Skip to main content
SpringerLink
Log in

Endogenous Configuration Space Approach in Robotics Research

  • Chapter
  • First Online:
Automatic Control, Robotics, and Information Processing

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 296))

Abstract

The Endogenous Configuration Space Approach (ECSA) was invented as a robotics research methodology providing a unified conceptual framework for dealing with robotic manipulators (holonomic robotic systems) and mobile robots (non-holonomic robotic systems). Conceptually, this approach has been derived from control theory. Taking as a point of departure a model of kinematics or dynamics of a mobile robot represented in the form of a non-linear control system with output function, the ECSA builds on an analogy between the kinematics map of a robotic manipulator and the input-output (end-point) map transforming control functions of the control system into the task space. Within this perspective, the derivative of the input-output map with respect to control defines the mobile robot’s Jacobian. Consequently, all Jacobian-oriented concepts and instruments are introduced, like regular and singular configurations, dexterity measures and, last but not least, Jacobian motion planning algorithms. Numerical computations within the ECSA are enabled by either parametric or non-parametric implementations of the Jacobian motion planning algorithms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

Bibliography of selected works devoted to the Endogenous Configuaration Space Approach, set in a chronological order

  1. Tchoń K, Muszyński, R.: Instantaneous kinematics and dexterity of mobile manipulators. In: Proc 2000 IEEE Int Conf Robot Automat, pp. 2493–2498, San Francisco, CA (2000)

    Google Scholar 

  2. Tchoń, K., Jakubiak, J., Muszyński, R.: Kinematics of mobile manipulators: a control theoretic perspective. Arch. Control Sci. 11, 195–221 (2001)

    MathSciNet  MATH  Google Scholar 

  3. Tchoń, K.: Repeatability of inverse kinematics algorithms for mobile manipulators. IEEE Trans. Autom. Control 47, 1376–1380 (2002)

    MathSciNet  MATH  Google Scholar 

  4. Tchoń, K., Jakubiak, J.: Extended Jacobian inverse kinematics algorithms for mobile manipulators. J. Robotic Syst. 19, 443–454 (2002)

    MATH  Google Scholar 

  5. Tchoń, K., Jakubiak, J.: Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms. Int. J. Control 76, 1387–1419 (2003)

    MathSciNet  MATH  Google Scholar 

  6. Tchoń, K., Jakubiak, J., Muszyński, R.: Regular Jacobian motion planning algorithms for mobile manipulators. In: Proc 15th IFAC World Congress, pp. 121–126, Barcelona Spain (2003)

    Google Scholar 

  7. Tchoń, K., Zadarnowska, K.: Kinematic dexterity of mobile manipulators: An endogenous configuration space approach. Robotica 21, 521–530 (2003)

    Google Scholar 

  8. Tchoń, K., Jakubiak, J.: Fourier vs. non-Fourier band-limited Jacobian inverse kinematics algorithms for mobile manipulators. In: Proc 10th IEEE Int Conf MMAR, Miȩdzyzdroje Poland, pp. 1005–1010 (2004)

    Google Scholar 

  9. Tchoń, K., Jakubiak, J., Zadarnowska, K.: Doubly non-holonomic mobile manipulators. In: Proc 2004 IEEE ICRA, pp. 4590– 4595, New Orleans LO (2004)

    Google Scholar 

  10. Tchoń, K., Jakubiak, J.: A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators. IEEE Trans. Syst. Man Cybernet. Part B Cybernet. 35, 1051–1057 (2005)

    Google Scholar 

  11. Tchoń, K., Jakubiak, J.: A hyperbolic, extended Jacobian inverse kinematics algorithm for mobile manipulators. In: Proc 16th IFAC World Congress, pp. 43–48, Prague, Czechia (2005)

    Google Scholar 

  12. Zadarnowska, K.: Dexterity Measures of Mobile Manipulators. Doctoral Dissertation, Wrocław University of Technology (in Polish) (2005)

    Google Scholar 

  13. Tchoń, K.: Repeatable, extended Jacobian inverse kinematics algorithm for mobile manipulators. Syst. Control Lett. 55, 87–93 (2006)

    MathSciNet  MATH  Google Scholar 

  14. Tchoń, K., Jakubiak, J.: Extended Jacobian inverse kinematics algorithm for nonholonomic mobile robots. Int. J. Control 79, 895–909 (2006)

    MathSciNet  MATH  Google Scholar 

  15. Zadarnowska, K., Tchoń, K.: A control theory framework for performance evaluation of mobile manipulators. Robotica 25, 703–715 (2007)

