Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T21:05:11.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Modeling, stability and walking pattern generators of biped robots: a review

Published online by Cambridge University Press:  05 December 2013

Hayder F. N. Al-Shuka ,
F. Allmendinger ,
B. Corves  and
Wen-Hong Zhu
Hayder F. N. Al-Shuka*
Affiliation:
Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany
F. Allmendinger
Affiliation:
Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany
B. Corves
Affiliation:
Department of Mechanism and Machine Dynamics, RWTH Aachen University, Aachen, Germany
Wen-Hong Zhu
Affiliation:
Canadian Space Agency, 6767, Route de l'Aéroport, Longueuil (St-Hubert), QC, Canada, J3Y 8Y9
*
*Corresponding author. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Biped robots have gained much attention for decades. A variety of researches have been conducted to make them able to assist or even substitute for humans in performing special tasks. In addition, studying biped robots is important in order to understand human locomotion and to develop and improve control strategies for prosthetic and orthotic limbs. This paper discusses the main challenges encountered in the design of biped robots, such as modeling, stability and their walking patterns. The subject is difficult to deal with because the biped mechanism intervenes with mechanics, control, electronics and artificial intelligence. In this paper, we collect and introduce a systematic discussion of modeling, walking pattern generators and stability for a biped robot.

Keywords

Biped robotStabilityZero moment pointOrbital stabilityWalking pattern generators
Type
Articles
Information
Robotica , Volume 32 , Issue 6 , September 2014 , pp. 907 - 934
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Lima, P. and Ribeiro, M. I., Mobile Robotics, Course handouts (Instituto Superior Técnico/Instituto de Sistemas e Robótica, Portugal, March 2002).Google Scholar
2. Silva, M. F. and Machado, J. T., “A literature review on the optimization of legged robots,” J. Vib. Control 18 (12), 1753–1767 (2012).Google Scholar
3. Bekey, G. A., Autonomous Robots: From Biological Inspiration to Implementation and Control (MIT Press, Cambridge, MA, 2005).Google Scholar
4. Vaughan, C. L., “Theories of bipedal walking: An odyssey,” J. Biomech. 36 (4), 513–523 (2003).CrossRefGoogle ScholarPubMed
5. Raibert, M. H., Legged Robots that Balance (MIT Press, Cambridge, MA, 1986).CrossRefGoogle Scholar
6. Vukobratovic, M. and Borovac, B., “Zero-moment point – thirty-five years of its life,” Int. J. Human. Robot. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
7. Vanderborght, B. et al. “Overview of the Lucy project: Dynamic stabilization of a biped powered by pneumatic artificial muscles,” Adv. Robot. 22 (10), 1027–1051, 2008.CrossRefGoogle Scholar
8. Golliday, C. L. and Hemami, H., “An Approach to Analyzing biped locomotion dynamics and Designing Robot locomotion controls,” IEEE Trans. Autom. Control AC 22 (6), 953–972 (1977, Dec.).Google Scholar
9. Kim, D., Seo, S.-J. and Park, G.-T., “Zero-moment point trajectory modeling of a biped walking robot using an Adaptive neuro-fuzzy system,” IEEE Proc. Control Theory Appl. 152 (4), 411–426 (2005).CrossRefGoogle Scholar
10. Chevallereau, C., Bessonnet, G., Abba, G. and Aoustin, Y., Bipedal Robots, Modeling, Design and Building Walking Robots (John Wiley, Malden MA, 2009).Google Scholar
11. Raibert, M., Tzafestas, S. and Tzafestas, C., “Comparative Simulation Study of Three Control Techniques Applied to a Biped Robot,” In: Proc. IEEE Int. Conf. on Systems, Man and Cybernetics, Le Touquet, France, Vol. 1 (1993) pp. 494–502.CrossRefGoogle Scholar
12. Zhu, W.-H, Virtual Decomposition Control: Towards Hyper Degrees of Freedom (Springer-Verlag, Berlin, Germany, 2010).Google Scholar
13. Park, I.-W., Kim, J.-Y. and Oh, J.-H., “Online Biped Walking Pattern Generation for Humanoid Robot KHR-3 (KAIST Humanoid Robot-3: HUBO),” In: IEEE-RAS International Conference on Humanoid Robots, Genova, Italy (Dec. 2006) pp. 398–403.Google Scholar
14. Dekker, M. H. P., “Zero-Moment Point Method for Stable Biped Walking,” Internship report, Eindhoven, Netherlands (2009).Google Scholar
15. Ozyurt, G., “3-D Humanoid Gait Simulation Using an Optimal Predictive Control,” MSc thesis (Middle East Technical University, Turkey, 2005).Google Scholar
16. Whittle, M. W., Gait Analysis: An Introduction, 4th Edn. (Butterworth-Heinemann, Edinburgh, UK, 2007).Google Scholar
17. Huang, Q., Kajita, S., Koyachi, N. and Kaneko, K., “A High Stability, Smooth Walking Pattern for a Biped Robot,” In: IEEE International Conference on Robotics and Automation, Detroit, MI, Vol. 1 (May 1999) pp. 65–71.Google Scholar
18. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., N. Koyachi and K. Tanie, “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17 (3), 280–289 (2001).CrossRefGoogle Scholar
19. Vadakkepat, P. and Goswami, D., “Biped locomotion: Stability, analysis and control,” Int. J. Smart Sens. Intell. Syst. 1 (1), 187–207 (2008).Google Scholar
20. Sato, T., Sakaino, S. and Ohnishi, K., “Trajectory Planning and Control for Biped Robot with Toe and Heel Joint,” In: IEEE International Workshop on Advanced Motion Control, Nagaoka, Japan (March 2010) pp. 129–136.Google Scholar
21. Lim, H.-O and Takanishi, A., “Compensatory motion control for a biped walking robot,” Robotica 23 (1), 1–11(2005).Google Scholar
22. Seireg, A. and Arvikar, R.J., “A mathematical model for evaluation of forces in lower extremities of the musculo-skeletal systems,” J. Biomech. 6 (3), 313–326 (1973).Google Scholar
23. Twonsend, M. A. and Seireg, A., “Effect of model complexity and gait criteria on the synthesis of bipedal locomotion,” IEEE Trans. Biomed. Eng. 20 (6), 433–444 (1973).CrossRefGoogle Scholar
24. Migliore, S. A., “The Role of Passive Joint Stiffness and Active Knee Control in Robotic Leg Swinging: Application to Dynamic Walking,” PhD thesis (Georgia Institute of Technology, Georgia, 2008).Google Scholar
25. Sangwan, V. and Agrawal, S. K., “Differentially flat design of bipeds ensuring limit-cycles,” IEEE/ASME Trans. Mechatronics 14 (6), 647–657 (2009).CrossRefGoogle Scholar
26. Miyazaki, F. and Arimoto, S., “A control theoretic study on dynamical biped locomotion,” J. Dyn. Syst. Meas. Control 102, 233–239 (1980).CrossRefGoogle Scholar
27. Spong, Mark. W. and Vidyasagar, M., Robot Dynamics and Control (John Wiley, New York, NY, 1989).Google Scholar
28. Samson, C., Le Borgne, M., Espiau, B., Robot Control: The Task Function Approach, Oxford Engineering Science Series (Oxford University Press, Clarendon, UK, 1991).Google Scholar
29. Shabana, A. A., Computational Dynamics, 3rd Edn. (John Wiley, Chichester, UK, 2010).CrossRefGoogle Scholar
30. Nikravesh, P. E., Computer Aided Analysis of Mechanical Systems (Prentice Hall, Englewood Cliffs, NJ, 1988).Google Scholar
31. Asada, H. and Slotine, J.-J. E., Robot Analysis and Control (John Wiley, New York, NY, 1986).Google Scholar
32. Zhu, W.-H., “Dynamics of general constrained robots derived from rigid bodies,” ASME J. Appl. Mech. 75 (3), 031005 (11 Pages) (May 2008).Google Scholar
33. Hamon, A. and Aoustin, Y., “Cross Four-Bar Linkage for the Knees of a Planar Bipedal Robot,” 10th IEEE-RAS International Conference on Humanoid Robots, Nashville, TN (Dec 2010) pp. 379–384.Google Scholar
34. Tzafests, S., Raibert, M. and Tzafestas, C., “Robust sliding mode control applied to 5-link biped robot,” J. Intell. Robot. Syst. 15, 67–133 (1996).CrossRefGoogle Scholar
35. Sonoda, N., Murakami, T. and Ohnishi, K., “An Approach of Biped Robot Control Utilizing Redundancy in Double Support Phase,” In: IEEE International Conference on Industrial Electronics, Control and Instrumentation, New Orleans, LA, Vol. 3 (Nov. 1997) pp. 1332–1336.Google Scholar
36. Choi, M. H. and Lee, B. H., “A Real-Time Optimal Load Distribution for Multiple Cooperating Robots,” In: IEEE International Conference on Robotics and Automation, Nagoya, Japan, Vol. 1 (May 1995) pp. 1211–1216.Google Scholar
37. Sano, A. and Furusho, J., “Control of Torque Distribution for the BLR-G2 Biped Robot,” In: 5th International Conference on Advanced Robotics, Pisa, Italy, Vol. 1 (June 1991) pp. 729–734.Google Scholar
38. Shih, C.-L. and Gurver, W. A., “Control of a biped robot in the double-support phase,” IEEE Trans. Syst. Man Cybern. 22 (4), 729–735 (1992).Google Scholar
39. Chevallereau, C., “Time-scaling control for an underactuated biped robot,” IEEE Trans. Robot. Autom. 19 (2), 362–368 (2003).CrossRefGoogle Scholar
40. Westervelt, E. R., Grizzle, J. W. and Koditschek, D. E., “Hybrid zero dynamics of planar biped walkers,” IEEE Trans. Autom. Control 48 (1), 42–56 (2003).Google Scholar
41. Duindam, V. and Stramigioli, S., Modeling and Control for Efficient Bipedal Walking Robot: A Port-Based Approach (Springer-Verlag, Berlin, Germany, 2009).Google Scholar
42. Iida, F., Rummel, J., Seyfarth, A., “Bipedal walking and running with spring-like biarticular muscles,” J. Biomech. 4 (3), 656–667 (2008).CrossRefGoogle Scholar
43. Rummel, J. and Seyfarth, A., “Stable running with segmented legs,” Int. J. Robot. Res. 27 (8), 919–934 (2008).CrossRefGoogle Scholar
44. Rummel, J., Blum, Y. and Seyfarth, A., “Robust and efficient walking with spring-like legs,” Bioinsp. Biomim. 5 (4), 1–13 (2010).CrossRefGoogle ScholarPubMed
45. Merker, A., Rummel, J. and Seyfarth, A., “Stable walking with asymmetric legs,” Bioinsp. Biomim. 6 (4), 1–13 (2011).Google Scholar
