Kinematic Analysis of Quadrotors with Manufacturing Errors

Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 14)

Abstract

We discuss the problem of calibrating quadrotors fabricated using inexpensive printing techniques used by the do-it-yourself community. Although it is easy to create prototypes rapidly, the rotor axes and positions in these prototypes may not be according to specifications. In such a case, operating the motors at the nominal speeds will not result in stable hovering. The fundamental equations that govern hovering are similar to those encountered in objects suspended with cables in that they couple the position and orientation variables with the forces required for equilibrium. We develop the kinematics and statics and derive the conditions for stable equilibrium with a numerical example to illustrate the basic ideas and point to approaches in which adaptation through software can rectify shortcomings in inexpensive manufacturing processors.

Keywords

Transportation Hunt Triad Librium 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
  2. 2.
  3. 3.
    Fink, J., Michael, N., Kim, S., Kumar, V.: Planning and control for cooperative manipulation and transportation with aerial robots. The International Journal of Robotics Research 30(3) (March 2011)Google Scholar
  4. 4.
    Hawkes, E., An, B., Benbernou, N., Tanaka, H., Kim, S., Demaine, E.D., Rus, D., Wood, R.J.: Programmable matter by folding. Proc. Nat. Acad. Sci. 107(28), 12441–12445 (2010)CrossRefGoogle Scholar
  5. 5.
    Hunt, K.H.: Kinematic Geometry of Mechanisms. Oxford University Press (1978)Google Scholar
  6. 6.
    Jiang, Q., Kumar, V.: Determination and stability analysis of equilibrium configurations of objects suspended from multiple aerial robots. Journal of Mechanisms and Robotics 4(2), 021005 (2012)CrossRefGoogle Scholar
  7. 7.
    Kumar, V., Michael, N.: Opportunities and challenges with autonomous micro aerial vehicles. In: Int. Symposium of Robotics Research, Flagstaff, AZ (August 2011)Google Scholar
  8. 8.
    Nanua, P., Waldron, K.J., Murthy, V.: Direct kinematic solution of a Stewart platform. IEEE Transactions on Robotics and Automation 6(4), 438–444 (1990)CrossRefGoogle Scholar
  9. 9.
    Phillips, J.: Freedom in Machinery, vol. 1. Cambridge University Press (1990)Google Scholar
  10. 10.
    Selig, J.M.: Geometric Fundamentals of Robotics. Springer (2005)Google Scholar
  11. 11.
    Waldron, K.J., Hunt, K.H.: Series-parallel dualities in actively coordinated mechanisms. The Int. Journal of Robotics Research 10(5), 473–480 (1991)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.University of PennsylvaniaPennsylvaniaUSA

Personalised recommendations