On the Computation of the Average of Planar Displacements

Q. Jeffrey Ge; Zihan Yu; Mona Arbab; Mark P. Langer

doi:10.1007/978-3-030-99826-4_20

On the Computation of the Average of Planar Displacements

Q. Jeffrey Ge
, Zihan Yu
, Mona Arbab
, Mark P. Langer

Mechanical Engineering

Stony Brook University
Indiana University-Purdue University Indianapolis

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

In this paper, we present four parametric representations of a planar displacements and studied the problem of how to compute the average displacement from a set of given planar displacements using these representations. It has been shown that the optimal average displacement is obtained by using planar quaternions and the concept of relative displacements. Examples are provided to show the comparisons of these methods.

Original language	English
Title of host publication	Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics
Editors	Pierre Larochelle, J. Michael McCarthy
Publisher	Springer Science and Business Media B.V.
Pages	232-242
Number of pages	11
ISBN (Print)	9783030998257
DOIs	https://doi.org/10.1007/978-3-030-99826-4_20
State	Published - 2022
Event	2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022 - Rapid City, United States Duration: May 19 2022 → May 21 2022

Publication series

Name	Mechanisms and Machine Science
Volume	118 MMS
ISSN (Print)	2211-0984
ISSN (Electronic)	2211-0992

Conference

Conference	2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022
Country/Territory	United States
City	Rapid City
Period	05/19/22 → 05/21/22

Keywords

Averaging displacements
Means and variance
Planar quaternions

Access to Document

10.1007/978-3-030-99826-4_20

Cite this

Ge, Q. J., Yu, Z., Arbab, M., & Langer, M. P. (2022). On the Computation of the Average of Planar Displacements. In P. Larochelle, & J. M. McCarthy (Eds.), Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics (pp. 232-242). (Mechanisms and Machine Science; Vol. 118 MMS). Springer Science and Business Media B.V.. https://doi.org/10.1007/978-3-030-99826-4_20

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abstract = "In this paper, we present four parametric representations of a planar displacements and studied the problem of how to compute the average displacement from a set of given planar displacements using these representations. It has been shown that the optimal average displacement is obtained by using planar quaternions and the concept of relative displacements. Examples are provided to show the comparisons of these methods.",

keywords = "Averaging displacements, Means and variance, Planar quaternions",

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note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022 ; Conference date: 19-05-2022 Through 21-05-2022",

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language = "English",

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Ge, QJ, Yu, Z, Arbab, M & Langer, MP 2022, On the Computation of the Average of Planar Displacements. in P Larochelle & JM McCarthy (eds), Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. Mechanisms and Machine Science, vol. 118 MMS, Springer Science and Business Media B.V., pp. 232-242, 2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022, Rapid City, United States, 05/19/22. https://doi.org/10.1007/978-3-030-99826-4_20

On the Computation of the Average of Planar Displacements. / Ge, Q. Jeffrey; Yu, Zihan; Arbab, Mona et al.
Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. ed. / Pierre Larochelle; J. Michael McCarthy. Springer Science and Business Media B.V., 2022. p. 232-242 (Mechanisms and Machine Science; Vol. 118 MMS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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