46. Rummel, J., Blum, Y., Maus, H. M., Rode, C. and Seyfarth, A., “Stable and Robust Walking with Compliant Legs,” In: IEEE International Conference on Robotics and Automation, Anchorage, AK (May 2010) pp. 5250–5255.Google Scholar
47. Pfeiffer, F. and Glocker, C., Multibody Dynamics with Unilateral Contacts (John Wiley, New York, NY, 1996).CrossRefGoogle Scholar
48. Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523–533 (1999).CrossRefGoogle Scholar
49. van Zutven, P., Kostic, D. and Nijmeijer, H., “On the Stability of Bipedal Walking,” SIMPAR 2010 (Ando, N. et al., eds.), LNAI 6472 (Springer-Verlag, Berlin, Germany, 2010) pp. 521–532.Google Scholar
50. Nicholls, E., “Bipedal Dynamic Walking in Robotics,” Honors thesis (Department of Electrical and Electronic Engineering, The University of Western Australia, 1998).Google Scholar
51. Pratt, J., Tedrake, R., “Velocity-based stability margins for fast bipedal walking,” Fast Motions Biomech. Robot. 340, 299–324 (2006).CrossRefGoogle Scholar
52. Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “Capture Point: A Step Toward Humanoid Push Recovery,” In: IEEE-RAS International Conference on Humanoid Robot, Genova, Italy (Dec 2006) pp. 200–207.Google Scholar
53. Wight, D. L., Kubica, E. G., Wang, D. W. L., “Introduction to the foot placement estimator: A dynamic measure of balance for bipedal robotics,” J. Comput. Nonlinear Dyn. 3, 1–9 (2008).Google Scholar
54. Vukobratovic, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15 (1–2), 1–37 (1972).Google Scholar
55. Kajita, S. and Espiau, B., “Legged robots,” In: Springer Handbook of Robotics (Siciliano, B. and Khatib, O., eds.) (Springer, Berlin, Germany, 2008), pp. 361–389.Google Scholar
56. Vundavilli, P. R. and Pratihar, D. K., “Gait planning of biped robots using soft computing: An attempt to incorporate intelligence,” In: Intelligent Autonomous Systems: Foundation and Applications (Pratihar, D. K. and Jain, L. C., eds.) (Springer-Verlag, Berlin, Germany, 2010) pp. 57–85.CrossRefGoogle Scholar
57. Alba, A. G and Zielinska, T., “Postural equilibrium criteria concerning feet properties for biped robots,” J. Autom. Mob. Robot. Intell. Syst. 6 (1), 22–27 (2012).Google Scholar
58. Pop, C., Khajepour, A., Huissoon, J. P. and Patla, A. E., “Experimental/analytical analysis of human locomotion using bondgraphs,” ASME J. Biomech. Eng. 125, 490–498 (2003).Google Scholar
59. Hobbelen, D. G. E. and Wisse, M., “Limit cycle walking,” In: Humanoid Robots: Human-Like Machines (Hackel, Matthias, ed.) (I-Tech, Vienna, Australia) pp. 277–294 (2007).Google Scholar
60. Or, J. and Takanishi, A., “A Biologically Inspired CPG-ZMP Control System for the Real-Time Balance of a Single-Legged Bally Dancing Robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, Vol. 1 (2004) pp. 931–936.Google Scholar
61. Park, J. H. and Kim, K. D., “Biped Robot Walking Using Gravity-Compensated Inverted Pendulum Mode and Computer Torque Control,” In: IEEE International Conference of Robotics & Automation, Leuven, Belgium, Vol. 4 (May 1998) pp. 3528–3533.Google Scholar
62. Huang, Q. and Ono, K., “Energy-efficient walking for biped using self-excited mechanism and optimal trajectory planning,” In: Humanoid Robots, New Developments (de Pina Filho, Armando Carlos, ed.) (I-Tech, Vienna, Austria, 2007) pp. 321–342.Google Scholar
63. Takanishi, A., Ishida, M., Yamazaki, Y. and Kato, I., “Realization of Dynamic Walking by the Biped Walking Robot WL-10RD,” In: Advanced Robotics: Proceedings of the 2nd International Conference (ICAR'85), Tokyo (1985) pp. 459–466.Google Scholar
64. Harada, K., Kajita, S., Kaneko, K. and Hirukawa, H., “Pushing manipulation by humanoid considering two-kinds of ZMPs,” In: IEEE International Conference on Robotics and Automation, Taipei, Taiwan, Vol. 2 (Sep. 2003) pp. 1627–1632.Google Scholar
65. Sardain, P. and Bessonnet, G., “Zero-moment point-measurement from a human walker wearing robot feet as shoes,” IEEE Tran. Syst. Man Cybern. A 34 (5), 638–648 (2004).CrossRefGoogle Scholar
66. Yüskel, B., Zhouand, C. and Leblebicioglu, K., “Ground Reaction Force Analysis of Biped Locomotion,” In: IEEE Conference on Robotics, Automation and Mechatronics, Singapore, Vol. 1 (Dec 2004) pp. 330–335.Google Scholar
67. Takanishi, A., Takeya, T., Karaki, H. and Kato, I., “A control method for dynamic biped walking under unknown external force,” In: IEEE International Workshop on Intelligent Robots and Systems (IROS'90), Ibaraki, Vol. 2 (Jul. 1990) pp. 795–801.Google Scholar
68. Sardain, P. and Bessonnet, G., “Force acting on a biped robot. Center of pressure-zero moment point,” IEEE Trans. Syst. Man Cybern. A 34 (5), 630–637 (2004).CrossRefGoogle Scholar
69. Tsuji, T. and Ohnishi, K., “A control of biped robot which applies inverted pendulum mode with virtual supporting leg,” In: Proceedings of the 7th International Workshop on Advanced Motion Control, Maribor, Solvenia (2002) pp. 478–483.Google Scholar
