Abstract
The center of mass (CoM) is a key descriptor in the understanding and the analysis of bipedal locomotion. Some approaches are based on the premise that humans minimize the CoM vertical displacement. Other approaches express walking dynamics through the inverted pendulum model. Such approaches are contradictory in that they lead to two conflicting patterns to express the CoM motion: straight line segments for the first approaches and arcs of a circle for the second ones. In this paper, we show that CoM motion is a trade-off between both patterns. Specifically, CoM follows a “curtate cycloid”, which is the curve described by a point rigidly attached to a wheel rolling on a flat surface. We demonstrate that all the three parameters defining a curtate cycloid only depend on the height of the subjects.
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Acknowledgements
We first thank the volunteers who took part in the experiment. We warmly thank Bruno Watier from LAAS-CNRS and University of Toulouse for helping us in the acquisition of motion capture data.
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This work was supported by the European Research Council through the Actanthrope Project and the French National Research Agency Project Loco3D.
Recommended by Associate Editor Hong Qiao
Justin Carpentier received the M. Sc. degree in applied mathematics and computer science from ENS Paris-Saclay, France in 2013. In 2014, he was a visiting student inside the Optimization, Robotics and Biomechanics Group at University of Heidelberg, Germany. Since 2014, he has been a Ph. D. degree candidate inside the Gepetto Team at Laboratory for Analysis and Architecture of Systems, Toulouse, France.
His research interests include the motion generation for humanoid robots, bipedal locomotion and numerical optimal control.
Mehdi Benallegue received the engineer degree from the Institute of Computer Science (INI), Algeria in 2007, the M. Sc. degree from the University of Paris 7, France in 2008, and the Ph.D. degree from University of Montpellier 2, France in 2011. Previously, he was a research associate with the Laboratory for Analysis and Architecture of Systems, France. He is now with the Humanoid Research Group, at the National Institute of Advanced Industrial Science and Technology, Japan.
His research interests include humanoid robotics, state observers, locomotion, imitation, learning, and computational geometry.
Jean-Paul Laumond is the research director LAAS-CNRS in Toulouse, France. He is a Member of the French Academy of Technology. His research is devoted to robot motion. In the 1990s, he has been the coordinator of two European Esprit projects, both dedicated to robot motion planning and control. In the early 2000s he created and managed Kineo CAM, a spinoff company from LAAS-CNRS devoted to develop and market motion planning technology. Siemens acquired Kineo CAM in 2012. In 2006, he launched the research team Gepetto dedicated to Human Motion studies. He teaches robotics at Ecole Normale Suprieure, France. He has published more than 150 papers in international journals and conferences in robotics, computer science, automatic control and recently in neurosciences. He has been the 2011–2012 recipient of the Chaire Innovation Technologique Liliane Bettencourt at Collège de France in Paris. His current project Actanthrope is devoted to the computational foundations of anthropomorphic action and it is supported by the European Research Council (ERC-ADG 340050).
His research interests include humanoid robotics, human locomotion, digital actor animation and motion planning.
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Carpentier, J., Benallegue, M. & Laumond, JP. On the centre of mass motion in human walking. Int. J. Autom. Comput. 14, 542–551 (2017). https://doi.org/10.1007/s11633-017-1088-5
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DOI: https://doi.org/10.1007/s11633-017-1088-5