Skip to main content
Log in

Identification of Parameters of a Model of a Movable Motion Platform

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We use specialized simulators to train drivers of vehicles difficult to drive. The environment created by such simulator for drivers must be as close to reality as possible. To simulate the overloads that occur during the motion of the simulated object, movable platform stands are used. Usually simulator software is developed for a particular imitation stand, which limits the use of such software for other equipment configuration. In addition, often the sensors in the mechanisms of the platform are either not precise enough or absent altogether, and the geometric parameters of the platform change with time due to deformations due to constant loads. These factors negatively affect the management of the platform and, therefore, the accuracy of dynamic simulation and the quality of coordination with visual and other types of simulation.

The purpose of this paper is to show that identification of platform parameters and platform positioning can be constructed without using measurements from internal sensors located in the mechanisms of the platform. To solve the problem, the authors developed an algorithm of semi-automatic identification of parameters of a platform model with a system of video analysis. Upon identification of parameters of a platform it is possible to monitor its angular motions without video analysis. Assessment of platform orientation is performed with angular velocity sensors (AVS) and accelerometers. The use of the suggested algorithms enables quick adaptation of stimulator software to any motion platform.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. V. Alexandrov, Mathematical Problems of Dynamic Simulation of Aerospace Flight [in Russian], MSU, Moscow (1995).

    Google Scholar 

  2. N. Andreff and P. Martinet, “Vision-based self-calibration and control of parallel kinematic mechanisms without proprioceptive sensing,” Intell. Serv. Robot., 2, No. 2, 71–80 (2009).

    Article  Google Scholar 

  3. N. S. Bakhvalov, Numerical Methods (Analysis, Algebra, Ordinary Differential Equations) [in Russian] Nauka, Moscow (1975).

    Google Scholar 

  4. I. V. Bardushkina, Methods of Decomposition in the Mathematical Modeling of the Dynamics of the Imitation Stand [in Russian], Abstract of Candidate’s Dissertation in Physics and Mathematics, Moscow (2001).

    Google Scholar 

  5. D. I. Bugrov, A. V. Lebedev, and V. A. Chertopolokhov, “Estimation of the angular rotation velocity of a body using a tracking system,” Moscow Univ. Mech. Bull., 69, No. 1, 25–27 (2014).

    Article  Google Scholar 

  6. Gao Meng, Li Tiemin, and Yin Wensheng, “Calibration method and experiment of Stewart platform using a laser tracker,” in: 2003 IEEE Int. Conf. on Systems, Man and Cybernetics (ICSMC) (2003).

    Google Scholar 

  7. V. N. Gordeev, Quaternions and Three-Dimensional Geometry, Kiev (2012).

  8. V. K. Isaev and V. V. Sonin, “A modification of Newton’s method of numerical solution of boundary-value problems,” J. Comput. Math. Math. Phys., 3, No. 6, 1114–1116 (1963).

    MathSciNet  Google Scholar 

  9. Ren C. Luo, Cheng-Hsun Hsieh, and Shih Che Chou, “Effective visual calibration system for parallel robot using decision tree with cooperative coevolution network approach,” in: 2015 IEEE Int. Conf. on Industrial Technology (ICIT) (2015).

    Google Scholar 

  10. Y. Meng and H. Zhuang, “Autonomous robot calibration using vision technology,” Robot. Comput.- Integr. Manuf., 23, No. 4, 436–446 (2007).

    Article  Google Scholar 

  11. J. A. Nelder and R. Mead, “A simplex method for function minimization,” Comput. J., 7, 308–313 (1965).

    Article  MathSciNet  Google Scholar 

  12. X.-D. Ren, Z.-R. Feng, C.-P. Su, “A new calibration method for parallel kinematics machine tools using orientation constraint,” Int. J. Machine Tools Manuf., 49, No. 9, 708–721 (2009).

    Article  Google Scholar 

  13. A. B. Sergiyenko, Digital Signal Processing, BHV-Peterburg, St. Petersburg (2011).

    Google Scholar 

  14. B. Shnaider, Applied Cryptography. Protocols, Algorithms and Source Code in C [in Russian], Triumph (2002).

  15. D. Stewart, “A platform with six degrees of freedom,” Aircraft Eng. Aerospace Technol., 38, No. 4, 30–35 (1966).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to D. S. Burlakov.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 2, pp. 73–88, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Burlakov, D.S., Latonov, V.V. & Chertopolokhov, V.A. Identification of Parameters of a Model of a Movable Motion Platform. J Math Sci 253, 806–817 (2021). https://doi.org/10.1007/s10958-021-05271-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-021-05271-z

Navigation