70. Waki, N., Matsumoto, K. and Kawamura, A., “Lateral sway motion generation for biped robots using virtual supporting point,” In: IEEE International Workshop on Advanced Motion Control, Nagaoka, Japan (Mar. 2010) pp. 124–128.Google Scholar
71. Herr, H. and Popovic, M., “Angular momentum in human walking,” J. Exp. Bio. 211, 467–481 (2008).Google Scholar
72. Popovic, M. B. and Herr, H., “Ground reference points in legged locomotion: Definitions, biological trajectories and control implications,” In: Mobile Robots Towards New Applications (Lazinica, A., ed) (Pro-Literatur-Verlag, Germany, 2006) pp. 79–104.Google Scholar
73. Cannon, R. C., Dynamics of Physical Systems (McGraw- Hill, New York, NY, 1967).Google Scholar
74. Schaefer, J., On the Bounded Control of Some Unstable Mechanical Systems, SUDAR Rep. 233 (Dept. of Aeronautics and Astronautics, Stanford University, Apr. 1965).Google Scholar
75. Witt, D. C., “A feasibility study of powered-limb prosthesis,” Proc. Inst. Mech. Eng. (Conf. Proc.) 183 (10), 18–25 (1968).Google Scholar
76. Hemami, H., Weimer, F. C. and Koozekanani, S. H., “Some aspects of the inverted pendulum problem for modeling of locomotion systems,” IEEE Trans. Autom. Control. 18 (6), 658–661(1973).Google Scholar
77. Gubina, F., Hemami, H. and McGhee, R. B., “On the dynamic stability of biped locomotion,” IEEE Trans. Biomed. Eng. 21 (2), 102–108 (1974).CrossRefGoogle ScholarPubMed
78. McGeer, T., “Passive dynamic walking,” Int. J. Robot. Res. 9 (2), 62–82 (1990).Google Scholar
79. McGeer, T., “Passive Walking with Knees,” In: IEEE International Conference on Robotics and Automation, Cincinnati, USA, Vol. 3 (May 1990) pp. 1640–1645.Google Scholar
80. Coleman, M. J. and Ruina, A., “Uncontrolled walking toy that cannot stand still,” Phys. Rev. Lett. 80 (16), 3658–3661 (1998).Google Scholar
81. Hirai, K., Hirose, M., Haikawa, Y. and Takenaka, T., “The development of humanoid Honda robot,” In: IEEE International Conference on Robotics and Automation, Leuven, Belgium, Vol. 2 (May 1998) pp. 1321–1326.Google Scholar
82. Goswami, A., Espiau, B. and Keramane, A., “Limit cycle and their stability in a passive bipedal gait,” In: IEEE International Conference on Robotics and Automation, Minneapolis, MN, Vol. 1 (Apr. 1996) pp. 246–251.Google Scholar
83. Adolfsson, J., “Passive Control of Mechanical Systems; Bipedal Walking and Autobalancing,” PhD thesis (Royal Institute of Technology, Stockholm, Sweden, 2001).Google Scholar
84. Adolfsson, J., Dankowicz, H. and Nordmark, A., “3D passive walkers: Finding periodic gaits in the presence of discontinuities,” Nonlinear Dyn. 24 (2), 205–229 (2001).Google Scholar
85. Asano, F. and Yamakita, M., “Virtual gravity and coupling control for robotic gait synthesis,” IEEE Trans. Syst. Man Cybern. A 31 (6), 737–745 (2001).Google Scholar
86. Goswarni, A., Thuilot, E. and Espiau, B., “A study of the passive gait of a compass-like biped robot: Symmetry and chaos,” Intern. J. Robot. Res. 17 (12), 1282–1301 (1998).Google Scholar
87. Hurmuzlu, Y., “Dynamics of bipedal gait; part ii: Stability analysis of a planar five-link biped,” ASME J. Appl. Mech. 60 (2), 337–343 (1993).Google Scholar
88. Kuo, A. D., “Stabilization of lateral motion in passive dynamic walking,” Int. J. Robot. Res. 18 (9), 917–930 (1999).Google Scholar
89. Piiroinen, P. T., “Recurrent Dynamics of Nonsmooth Systems with Application to human Gait,” PhD thesis (Royal Institute of Technology, Stockholm, Sweden, 2002).Google Scholar
90. Spong, M. W. and Bullo, F., “Controlled symmetries and passive walking,” IEEE Trans. Autom. Control 50 (7), 1025–1031 (2005).CrossRefGoogle Scholar
91. Van Der Linde, R. Q., “Active leg compliance for passive walking,” In: Proceedings of IEEE International Conference on Robotics and Automation, Leuven, Belgium, Vol. 3 (May 1998) pp. 2339–2344.Google Scholar
92. Van Der Linde, R. Q., “Design, analysis, and control of a low power joint for walking robots, by phasic activation of McKibben muscles,” IEEE Trans. Robot. Autom. 15 (4), 599–604 (1999).Google Scholar
93. Van Der Linde, R. Q., “Passive bipedal walking with phasic muscle contraction,” Biol. Cybern. 81 (3), 227–237 (1999).Google Scholar
94. Hosoda, K., Takuma, T., Nakamoto, A. and Hayashi, S., “Biped robot design powered by antagonistic pneumatic actuators for multi-modal locomotion,” Robot. Auton. Syst. 56 (2008), 46–53 (2007).Google Scholar
95. Honda, “Humanoid robot,” available at: http://world.honda.com/ASIMO/ (accessed May 1, 2013).Google Scholar
96. Tajima, R., Honda, D. and Suga, K., “Fast Running Experiments Involving a Humanoid Robot,” In: IEEE International Conference on Robotics and Automation, Kone, Japan (May 2009) pp. 1571–1576.Google Scholar
