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Applied Computational Intelligence and Soft Computing
Volume 2010 (2010), Article ID 413179, 12 pages
http://dx.doi.org/10.1155/2010/413179
Review Article

A Review of Gait Optimization Based on Evolutionary Computation

School of Electronic Information and Control Engineering, Beijing University of Technology, Beijing 100124, China

Received 1 September 2009; Revised 21 March 2010; Accepted 22 April 2010

Academic Editor: Oliver Kramer

Copyright © 2010 Daoxiong Gong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Chen, P. Yang, Z. Liu, H. Chen, and X. Guo, “Gait optimization of biped robot based on mix-encoding genetic algorithm,” in Proceedings of the 2nd IEEE Conference on Industrial Electronics and Applications (ICIEA '07), pp. 1623–1626, May 2007. View at Publisher · View at Google Scholar
  2. S. Chernova and M. Veloso, “An evolutionary approach to gait learning for four-legged robots,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '04), pp. 2562–2567, October 2004.
  3. M. Srinivasan and A. Ruina, “Computer optimization of a minimal biped model discovers walking and running,” Nature, vol. 439, no. 7072, pp. 72–75, 2006. View at Publisher · View at Google Scholar · View at PubMed
  4. J. E. A. Bertram and A. Ruina, “Multiple walking speed-frequency relations are predicted by constrained optimization,” Journal of Theoretical Biology, vol. 209, no. 4, pp. 445–453, 2001. View at Publisher · View at Google Scholar · View at PubMed
  5. R. M. Alexander, “Optimization and gaits in the locomotion of vertebrates,” Physiological Reviews, vol. 69, no. 4, pp. 1199–1227, 1989.
  6. R. M. Alexander, “Optimum walking techniques for quadrupeds and bipeds,” Journal of Zoology, vol. 192, pp. 97–117, 1980.
  7. R. M. Alexander, “Energetics and optimization of human walking and running: the 2000 Raymond Pearl Memorial Lecture,” American Journal of Human Biology, vol. 14, no. 5, pp. 641–648, 2002. View at Publisher · View at Google Scholar · View at PubMed
  8. R. M. Alexander, “Design by numbers,” Nature, vol. 412, no. 6847, p. 591, 2001. View at Publisher · View at Google Scholar · View at PubMed
  9. J. E. A. Bertram, “Constrained optimization in human walking: cost minimization and gait plasticity,” The Journal of Experimental Biology, vol. 208, no. 6, pp. 979–991, 2005. View at Publisher · View at Google Scholar · View at PubMed
  10. A. K. Gutmann, B. Jacobi, M. T. Butcher, and J. E. A. Bertram, “Constrained optimization in human running,” The Journal of Experimental Biology, vol. 209, no. 4, pp. 622–632, 2006. View at Publisher · View at Google Scholar · View at PubMed
  11. D. F. Hoyt and C. R. Taylor, “Gait and the energetics of locomotion in horses,” Nature, vol. 292, no. 5820, pp. 239–240, 1981.
  12. F. Saibene, “The mechanisms for minimizing energy expenditure in human locomotion,” European Journal of Clinical Nutrition, vol. 44, no. 1, pp. 65–71, 1990.
  13. J. Yang, B. Hong, S. Piao, and Q. Huang, “An efficient strategy of penalty kick and goal keep based on evolutionary walking gait for biped soccer robot,” Information Technology Journal, vol. 6, no. 8, pp. 1120–1129, 2007.
  14. C. Zhou, P. K. Yue, J. Ni, and S.-B. Chan, “Dynamically stable gait planning for a humanoid robot to climb sloping surface,” in Proceedings of the IEEE Conference on Robotics, Automation and Mechatronics, pp. 341–346, Singapore, December 2004.
  15. L. Hu and C. Zhou, “EDA-Based optimization and learning methods for biped gait generation,” in Robotic Welding, Intelligence and Automation, T.-J. Tarn, et al., Ed., vol. 362 of Lecture Notes in Control and Information Sciences, pp. 541–549, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar
  16. M. Shrivastava, A. Dutta, and A. Saxena, “Trajectory generation using GA for an 8 DOF biped robot with deformation at the sole of the foot,” Journal of Intelligent and Robotic Systems: Theory and Applications, vol. 49, no. 1, pp. 67–84, 2007. View at Publisher · View at Google Scholar
  17. K. Seo and S. Hyun, “Genetic programming based automatic gait generation for quadruped robots,” in Proceedings of the 10th Annual Genetic and Evolutionary Computation Conference (GECCO '08), pp. 293–294, July 2008.
