Towards Manipulability of Interactive Lagrangian Systems

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.