97. Tajima, R. and Suga, K., “Motion having a flight phase: Experiments involving a one-legged robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China (Oct. 2006) pp. 1726–1731.Google Scholar
98. Löffler, K., Gienger, M. and Pfeiffer, F., “Sensor and Control Design of a Dynamically Stable Biped Robot,” In: IEEE International Conference on Robotics and Automation, Taipei, Taiwan, Vol. 1 (Sep. 2003) pp. 484–490.Google Scholar
99. Löffler, K., Gienger, M., Pfeiffer, F. and Ulbrich, H., “Sensors and control concept of a biped robot,” IEEE Trans. Ind. Electron. 51 (3), 972–980 (2004).Google Scholar
100. Chevallereau, C., Abba, A., Aoustin, Y., Plestan, F., Westervelt, E. R., C. Canudas-de-Wit and Grizzle, J. W., “RABBIT: A test bed for advanced control theory,” IEEE Control Syst. Mag. 23 (5), 57–79 (2003).Google Scholar
101. Tesio, L., Lanzi, D. and Detrembleur, C., “The 3-D motion of the centre of gravity of the human body during level walking. I. Normal subjects at low and intermediate walking speeds,” Clin. Biomech. 13 (2), 77–82 (1998).CrossRefGoogle ScholarPubMed
102. Collins, S., Ruina, A., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamics walkers,” Science 307 (5712), 1082–1085 (2005).Google Scholar
103. Forner-Cordero, A., Pons, J. L. and Wisse, M., “Basis for bioinspiration and biomechanism in wearable robots,” In: Wearable Robots: Biomechatronic Exoskeletons (Pons, J. L., ed.) (John Wiley, West Sussex, England, 2008).Google Scholar
104. Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19 (N5), 557–569 (2001).CrossRefGoogle Scholar
105. Westervelt, E. R. and Grizzle, J. W., “Design of asymptotically stable walking for a 5-link planar biped walker via optimization,” In: IEEE International Conference on Robotics and Automation, Washington, WA, Vol. 3 (May 2002) pp. 3117–3122.Google Scholar
106. Chevallereau, C., Fomal'sky, A. and Djoudi, D., “Tracking a joint path for the walk of under actuated biped,” Robotica 22 (1), 15–28 (2004).Google Scholar
107. Vukobraovic, M. and Juicic, D., “Contribution to the synthesis of biped gait,” IEEE Trans. Biomed. Eng. (BME) 16 (1), 1–6 (1969).Google Scholar
108. Azvedo, C., Espiau, B., Amblard, B. and Assaiante, C., “Bipedal locomotion: Towards unified concepts in robotics and neuroscience,” Biol. Cybern. 96 (2), 209–228 (2007).Google Scholar
109. Yin, Y. and Hosoe, S., “Mixed logic dynamical modeling and online optimal control of biped robot,” In: Humanoid Robots: Human-Like Machines (Hackel, Matthias, ed.) (Itech, Vienna, Austria, 2007) Chap. 16, pp. 315–328.Google Scholar
110. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K. and Hirukawa, H., “Biped walking pattern generation by using preview control of zero-moment point,” In: IEEE International Conference on Robotics & Automation, Taipei, Taiwan, Vol. 2 (Sep. 2003) pp. 1620–1626.Google Scholar
111. Azevedo, C., Poignet, P. and Espiau, B., “On Line Optimal Control for Biped Robots,” IFAC, 15th Triennial World Congress, Barcelona, Spain (2002).Google Scholar
112. Wieber, P. -B., “Trajectory-Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations,” In: IEEE-RAS International Conference on Humanoid Robots, Genova, Italy (Dec. 2006) pp. 137–142.Google Scholar
113. Zheng, Y. F., “A neural gait synthesizer for autonomous biped robots,” In: IEEE International Workshop on Intelligent Robots and Systems (IROS'90), Ibaraki, Japan, Vol. 2 (Jul. 1990) pp. 601–608.Google Scholar
114. Sugihara, T., “Mobility Enhancement Control of Humanoid Robot Based on Reaction Force Manipulator via Whole Body Motion,” PhD thesis (University of Tokyo, Tokyo, Japan, 2004).Google Scholar
115. Yüksel, B., “Towards the Enhancement of the Biped Locomotion and Control Techniques,” PhD thesis (Middle East Technical University, Turkey, 2008).Google Scholar
116. Zarrugh, M. Y. and Radcliffe, C. W., “Computer generation of human gait kinematics,” J. Biomech. 12 (2), 99–111 (1979).CrossRefGoogle ScholarPubMed
117. Dasgupta, A. and Nakamura, Y., “Making Feasible Walking Motion of Humanoid Robots from Human Motion Capture Data,” In: IEEE International Conference on Robotics & Automation, Detroit, USA, Vol. 2 (May 1999) pp. 1044–1049.Google Scholar
118. Cheng, I. S., Koozekanani, S. H. and Fatebi, M.T., “A simple computer-television interface system for gait analysis,” IEEE Trans. Biomed. Eng. (BME) 22 (3), 259–260 (1975).Google Scholar
119. Hemami, H. and Farnsworth, R. L., “Postural and gait stability of a planar five link biped by simulation,” IEEE Trans. Autom. Control 22 (3), 452–458 (1976).Google Scholar
120. Juang, J. -G. and Lin, C.-S., “Gait Synthesis of a Biped Robot Using Backpropagation Through Time Algorithms,” IEEE International Conference on Neural Networks, Washington, DC, Vol. 3 (Jun 1996) pp. 710–715.Google Scholar