  18. M. R. Heinen and F. S. Osório, “Gait control generation for physically based simulated robots using genetic algorithms,” in Proceedings of the 2nd International Joint Conference on Advances in Artificial Intelligence—IBERAMIA-SBIA, J. S. Sichman, et al., Ed., vol. 4140 of Lecture Notes in Computer Science, pp. 562–571, Ribeirão Preto, Brazil, October 2006.
  19. B.-I. Koh, J. A. Reinbolt, A. D. George, R. T. Haftka, and B. J. Fregly, “Limitations of parallel global optimization for large-scale human movement problems,” Medical Engineering and Physics, vol. 31, no. 5, pp. 515–521, 2009. View at Publisher · View at Google Scholar · View at PubMed
  20. Z. Tang, C. Zhou, and Z. Sun, “Humanoid walking gait optimization using GA-based neural network,” in Proceedings of the 1st International Conference on Natural Computation (ICNC '05), L. Wang, K. Chen, and Y. S. Ong , Eds., vol. 3611 of Lecture Notes in Computer Science, pp. 252–261, August 2005.
  21. T. Arakawa and T. Fukuda, “Natural motion trajectory generation of biped locomotion robot using genetic algorithm through energy optimization,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, pp. 1495–1500, October 1996.
  22. C. Paul and J. C. Bongard, “The road less travelled: morphology in the optimization of biped robot locomotion,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '01), vol. 1, pp. 226–232, Maui, Hawaii, USA, October 2001.
  23. J. Pettersson, H. Sandholt, and M. Wahde, “A flexible evolutionary method for the generation and implementation of behaviors for humanoid robots,” in Proceedings of the IEEE-RAS International Conference on Humanoid Robotics, pp. 279–286, November 2001.
  24. K. Wolff, J. Pettersson, A. Heralić, and M. Wahde, “Structural evolution of central pattern generators for bipedal walking in 3D simulation,” in Proceedings of IEEE International Conference on Systems, Man and Cybernetics (SMC '06), vol. 1, pp. 227–234, Taipei, Taiwan, October 2007. View at Publisher · View at Google Scholar
  25. P. R. Vundavilli and D. K. Pratihar, “Soft computing-based gait planners for a dynamically balanced biped robot negotiating sloping surfaces,” Applied Soft Computing Journal, vol. 9, no. 1, pp. 191–208, 2009. View at Publisher · View at Google Scholar
  26. M. F. Silva, R. S. Barbosa, and J. A.T. Machado, “Development of a genetic algorithm for the optimization of hexapod robot parameters,” in Proceedings of the IASTED International Conference on Applied Simulation and Modelling (ASM '09), pp. 77–82, Palma de Mallorca, Spain, 2009.
  27. G. Dip, V. Prahlad, and P. D. Kien, “Genetic algorithm-based optimal bipedal walking gait synthesis considering tradeoff between stability margin and speed,” Robotica, vol. 27, no. 3, pp. 355–365, 2009. View at Publisher · View at Google Scholar
  28. M. R. Heinen and F. S. Osório, “Applying genetic algorithms to control gait of physically based simulated robots,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '06), pp. 1823–1830, July 2006.
  29. T. Röfer, “Evolutionary gait-optimization using a fitness function based on proprioception,” in RoboCup Symposium, pp. 310–322, Springer, Lisbon, Portugal.
  30. N. Kohl and P. Stone, “Machine learning for fast quadrupedal locomotion,” in Proceedings of the 19th National Conference on Artificial Intelligence (AAAI '04), pp. 611–616, San Francisco, Calif, USA, July 2004.
  31. E. Kim, M. Kim, and J.-W. Kim, “Optimal trajectory generation for walking up and down a staircase with a biped robot using genetic algorithm (GA),” in FIRA RoboWorld Congress, J.-H. Kim, et al., Ed., vol. 5744 of Lecture Notes in Computer Science, pp. 103–111, August 2009. View at Publisher · View at Google Scholar
  32. K. Wolff and P. Nordin, “Evolutionary learning from first principles of biped walking on a simulated humanoid robot,” http://fy.chalmers.se/~wolff/WN_gecco03.pdf.
  33. J. E. Murphy, H. Carr, and M. O'Neill, “Grammatical evolution for gait retargeting,” in Eurographics UK Symposium on Theory and Practice of Computer Graphics (TPCG '08), pp. 159–162, Manchester, UK, June 2008.
