maximizing transparency, while guaranteeing stability, into a set of matrix inequalities. Then we propose a numerical procedure to solve the matrix inequalities based on the cone complementarity algorithm. With this formulation one can also incorporate other design tasks, such as robustness to parameter variations, by introducing additional norm conditions and solving Hinfin or mixed norm problems. A numerical example is used to illustrate the design methodology