121. Kurematsu, Y., Kitarnura, S. and Kondo, Y., “Trajectory planning and control of a biped locomotive robot-simulation and experiment,” In: Robotics and Manufacturing, Recent Trends in Research, Education and Applications, Vol. 2 (Jamshidi, M., ed.) (ASME Press, New York, NY, 1988) pp. 65–72.Google Scholar
122. Koivo, A. J., Fundamentals for Control of Robotic Manipulators (John Wiley, New York, NY, 1989).Google Scholar
123. Brotman, L. S. and Netravali, A.N., “Motion interpolation by optimal control,” Comput. Graph. 22 (4), 309–315 (1988).Google Scholar
124. Shih, C. L., “Gait synthesis for a biped robot,” Robotica 15, 599–607 (1997).Google Scholar
125. Mu, X. and Wu, Q., “Synthesis of a complete Sagittal cycle for a five-link biped robot,” Robotica 21, 581–587 (2003).Google Scholar
126. Kajita, S. and Tani, K., “Experimental Study of Biped Dynamic Walking in the Linear Inverted Pendulum Mode,” In: IEEE International Conference on Robotics and Automation, Nagoya, Japan, Vol. 3 (May 1995) pp. 2885–2891.Google Scholar
127. Kajita, S. and Tani, K., “Experimental study of biped dynamic walking,” IEEE Control Syst. 16 (1), 13–19 (1996).Google Scholar
128. Miura, H. and Shimoyama, I., “Dynamic walk of a biped,” Int. J. Robot. Res. 3 (2), 60–74 (1984).Google Scholar
129. Kajita, S., Yamaura, T. and Kobayashi, A., “Dynamic walking control of a biped robot along a potential conserving orbit,” IEEE Trans. Robot. Autom. 8 (4), 431–438 (1992).Google Scholar
130. Shibuya, M., Suzuki, T. and Ohnishi, K., “Trajectory Planning of Biped Robot Using Linear Pendulum Mode for Double Support Phase,” In: Proceedings of the 32nd Annual IEEE Industrial Electronics Conference (IECON 2006) (2006) pp. 4094–4099.Google Scholar
131. Kudoh, S. and Komura, T., “C2 Continuous Gait-Pattern Generation for Biped Robots,” In: Proceedings of 2003 IEEE/RSJ Intelligent Robots and Systems Conference, Vol. 2 (2003) pp. 1135–1140.Google Scholar
132. Al-Shuka, H. F. N. and Corves, B., “On the walking pattern generators of biped robot,” J. Autom. Control (JOACE) 1 (2), 149–155 (2013).Google Scholar
133. Albert, A. and Gerth, W., “Analytic path planning algorithms for bipedal robots without a trunk,” J. Intell. Robot. Syst. 36 (2), 109–127 (2003).Google Scholar
134. Takanishi, A., Tochizawa, M., Karaki, H. and Kato, I., “Dynamic Biped Walking Stabilized with Optimal Trunk and Waist Motion,” In: IEEE/RSJ International Workshop on Intelligent Robots and Systems, Tsukuba, Japan (Sep. 1989) pp. 187–192.Google Scholar
135. Ha, T. and Choi, Chong-Ho, “An effective trajectory generation method for bipedal walking,” Robot. Auton. Syst. 55 (10), 795–810 (2007).Google Scholar
136. Betts, J. T., “Survey of numerical methods for trajectory optimization,” J. Guid. Control Dyn. 21 (2), 193–207 (1998).CrossRefGoogle Scholar
137. Al-Shuka, H. F. N., Corves, B. and Zhu, W.-H, “On the dynamic optimization of biped robot,” Lecture Notes Softw. Eng. 1 (3), 237–243 (2013).Google Scholar
138. Robinett, R. D. III, Wilson, D. G., Eislerand, G. R. and Hurtado, H. E., Applied Dynamic Programming for Optimization of Dynamical Systems (SIAM, Philadelphia, PA, 2005).Google Scholar
139. Pandy, M. G., Anderson, F. C. and Hull, D. G., “A parameter optimization approach for the optimal control of large-scale musculoskeletal,” J. Biomech. Eng. 114 (4), 450–460 (1992).Google Scholar
140. Diehl, M., Numerical Optimal Control, lecture notes (Optimization in Engineering Center (OPTEC) and Electrical Engineering Department (ESAT), KU Leuven, Belgium, 2011).Google Scholar
141. Seguin, P. and Bessonnet, G., “Generating optimal walking cycles using spline-base state parameterization,” Int. J. Hum. Robot. 2 (1), 47–80 (2005).Google Scholar
142. Rostami, M. and Bessonnet, G., “Sagittal gait of a biped robot during the single support phase. Part 2: Optimal motion,” Robotica 19, 241–253 (2001).Google Scholar
143. Bessonnet, G., Chesse, S. and Sardain, P., “Generating optimal gait of a human-sized biped robot,” In: The 5th International Conference Climbing and Walking Robots, Paris (2002) pp. 241–253.Google Scholar
144. Hull, D. G., Conversion of Optimal Control Problems into Parameter Optimization Problems (AIAA, Guidance, Navigation and Control Performance, San Diego, 1996).Google Scholar
145. Goh, C. J. and Teo, K. L., “Control parameterization, a unified approach to optimal problem with general constraints,” Automatica 24 (1), 3–18 (1988).Google Scholar
146. Matsuoka, K., “Mechanisms of frequency and pattern control in the neural rhythm generators,” Biol. Cybern. 56, 345–353(1987).CrossRefGoogle ScholarPubMed
147. Zielinska, T., “Coupled oscillators utilized as gait rhythm generators of a two-legged walking machine,” Biol. Cybern. 74 (3), 263–273 (1996).Google Scholar
148. Yang, W., Chong, N. Y., Ra, S., Kim, C. H., You, B. J., “Self-Stabilizing Biped Locomotion Employing Neural Oscillators,” In: IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea (Dec. 2008) pp. 8–15.Google Scholar