    Google Scholar 

  16. Muszyński, R., Jakubiak, J.: On predictive approach to inverse kinematics of mobile manipulators. In: Proc IEEE Int Conf Control Automation, pp. 2423–2428, Guangzhou, China (2007)

    Google Scholar 

  17. Kabała, M.: Practical Realization of Robot Control Algorithms Based on the Model of Dynamics: Sperical Robot RoBall—Design, Modeling, Motion Planning. Doctoral Dissertation, Wrocław University of Technology (in Polish) (2008)

    Google Scholar 

  18. Janiak, M.: Jacobian Inverse Kinematics Algorithms for Mobile Manipulators with Constraints on State, Control, and Performance. Doctoral Dissertation, Wrocław University of Technology (in Polish) (2009)

    Google Scholar 

  19. Małek, Ł.: Convergence of Jacobian Inverse Kinematics Algorithms Based on the Method of Homotopy. Doctoral Dissertation, Wrocław University of Technology (in Polish) (2009)

    Google Scholar 

  20. Tchoń, K., Jakubiak, J., Małek, Ł.: Motion planning of nonholonomic systems with dynamics. Computational Kinematics, Springer-Verlag, pp.125–132 (2009)

    Google Scholar 

  21. Tchoń, K., Małek, Ł.: On dynamic properties of singularity robust Jacobian inverse kinematics. IEEE Trans. Autom. Contr. 54, 1402–1406 (2009)

    MathSciNet  MATH  Google Scholar 

  22. Tchoń, K.: Iterative learning control and the singularity robust Jacobian inverse for mobile manipulators. Int. J. Control. 83, 2253–2260 (2010)

    MathSciNet  MATH  Google Scholar 

  23. Karpińska, J., Ratajczak, A., Tchoń, K.: Task-priority motion planning of underactuated systems: An endogenous configuration space approach. Robotica 28, 885–892 (2010)

    Google Scholar 

  24. Jakubiak, J., Tchoń, K., Magiera, W.: Motion planning in velocity affine mechanical systems. Int. J. Control 83, 1965–1974 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Janiak, M., Tchoń, K.: Towards constrained motion planning of mobile manipulators. In: Proc 2010 IEEE ICRA, pp. 4990–4995, Anchorage, Alaska (2010)

    Google Scholar 

  26. Janiak, M., Tchoń, K.: Constrained motion planning of nonholonomic systems. Syst. Control Lett. 60, 625–631 (2011)

    MathSciNet  MATH  Google Scholar 

  27. Ratajczak, A.: Motion Planning of Underactuated Robotic Systems. Doctoral Dissertation, Wrocław University of Science and Technology (in Polish) (2011)

    Google Scholar 

  28. Ratajczak, A., Tchoń, K.: Motion planning of a balancing robot with threefold sub-tasks: An endogenous configuration space approach. In: Proc 2011 ICRA, pp. 6096–6101, Shanghai, China (2011)

    Google Scholar 

  29. Paszuk, D., Tchoń, K., Pietrowska, Z.: Motion planning of the trident snake robot equipped with passive or active wheels. Bull. Polish Ac. Sci. Ser. Tech. Sci. 60, 547–554 (2012)

    Google Scholar 

  30. Kȩdzierski, K.: Control System of a Social Robot. Doctoral Dissertation, Wrocław University of Science and Technology (in Polish) (2013)

    Google Scholar 

  31. Ratajczak, A., Tchoń, K.: Multiple-task motion planning of non-holonomic systems with dynamics. Mech. Sci. 4, 153–166 (2013)

    Google Scholar 

  32. Pietrowska, Z., Tchoń, K.: Dynamics and motion planning of trident snake robot. J. Intell. Robotic Syst. 75, 17–28 (2014)

    Google Scholar 

  33. Jakubiak, J., Magiera, W., Tchoń, K.: Control and motion planning of a non-holonomic parallel orienting platform. J. Mech. Robotics 7 (2015). https://doi.org/10.1115/1.4029891

  34. Ratajczak, J.: Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse. Arch. Control Sci. 25, 35–50 (2015)

    MathSciNet  Google Scholar 

  35. Tchoń, K., Ratajczak, A., Góral, I.: Lagrangian Jacobian inverse for nonholonomic robotic systems. Nonlinear Dyn. 82, 1923–1932 (2015)

