Input-to-state stable approach to release the conservatism of passivity-based stable haptic interaction

Abstract

Passivity has been a major criterion on designing a stable haptic interface due to many advantages. However, passivity has been suffering from its intrinsic conservatism since it only represents a small set of the whole stable region. Therefore, there was always limitation to increase the performance due to the small design margin from the passivity criterion. In most of the cases, stability and performance has trade-off relationship. In this paper, we propose a less conservative control approach for stable haptic interaction based on Input to State Stable (ISS) criterion. The proposed approach is inspired from the analogy between virtual environments and systems with hysteresis nonlinearities. A system with hysteresis nonlinearity has sector bounded property, which allows us to guarantee that only a finite amount of energy can be extracted from the system, which leads the system to be dissipative [1] and also the states to be bounded by a function of the input [2]. Since the finite amount of energy is allowed to be extracted from the system, the proposed ISS approach has less conservative constraint compared with passivity-based approaches. Moreover, the proposed approach has a simple structure and does not use any system parameters which make it suitable for practical implementations. Experimental evaluation validates the effectiveness of the proposed approach.