Abstract
In ankle joint trajectory planning of biped robots, the spline interpolation generally leads to acceleration mutations on the key points, which weakens the stability of the biped robot. To solve this problem, a smooth function fitting method on ankle joint trajectory planning is proposed in this paper. In this method, the higher order derivatives of the ankle joint trajectory is smooth, and the acceleration mutation can be avoided. The biped robot gait planning of a whole cycle is accomplished by calculating the joint angle sequences of hip, knee and ankle. The effectiveness of the proposed method is demonstrated by numerical simulations on NAO robot gait planning. Experimental results show that the proposed method can improve the stability of the zero moment point (ZMP) margin effectively when it is applied to the bipedal robot gait planning on the non-horizontal ground.
Similar content being viewed by others
References
A. S. Go, D. Mozaarian, and V. L. Roger, “American heart association statistics committee and stroke statistics subcommittee. Heart disease and stoke statistics-2014 update: a report from the American heart association,” vol. 129, no. 3, pp. 280–292, 2014.
J. Hu, Z. G. Hou, Y. X. Chen, and F. Zhang, “Lower limb rehabilitation robots and interactive control methods,” Acta Automatica Sinica, vol. 40, no. 11, pp. 2377–2390,2014.
P. Liang, Z. G. Hou, and W. Q. Wang, “Synchronous active interaction control and its implementation for a rehabilitation robot,” Acta Automatica Sinica, vol. 41, no. 11, pp. 1837–1846, 2015.
S. Y. Je, P. Hyeon, and Member, “A fast turning method for biped robots with foot slip during single-support phase,” IEEE/ASME Transactions on Mechatronics, vol. 19, no. 6, pp. 1847–1858, 2014. [click]
H. Reza and F. Mohammad, “Robust model predictive control of biped robots with adaptive on-line gait generation,” International Journal of Control Automation & Systems, vol. 15, no. 1, pp. 329–344, 2017. [click]
A. S. Haghighi, I. Zare, and A. B. Mohammad, “Modeling of bio-inspired thunnus albacares and inchwormgammarus with micro actuators in one structure,” International Journal of Science and Qualitative Analysis, vol. 1, no. 3, pp. 54–63, 2015. [click]
S. H. AliReza, Z. Iman, and F. AliReza, “Bio-inspired micro-robot with micro-actuators ICPF and floating collector skimmer,” Proc. of 7th Iranian Conference on Electrical and Electronics Engineering (ICEEE2015) Islamic Azad University Gonabad Branc, pp. 131–139, 2015.
Q. Li, A. Takanishi, and I. Kato, “Learning control of compensation trunk motion for biped walking robot based on ZMP stability criterion,” Proceedings of IEEE IntConfon Robotics System, Yokohama, pp. 597–603,1992.
K. Hirai, M. Hirose, and T. Takenaka, “Current and future perspective of honda humanoid robot,” Proceedings of IEEE/RSJ International Confon Intelligent Robots and Systems, Tokyo, pp. 500–508, 1998.
J. Zhang, L. Liu, C. S. Li, and K. Chen, “Parametricomnidirectional gait planning of humanoid robots,” Robot, vol. 36, no. 2, pp. 210–217, 2014.
L. Chen, G. L. Zhang, and W. P. Zhang, “Biped robot dynamic gait planning,” Computer Engineering and Application, vol. 50, no. 1, pp. 267–270, 2015.
Y. Ou, W. Xiao, G. Pan, and L. Yu, “Time-variant gait planning for under-actuated biped robot via optimization,” Lecture Notes in Electrical Engineering, vol. 256, pp. 323–332, 2013.
J. Seok, W. Yoo, and S. Won, “Inertia-related coupling torque compensator for disturbance observer based position control of robotic manipulators,” International Journal of Control, Automation, and System, vol. 10, no. 4, pp. 753–760, 2012. [click]
Z. J. Li, Y. Kun, B. Stjepan, and X. Bugong, “On motion optimization of robotic manipulators with strong nonlinear dynamic coupling using support area level set al.gorithm,” International Journal of Control, Automation, and System, vol. 11, no. 6 pp. 1266–1275, 2013. [click]
Z. Q. Deng, Y. Q. Liu, D. Liang, and H. B. Gao, “Motion planning and simulation verification of a hydraulic hexapod robot based on reducing energy/flow consumption,” Journal of Mechanical Science and Technology, vol. 29, no. 10 pp. 4427–4436, 2015.