  34. J. E. Murphy, M. O'Neill, and H. Carr, “Exploring grammatical evolution for horse gait optimisation,” in Proceedings of the 12th European Conference on Genetic Programming (EuroGP '09), vol. 5481 of Lecture Notes in Computer Science, pp. 183–194, Springer, 2009. View at Publisher · View at Google Scholar
  35. M. Hebbel, R. Kosse, and W. Nistico, “Modeling and learning walking gaits of biped robots,” in Proceedings of the Workshop on Humanoid Soccer Robots of the IEEE-RAS International Conference on Humanoid Robots, pp. 40–48, Genoa, Italy, 2006.
  36. M. Hebbel, W. Nistico, and D. Fisseler, “Learning in a high dimensional space: fast omnidirectional quadrupedal locomotion,” in Proceedings of the 10th RoboCup International Symposium, G. Lakemeyer, et al., Ed., vol. 4434 of Lecture Notes in Computer Science, pp. 314–321, Bremen, Germany, June 2007.
  37. K. Wolff, D. Sandberg, and M. Wahde, “Evolutionary optimization of a bipedal gait in a physical robot,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '08), pp. 440–445, June 2008. View at Publisher · View at Google Scholar
  38. K. Wampler and Z. Popovi, “Optimal gait and form for animal locomotion,” ACM Transactions on Graphics, vol. 28, no. 3, article 60, 8 pages, 2009. View at Publisher · View at Google Scholar
  39. L. Hu, C. Zhou, and Z. Sun, “Biped gait optimization using spline function based probability model,” in Proceedings of IEEE International Conference on Robotics and Automation, pp. 830–835, Orlando, Fla, USA, May 2006. View at Publisher · View at Google Scholar
  40. C. Zhou, L. Hu, C. A. A. Acosta, and P. K. Yue, “Humanoid soccer gait generation and optimization using probability distribution models,” in Proceedings of the Workshop on Humanoid Soccer Robots of the IEEE-RAS International Conference on Humanoid Robots, pp. 49–55, Genoa, Italy, December, 2006.
  41. J. I. Alonso-Barba, J. A. Gámez, J. M. Puerta, and I. García-Varea, “Gait optimization in AIBO robots using an estimation of distribution algorithm,” in Proceedings of the 8th International Conference on Hybrid Intelligent Systems (HIS '08), pp. 150–155, September 2008. View at Publisher · View at Google Scholar
  42. J. Eperješi, “Gait optimization of AIBO robot based on interactive evolutionary computation,” in Proceedings of the 6th International Symposium on Applied Machine Intelligence and Informatics (SAMI '08), pp. 236–240, January 2008. View at Publisher · View at Google Scholar
  43. M. A. Lewis, A. H. Fagg, and G. A. Bekey, “Genetic algorithms for gait synthesis in a hexapod robot,” in Recent Trends in Mobile Robots, V. Zheng, Ed., pp. 317–331, World Scientific, River Edge, NJ, USA, 1994.
  44. G. Capi, Y. Nasu, M. Yamano, and K. Mitobe, “Multicriteria optimal humanoid robot motion generation,” in Humanoid Robots, A. C. de Pina Filho, Ed., pp. 157–170, Advanced Robotic Systems International and I-Tech, Vienna, Austria, 2007.
  45. S. Bi, H. Min, Q. Liu, and X. Zheng, “Multi-objective optimization for a humanoid robot climbing stairs based on genetic algorithms,” in Proceedings of the IEEE International Conference on Information and Automation (ICIA '09), pp. 66–71, Zhuhai, China, 2009. View at Publisher · View at Google Scholar
  46. G. Capi, M. Yokota, and K. Mitobe, “A new humanoid robot gait generation based on multiobjective optimization,” in Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM '05), vol. 1, pp. 450–454, Monterey, Calif, USA, July 2005.
  47. D. Golubovic and H. Hu, “Parameter optimisation of an evolutionary algorithm for on-line gait generation of quadruped robots,” in Proceedings of the IEEE International Conference on Industrial Technology (ICIT '03), vol. 1, pp. 221–226, December 2003.
  48. Z. Peng, Q. Huang, X. Zhao, T. Xiao, and K. Li, “Online trajectory generation based on off-line trajectory for biped humanoid,” in Proceedings of IEEE International Conference on Robotics and Biomimetics (ROBIO '04), pp. 752–756, Shenyang, China, August 2004.
  49. G. S. Hornby, M. Fujita, S. Takamura, T. Yamamoto, and O. Hanagata, “Autonomous evolution of gaits with the Sony quadruped robot,” in Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1297–1304, Morgan Kaufmann, San Mateo, Calif, USA, 1999.
  50. Q. Wang, C. Rong, G. Xie, and L. Wang, “Collaborative localization and gait optimization of SharPKUngfu team,” in Robotic Soccer, P. Lima, Ed., pp. 549–574, Itech Education and Publishing, Vienna, Austria, 2007.
