An Evolutionary Optimization Approach for Optimal Hopping of Humanoid Robots

  • Hong, Young-Dae
  • Received : 2015.05.27
  • Accepted : 2015.08.12
  • Published : 2015.11.01


This paper proposes an evolutionary optimization approach for optimal hopping of humanoid robots. In the proposed approach, the hopping trajectory is generated by a central pattern generator (CPG). The CPG is one of the biologically inspired approaches, and it generates rhythmic signals by using neural oscillators. During the hopping motion, the disturbance caused by the ground reaction forces is compensated for by utilizing the sensory feedback in the CPG. Posture control is essential for a stable hopping motion. A posture controller is utilized to maintain the balance of the humanoid robot while hopping. In addition, a compliance controller using a virtual spring-damper model is applied for stable landing. For optimal hopping, the optimization of the hopping motion is formulated as a minimization problem with equality constraints. To solve this problem, two-phase evolutionary programming is employed. The proposed approach is verified through computer simulations using a simulated model of the small-sized humanoid robot platform DARwIn-OP.


Humanoid robot;Hopping motion;Evolutionary optimization;Central pattern generator


  1. Y.-D. Hong, B.-J. Lee, and J.-H. Kim, “Command state-based modifiable walking pattern generation on an inclined plane in pitch and roll directions for humanoid robots,” IEEE/ASME Trans. Mechatron., vol. 16, no. 4, pp. 783-789, 2011.
  2. Y. Sakagami, R. Watanabe, C. Aoyama, S. Matsunaga, N. Higaki, and K. Fujimura, “The intelligent ASIMO: System overview and integration,” in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., 2002, pp. 2478-2483.
  3. K. Akachi, K. Kaneko, N. Kanehira, S. Ota, G. Miyamori, M. Hirata, S. Kajita, and F. Kanehiro, “Development of humanoid robot HRP-3P,” in Proc. IEEE-RAS Int. Conf. Humanoid Robots, 2005, pp. 50-55.
  4. Y.-D. Hong and J.-H. Kim, “3-D command state-based modifiable bipedal walking on uneven terrain,” IEEE/ASME Trans. Mechatron., vol. 18, no. 2, pp. 657-663, 2013.
  5. Y.-D. Hong and B.-J. Lee, “Experimental study on modifiable walking pattern generation for handling infeasible navigational commands,” J. Elect. Eng. Technol., 2015 (to be published).
  6. S. Kajita, K. Kaneko, M. Morisawa, A. Nakaoka, and H. Hirukawa, “ZMP-based biped running enhanced by toe springs,” in Proc. IEEE Int. Conf. Robot. Autom., 2007, pp. 3963-3969.
  7. S. Kajita, T. Nagasaki, K. Kaneko, and H. Hirukawa, “ZMP-based biped running control,” IEEE Robot. Autom. Mag., vol. 14, no. 2, 2007, pp. 63-72.
  8. B. Cho, J. Kim, and J. Oh, “Online balance controllers for a hopping and running humanoid robot,” Adv. Robot., vol. 25, no. 9-10, 2011, pp. 1209-1225.
  9. B. Ugurlu, and A. Kawamura, “ZMP-based online jumping trajectory generation for a one-legged robot,” IEEE Trans. Ind. Electron., vol. 57, no. 5, 2010, pp. 1701-1709.
  10. K.-H. Han and J.-H. Kim, “Quantum-inspired evolutionary algorithms with a new termination criterion, Hε gate, and two phase scheme,” IEEE Trans. Evol. Comput., vol. 8, no. 2, pp. 156-169, 2004.
  11. B. Ugurlu and A. Kawamura, “On the backwards problem of legged robots,” IEEE Trans. Ind. Electron., vol. 61, no. 3, pp. 1632-1634, 2014.
  12. B. Ugurlu, J. A. Saglia, N. G. Tsagarakis, S. Morfey, and D. G. Caldwell, “Bipedal hopping pattern generation for passively compliant humanoids: exploiting the resonance,” IEEE Trans. Ind. Electron., vol. 61, no. 10, 2014, pp. 5431-5443.
  13. K.-H. Han and J.-H. Kim, “Quantum-inspired evolutionary algorithm for a class of combinatorial optimization,” IEEE Trans. Evol. Comput., vol. 6, no. 6, pp. 580-593, 2002.
  14. Y.-D. Hong, C.-S. Park, and J.-H. Kim, “Stable bipedal walking with a vertical center of mass motion by an evolutionary optimized central pattern generator,” IEEE Trans. Ind. Electron., vol. 61, no. 5, pp. 2246-2355, May. 2014.
  15. C.-S. Park, Y.-D. Hong, and J.-H. Kim, “Evolutionary optimized central pattern generator for stable modifiable bipedal walking,” IEEE/ASME Trans. Mechatron., vol. 19, no. 6, pp. 1374-1383, 2014.
  16. Y.-D. Hong, Y.-H. Kim, J.-H. Han, J.-K. Yoo, and J.-H. Kim, “Evolutionary multiobjective footstep planning for humanoid robots,” IEEE Trans. Syst. Man. Cybern. C, Appl. Rev., vol. 41, no. 4, pp. 520-532, Jul. 2011.
  17. Y.-D. Hong and J.-H. Kim, “An evolutionary optimized footstep planner for the navigation of humanoid robots,” Int. J. Humanoid Robot., vol. 9, no. 1, Mar. 2012.
  18. J.-H. Kim and H. Myung, “Evolutionary programming techniques for constrained optimization problems,” IEEE Trans. Evol. Comput., vol. 1, no. 2, pp. 129-140, 1997.
  19. I.-W. Park and K.-B. Lee and J.-H. Kim, “Multi-objective evolutionary algorithm-based optimal posture control of humanoid robots,” in Proc. IEEE Congr. Evol. Comput., 2012, pp. 1-7.
  20. G. Taga, “A model of the neuro-musculo-skeletal system for human locomotion,” Biol. Cybern., vol. 73, no. 2, pp. 97-111, Jul. 1995.
  21. K. Matsuoka, “Mechanisms of frequency and pattern control in the neural rhythm generators,” Biol. Cybern., vol. 56, no. 5, pp. 345-353, 1987.
  22. O. Michel, “Cyberbotics Ltd. WebotsTM: Professional mobile robot simulation,” Int. J. Adv. Robot. Syst., vol. 1, no. 1, pp. 39-42, 2004.

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