H. P. Jong and C. Seunghyun, “Optimal locomotion trajectory for biped robot ‘D2’ with knees stretched,heel-contact landings, and toe-off liftoffs,” Journal of Mechanical Science and Technology, vol. 25, no. 12 pp. 3231–3241, 2011.
G. B. Wang, D. S. Chen, K. W. Chen, and Z. Q. Zhang, “The current research status and development strategy on biomimetic robot,” Journal Of Mechanical Engineering, vol. 51, no. 13 pp. 27–44, 2015.
M. Tan and S. Wang, “Research progress on robotics,” Acta Automatica Sinica, vol. 39, no. 7 pp. 963–942, 2013.
G. P. Fu, Y. M. Zhang, J. P. Chen, and J. Li, “Walking control for humanoid robot based on ZMP errorcorrection,” Robot, vol. 35, no. 1 pp. 39–44, 2013.
H. Y. Wang and Y. B. Li, “Realization of a biped robot lower limb walking without double support phase on uneven terrain,” Journal of Control Science and Engineering, vol. 2013 pp. 8, 2013.
M. B. Amir, Z. Ali, S. Yaser, and A. S. Mahdi, “A hybrid controller based on CPG and ZMP for biped locomotion,” Journal of Mechanical Science and Technology, vol. 27, no. 11 pp. 3473–3486, 2013.
C. Zhao and D. S. Chen, “Gait planning of biped robot NAO climbing stairs,” Robot Technique And Application, vol. 4, pp. 31–36, 2013.
S. Kim and Y. Sankai, “Stair climbing task of humanoid robot by phase composition and phase sequence,” IEEE International Workshop on Robotsand Human Interactive Communication, pp. 531–536, 2005. [click] 24.
X. T. Wang, J. X. Zhang, and L. P. Yin, “Research on design and gait planning of biped robot,” Manufacturing Automation, vol. 35, no. 2 pp. 50–53, 2013.
Z. Li and S. S. Ge, “Adaptive robust controls of biped robots,” IET Control Theory & Application, vol. 7, no. 2 pp. 161–175, 2013. [click]
W. Indrajit and A. Muis, “Development of whole body motionimitation in humanoid robot,” Proceeding of 2013 International Conference on QiR (Quality in Research), Yogyakarta, IEEE, pp. 138–141, 2013.
K. Chen and C. L. Fu, Humanoid Robot Theory and Technology, Tsinghua University Press, Beijing, 2010.
Y. Okumura, T. Tawara, and K. Endo, “Realtime ZMP compensation for biped walking robot using adaptive inertia force control,” Proc. of IEEE/RSJ Conference on Intelligent Robots and Systems, pp. 335–339, 2003.
O. Kurt and K. Erbatur, “Biped robot reference generation with natural ZMP trajectories,” IEEE International Workshop on Advanced Motion Control, IEEE, pp. 403–410, 2006.
J. E. Machado, H. M. Becerra, and M. Moreno-Rocha, “Modeling and finite-time walking control of a biped robot with feet,” Mathematical Problems in Engineering, vol. 2015, Article ID 963496, 17 pages, 2015.
H. F. Yu, E. H. K. Fung, and X. J. Jing, “An improved ZMP-based CPG model of robot walking searched by SaDE,” ISRN Robotics, vol. 17, pp. 1–16, 2014.
T. Franco and C. Giuseppe, “Hexapod walking robot locomotion,” Mechanisms and Machine Science, vol. 29, pp. 439–468, 2015. [click]
S. Byung-Rok, T. Hwan, and B. J. Yi, “ZMP-based motion planning algorithm for kinematiccally redundant manipulator standing on the ground,” Intelligent Service Robotics, vol. 8, no. 1, pp. 35–44, 2015. [click]
M. K. Duong, H. Cheng, H. Tran, and Q. Jing, “Minimizing human-exoskeleton interaction force by using global fast sliding mode control,” International Journal of Control, Automation and Systems, vol. 14, no. 2, pp. 1–10, 2016.
C. Y. Chen, B. Y. Shih, and C. H. Shih, “Design modeling and stability control for an actuated dynamic walking planar bipedal robot,” Journal of Vibration And Control, vol. 19, no. 3, pp. 376–384, 2013.
