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Optimization-based gait planning and control for biped robots utilizing the optimal allowable ZMP variation region

Hongbo Zhu (Anhui University of Science and Technology, Huainan, China)
Minzhou Luo (Hohai University - Changzhou Campus, Changzhou, China)
Jingzhao Li (Anhui University of Science and Technology, Huainan, China)

Industrial Robot

ISSN: 0143-991x

Article publication date: 11 July 2018

Issue publication date: 29 August 2018




The purpose of this study is to present an optimization-based gait planning method for biped robots according to the conditions of terrain, which takes fully the relationship between walking stability margin and energy efficiency into account.


First, the authors newly designed a practical gait motion synthesis algorithm by using the optimal allowable zero moment point (ZMP) variation region (OAZR), which can generate different gait motions corresponding to different terrains based on the modifiability of ZMP in lateral (y-axis) direction. Second, an effective gait parameter optimization algorithm is performed to find the optimal set of key gait parameters (step length, duration time of gait cycle, average height of center of mass (CoM), amplitude of the vertical CoM motion and double support ratio), which maximizes either the walking stability margin or the energy efficiency with certain walking stability margin under practical constraints (mechanical constraints of all joint motors, geometric constraints, friction force limit and yawing moment limit) according to the conditions of terrain. Third, the necessary controllers for biped robots have been introduced briefly.


The experiment data and results are described and analyzed, showing that the proposed method was verified through simulations and implemented on a DRC-XT biped robot.


The main contribution is that the OAZR has been defined based on AZR, which could be used to plan and generate the various feasible gait motions to help a biped robot to adapt effectively to various terrains.



This research has been supported by National Nature Science Foundation of China (Grant No. 51405469).


Zhu, H., Luo, M. and Li, J. (2019), "Optimization-based gait planning and control for biped robots utilizing the optimal allowable ZMP variation region", Industrial Robot, Vol. 45 No. 4, pp. 469-480.



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