Issue 4 (190), article 3


Kibern. vyčisl. teh., 2017, Issue 4 (190), pp.

Melnichuk S.V., Dr (Engineering),
Researcher of Dynamic Systems Control Ddepartment
Gubarev V.F., Professor,
Dr (Engineering), Professor,
Corresponding Member of NAS of Ukraine,
Head of Dynamic Systems Control Department
Salnikov N.N., (Engineering),
Senior Researcher of Dynamic Systems Control Department
Space Research Institute National Academy of Sciences of Ukraine
and State Space Agency of Ukraine
Acad. Glushkov av. 40, 4/1, 03680, Kyiv 187, Ukraine


Introduction. Autonomous rendezvous and docking is an important technological capability that enables various spacecraft missions. It requires the real-time relative pose estimation i.e. determination of the position and attitude of a target object relative to a chaser. The usage of techniques based on optical measurement has certain advantages at close range phases of docking.
The purpose of the paper is to create a computer vision system, that estimates position and attitude of the target relative to the chaser. To develop the design of a computer vision system and suited mathematical methods. To use a new learning-based method, which can be implemented for the real-time execution with limited computing power.
Methods. A non-standard approach to solving the problem was used. A combination of image processing techniques, machine learning, decision trees and piecewise linear
approximation of functions were used. The tool of informative features computed by images was essentially used.
Results. A two-stage algorithm, which involves training the computer vision system to recognize the attitude and position of the target in a changing lighting environment was developed. The calculation of the camera parameters was carried out to ensure a given accuracy of the solution of the problem.
Conclusion. It was shown that the informative features can be used to create a high-performance on-board system for estimating relative attitude and position. Implementation of the proposed algorithm allows to create a competitive device for docking in space.
Keywords: autonomous rendezvous, uncooperative pose estimation, model-based pose estimation, vision-based pose estimation, computer vision, decision tree, linear approximation, informative features, image processing, machine learning, identification, relative position and attitude estimation.

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1 Gubarev V.F., et al. Using Vision Systems for Determining the Parameters of Relative Motion of Spacecrafts. Journal of Automation and Information Sciences, 2016. No11. P. 23–39.

2 Shi J.-F., et al. Uncooperative Spacecraft Pose Estimation Using an Infrared Camera During Proximity Operations. AIAA Space 2015 Conference and Exposition. Issue AIAA 2015–4429. 17 pp.

3 Kelsey J.M., et. al. Vision-Based Relative Pose Estimation for Autonomous Rendezvous and Docking. 2006 IEEE Aerospace Conference. 20 pp.

4 Zorich V.A. Mathematical Analysis. Part 2. Moskow: Nauka, 1984. 640 p.

5 David, P. et. al. SoftPOSIT: Simultaneous Pose and Correspondence Determination. Interational Journal of Computer Vision. 2004. Vol. 59. I. 3. P. 259–284.

6 Philip N.K., Ananthasayanam M.R. Relative position and attitude estimation and control schemes for the final phase of an autonomous docking mission of spacecraft. Acta Astronautica. 2003. Vol. 52. I. 7. P. 511–522.

7 Shijie Monocular Vision-based Two-stage Iterative Algorithm for Relative Position and Attitude Estimation of Docking Spacecraft. Chinese Journal of Aeronautics, 2010. Vol. 23. I. 2. P. 204–210.

8 Vassilieva N.S. Content-based image retrieval methods. Programming and Computer Software. 2009. Vol. 35. No 3. P. 158–180.

9 Prewitt J.M.S. Object enhancement and extraction. Picture Processing and Psychopictorics, B. Lipkin and A. Rosenfeld. New York: Academic Press. 1970. P. 75–149.

10 Sobel I., Feldman G. A 3×3 isotropic gradient operator for image processing, presented at a talk at the Stanford Artificial. Project in Pattern Classification and Scene Analysis, R. Duda and P. Hart. Eds.: John Wiley & Sons, 1968. P. 271–272.

