# Dynamic Interconnection and Damping Injection for Input-to-State Stable Bilateral Teleoperation

## TL;DR

This paper introduces a novel control strategy for bilateral teleoperation that ensures exponential input-to-state stability despite time-varying delays and unpredictable user and environment forces, without requiring their explicit modeling.

## Contribution

It proposes a dynamic interconnection and damping injection controller that robustly synchronizes master and slave robots under uncertain conditions, ensuring stability and convergence.

## Key findings

- Ensures exponential input-to-state stability in teleoperation with delays.
- Confines position error to an invariant set and drives it exponentially to a global attractor.
- Robustly synchronizes master and slave robots under user and environment perturbations.

## Abstract

In bilateral teleoperation, the human who operates the master and the environment which interacts with the slave are part of the force feedback loop. Yet, both have time-varying and unpredictable dynamics and are challenging to model. A conventional strategy for sidestepping the demand for their models in the stability analysis is to assume passive user and environment, and to control the master-communications-slave system to be passive as well. This paper circumvents the need to model the user and environment in a novel way: it regards their forces as external excitations for a semi-autonomous force feedback loop, which it outfits with a dynamic interconnection and damping injection controller that renders bilateral teleoperation with time-varying delays exponentially input-to-state stable. The controller uses the position and velocity measurements of the local robot and the delayed position transmitted from the other robot to robustly synchronize the master and slave under the user and environment perturbations. Lyapunov-Krasovskii stability analysis shows that the proposed strategy (i) can confine the position error between the master and slave to an invariant set, and (ii) can drive it exponentially to a globally attractive set. Thus, the dynamic interconnection and damping injection approach has practical relevance for telemanipulation tasks with given precision requirements.