Towards Manipulability of Interactive Lagrangian Systems

TL;DR

This paper introduces a unified framework for ensuring infinite manipulability in interactive Lagrangian systems, enabling robust adaptive control under uncertainties and communication constraints, and solving longstanding teleoperation issues.

Contribution

It formulates the concept of infinite manipulability for dynamical systems and develops adaptive controllers that guarantee this property along with robustness in interactive robotic systems.

Findings

Proposes a new dynamic feedback-based adaptive control paradigm.

Achieves infinite manipulability and robustness in Lagrangian systems.

Resolves the nonlinear bilateral teleoperation problem with unknown delays.

Abstract

This paper investigates manipulability of interactive Lagrangian systems with parametric uncertainty and communication/sensing constraints. Two standard examples are teleoperation with a master-slave system and teaching operation of robots. We here systematically formulate the concept of infinite manipulability for general dynamical systems, and investigate how such a unified motivation yields a design paradigm towards guaranteeing the infinite manipulability of interactive dynamical systems and in particular facilitates the design and analysis of nonlinear adaptive controllers for interactive Lagrangian systems. Specifically, based on a new class of dynamic feedback, we propose adaptive controllers that achieve both the infinite manipulability of the controlled Lagrangian systems and the robustness with respect to the communication/sensing constraints, mainly owing to the resultant dynamic-cascade framework. The proposed paradigm yields the desirable balance between network coupling requirements and controlled dynamics of human-system interaction. We also show that a special case of our main result resolves the longstanding nonlinear bilateral teleoperation problem with arbitrary unknown time-varying delay. Simulation results show the performance of the interactive robotic systems under the proposed adaptive controllers.