Dynamic balance preservation and prevention of sliding for humanoid robots in the presence of multiple spatial contacts


The main indicator of dynamic balance is the \(\mathit{ZMP}\). Its original notion assumes that both feet of the robot are in contact with the flat horizontal surface (all contacts are in the same plane) and that the friction is high enough so that sliding does not occur. With increasing capabilities of humanoid robots and the higher complexity of the motion that needs to be performed, these assumptions might not hold. Having in mind that the system is dynamically balanced if there is no rotation about the edges of the feet and if the feet do not slide, we propose a novel approach for testing the dynamic balance of bipedal robots, by using linear contact wrench conditions compiled in a single matrix (Dynamic Balance Matrix). The proposed approach has wide applicability since it can be used to check the stability of different kinds of contacts (including point, line, and surface) with arbitrary perimeter shapes. Motion feasibility conditions are derived on the basis of the conditions which the wrench of each contact has to satisfy. The approach was tested by simulation in two scenarios: biped climbing up and walking sideways on the inclined flat surface which is too steep for a regular walk without additional support. The whole-body motion was synthesized and performed using a generalized task prioritization framework.

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  1. 1.

    In this context “stable contact” represents the situation where there is no relative motion between the bodies in contact. In our opinion term “stable contact” is not the most suitable to describe the state of the contact when there is no sliding and no separation. It seems that terms such as “reliable, sustainable” are more descriptive.

  2. 2.

    One exception appears to be when the robot grasps the environment, so it can both push and pull. When looking at the grasp, it actually comprises several unilateral contacts, positioned in such a way that all directions of contact forces are possible. The only real exception of this assumption is when there is adhesion between the robot and the environment.

  3. 3.

    An on-line demo showing calculation of the DBM can be found at the author’s website www.milutinnikolic.info/dbm/.


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This work was funded by the Ministry of Science and Technological Development of the Republic of Serbia in part under contract TR35003 and in part under contract III44008.

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Correspondence to Milutin Nikolić.

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Nikolić, M., Borovac, B. & Raković, M. Dynamic balance preservation and prevention of sliding for humanoid robots in the presence of multiple spatial contacts. Multibody Syst Dyn 42, 197–218 (2018). https://doi.org/10.1007/s11044-017-9572-9

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  • Humanoid robots
  • Contact stability
  • Whole-body motion