  51. K. Wolff, D. Sandberg, and M. Wahde, “Evolutionary optimization of a bipedal gait in a physical robot,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '08), pp. 440–445, June 2008. View at Publisher · View at Google Scholar
  52. G. S. Hornby, S. Takamura, T. Yamamoto, and M. Fujita, “Autonomous evolution of dynamic gaits with two quadruped robots,” IEEE Transactions on Robotics, vol. 21, no. 3, pp. 402–410, 2005. View at Publisher · View at Google Scholar
  53. W. Chen, “Odometry Calibration and Gait Optimization,” Tech. Rep., School of Computer Science and Engineering, The University of New South Wales, 2005, http://www.cse.unsw.edu.au/~robocup/2005site/reports05/RobocupThesis2005_weiming.pdf.
  54. T. Mericli, H. L. Akin, C. Mericli, K. Kaplan, and B. Celik, “The Cerberus'05 Team Report,” http://robot.cmpe.boun.edu.tr/~cerberus/wiki/uploads/Downloads/Cerberus2005-TR.pdf.
  55. C. Niehaus, T. Roefer, and T. Laue, “Gait optimization on a humanoid robot using particle swarm optimization,” http://www.informatik.uni-bremen.de/kogrob/papers/Humanoids-Niehaus-etal-07.pdf.
  56. J. H. Park and M. Choi, “Generation of an optimal gait trajectory for biped robots using a genetic algorithm,” JSME International Journal, Series C, vol. 47, no. 2, pp. 715–721, 2004. View at Publisher · View at Google Scholar
  57. G. Capi, S. Kaneko, K. Mitobe, L. Barolli, and Y. Nasu, “Optimal trajectory generation for a prismatic joint biped robot using genetic algorithms,” Robotics and Autonomous Systems, vol. 38, no. 2, pp. 119–128, 2002. View at Publisher · View at Google Scholar
  58. W. I. Sellers, L. A. Dennis, W.-J. Wang, and R. H. Crompton, “Evaluating alternative gait strategies using evolutionary robotics,” Journal of Anatomy, vol. 204, no. 5, pp. 343–351, 2004. View at Publisher · View at Google Scholar · View at PubMed
  59. S. Fan and M. Sun, “Gait parameters optimization and real-time trajectory planning for humanoid robots,” in Proceedings of the 3rd International Conference on Intelligent Computing (ICIC '07), D.-S. Huang, L. Heutte, and M. Loog, Eds., vol. 4682 of Lecture Notes in Computer Science, pp. 35–46, 2007.
  60. G. Capi, Y. Nasu, L. Barolli, K. Mitobe, M. Yamano, and K. Takeda, “A new gait optimization approach based on genetic algorithm for walking biped robots and a neural network implementation,” Information Processing Society of Japan (IPSJ) Journal, vol. 43, no. 4, pp. 1039–1049, 2002.
  61. T. Arakawa and T. Fukuda, “Natural motion generation of biped locomotion robot using hierarchical trajectory generation method consisting of GA, EP layers,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '97), pp. 211–216, April 1997.
  62. G. Capi, Y. Nasu, L. Barolli, K. Mitobe, and M. Yamano, “Real time generation of humanoid robot optimal gait for going upstairs using intelligent algorithms,” Industrial Robot, vol. 28, no. 6, pp. 489–497, 2001. View at Publisher · View at Google Scholar
  63. G. Capi, S. Kaneko, K. Mitobe, L. Barolli, and Y. Nasu, “Optimal trajectory generation for a prismatic joint biped robot using genetic algorithms,” Robotics and Autonomous Systems, vol. 38, no. 2, pp. 119–128, 2002. View at Publisher · View at Google Scholar
  64. Y. Hasegawa, T. Arakawa, and T. Fukuda, “Trajectory generation for biped locomotion robot,” Mechatronics, vol. 10, no. 1-2, pp. 67–89, 2000. View at Publisher · View at Google Scholar
  65. G. Capi and M. Yokota, “Optimal multi-criteria humanoid robot gait synthesis—an evolutionary approach,” International Journal of Innovative Computing, Information and Control, vol. 2, no. 6, pp. 1249–1258, 2006.
  66. M.-Y. Cheng and C.-S. Lin, “Genetic algorithm for control design of biped locomotion,” Journal of Robotic Systems, vol. 14, no. 5, pp. 365–373, 1997.
