A Comparison Between Lie Group- and Lie Algebra- Based Potential Functions for Geometric Impedance Control
CoRR(2024)
摘要
In this paper, a comparison analysis between geometric impedance controls
(GICs) derived from two different potential functions on SE(3) for robotic
manipulators is presented. The first potential function is defined on the Lie
group, utilizing the Frobenius norm of the configuration error matrix. The
second potential function is defined utilizing the Lie algebra, i.e., log-map
of the configuration error. Using a differential geometric approach, the
detailed derivation of the distance metric and potential function on SE(3) is
introduced. The GIC laws are respectively derived from the two potential
functions, followed by extensive comparison analyses. In the qualitative
analysis, the properties of the error function and control laws are analyzed,
while the performances of the controllers are quantitatively compared using
numerical simulation.
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