Research Papers

An Algorithm for Rigid-Body Angular Velocity and Attitude Estimation Based on Isotropic Accelerometer Strapdowns

[+] Author and Article Information
Ting Zou

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

Jorge Angeles

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

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 12, 2017; final manuscript received February 21, 2018; published online April 5, 2018. Assoc. Editor: Walter Lacarbonara.

J. Appl. Mech 85(6), 061010 (Apr 05, 2018) (10 pages) Paper No: JAM-17-1368; doi: 10.1115/1.4039435 History: Received July 12, 2017; Revised February 21, 2018

A novel algorithm for the estimation of rigid-body angular velocity and attitude—the most challenging part of pose-and-twist estimation—based on isotropic accelerometer strapdowns, is proposed in this paper. Quaternions, which employ four parameters for attitude representation, provide a compact description without the drawbacks brought about by other representations, for example, the gimbal lock of Euler angles. Within the framework of quaternions for rigid-body angular velocity and attitude estimation, the proposed methodology automatically preserves the unit norm of the quaternion, thus improving the accuracy and efficiency of the estimation. By virtue of the inherent nature of isotropic accelerometer strapdowns, the centripetal acceleration is filtered out, leaving only its tangential counterpart, to be estimated and updated. Meanwhile, using the proposed integration algorithm, the angular velocity and the quaternion, which are dependent only on the tangential acceleration, are calculated and updated at appropriate sampled instants for high accuracy. This strategy, which brings about robustness, allows for relatively large time-step sizes, low memory demands, and low computational complexity. The proposed algorithm is tested by simulation examples of the angular velocity and attitude estimation of a free-rotating brick and the end-effector of an industrial robot. The simulation results showcase the algorithm with low errors, as estimated based on energy conservation, and high-order rate of convergence, as compared with other algorithms in the literature.

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Fig. 1

Simplicial biaxial accelerometer

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Fig. 2

Isotropic tetrahedron SBA strapdown

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Fig. 3

A rigid brick with accelerometer strapdown

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Fig. 4

Comparison of the estimation of the angular-velocity time-history for three integration algorithms

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Fig. 5

Error in kinetic energy for three integration algorithms

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Fig. 7

PUMA 560 industrial robot

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Fig. 8

PUMA 560 operation point trajectory

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Fig. 9

PUMA 560 end effector angular acceleration component ω˙x

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Fig. 10

PUMA 560 end effector estimated angular velocity component ωx

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Fig. 11

Quaternion components of the end-effector attitude

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Fig. 12

Time-history of the computed norm of the quaternion

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Fig. 13

Log–log plot of error in ωx versus the inverse of time-step 1/Δt




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