TY - GEN
T1 - ON THE CONSTRUCTION OF CONFIDENCE REGIONS FOR UNCERTAIN PLANAR DISPLACEMENTS
AU - Yu, Zihan
AU - Ge, Qiaode Jeffrey
AU - Langer, Mark P.
AU - Arbab, Mona
N1 - Publisher Copyright:
© 2023 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 2023
Y1 - 2023
N2 - This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.
AB - This paper studies the statistical concept of confidence region for a set of uncertain planar displacements with a certain level of confidence or probabilities. Three different representations of planar displacements are compared in this context and it is shown that the most commonly used representation based on the coordinates of the moving frame is the least effective. The other two methods, namely the exponential coordinates and planar quaternions, are equally effective in capturing the group structure of SE(2). However, the former relies on the exponential map to parameterize an element of SE(2), while the latter uses a quadratic map, which is often more advantageous computationally. This paper focus on the use of planar quaternions to develop a method for computing the confidence region for a given set of uncertain planar displacements. Principal component analysis (PCA) is another tool used in our study to capture the dominant direction of movements. To demonstrate the effectiveness of our approach, we compare it to an existing method called rotational and translational confidence limit (RTCL). Our examples show that the planar quaternion formulation leads to a swept volume that is more compact and more effective than the RTCL method, especially in cases when off-axis rotation is present.
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U2 - 10.1115/DETC2023-117185
DO - 10.1115/DETC2023-117185
M3 - Conference contribution
AN - SCOPUS:85178618466
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 47th Mechanisms and Robotics Conference (MR)
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2023
Y2 - 20 August 2023 through 23 August 2023
ER -