Stable Interaction Control of Networked Lagrangian Systems with Uncertain Dynamics

This paper investigates the coupled stability problem of networked Lagrangian systems with arbitrarily bounded time-varying delays and with uncertainties in dynamics when interacting mechanically with human operators and operating environment. With the assumption that the external torques exerted on the Lagrangian systems are modeled as spring-damper systems, we propose two adaptive controllers with the external torque being directly compensated. The first controller utilizes only the relative positions from the neighbors to yield the linear consensus protocol. To improve the transparency, the relative damping is also incorporated in the second controller. Both of the adaptive controllers guarantee the coupled stability of the systems and render the external torques uniformly asymptotically converge to constant vectors with the robustness to the time-varying delays by exploiting the Laplacian structure of the linear reference dynamics and the dynamic-cascade property of the whole system.