A Small Gain Framework for Networked Cooperative Teleoperation

Abstract

A small gain approach for stability analysis of cooperative network-based force reflecting teleoperator systems is presented. The approach is based on a new version of inputto-output stability (IOS) nonlinear small gain theorem that is applicable to stability analysis of large-scale network-based interconnections. Using the small-gain theorem presented, we show that stability of the cooperative teleoperator system can always be achieved by choosing some of the system' gains appropriately.

Adaptive stabilization of nonlinear teleoperation systems: An SIIOS approach

“…The similar assumption can be seen in [23], in which these torques are assumed to be uniformly bounded with unknown (finite) bound. Contrary to the usual formulation of the telerobotics problem, no assumptions (e.g., passivity) are imposed on the dynamics of environment as well as human operator, which reduces the application restrictive to some extent [12].…”

“…Firstly, to simplify the expression, the next definitions are needed, which can be seen in [12,26,27].…”

“…Over the past 60 years, the teleoperation system has received considerable attentions [1][2][3]. Many control schemes are proposed to cope with various practical control problems including time-delay, actuator saturation and model uncertainty, for example, adaptive control [4][5][6], saturation-based control [7,8], passivity-based control [3], sliding-mode control [9,10], small-gain approach [11,12], and the proportional derivative like control scheme [8,13,14], just to name a few. Recently, as a useful tool, the linear matrix inequality (LMI) approach has also been applied to teleoperation control system [15][16][17][18][19][20][21][22].…”

“…Finally, the numerical example is given to demonstrate the effectiveness. ADAPTIVE STABILIZATION OF TELEOPERATION SYSTEMS: AN SIIOS APPROACH 3697 Recently, to avoid the passive restrictive of the external torques applied by human operator or environment, an alternative control approach based on the point of view of ISS/IOS is also developed for the teleoperation systems [11,12,17,23]. In [23], a nonlinear control scheme is proposed, which makes the teleoperator system input-to-state stable regardless of the communication delays.…”

“…To obtain the timedependent stability criterion, a Lyapunov-Krasovskii method incorporated with ISS is developed in [17]. Compared with the usual formulation of the telerobotics problem, no passive assumptions are imposed on the dynamics of the environment and human operator in the ISS/IOS-based scheme, and hence, it reduces the restrictive for these external torques to some extent [12]. However, the joint position should also be one of the components of the complete state of the closed-loop system in this conventional ISS/IOS framework, which thus results in several application limitations of the existing conclusions.…”