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Autonomous Robots

, Volume 35, Issue 2–3, pp 161–176 | Cite as

Centroidal dynamics of a humanoid robot

  • David E. Orin
  • Ambarish GoswamiEmail author
  • Sung-Hee Lee
Article

Abstract

The center of mass (CoM) of a humanoid robot occupies a special place in its dynamics. As the location of its effective total mass, and consequently, the point of resultant action of gravity, the CoM is also the point where the robot’s aggregate linear momentum and angular momentum are naturally defined. The overarching purpose of this paper is to refocus our attention to centroidal dynamics: the dynamics of a humanoid robot projected at its CoM. In this paper we specifically study the properties, structure and computation schemes for the centroidal momentum matrix (CMM), which projects the generalized velocities of a humanoid robot to its spatial centroidal momentum. Through a transformation diagram we graphically show the relationship between this matrix and the well-known joint-space inertia matrix. We also introduce the new concept of “average spatial velocity” of the humanoid that encompasses both linear and angular components and results in a novel decomposition of the kinetic energy. Further, we develop a very efficient \(O(N)\) algorithm, expressed in a compact form using spatial notation, for computing the CMM, centroidal momentum, centroidal inertia, and average spatial velocity. Finally, as a practical use of centroidal dynamics we show that a momentum-based balance controller that directly employs the CMM can significantly reduce unnecessary trunk bending during balance maintenance against external disturbance.

Keywords

Centroidal momentum matrix Angular momentum Robot dynamics algorithms Average spatial velocity Humanoid balance controller Momentum based balance control 

Notes

Acknowledgments

The authors gratefully thank Ghassan Bin Hammam for testing the recursive centroidal dynamics algorithm on a PC. Support for this work for David Orin was provided in part by Grant No. CNS-0960061 from NSF with a subaward to The Ohio State University. S.-H. Lee was partly supported by the Global Frontier R&D Program, NRF (NRF-2012M3A6A3055690).

Supplementary material

10514_2013_9341_MOESM1_ESM.mpg (8.5 mb)
Supplementary material 1 (mpg 8710 KB)

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • David E. Orin
    • 1
  • Ambarish Goswami
    • 2
    Email author
  • Sung-Hee Lee
    • 3
  1. 1.Department of Electrical and Computer EngineeringThe Ohio State UniversityColumbusUSA
  2. 2.Honda Research InstituteMountain ViewUSA
  3. 3.Graduate School of Culture TechnologyKorea Advanced Institute of Science and Technology (KAIST)DaejeonSouth Korea

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