Dynamics Analysis: Equations of Motion

  • Tomomichi Sugihara
  • Yasutaka FujimotoEmail author
Reference work entry


This chapter provides dynamics analyses of a humanoid robot as a mechanical system. It is modeled as a floating-base tree structure that exchanges forces with the environment through contacts. Lagrange’s equation of motion of the system is derived in order to focus on how to read it rather than how to compute it. The dominant dynamics of the robot embedded in the centroidal momentum is then discussed. Issues around the contact force are also addressed. Some useful ground references are introduced in order to intuitively associate the contact constraints with the whole-body motion. Finally, the equation of motion of a planar humanoid robot is explicitly derived in a different way from the above, which helps readers understand another mathematical structure of the dynamics.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Adaptive Machine Systems, Graduate School of EngineeringOsaka UniversitySuita/OsakaJapan
  2. 2.Department of Electrical and Computer EngineeringYokohama National UniversityYokohamaJapan

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