Generation of Walking Patterns for Biped Robots Based on Dynamics of 3D Linear Inverted Pendulum

  • Artem Kovalev
  • Nikita Pavliuk
  • Konstantin Krestovnikov
  • Anton Saveliev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11659)


Biped humanoid robot dynamics is approximated by dynamics of 3D linear inverted pendulum, which can be derived from dynamics of ordinary 3D inverted pendulum. Based on this approximation of biped robot dynamics we can generate walking patterns, which are specified by step parameters, that specify desired zero moment point (ZMP) trajectory. To track desired center of mass (CoM) trajectory, modified foot positions are calculated by minimizing an error function in closed form. Different forces acting on biped robot are taken into account during calculation of robot dynamics for plain surface as well for uneven terrain. Some walking patterns and walking primitives are expressed algorithmically for different 3D cases in terms of ground-fixed coordinate frame. Some dynamic constraints applicable in this setting are presented.


Linear inverted pendulum Walking pattern generation Biped robots 



This research is supported by RSF grant No. 16-19-00044P.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.St. Petersburg Institute for Informatics and Automation of the Russian Academy of Sciences (SPIIRAS)St. PetersburgRussia

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