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Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra

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Abstract

Local controllability of a three link robotic snake is solved by means of 5D conformal geometric algebra. The non-holonomic kinematic equations are assembled, their role in the geometric control theory is discussed and the control solution is found. The functionality is demonstrated on a virtual model in CLUCalc programme. Finally, the snake robot dynamics is elaborated.

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References

  1. Gonzalez-Jimenez L., Carbajal-Espinosa O., Loukianov A., Bayro-Corrochano E.: Robust Pose Control of Robot Manipulators Using Conformal Geometric Algebra. Adv. Appl. Clifford Algebr. 24(2), 533–552 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hildenbrand, D.: Foundations of Geometric Algebra Computing. Springer, Heidelberg (2013)

  3. Hrdina, J., Vašík, P.: Notes on differential kinematics in conformal geometric algebra approach. In: Matoušek, R. (ed.) Mendel 2015, Advances in Intelligent Systems and Computing, vol. 378, pp. 375–385. Springer (2015)

  4. Liljebäck, P., Pettersen, K.Y., Stavdahl, Ø., Gravdahl, J.T.: Snake Robots, Modelling, Mechatronics and Control. Springer, London (2013)

  5. Matoušek, R., Návrat, A.: Trident snake control based on CGA. In: Matoušek, R. (ed.) Mendel 2015, Advances in Intelligent Systems and Computing, vol. 378, pp. 375–385. Springer, Heidelberg (2015)

  6. Murray, R.M., Zexiang, L., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

  7. Perwass, Ch.: Geometric Algebra with Applications in Engineering. Springer, Heidelberg (2009)

  8. Selig, J.M.: Geometric Fundamentals of Robotics. Springer, New York (2004)

  9. Zamora-Esquivel, J., Bayro-Corrochano, E.: Kinematics and differential kinematics of binocular robot heads. In: Proceedings of the 2006 IEEE International Conference on Robotics and Automation, pp. 4130–4135. IEEE, Orlando, FL (2006)

  10. Zamora-Esquivel, J., Bayro-Corrochano, E.: Parallel Forward Dynamics: a geometric approach. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2377–2382. IEEE, Taipei (2010)

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Authors and Affiliations

  1. Institute of Mathematics, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    Jaroslav Hrdina, Aleš Návrat & Petr Vašík

Authors
  1. Jaroslav Hrdina
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  2. Aleš Návrat
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  3. Petr Vašík
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Corresponding author

Correspondence to Jaroslav Hrdina.

Additional information

The authors were supported by a Grant No. FSI-S-14-2290.

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Hrdina, J., Návrat, A. & Vašík, P. Control of 3-Link Robotic Snake Based on Conformal Geometric Algebra. Adv. Appl. Clifford Algebras 26, 1069–1080 (2016). https://doi.org/10.1007/s00006-015-0621-2

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  • DOI: https://doi.org/10.1007/s00006-015-0621-2

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