149. Kai, F., “Biologically Inspired Locomotion Control of Bipedal Robot,” MSc thesis (National University of Singapore, 2006).Google Scholar
150. Jalics, L., Hemami, H. and Zheng, Yuan F., “Pattern generation using coupled oscillators for robotic and biorobotic adaptive periodic movement,” In: IEEE Conference on Robotics and Automation, Albuquerque, NM, Vol. 1 (Apr. 1997) pp. 179–184.Google Scholar
151. Kurematsu, Y., Maeda, T. and Kitamura, S., “Autonomous trajectory generation of a biped locomotive robot using neuro oscillator,” In: IEEE International Conference on Neural Networks, San Francisco, CA, Vol. 3 (Apr. 1993) pp. 1961–1966.Google Scholar
152. Yang, W., Chong, N. Y. and You, B. -J., “Biologically inspired robotic system control: Multi-DOF robotic arm control,” ISBN: 978-3-639-23071-0, VDM Verlag Dr. Müller, Germany, 2010.Google Scholar
153. Ijspeert, A. J., “Central pattern generators for locomotion control in animals and robots: A review,” Neural Netw. 21, 642–653 (2008).Google Scholar
154. Katic, D. and Vukobratovic, M., “Survey of intelligent control techniques for humanoid robots,” J. Intell. Robot. Syst. 37 (2), 117–141 (2003).Google Scholar
155. Collins, S. H., Wisse, M. and Ruina, A., “A 3-D passive-dynamic walking robot with two legs and knees,” Int. J. Robot. Res. 20 (7), 607–615 (2001).CrossRefGoogle Scholar
156. Collins, S. H. and Ruina, A. (2005), “A Bipedal Walking Robot with Efficient and Human-Like Gait,” In: IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005) pp. 1983–1988.Google Scholar
157. Wisse, M., Feliksdal, G., Van Frankkenhuyzen, J. and Moyer, B., “Passive-based walking robot,” IEEE Robot. Autom. Mag. 14 (2), 52–62 (2007).Google Scholar
158. Pratt, J. E. and Pratt, G.A., “Exploiting Natural Dynamics in the Control of a Planar Bipedal Walking Robot,” Proceedings of the Thirty-Sixth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois (Sep. 1998).Google Scholar
159. Pratt, J. E. and Pratt, G.A., “Exploiting Natural Dynamics in the Control of a 3D Bipedal Walking, Simulation,” International Conference on Climbing and Walking Robots (CLAWAR99), Portsmouth, UK (1999).Google Scholar
160. Pratt, J., Dilworth, P. and Pratt, G., “Virtual Model Control of a Bipedal Walking Robot,” In: IEEE International Conference on Robotics and Automation, Albuquerque, NM, Vol. 1 (Apr 1997) pp. 193–198.Google Scholar
161. Pratt, J. and Pratt, G., “Intuitive Control of a Planar Bipedal Walking Robot,” In: IEEE International Conference on Robotics and Automation, Leuven, Belgium, Vol. 3 (May 1998) pp. 2014–2021.Google Scholar
162. Pratt, J., Chew, C., Torres, A., Dilworth, P. and Pratt, G., “Virtual model control: An intuitive approach for bipedal locomotion,” Int. J. Robot. Res. 20 (2), 129–143 (Feb. 2001).Google Scholar
Hun-ok Lim and Takanishi, A., “Biped walking robots created at Waseda University: WL and WABIAN family,” Phil. Trans. R. Soc. A. 365 (1850), 49–64 (2007).Google Scholar
164. McGeer, T., “Powered Flight, Child's Play, Silly Wheels and Walking Machines,” In: IEEE International Conference on Robotics and Automation, Scottsdale, AZ, Vol. 3 (May 1989) pp. 1592–1597.Google Scholar
165. Hirai, K., “Current and Future Perspective of Honda Humanoid,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Grenoble (Sep. 1997) pp. 500–508.Google Scholar
166. Hirai, K., “The Honda humanoid robot: Development and future perspective” Ind. Robot 26 (4), 260–266 (1999).Google Scholar
167. Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N. and Fujimura, K., “The Intelligent ASIMO: System Overview and Integration,” In: IEEE/RSJ International Conference on Intelligent Robots and System (IROS 2002), Vol. 3 (2002) pp. 2478–2483.Google Scholar
168. Ogura, Y., Aikawa, H., Shimomura, K., Morishima, A., Hon-ok Lim and Takanishi, A., “Development of a new humanoid robot WABIAN-2,” In: IEEE International Conference on Robotics and Autonomous, Orlando, FL (May 2006) pp. 76–81.Google Scholar
169. Setiawan, S. A., Yamaguchi, J., Hyon, Sang-Ho and Takanishi, A., “Physical Interaction Between Human and a Bipedal Humanoid Robot-Realization Of Human-Fellow Walking,” In: IEEE International Conference on Robotics and Automation, Detroit, MI, Vol. 1 (May 1999) pp. 361–367.Google Scholar
Hun-ok Lim, Ishii, A. and Takanishi, A., “Emotion Expression of Biped Personal Robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Takamatsu, Vol. 1 (Nov 2000) pp. 191–196.Google Scholar
171. Miwa, H., Okuchi, T., Takanobu, H. and Takanishi, A., “Development of a New Human-Like Head Robot WE-4,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, Vol. 3 (Oct. 2002) pp. 2443–2448.Google Scholar
