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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Yazdi, N. , Ayazi, F. , and Najafi, K. , 1998, “ Micromachined Inertial Sensors,” Proc. IEEE, 86(8), pp. 1640–1659. [CrossRef]
Mital, N. K. , and King, A. I. , 1979, “ Computation of Rigid-Body Rotation in Three-Dimensional Space From Body-Fixed Linear Acceleration Measurements,” ASME J. Appl. Mech., 46(4), pp. 925–930. [CrossRef]
Pamadi, K. B. , Ohlmeyer, E. J. , and Pepitone, T. R. , 2004, “ Assessment of a GPS Guided Spinning Projectile Using an Accelerometer-Only IMU,” AIAA Paper No. 2004-4881.
Barbour, N. , and Schmidt, G. , 2001, “ Inertial Sensor Technology Trends,” IEEE Sens., 1(4), pp. 332–339. [CrossRef]
Cappa, P. , Patanè, F. , and Rossi, S. , 2008, “ Two Calibration Procedures for a Gyroscope-Free Inertial Measurement System Based on a Double-Pendulum Apparatus,” Meas. Sci. Technol., 19(5), pp. 32–38. [CrossRef]
Comi, C. , Corigliano, A. , Langfelder, G. , Longoni, A. , Tocchio, A. , and Simon, B. , 2011, “ A New Biaxial Silicon Resonant Micro Accelerometer,” IEEE 24th International Conference on Micro Electro Mechanical Systems (MEMS), Cancun, Mexico, Jan, 23–27, pp. 529–532.
Zou, Q. , Tan, W. , Kim, E. , Singh, J. , and Loeb, G. E. , 2004, “ Implantable Biaxial Piezoresistive Accelerometer for Sensorimotor Control,” 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (IEMBS'04), San Francisco, CA, Sept. 1–5, pp. 4279–4282.
Cardou, P. , and Angeles, J. , 2007, “ Simplectic Architectures for True Multi-Axial Accelerometers: A Novel Application of Parallel Robots,” IEEE International Conference on Robotics and Automation (ICRA), Rome, Italy, Apr. 10–14, pp. 181–186.
Zou, T. , and Angeles, J. , 2014, “ Structural and Instrumentation Design of a Microelectromechanical Systems Biaxial Accelerometer,” Proc. Inst. Mech. Eng., Part C, 228(13), pp. 2440–2455. [CrossRef]
Zou, T. , and Angeles, J. , 2014, “ The Decoupling of the Cartesian Stiffness Matrix in the Design of Microaccelerometers,” Multibody Syst. Dyn., 34(1), pp. 1–21. [CrossRef]
Zou, T. , and Angeles, J. , 2014, “ Isotropic Accelerometer Strapdowns and Related Algorithms for Rigid-Body Pose and Twist Estimation,” ASME J. Appl. Mech., 81(11), p. 111001. [CrossRef]
Spring, K. W. , 1986, “ Euler Parameters and the Use of Quaternion Algebra in the Manipulation of Finite Rotations: A Review,” Mech. Mach. Theory, 21(5), pp. 365–373. [CrossRef]
Terze, Z. , Müller, A. , and Zlatar, D. , 2015, “ Lie-Group Integration Method for Constrained Multibody Systems in State Space,” Multibody Syst. Dyn., 34(3), pp. 275–305. [CrossRef]
Treven, A. , and Saje, M. , 2015, “ Integrating Rotation and Angular Velocity From Curvature,” Adv. Eng. Software, 85, pp. 26–42. [CrossRef]
Kosenko, I. , 1998, “ Integration of the Equations of a Rotational Motion of a Rigid Body in Quaternion Algebra, the Euler Case,” J. Appl. Math. Mech., 62(2), pp. 193–200. [CrossRef]
Linne, M. , 2002, Spectroscopic Measurement: An Introduction to the Fundamentals, Academic Press, San Diego, CA.
Eberly, D. , 2002, Rotation Representations and Performance Issues, Magic Software Inc., Chapel Hill, NC.
Kuiper, J. , 1999, Quaternions and Rotation Sequences, Princeton University Press, Princeton, NJ.
Reich, S. , 1996, “ Symplectic Integrators for Systems of Rigid Bodies,” Integration Algorithms for Classical Mechanics (Fields Institute Communications, Vol. 10), J. E. Marsden, G. W. Patrick, and W. F. Shadwick, eds., American Mathematical Society, Providence, RI, pp. 181–191. [CrossRef]
Seelen, L. , Padding, J. , and Kuipers, J. , 2016, “ Improved Quaternion-Based Integration Scheme for Rigid Body Motion,” Acta Mech., 227(12), pp. 3381–3389. [CrossRef]
Andrle, M. , and Crassidis, J. , 2013, “ Geometric Integration of Quaternions,” AIAA J. Guid. Control Dyn., 36(6), pp. 1762–1767. [CrossRef]
Zupan, E. , and Saje, M. , 2011, “ Integrating Rotation From Angular Velocity,” Adv. Eng. Software, 42(9), pp. 723–733. [CrossRef]
Betsch, P. , and Siebert, R. , 2009, “ Rigid Body Dynamics in Terms of Quaternions: Hamiltonian Formulation and Conserving Numerical Integration,” Int. J. Numer. Methods Eng., 79(4), pp. 444–473. [CrossRef]
Whitmore, S. , 2000, “Closed-Form Integrator for the Quaternion (Euler Angle) Kinematics Equations,” National Aeronautics and Space Administration, Washington, DC, U.S. Patent No. US6061611.
Zhao, F. , and van Wachem, B. , 2013, “ A Novel Quaternion Integration Approach for Describing the Behaviour of Non-Spherical Particles,” Acta Mech., 224(12), pp. 3091–3109. [CrossRef]
Kreyszig, E. , 1997, Advanced Engineering Mathematics, Wiley, New York.
Angeles, J. , 2004, “ The Qualitative Synthesis of Parallel Manipulators,” ASME J. Mech. Des., 126(4), pp. 617–624. [CrossRef]
Angeles, J. , 2014, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 4th ed., Springer, New York. [CrossRef]
Baltes, H. , Brand, O. , Fedder, G. , Hierold, C. , Korvink, J. , and Tabata, O. , 2005, Circuit and System Integration, Vol. 2, Wiley-VCH, Weinheim, Germany.
Julier, S. J. , Uhlmann, J. K. , and Durrant-Whyte, H. , 1995, “ A New Approach for Filtering Nonlinear Systems,” American Control Conference, Seattle, WA, June 21–23, pp. 1628–1632.
Julier, S. J. , and Uhlmann, J. K. , 1997, “ New Extension of the Kalman Filter to Nonlinear Systems,” Proc. SPIE, 3068, pp. 182–193.
Julier, S. J. , and Uhlmann, J. K. , 2004, “ Unscented Filtering and Nonlinear Estimation,” Proc. IEEE, 92(3), pp. 401–422. [CrossRef]
Corke, P. I. , 2011, Robotics, Vision & Control: Fundamental Algorithms in MATLAB, Springer, Berlin. [CrossRef]
Brand, L. , 1965, Advanced Calculus, Wiley, New York.
Brogan, W. L. , 1991, Modern Control Theory, Prentice Hall, Englewood Cliffs, NJ.


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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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