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

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

3 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 (US)
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
Externally published	Yes
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	5/19/22 → 5/21/22

Keywords

Averaging displacements
Means and variance
Planar quaternions

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering

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

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

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, 5/19/22. https://doi.org/10.1007/978-3-030-99826-4_20

@inproceedings{165b65c2f0e14785b77a9f71a91c0f86,

title = "On the Computation of the Average of Planar Displacements",

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",

author = "Ge, {Q. Jeffrey} and Zihan Yu and Mona Arbab and Langer, {Mark P.}",

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",

year = "2022",

doi = "10.1007/978-3-030-99826-4_20",

language = "English (US)",

isbn = "9783030998257",

series = "Mechanisms and Machine Science",

publisher = "Springer Science and Business Media B.V.",

pages = "232--242",

editor = "Pierre Larochelle and McCarthy, {J. Michael}",

booktitle = "Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics",

}

TY - GEN

T1 - On the Computation of the Average of Planar Displacements

AU - Ge, Q. Jeffrey

AU - Yu, Zihan

AU - Arbab, Mona

AU - Langer, Mark P.

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Averaging displacements

KW - Means and variance

KW - Planar quaternions

UR - http://www.scopus.com/inward/record.url?scp=85128708332&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85128708332&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-99826-4_20

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

M3 - Conference contribution

AN - SCOPUS:85128708332

SN - 9783030998257

T3 - Mechanisms and Machine Science

SP - 232

EP - 242

BT - Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics

A2 - Larochelle, Pierre

A2 - McCarthy, J. Michael

PB - Springer Science and Business Media B.V.

T2 - 2nd USCToMM Symposium on Mechanical Systems and Robotics, USCToMM MSR 2022

Y2 - 19 May 2022 through 21 May 2022

ER -