S. Shimmyo, T. Sato, and K. Ohnishi, “Biped walking pattern generation by using preview control based on threemass model,” IEEE Transactions on Industrial Electronics, vol. 60, no. 11, pp. 5137–5147, 2014. [click]
J. Q. Zhang, F. Gao, and X. L. Han, “Trot gait design and CPG method for a quadruped robot,” Journal of Bionic Engineering, vol. 11, no. 1, pp. 18–25, 2014.
W. D. Ke, Z. P. Peng, Z. S. Cai, S. H. Piao, and K. Chen, “Study of trajectory tracking control for humanoid robot based on Similarity Locomotion,” Acta Automatica Sinica, vol. 40, no. 11, pp. 2404–2413, 2014.
H. Y. Wang, Y. B. Li, and L. X. Ning, “Realization of a hydraulic actuated biped robot walking without double support phase,” International Journal of Control, Automation, and Systems, vol. 12, no. 4, pp. 843–851, 2014. [click]
W. Luo, P. H. You, R. X. Lu, and K. Z. Yan, “Design of humanoid robot foot structure with sensing system and the ZMP algorithm,” Intelligence Engineering, vol. 10, no. 8, pp. 67–70, 2013.
G. B. Sun, H. Wang, Z. G. Lu, and F. W. Wang, “Humanoid walking planning based on EMG from human footbottom,” Acta Automatica Sinica, vol. 41, no. 5, pp. 874–884, 2015.
X. Y. Wang, J. H. Qin, H. Qiu, G. Q. Chen, and Z. Z. Qiu, “Walking stability control of a new biped-imitating walking mechanism based on ZMP,” Mechanical Science and Technology for Aerospace Engineering, vol. 33, no. 6, pp. 802–806, 2014.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Recommended by Associate Editor Sooyeong Yi under the direction of Editor Hyun-Seok Yang. This paper was supported by the National Natural Science Foundation (61203138); The Foundation of the Application Base and Frontier Technology Research Project of Tianjin (15JCYBJC51800); The City of Tianjin Higher School Science and Technology Development Fund Planning Project (20120829) and South African National Research Foundation Incentive Grants (No. 81705).
Dong En Zeng received the Doctoral degree in Opertional Research and Cybernetics, Nankai University, Tianjin, China in 2006. Currently, he is a Professor in School of Electrical Engineering, Tianjin University of Technology. He is mainly working on intelligent control theory and applications, image and video processing, and brain-computer interface (BCI).
Wang Dan Dan received her Bachelor degree in electrical engineering and automation from Hebei University of Agricultural, China, in 2014. She was a graduate student at Tianjin Univercity of Technology in control science and Engineering in 2014. Her research interests include control applications, biped robot gait planning, and human-robot interaction, and so on.
Tong Ji Gang received the B.S. degree from Liaoning University of Technology, Jinzhou, China, in 1998, and the M.S. and Ph.D degrees in control engineering from NanKai University, TianJin, China, in 2006 and 2010, respectively. Currently, he is a teacher at the School of Electrical Engineering, Tianjin University of Technology. His research interests include embedded system, human-computer interaction techniques.
Chen Chao received his Bachelor degree in Automation, and his Master degree in Pattern Recognition and Intelligent System from Northeastern University, Shenyang, China in 2005 and 2008. In 2014, He got his Ph.D. degree from Tokyo Institute of Technology, Japan. Currently, he is an Associate professor in School of Electrical Engineering, Tianjin University of Technology. He mainly works on invasive and non-invasive brain-computer interface (BCI), pattern recognition and intelligent algorithm.
Wang Zeng Hui graduated with Doctoral degree in Control Theory and Control Engineering, Nankai University, China in 2007. He is currently a Professor in the Department of Electrical and Mining Engineering at University of South Africa. He has about 70 peer-reviewed journal and conference publications. His research interest is in the fields of evolutionary optimization, image and video processing, adaptive control and predictive control for nonlinear systems, artificial Intelligence, and so on.
Rights and permissions
About this article
Cite this article
Dong, E.Z., Wang, D.D., Tong, J.G. et al. A Stable Gait Planning Method of Biped Robot Based on Ankle motion Smooth Fitting. Int. J. Control Autom. Syst. 16, 284–294 (2018). https://doi.org/10.1007/s12555-016-0263-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-016-0263-8