  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.