    MathSciNet  MATH  Google Scholar 

  36. Tchoń, K., et al.: Modeling and control of a skid-steering mobile platform with coupled side wheels. Bull. Polish Ac. Sci. Ser. Tech. Sci. 63, 807–818 (2015)

    Google Scholar 

  37. Chojnacki, Ł.: Framework for ECSA Algorithms. Research report, Department of Cybernetics and Robotics, Wrocław University of Science and Technology (in Polish) (2016)

    Google Scholar 

  38. Ratajczak, A.: Trajectory reproduction and trajectory tracking problem for the nonholonomic systems. Bull. Polish Ac. Sci. Ser. Tech. Sci. 64, 63–70 (2016)

    Google Scholar 

  39. Ratajczak, J., Tchoń, K.: Dynamically consistent Jacobian inverse for mobile manipulators. Int. J. Control 89, 1159–1168 (2016)

    MathSciNet  MATH  Google Scholar 

  40. Tchoń, K., Ratajczak, J.: Dynamically consistent Jacobian inverse for nonholonomic systems. Nonlinear Dyn. 85, 107–122 (2016)

    MATH  Google Scholar 

  41. Ratajczak, J., Tchoń, K.: On dynamically consistent Jacobian inverse for non-holonomic robotic systems. Arch. Control Sci. 27, 555–573 (2017)

    MathSciNet  MATH  Google Scholar 

  42. Tchoń, K.: Endogenous configuration space approach: An intersection of robotics and control theory. In: Nonlinear Systems, pp. 209–233, Springer (2017)

    Google Scholar 

  43. Góral, I., Tchoń, K.: Lagrangian Jacobian motion planning: A parametric approach. J. Intell. Robotic Syst. 85, 511–522 (2017)

    Google Scholar 

  44. Ratajczak, A.: Egalitarian vs. prioritarian approach in multiple task motion planning for nonholonomic systems. Nonlinear Dyn. 88, 1733–1747 (2017)

    Google Scholar 

  45. Tchoń, K., Góral, I.: Optimal motion planning for non-holonomic robotic systems. In: Proc 20th IFAC World Congress, pp. 1946–1951 Toulouse, France (2017)

    Google Scholar 

  46. Zadarnowska, K.: Switched modeling and task-priority motion planning of wheeled mobile robots subject to slipping. J. Intell. Robotic Syst. 85, 449–469 (2017)

    Google Scholar 

  47. Tchoń, K., Ratajczak, J.: General Lagrange-type Jacobian inverse for nonholonomic robotic systems. IEEE Trans. Robotics 34, 256–263 (2018)

    Google Scholar 

  48. Ratajczak, A.: Motion planning for nonholonomic systems with earlier destination reaching. Arch. Control Sci. 27, 269–283 (2018)

    MathSciNet  MATH  Google Scholar 

  49. Ratajczak, J., Tchoń, K.: Dynamic nonholonomic motion planning by means of dynamically consistent Jacobian inverse. IMA J. Math. Control Inf. 35, 479–489 (2018)

    MATH  Google Scholar 

  50. Tchoń, K., Respondek, W., Ratajczak, J.: Normal forms and configuration singularities of a space manipulator. J. Intell. Robotic Syst. 93, 621–634 (2019)

    Google Scholar 

  51. Tchoń, K., Ratajczak, J.: Singularities, Normal Forms, and Motion Planning for Non-holonomic Robotic System. In: Proc. 6th Int. Conf. Control, Dynamic Systems, Robotics (CDSR’19), Ottawa, Canada, CDSR 127-1–cdsr-127-8 (2019)

    Google Scholar 

  52. Tchoń, K., Ratajczak, J.: Feedback equivalence and motion planning of a space manipulator. In: Advances in Mechanism and Machine Science, Mechanisms and Machine Science, vol. 73, T. Uhl (ed.), pp. 1691–1700, Springer Nature Switzerland AG (2019)

    Google Scholar 

  53. Ratajczak, A., Ratajczak, J.: Trajectory Reproduction Algorithm in Application to an On–Orbit Docking Maneuver with Tumbling Target. In: Proc. 12th Int. Workshop RoMoCo, vol. 8–10, pp. 172–177, Poznań University of Technology, Poznań, Poland (2019)

    Google Scholar 

References

  1. Allgower, E.L., Georg, K.: Numerical Continuation Methods. Springer-Verlag, Berlin (1990)

    MATH  Google Scholar 

  2. Alouges, F., Chitour, Y., Long, R.: A motion-planning algorithm for the rolling-body problem. IEEE Trans. Robot. 26, 827–836 (2010)

