Abstract
We solve the open problem of global tracking control of 2nd-degree under-actuated lossless (without friction) Lagrangian systems via position measurements only. For flexible-joint robots, we design a dynamic controller which is based on measurements of link and joint positions only. Then, approximate differentiation is used for link velocities and a simple Luenberger observer for rotor velocities. The main results constitute a significant extension of recent work on observerless output-feedback control of Lagrangian systems. Strictly speaking, we establish uniform global asymptotic stability for the closed loop system.
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