  67. X. Ke and Z. Gong, “Non-time reference gait planning and optimization for a stable bipedal walking,” in Proceedings of the IEEE International Symposium on Industrial Electronics (ISIE '08), pp. 1400–1405, July 2008. View at Publisher · View at Google Scholar
  68. D. L. Wight, E. G. Kubica, and D. W. L. Wang, “Introduction of the foot placement estimator: a dynamic measure of balance for bipedal robotics,” Journal of Computational and Nonlinear Dynamics, vol. 3, no. 1, 2008. View at Publisher · View at Google Scholar
  69. K. S. Jeon, O. Kwon, and J. H. Park, “Optimal trajectory generation for a biped robot walking a staircase based on genetic algorithms,” in Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS '04), pp. 2837–2842, October 2004.
  70. G. S. Hornby, S. Takamura, J. Yokono, O. Hanagata, T. Yamamoto, and M. Fujita, “Evolving robust gaits with AIBO,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA '00), pp. 3040–3045, April 2000.
  71. K. Wolff and P. Nordin, “Evolution of efficient gait with an autonomous biped robot using visual feedback,” http://fy.chalmers.se/~wolff/Papers/WN_gecco01.pdf.
  72. M. Eaton and T. J. Davitt, “Automatic evolution of bipedal locomotion in a simulated humanoid robot with many degree of freedom,” in Proceedings of the 11th International Symposium on Artificial Life and Robotics, pp. 23–25, Beppu, Japan, 2006.
  73. S. Ha, Y. Han, and H. Hahn, “Adaptive gait pattern generation of biped robot based on human's gait pattern analysis,” International Journal of Mechanical Systems Science and Engineering, vol. 1, no. 2, pp. 80–85, 2007.
  74. J. C. Zagal and J. Ruiz-Del-Solar, “Combining simulation and reality in evolutionary robotics,” Journal of Intelligent and Robotic Systems: Theory and Applications, vol. 50, no. 1, pp. 19–39, 2007. View at Publisher · View at Google Scholar
  75. N. Shafii, A. Khorsandian, A. Abdolmaleki, and B. Jozi, “An optimized gait generator based on Fourier series towards fast and robust biped locomotion involving arms swing,” in Proceedings of the IEEE International Conference on Automation and Logistics (ICAL '09), pp. 2018–2023, Shenyang, China, August 2009. View at Publisher · View at Google Scholar
  76. N. Shafii, S. Aslani, O. M. Nezami, and S. Shiry, “Evolution of biped walking using truncated Fourier series and particle swarm optimization,” in Proceedings of the 13th RoboCup International Symposium, vol. 5949 of Lecture Notes in Computer Science, pp. 344–354, Graz, Austria, 2010. View at Publisher · View at Google Scholar
  77. B. Jiao, Z. Lian, and X. Gu, “A dynamic inertia weight particle swarm optimization algorithm,” Chaos, Solitons & Fractals, vol. 37, no. 3, pp. 698–705, 2008. View at Publisher · View at Google Scholar
  78. C. Rong, Q. Wang, Y. Huang, G. Xie, and L. Wang, “Autonomous evolution of high-speed quadruped gaits using particle swarm optimization,” in Proceedings of the 12th Annual RoboCup International Symposium (RoboCup '08), L. Iocchi, et al., Ed., vol. 5399 of Lecture Notes in Computer Science, pp. 259–270, Suzhou, China, July 2009. View at Publisher · View at Google Scholar
  79. E.-S. Kim, J.-H. Kim, and J.-W. Kim, “Generation of optimal trajectories for ascending and descending a stair of a humanoid based on uDEAS,” in Proceedings of the IEEE International Conference on Fuzzy Systems, pp. 660–665, Jeju, Korea, August 2009. View at Publisher · View at Google Scholar
  80. M. R. Heinen and F. S. Osório, “Evolving morphologies and gaits of physically realistic simulated robots,” in Proceedings of 24th Annual ACM Symposium on Applied Computing (SAC '09), pp. 1161–1165, Honolulu, Hawaii, USA, March 2009. View at Publisher · View at Google Scholar
  81. J. Rieffel, F. Saunders, S. Nadimpalli, et al., “Evolving soft robotic locomotion in PhysX,” in Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference, pp. 2499–2504, 2009.
  82. L. Yang, C.-M. Chew, T. Zielinska, and A.-N. Poo, “A uniform biped gait generator with offline optimization and online adjustable parameters,” Robotica, vol. 25, no. 5, pp. 549–565, 2007. View at Publisher · View at Google Scholar
  83. T. Laue and M. Hebbel, “Automatic parameter optimization for a dynamic robot simulation,” in Proceedings of the 12th Annual RoboCup International Symposium (RoboCup '08), vol. 5399 of Lecture Notes in Computer Science, pp. 121–132, Suzhou, China, July 2009. View at Publisher · View at Google Scholar