    Google Scholar 

  3. Baillieul, J.: Kinematic programming alternatives for redundant manipulators, pp. 722–728. Proc IEEE ICRA, St. Luois, MO (1985)

    Google Scholar 

  4. Bayle, B., Fourquet, J.Y., Renaud, M.: Manipulability of wheeled mobile manipulators: application to motion generation. Int. J. Robot. Res. 22, 565–581 (2003)

    Google Scholar 

  5. Bonnard, B., Chyba, M.: Singular Trajectories and Their Role in Control Theory Springer. Paris (2003)

    Google Scholar 

  6. Brockett, R.W.: Robotic manipulators and the product of exponentials formula. W: Mathematical Theory of Networks and Systems. Springer-Berlin, pp. 120–129 (1984)

    Google Scholar 

  7. Chelouah, A., Chitour, Y.: On the motion planning of rolling surfaces. Forum Math. 15, 727–758 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Chitour, Y.: A homotopy continuation method for trajectories generation of nonholonomic systems. ESAIM: Control Optim. Calc. Var. 12, 139–168 (2006)

    Google Scholar 

  9. Chitour, Y., Sussmann, H.J.: Motion planning using the continuation method. In: W. Baillieul, J., Sastry, S.S., Sussmann, H.J. (eds.), 91–125, Essays on Mathematical Robotics, Springer-Verlag, New York (1998)

    Google Scholar 

  10. Chitour, Y., Jean, F., Trélat, E.: Singular trajectories of control-affine systems. SIAM J. Contr. Opt. 47, 1078–1095 (2008)

    MathSciNet  MATH  Google Scholar 

  11. Choi, Y., et al.: Multiple task manipulation for a robotic manipulator. Adv. Robot. 18, 637–653 (2004)

    Google Scholar 

  12. Davidenko, D.: On a new method of numerically integrating a system of nonlinear equations. Dokl Akad Nauk SSSR 88, 601–604 (1953)

    MathSciNet  Google Scholar 

  13. Deuflhard, P.: Newton Methods for Nonlinear Problems. Springer, Berlin (2004)

    MATH  Google Scholar 

  14. Divelbiss, A.W., Seereeram, S., Wen, J.T.: Kinematic path planning for robots with holonomic and nonholonomic constraints. In: Sastry, S.S., Sussmann, H.J. (eds.) Baillieul J, pp. 127–150. Essays on Mathematical Robotics, Springer-Verlag, New York (1998)

    Google Scholar 

  15. Dulȩba, I.: Algorithms of Motion Plannng for Nonholonomic Robots. Oficyna Wydawnicza PWr, Wrocław (1998)

    MATH  Google Scholar 

  16. Dulȩba, I., Khefifi, W., Karcz-Dulȩba, I.: Layer, Lie algebraic method of motion planning for nonholonomic systems. J. Franklin Inst. 349, 201–215 (2012)

    MathSciNet  MATH  Google Scholar 

  17. Dulȩba, I., Sa̧siadek, J.Z.: Non-holonomic motion planning based on Newton algorithm with energy optimization. IEEE Trans. Contr. Syst. Technol. 11, 355–363 (2003)

    Google Scholar 

  18. Galicki, M.: Inverse kinematics solution to mobile manipulators. Int. J. Robot. Res. 22, 1041–1064 (2003)

    Google Scholar 

  19. Galicki, M.: Tracking the kinematically optimal trajectories by mobile manipulators. J. Intell. Robot. Syst. (2018). https://doi.org/10.1007/s10846-018-0868-7

    Article  Google Scholar 

  20. Ishikawa, M., Minati, Y., Sugie, T.: Development and control experiment of the trident snake robot. IEEE/ASME Trans. Mech. 15, 9–15 (2010)

    Google Scholar 

  21. Jakubczyk, B.: Equivalence and invariants of nonlinear control systems. W: Nonlinear Controllability and Optimal Control, pp. 177–218, M. Dekker, New York (1990)

    Google Scholar 

  22. Johnson, C.D., Gibson, J.E.: Singular solutions in problems of optimal control. IEEE Trans. Autom. Contr. 8, 4–15 (1963)

    MathSciNet  Google Scholar 

  23. Jung, S., Wen, J.T.: Nonlinear model predictive control for the swing-up of a rotary inverted pendulum. Trans. ASME 126, 666–673 (2004)

    Google Scholar 

  24. Khatib, O.: Motion/Force redundancy of manipulators. W: Proc Japan-USA Symposium on Flexible Automation: A Pacific Rim Conference, pp. 337–342, The Institute, Kyoto (1990)

