Comparative stable walking gait optimization for small-sized biped robot using meta-heuristic optimization algorithms

Tran Thien Huan, Ho Pham Huy Anh


This paper proposes a new way to optimize the biped walking gait design for biped robots that permits stable and robust stepping with pre-set foot lifting magnitude. The new meta-heuristic CFO-Central Force Optimization algorithm is initiatively applied to optimize the biped gait parameters as to ensure to keep biped robot walking robustly and steadily. The efficiency of the proposed method is compared with the GA-Genetic Algorithm, PSO-Particle Swarm Optimization and Modified Differential Evolution algorithm (MDE). The simulated and experimental results carried on the prototype small-sized humanoid robot demonstrate that the novel meta-heuristic CFO algorithm offers an efficient and stable walking gait for biped robots with respect to a pre-set of foot-lift height value.


biped robot; meta-heuristic optimization algorithm; Central Force Optimization (CFO) algorithm

Full Text:



W. T. Miller. Real-time neural network control of a biped walking robot. IEEE Control Systems, 14, (1), (1994), pp. 41–48.

C.-L. Shih. Ascending and descending stairs for a biped robot. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 29, (3), (1999), pp. 255–268.

S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, and H. Hirukawa. Biped walking pattern generation by using preview control of zero-moment point. In Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan, (2003). pp. 14–19.

Y.-F. Ho, T.-H. S. Li, P.-H. Kuo, and Y.-T. Ye. Parameterized gait pattern generator based on linear inverted pendulum model with natural ZMP references. The Knowledge Engineering Review, 32, (2017).

J. Mrozowski, J. Awrejcewicz, and P. Bamberski. Analysis of stability of the human gait. Journal of Theoretical and Applied Mechanics, 45, (1), (2007), pp. 91–98.

Q. Huang, K. Yokoi, S. Kajita, K. Kaneko, H. Arai, N. Koyachi, and K. Tanie. Planning walking patterns for a biped robot. IEEE Transactions on Robotics and Automation, 17, (3), (2001), pp. 280–289.

V.-H. Dau, C.-M. Chew, and A.-N. Poo. Optimal trajectory generation for bipedal robots. In Proceedings IEEE-RAS International Conference on Humanoid Robot, Pittsburgh, PA, USA, (2007). IEEE, pp. 603–608.

G. Dip, V. Prahlad, and P. D. Kien. Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed. Robotica, 27, (3), (2009), pp. 355–365.

M. R. Maximo, E. L. Colombini, and C. H. C. Ribeiro. Stable and fast model-free walk with arms movement for humanoid robots. International Journal of Advanced Robotic Systems, 14, (3), (2017).

R. Khusainov, A. Klimchik, and E. Magid. Kinematic and dynamic approaches in gait optimization for humanoid robot locomotion. In Informatics in Control, Automation and Robotics. Springer, (2018), pp. 293–320.

T. T. Huan and H. P. H. Anh. Novel stable walking for humanoid robot using particle swarm optimization algorithm. Journal of Advances in Intelligent Systems Research, 123, (2015), pp. 322–325.

T. T. Huan and H. P. H. Anh. Stable gait optimization for small-sized humanoid robot using modified differential evolution (MDE) algorithm. Special Issue of Measurement-Control and Automation Journal, 21, (1), (2018), pp. 63–74. (in Vietnamese).

N. N. Son, H. P. H. Anh, and T. D. Chau. Inverse kinematics solution for robot manipulator based on adaptive MIMO neural network model optimized by hybrid differential evolution algorithm. In Proceedings of the 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO). IEEE, (2014), pp. 2019–2024.

N. Shafii, L. P. Reis, and N. Lau. Biped walking using coronal and sagittal movements based on truncated Fourier series. In RoboCup-2010: Robot Soccer World Cup XIII. Springer, (2011), pp. 324–335.

E. Yazdi, V. Azizi, and A. T. Haghighat. Evolution of biped locomotion using bees algorithm, based on truncated Fourier series. In Proceedings of the World Congress on Engineering and Computer Science. Citeseer, (2010), pp. 378–382.

Y. Farzaneh, A. Akbarzadeh, and A. A. Akbari. Online bio-inspired trajectory generation of seven-link biped robot based on T-S fuzzy system. Applied Soft Computing, 14, (2014), pp. 167–180.

D. Gong, J. Yan, and G. Zuo. A review of gait optimization based on evolutionary computation. Applied Computational Intelligence and Soft Computing, 2010, (2010), pp. 1–12.

P. H. Anh. An evolutionary-based optimization algorithm for truss sizing design. Vietnam Journal of Mechanics, 38, (4), (2016), pp. 307–317.

C.-F. Juang and Y.-T. Yeh. Multiobjective evolution of biped robot gaits using advanced continuous ant-colony optimized recurrent neural networks. IEEE Transactions on Cybernetics, 48, (6), (2018), pp. 1910–1922.

B. H. Le and T. M. Thuy. Optimal design for eigen-frequencies of a longitudinal bar using Pontryagin’s maximum principle considering the influence of concentrated mass. Vietnam Journal of Mechanics, 39, (1), (2017), pp. 1–12.

T. T. Huan and H. P. H. Anh. Implementation of novel stable walking method for small-sized biped robot. In Proceedings The 8th Viet Nam Conference on Mechatronics (VCM), (2016), pp. 283–292.

R. A. Formato. Central force optimization: A new metaheuristic with applications in applied electromagnetics. In Progress in Electromagnetics Research (PIER), Vol. 77, (2007), pp. 425–491.



  • There are currently no refbacks.

Copyright (c) 2018 Vietnam Academy of Science and Technology



Editorial Office of Vietnam Journal of Mechanics

3rd Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam

Tel: (+84) 24 3791 7103