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A dynamic human motion: coordination analysis

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Abstract

This article is concerned with the generic structure of the motion coordination system resulting from the application of the method of virtual holonomic constraints (VHCs) to the problem of the generation and robust execution of a dynamic humanlike motion by a humanoid robot. The motion coordination developed using VHCs is based on a motion generator equation, which is a scalar nonlinear differential equation of second order. It can be considered equivalent in function to a central pattern generator in living organisms. The relative time evolution of the degrees of freedom of a humanoid robot during a typical motion are specified by a set of coordination functions that uniquely define the overall pattern of the motion. This is comparable to a hypothesis on the existence of motion patterns in biomechanics. A robust control is derived based on a transverse linearization along the configuration manifold defined by the coordination functions. It is shown that the derived coordination and control architecture possesses excellent robustness properties. The analysis is performed on an example of a real human motion recorded in test experiments.

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Notes

  1. A motion generator is a dynamical system of low dimension whose solutions define the evolution of all degrees of freedom of a higher-dimensional mechanical system.

  2. The assumption of passivity of the ankle joint is routinely applied in nonlinear control theory in the analysis of periodic gates of walking mechanisms. This assumption will be confirmed later in the text of the article by the existence of a humanlike dynamical motion along a chosen trajectory.

  3. We retain the notations used in [18].

  4. It is assumed that the inclination of the head and the configuration of the hands are fixed with respect to the torso.

  5. It should be mentioned that the exact values \(k_{ij}\) of (3), (4) found in [18] in the course of reconstructing the human motion are of limited use for planning such motion for the robot. The easiest way to verify this is to run simulations and observe abnormal motions of the robot’s dynamics with such synchronization functions. These results are not reported here due to space limitation.

  6. The ranges of joint variables can vary and depend on specifications of initial and final configuration of (2). The velocities for all joint variables in the initial point are usually taken as zero, while in the final position, e.g. when the robot hits a chair, the velocities are not necessarily zero, but expected to be small as well as the accelerations.

  7. The existence of multiple local minima is a surprising result, which we cannot explain at the moment. The solution with the best optimization index value has been chosen among the found solutions. Unfortunately we cannot guarantee that all local minima were found. This is a topic for future research.

  8. The solution was found using standard subroutines of Matlab optimization package.

  9. In a similar way, various additional constraints can be systematically handled in a step-by-step manner without attempting a too computationally difficult numerical task.

  10. Other nonlinear feedback strategies can be used here instead of (20) as a basis for synthesizing a controller for contraction to the motion of the nonlinear system (9), but they are not elaborated since the steps for redesign will be conceptually similar.

  11. Instead of (23) one can consider the solution of

    $$\begin{aligned}&\frac{d}{d\tau } P(\tau )+A(\tau )^{\scriptscriptstyle T}P(\tau )+P(\tau )A(\tau )-G(\tau )\\&\quad -\,\left[ P(\tau )B(\tau )-g(\tau )\right] \varGamma (\tau )^{-1}\left[ P(\tau )B(\tau )-g(\tau )\right] ^{\scriptscriptstyle T}\end{aligned}$$

    with the initial condition \(P(0)=Q\) at the beginning of the interval \(\tau =0\).

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Authors and Affiliations

  1. Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7491, Trondheim, Norway

    Stepan Pchelkin, Anton S. Shiriaev & Leonid Paramonov

  2. Department of Applied Physics and Electronics, Umeå University, 901 87, Umeå, Sweden

    Leonid B. Freidovich

  3. Department of Transmission and Hybrid Systems, IAV Automotive Engineering, 10587, Berlin, Germany

    Uwe Mettin

  4. Department of General Mathematics and Informatics, St. Petersburg State University, St. Petersburg, Russia

    Sergei V. Gusev

  5. Samsung Advanced Institute of Technology, Nongseo-dong, Giheung-gu, Yongin-si, Gyeonggi-do, 446-712, Korea

    Woong Kwon

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  1. Stepan Pchelkin
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  2. Anton S. Shiriaev
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  3. Leonid B. Freidovich
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  4. Uwe Mettin
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  5. Sergei V. Gusev
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  6. Woong Kwon
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  7. Leonid Paramonov
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Correspondence to Stepan Pchelkin.

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Pchelkin, S., Shiriaev, A.S., Freidovich, L.B. et al. A dynamic human motion: coordination analysis. Biol Cybern 109, 47–62 (2015). https://doi.org/10.1007/s00422-014-0624-4

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