Abstract
Motivated by the need to develop responsive teleoperation systems, the responsiveness performance of leader-follower systems is studied in this article. A new performance metric, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> gain, is proposed and analyzed. It is proved that the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> gain changes monotonically with respect to edge weights and that it is closely related to the coherence metric of leader-follower systems. Explicit bounds are obtained for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> gain of classic leader-follower systems when the underlying graph is a tree or a growth-limited graph. Based on these findings, the performance of an observer-based leader-follower system is studied and conditions under which the observer-based system behaves better are obtained. Numerical experiments are also conducted showing that the observer-based leader-follower system can perform better than the classic leader-follower system for 2-D grid graphs in practical conditions. These results contribute to the design of teleoperation systems in the future.
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