11 Canny, J. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1986. No 8(6). P. 679–698.

12 Arbelaez P., et al. Contour Detection and Hierarchical Image Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2010. P. 898–916.

13 Bentley J.L. Multidimensional binary search trees used for associative searching. Communications of the ACM. 1975. Vol. 18. I. 9. P. 509–517.

14 Samet H. The Design and Analysis of Spatial Data Structures. 1990. 493 p.

Received 14.06.2017

Issue 186, article 4


KVT, 2016, Issue 186, pp.30-46

UDC 519.71


Gubarev V.F.

Space Research Institute NAS Ukraine and SSA Ukraine, Kiev, Ukraine

Introduction. Very significant for application model reduction problem of large-scale time-invariant system to more simple small order is considered and developed in the paper. Real and approximate models fitting is determined by norms which establish the difference between impulse response of these two models.

The purpose of the article is to propose a new approach of setting the model reduction problem and to develop methods based on variational principle of its solving.

Methods. It is proposed to set model reduction problem as optimization. For this initial state space model was transformed to equivalent description in form of input-output relation using analytical expression for impulse response. Such form allows to apply conception of fit between real system and its low-order approximation widely used in identification. Parameters of approximate model and its dimention are determined from optimization problem with different measure of fit writing as norm. Algorithms of numerical solving the optimization problems and needed for this data are considered in the paper. Besides the modified subspace method that permits to construct the observability matrix directly from output data using SVD factorization is proposed and described. Singular values of SVD-decomposition indicate as the best way to truncate full model.

Results. Some results dealing with mutual disposition of eigenvalues of real model and reduced one are demonstrated.

Conclusion. Developed methods may be used both for systems with scalar input and output and for multi-input and multi-output system as well. Results obtained by modelling show efficiency of all worked out methods.

Keywords: model reduction, approximation, optimization, model fit, state-space model.

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1 Mischenko E.F., Rozov N.H. Differential equations with small parameter and relaxation oscillations. M.: Nauka. 1975, 248 p. (in Russian).

2 Antoulas A.C., Sorenson D.C., Gugercin S.A. A survey of model reduction methods for large-scale systems. Contemporary Mathematics. 2001, Vol. 280, pp. 193–219.

3 Reis T., Stykel T. A survey on model reduction of coupled systems. Model order Reduction. Theory, Research Aspects and Applications. 2008.

4 Gubarev V.F. Method of iterative identification of multivariable systems over inexact data. Part 1. Theoretical aspects. Journal of Automation and Information Sciences, 2006, No5,pp. 16–31 (in Russian).

5 Gubarev V.F. and Melnichuk S.V. Identification of multivariable systems using steady-state parameters. Journal of Automation and Information Sciences, 2012, No 5, pp. 26–42 (in Russian).

6 Rainer S., Price K. Differential evolution – a simple and efficient adaptive scheme for global optimization over continuous spaces. Journal of Global Optimization, 1997, No 11, pp. 341–359.

7 Golub G.H. and Van Loan Ch.F. Matrix Computations. Baltimore and London: John Hopkins University Press, 1999, 550 p.

8 Melnichuk S.V. Method of structural parametric multivariable systems identification using frequency characteristics. Kibernetika i vycislitel’naa tehnika, 2015, No 181, p. 66–79 (in Russian).


Received 15.09.16

Issue 185, article 4


KVT, 2016, Issue 185, pp.35-47

UDC 629.7.05


Simakov V.A., Gubarev V.F., Salnikov N.N., Melnichuk S.V.

Space Research Institute of the National Academy of Science of Ukraine and State Space Agency of Ukraine, Kyiv, Ukraine , , ,

Introduction. Automatic orbital berthing systems require permanent availability of relative position and attitude of a target spacecraft. In the most general case the only source of information is video filming. Extracting mutual disposition parameters from a video frame is based upon special techniques which can be divided into two large groups: feature-based and model-based. Major difference between them is defined by data structure used for the target description (individual points for feature-based approach vs. rigorous visual model for model-based one). This article is devoted to the research of mathematical problem that appears in considering pose estimation for two orbital spacecraft in the presence of wireframe model of the target when only video filming is available.

