Asymptotic stability of teleoperators with variable time-delays

This paper extends the previous results on position tracking for bilateral teleoperators with constant time-delays, reported in Nũno et al. IEEE Trans. Robot., vol. 24, no. 3, pp. 753-758, June 2008, to the case of variable time-delays in the teleoperator's communications. The key part is the extension of a previous Lemma that is used to prove that P+d or PD+d controllers can stabilize the teleoperator under variable timedelays, and moreover, they provide position tracking. The paper outlines the conditions under which velocities and position errors, of the nonlinear teleoperator, are bounded, and using Barbǎlat's Lemma, it is proved asymptotic converge to zero if the local manipulator stands still and the remote manipulator does not interact with the environment. Simulations and real experiments validate the proposed schemes. The experiments have been performed using the Internet as communication channel between Urbana-Champaign, USA and Barcelona, Spain.