    Google Scholar 

  25. Khatib, O.: Inertial properties in robotics manipulation: An object-level framework. Int. J. Robot. Res. 14, 19–36 (1995)

    Google Scholar 

  26. Klein, ChA, Blaho, B.E.: Dexterity measures for the design and control of kinematically redundant manipulators. Int. J. Robot. Res. 6, 72–82 (1987)

    Google Scholar 

  27. L’Affito, A., Haddad, W.M.: Abnormal optimal trajectory planning of multi-body systems in the presence of holonomic and nonholonomic constraints. J. Intell. Robot. Syst. 89, 51–67 (2018)

    Google Scholar 

  28. Li, Z., Ge, S.: Fundamentals in modelling and control of mobile manipulators. CRC Press, Boca Raton (2013)

    Google Scholar 

  29. Mazur, A.: Model-based Control of Non-holonomic Mobile Manipulators. Oficyna Wydawnicza PWr, Wrocław (in Polish) (2009)

    Google Scholar 

  30. Nakamura, Y., Hanafusa, H., Yoshikawa, T.: Task-priority based redundancy control of robot manipulators. Int. J. Robot. Res. 6, 3–15 (1987)

    Google Scholar 

  31. Nijmeijer, H., van der Schaft, A.J.: Nonlinear Dynamical Control Systems. Springer, New York (1990)

    MATH  Google Scholar 

  32. Popa, D.O., Wen, J.T.: Singularity computation for iterative control of nonlinear affine systems. Asian J. Control 2, 57–75 (2000)

    Google Scholar 

  33. Rugh, W.J.: Linear System Theory. Prentice Hall, Englewood Cliffs (1993)

    Google Scholar 

  34. Rybus, T., Seweryn, K.: Planar air-bearing microgravity simulators: review of applications, existing solutions and design parameters. Acta Astronaut. 120, 239–259 (2016)

    Google Scholar 

  35. Sciavicco, L., Siciliano, B.: Coordinate transformation: A solution algorithm for one class of robots. IEEE Trans. Syst. Man Cybernet. 16, 550–559 (1986)

    MATH  Google Scholar 

  36. Sontag, E.D.: Mathematical Control Theory. Springer-Verlag, New York (1990)

    MATH  Google Scholar 

  37. Sontag, E.D.: A general approach to path planning for systems without drift. In: Baillieul, J., Sastry, S.S., Sussmann, H.J. (eds.) Essays on Mathematical Robotics, pp. 151–168. Springer-Verlag, New York (1998)

    Google Scholar 

  38. Sussmann, H.J.: A continuation method for nonholonomic path finding problems. W: Proc 32nd IEEE CDC, pp. 2718–2723, San Antonio, TX (1993)

    Google Scholar 

  39. Tchoń, K., Muszyński, R.: Singular inverse kinematic problem for robotic manipulators: A normal form approach. IEEE Trans. Robot. Automat. 14, 93–104 (1998)

    Google Scholar 

  40. Tzafestas, S.G.: Introduction to Mobile Robot Control. Elsevier, Amsterdam (2014)

    Google Scholar 

  41. Ważewski, T.: Sur l’évaluation du domaine d’existence des fonctions implicites réelles ou complexes. Ann. Soc. Pol. Math. 20, 81–120 (1947)

    MATH  Google Scholar 

  42. Yoshikawa, T.: Manipulability of robotic mechanisms. Int. J. Robot. Res. 4, 3–9 (1985)

    Google Scholar 

Download references

Acknowledgements

This research has been supported by Wrocław University of Science and Technology under a statutory research project.

Author information

Authors and Affiliations

  1. Department of Cybernetics and Robotics, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego street 27, 50-370, Wrocław, Poland

    Krzysztof Tchoń

Authors
  1. Krzysztof Tchoń
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Krzysztof Tchoń .

Editor information

Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Piotr Kulczycki

  2. Institute of Control and Computation Engineering, University of Zielona Góra, Zielona Góra, Poland

    Józef Korbicz

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tchoń, K. (2021). Endogenous Configuration Space Approach in Robotics Research. In: Kulczycki, P., Korbicz, J., Kacprzyk, J. (eds) Automatic Control, Robotics, and Information Processing. Studies in Systems, Decision and Control, vol 296. Springer, Cham. https://doi.org/10.1007/978-3-030-48587-0_14

Download citation

Publish with us

Policies and ethics

Search

Navigation