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Normal Forms of Robotic Systems with Affine Pfaffian Constraints: A Case Study

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Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 8))

Abstract

We study robotic systems subject to Pfaffian constraints in the affine form. A control system representation of such a system is given in the form of a control-affine system. Normal forms under feedback are considered and used both as a description of configuration singularities of the robotic system as well as a tool for solving the motion planning problem. An example of a space manipulator is analysed in detail to illustrate the theoretical concepts.

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References

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

    Article  Google Scholar 

  2. Tchoń, K.: Endogenous configuration space approach: an intersection of robotics and control theory. In: van de Wouw, N., Lefeber, E., Lopez Arteaga, I. (eds.) Nonlinear Systems. LNCIS, vol. 470, pp. 209–234. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-30357-4_10

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  3. Tchoń, K., Respondek, W., Ratajczak, J.: Normal forms and configuration singularities of a space manipulator. J. Intell. Robot. Syst. (2018). https://doi.org/10.1007/s10846-018-0883-8

  4. Roberts, R.G., Maciejewski, A.A.: Nearest optimal repeatable control strategies for kinematically redundant manipulators. IEEE Trans. Autom. Control 8, 327–337 (1992)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Rybus, T.: Control of a satellite manipulator during the interception maneuver and the motion stabilization. Ph.D. dissertation. Wrocław University of Science and Technology (2016)

    Google Scholar 

  7. Murray, R.M., Li, Z., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    MATH  Google Scholar 

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Acknowledgement

Author 2 was assisted by the National Science Centre Poland, grant decision No. 2015/17/B/ST7/03995. Authors 1 and 3 were supported by the Wrocław University of Science and Technology under a research project number 0401/0143/17.

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Correspondence to Krzysztof Tchoń .

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Tchoń, K., Ratajczak, J., Jakubiak, J. (2019). Normal Forms of Robotic Systems with Affine Pfaffian Constraints: A Case Study. In: Lenarcic, J., Parenti-Castelli, V. (eds) Advances in Robot Kinematics 2018. ARK 2018. Springer Proceedings in Advanced Robotics, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-93188-3_29

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