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Research Papers

Isotropic Accelerometer Strapdowns and Related Algorithms for Rigid-Body Pose and Twist Estimation

[+] Author and Article Information
Ting Zou

Post-doc Fellow
Centre for Intelligent Machines,
Department of Mechanical Engineering,
McGill University,
Montréal, QC H3A 0C3, Canada
e-mail: ting@cim.mcgill.ca

Jorge Angeles

Fellow ASME
Centre for Intelligent Machines,
Department of Mechanical Engineering,
McGill University,
Montréal, QC H3A 0C3, Canada
e-mail: angeles@cim.mcgill.ca

In the cited reference, the authors dub their architectures simplectic, which is a misnomer.

Superscripts and are to be read “perp” and “par,” respectively.

In mathematical programming, a “simplex” is a polyhedron in Rn with the minimum number of vertices, i.e., n + 1 [17].

This concept refers to the second moment of the array of vertices of the isotropic polyhedral, a.k.a. geometric moment-of-inertia tensor, with three identical eigenvalues.

The axial vector of a 3 × 3 matrix A is defined as avect(A)(1/2)[a32-a23a13-a31a21-a12]T, a vector invariant of A [16].

The Buckyball is also known as the 60-vertex truncated icosahedron, whose shape appears in soccer balls.

For any Platonic solid, its dual polyhedron is constructed in such way that each vertex of the latter coincides with the centroid of the corresponding face of the former.

1Corresponding author.

Manuscript received April 7, 2013; final manuscript received August 24, 2014; accepted manuscript posted August 27, 2014; published online September 10, 2014. Assoc. Editor: Alexander F. Vakakis.

J. Appl. Mech 81(11), 111003 (Sep 10, 2014) (13 pages) Paper No: JAM-13-1150; doi: 10.1115/1.4028405 History: Received April 07, 2013; Revised August 24, 2014; Accepted August 27, 2014

A novel design of accelerometer strapdown, intended for the estimation of the rigid-body acceleration and velocity fields, is proposed here. The authors introduce the concept of isotropic-polyhedral layout of simplicial biaxial accelerometers (SBA), in which one SBA is rigidly attached at the centroid of each face of the polyhedron. By virtue of both the geometric isotropy of the layout and the structural planar isotropy of the SBA, the point tangential relative acceleration is decoupled from its centripetal counterpart, which is filtered out, along with the angular velocity. The outcome is that the rigid-body angular acceleration can be estimated independent of the angular velocity, thereby overcoming a hurdle that mars the estimation process in current accelerometer strapdowns. An estimation algorithm, based on the extended Kalman filter, is included. Simulation results show an excellent performance of the proposed strapdowns in estimating the acceleration and velocity fields of a moving object along with its pose.

Copyright © 2014 by ASME
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References

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Figures

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Fig. 1

A rigid body carrying n uniaxial accelerometers

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Fig. 2

Acceleration field of a rigid body: (a) tangential and (b) centripetal components

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Fig. 3

Layout of simplicial accelerometers: (a) SUA; (b) SBA; and (c) STA

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Fig. 4

Compliant realization of the Π-joint with: (a) a pair of long beams and (b) four notched hinges

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Fig. 5

SBA design with its dimensions

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Fig. 6

Two instances of accelerometer strapdowns: (a) nonisotropic and (b) isotropic

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Fig. 7

A rigid rotating disk with strapdowns: (a) tetrahedral and (b) general

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Fig. 8

Estimated acceleration of the disk of Fig. 7(a) using a tetrahedral SBA strapdown

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Fig. 9

Estimated twist of the disk of Fig. 7(a) using a tetrahedral SBA strapdown

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Fig. 10

Estimated pose of the disk of Fig. 7(a) using a tetrahedral SBA strapdown

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Fig. 11

Estimated acceleration of the disk of Fig. 7(b) using a brick SBA strapdown

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Fig. 12

Estimated twist of the disk of Fig. 7(b) using a brick SBA strapdown

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Fig. 13

Estimated pose of the disk of Fig. 7(b) using a brick SBA strapdown

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Fig. 14

A rigid brick with accelerometer strapdowns: (a) tetrahedral and (b) general

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Fig. 15

Measured acceleration of the brick through isotropic SBA strapdown

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Fig. 16

Measured twist of the brick through isotropic SBA strapdown

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Fig. 17

Measured attitude of the brick through isotropic SBA strapdown

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Fig. 18

Measured acceleration of the brick through a brick SBA strapdown

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Fig. 19

Measured twist of the brick through a brick SBA strapdown

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Fig. 20

Measured attitude of the brick through a brick SBA strapdown

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Fig. 21

Illustration of the tetrahedral strapdown with its local and global coordinate frame

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Fig. 22

Illustration of the brick strapdown with local and global coordinate frames

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