The purpose of the article is to construct a model-based method that provides fast and accurate estimation of relative position and attitude of the target spacecraft. We discuss possible drawbacks of direct procedures based on straightforward (pixel-wise) image fitting and propose a subtle algorithm which satisfies formulated conditions.

Results. The algorithm composed of three independent parts (initialization, pose refinement and pose tracking) has been developed and tested on simple initial datum. Initialization stage, responding for rough estimation in the absence of preliminary information, has given relatively poor but quite enough accuracy for the aims of initial approximation. Pose refinement stage which is implemented as iterative procedure based on closeness of neighboring frames demonstrated almost total matching with actual values. Pose tracking (state estimation based on equations of motion) was redundant for our simple example as it could not improve the result provided by pose refinement.

Conclusions. Constructed algorithm has been tested on simplified situation and demonstrated very high precision. More realistic conditions including noises and occlusions can bring to corrupted result that should be recovered. This requires introducing additional steps into the algorithm which are reflected in the text. The notable feature of the algorithm is its high modularity which allows each stage to be implemented and configured independently according to available resources and mission requirements.

Keywords: orbital rendezvous, pose estimation, orbital video filming, computer vision.

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1 Lowe D.G. Distinctive Image Features from Scale-Invariant Keypoints. International Journal of Computer Vision, 2004, 60 (2), pp. 91–110.

2 David P. SoftPOSIT: Simultaneous Pose and Correspondence Determination. International Journal of Computer Vision, 2004, 59 (3), pp. 259–284.

3 Black M.J., Jepson A.D. EigenTracking: Robust Matching and Tracking of Articulated Objects Using a View-Based Representation. International Journal of Computer Vision, 1998, 26 (1), pp. 63–84.

4 Trefethen L.N., Bau D. Numerical Linear Algebra. Philadelphia: SIAM, 1997, 361p.

5 Drummond T., Cipolla R. Real-Time Visual Tracking of Complex Structures. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24 (7), pp. 932–946.

6 Hartley R., Zisserman, A. Multiple View Geometry in Computer Vision. 2nd Edition. Cambridge University Press, 2004, 655p.

7 Paterson M.S., Yao, F.F. Efficient Binary Space Partitions for Hidden-Surface Removal and Solid Modeling. Discrete and Computational Geometry, 1990, 5, pp. 485–503.

8 Kelsey J.M., et. al. Vision-Based Relative Pose Estimation for Autonomous Rendezvous and Docking. 2006 IEEE Aerospace Conference. — 20 p.

9 Wenfu X., et al. Autonomous Rendezvous and Robotic Capturing of Non-Cooperative Target in Space. Robotica, 2010, 28, pp. 705–718.

10 Fehse W. Automated Rendezvous and Docking of Spacecraft. Cambridge University Press, 2003, 495 p.

Received 10.06.16

Issue 183, article 4

Gubarev Viacheslav F., Corresponding Member of NAS of Ukraine, Dr Technics, Head of Control of Dynamic Systems Department of Space Research Institute the National Academy of Sciences of Ukraine and of State Space Agency of Ukraine, av.Acad.Glushkova, 40, build. 4/1, c. Kiev, 03680,

Diadenko O.N., Postgraduate (PG) of National Technical University of Ukraine “Kiev Polytechnical Institute”, av. Pobedy, 37, Kiev, 03056,

OBSERVABILITY ANALYSIS OF SPACECRAFTS’ ATTITUDE MEASUREMENT SYSTEMS. Kibernetika i vyčislitel’naâ tehnika, 2016, issue 183, pp.51-68.

Introduction. One of the important tasks for small spacecrafts is the optimization of onboard measurement equipment, which on the one hand is not excessive and on the other — allows to estimate all attitude parameters with required accuracy.

The purpose of the artecle is to conduct observability analysis of the most commonly used measurement systems, such as magnetometer, star and angular velocity sensors, local vertical builder in order to identify the minimum required set of onboard measurement equipment, which ensures observability of the spacecraft.

