This tutorial revisits several of the most recent passivity-based controllers for nonlinear bilateral teleoperators with guaranteed stability properties. These schemes, which include scattering–based, damping injection and adaptive controllers, ensure asymptotic stability in multiple situations that range from constant to variable time-delays, with or without scattering transformation and with or without position tracking capabilities. Although all controllers exploit the basic property of passivity of the teleoperators, they have been developed invoking various analysis and design tools, which complicates their comparison and relative performance assessment. The objective of this paper is to present a unified theoretical framework—based on a general Lyapunov–like function—that, upon slight modification, allows to analyze the stability of all the schemes.

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