Approach and Methods. Measurement systems observability assessment utilizes existing methods of dynamic systems observability theory and is based on observation and spacecraft’s angular motion equations. Model of the spacecraft’s motion is described using quaternion components as positional parameters. Since the models are essentially nonlinear, obtaining the overall global observability conditions for such system is a complex problem. Therefore, linearization procedure is applied and local observability conditions are assessed based on the rank and condition numbers of observability matrices of the linear approximation.

Results. Astro-measurement system ensures the most effective observability and may be used as the simplest measurement system. Magnetometer with three orthogonal magnetically sensitive probes does not ensure practical observability of the system, unless local vertical builder is added.

Keywords: State estimation, observability, quarternion, spacecraft, magnetometer, star sensor, local vertical builder.

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1 Lebedev D.I., Tkachenko A.I. Control of the spherical motion of the spacecraft in the Earth’s magnetic field. Part 1: Information Support. Problemy upravleniya i informatiki, 1995, Vol. 6, pp. 5–18. (in Russian)

2 Tkachenko A.I. Determination of the orientation of the spacecraft based on the testimony of two magnetometers. Kosmicheskie issledovaniya, 2000, Vol. 38, No 3,pp. 322–330. (in Russian)

3 Psiaki M.L., Martel F., Pal P.K. Three-axis attitude determination via Kalman filtering of magnetometer data. J. Guid., Control and Dynamics, 1990, Vol. 13, No 3,pp. 506–514.

4 Solov’ev I.V. Spacecraft’s attitude and angular velocity estimation algorithms with the use of star sensor. Aviakosmicheskoe priborostroenie, 2013, Vol. 7, pp. 10–26. (in Russian)

5 Control theory handbook . Under edition of. A.A. Krasovskiy. Moscow: Science, 1987, 712 p. (in Russian).

6 Karpenko S.O. Means of onboard orientation determination for small spacecrafts. Bauman Moscow State Technical Universityoverview, 2004.(in Russian).

7 Agutin A.M., Babenko V.G., Nepotyuk I.V. Astromeasurement system for spacecraft attitude estimation. IV International scientific-technical conference “Gyrotechnology, navigation, traffic management and the construction of aerospace engineering”, Proceedings of the Part 1. NTUU “KPI”, 2003, pp. 340–345. (in Russian)

8 Brady T., Tillier C., Brown R. et al. The inertial stellar compass: A new direction spacecraft attitude determination. Paper SSCO2 II — 1. 16th annual USU conference on small satellites, 2002.

9 Bessonov R.V., Dyatlov S.A., Kurkina A.N.Features of construction and operation of the astroorientation equipment BOC 3 with built-in angular velocity sensors. Proc. of Russian Space Research Institute, 2009, pp. 32–40. (in Russian)

10 Raushenbah B.V., Tokar’ E.N. Spacecrafts orientation control. Moscow: Science, 1974, 600p. (in Russian)

11 Branec V.N., Shmyglevskij I.P. Introduction to the Theory of strapdown navigation systems. Moscow: Science, 1992, 280p. (in Russian)

12 Volosov V.V., Tyutyunnik L.I. Synthesis of spacecraft attitude control with the use of quaternions. Kosmichna nauka ta tekhnologiya, 1999, Vol. 5, No. 4, pp.61–39. (in Russian)

13 Volosov V.V., Hlebnikov M.V., Shevchenko V.N. Spacecraft’s attitude control precision algorithm under uncontrolled perturbation. Problemy upravleniya i informatiki, 2011, No. 2, pp.114–121. (in Russian)

14 Wittenburg J. Dynamics of Systems of Rigid Bodies. Moscow: World, 1990, 292p. (in Russian)

15 Solov’ev I.V. Algorithm “ORIENT” for the spacecraft attitude estimation based on astro measurements. Aviakosmicheskoe priborostroenie, 2012, No. 12, pp. 11–19. (in Russian)

16 Golub Dzh., Van Loun CH. Matrix calculations. Moscow: World, 1999, pp. 548.

Received 21.12.2015