172. Zecca, M., Endo, N., Momoki, S., Itoh, K. and Takanishi, A., “Design of the Humanoid Robot KOBIAN – Preliminary Analysis of Facial and Whole Body Emotion Capabilities,” In: IEEE-RAS International Conference on Humanoids, Daejeon, Korea (Dec. 2008) pp. 487–492.Google Scholar
173. Zecca, M., Mizoguchi, Y., Endo, K., Lida, F., Kawabata, Y., Endo, N., Itoh, K. and Takanishi, A., “Whole Body Emotion Expressions for Kobian Humanoid Robot-Preliminary Experiments with Different Emotional Patterns,” In: IEEE International Symposium on Robot and Human Interactive Communication, Toyama, Japan (Sep. 2009) pp. 381–386.Google Scholar
174. Pratt, J. E., “Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots,” PhD thesis (MIT, Cambridge, MA, 2000).Google Scholar
175. Pratt, J., Torres, A., Dilworth, P. and Pratt, G., “Virtual Actuator Control,” In: Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS'96), Osaka, Japan, Vol. 3 (Nov. 1996) pp. 1219–1226.Google Scholar
176. Pratt, G. A. and Williamson, M. M., “Series Elastic Actuator,” In: IEEE/RSJ International Conference on Cooperative Robots, Pittsburgh, PA, Vol. 1 (Aug 1995) pp. 399–406.Google Scholar
177. Partt, G. A., Williamson, M. M., Dillworth, P., Pratt, J. and Wright, A., “Stiffness Isn't Everything,” In: Experimental Robotics IV, Lecture Notes in Control and Information Science, Vol. 223 (Springer-Verlag, Berlin, Germany, 1997) pp. 253–262.Google Scholar
178. Westervelt, E. R., Grizzle, J. W. and Koditschek, D. E., “Hybrid zero dynamics of planar biped walkers,” IEEE Trans. Autom. Control 48 (1), 42–56 (2003).Google Scholar
179. Canudas-de-Wit, C., “On the concept of virtual constraints as a tool for walking robot control and balancing,” Annu. Rev. Control 28 (2), 157–166 (2004).Google Scholar
180. Kuroki, Y., Blank, B., Mikami, T., Mayeux, P., Miyamoto, A., Playter, R., Nagasaka, K., Raibert, M., Nagano, M. and Yamaguchi, J., “Motion creating system for a small biped entertainment robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, Nevada, Vol. 2 (Oct. 2003) pp. 1394–1399.Google Scholar
181. Ishida, T., Kuroki, Y., Yamaguchi, J., Fujita, M. and Doi, T. T., “Motion Entertainment by a Small Humanoid Robot Based on Open-R,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, USA, Vol. 2 (Nov. 2001) pp. 1079–1086.Google Scholar
182. Ishida, T., Kuroki, Y. and Yamaguchi, J., “Mechanical Systems of a Small Biped Entertainment Robot,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Las Vegas, Nevada, Vol. 2 (Oct. 2003) pp. 1129–1134.Google Scholar
183. Ishida, T., “Development of a Small Biped Entertainment Robot Qrio,” In: Proceedings of the International Symposium on Micro-Nanomechatronics and Human Science (2004) pp. 23–28.Google Scholar
184. Kuroki, Y., “A Small Biped Entertainment Robot,” In: IEEE International Symposium on Micromechatronics and Human Science, Nagoya, Japan (Sep. 2001) pp. 3–4.Google Scholar
185. Endo, G., Nakanishi, J., Morimoto, J. and Cheng, G., “Experimental Studies of a Neural Oscillator for Biped Locomotion with QRIO,” In: Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005) pp. 596–602.Google Scholar
186. Kuroki, Y., Fujita, M., Ishida, T. and Nagasaka, K., “A Small Biped Entertainment Robot Exploring Attractive Applications,” In: IEEE International Conference on Robotics and Automation, Taipei, Taiwan, Vol. 1 (Sep. 2003) pp. 471–476.Google Scholar
187. Suleiman, W., Kanehiro, F., Miura, K., Yoshida, E., “Improving ZMP-Based Control Model Using System Identification Technique,” In: IEEE-RAS International Conference on Humanoid Robots, Paris (Dec. 2009) pp. 74–90.Google Scholar
188. Miura, K., Morisawa, M., Nakaoka, S., Kanehiro, F., Harada, K., Kaneko, K. and Kajita, S., “Robot Motion Remix Based on Motion Capture Data Towards Human-Like Locomotion Of Humanoid Robots,” In: IEEE-RAS International Conference on Humanoid Robots, Paris (Dec. 2009) pp. 596–603.Google Scholar
189. Kaneko, K., Kanehiro, F., Morisawa, M., Tsuji, T., Miura, K., Nakaoka, S., Kajita, S. and Yokoi, K., “Hardware Improvement of Cybernetic Human HRP-4C for Entertainment Use,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), San Francisco, CA (Sep. 2011) pp. 4392–4399.Google Scholar
190. Kaneko, K., Kanehiro, F., Morisawa, M., Miura, K., Nakaoka, S. and Kajita, S., “Cybernetic Human HRP-4C. In: IEEE-RAS International Conference on Humanoid Robots (Humanoids 2009), Paris (Dec. 2009) pp. 7–14.Google Scholar
191. Miura, K., Kanehiro, F., Kaneko, K., Kajita, S. and Yokoi, K., “Quick Slip-Turn of HRP-4C on Its Toes,” In: IEEE International Conference on Robotics and Automation, Saint Paul, MN (May 2012) pp. 3527–3528.Google Scholar
192. Kaneko, K., Kanehiro, F., Kajita, S., Yokoyama, K., Akachi, K., Kawasaki, T., Ota, S. and Isozumi, T., “Design of Prototype Humanoid Robotics Platform for HRP,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, Vol. 3 (Oct. 2002) pp. 2431–2436.Google Scholar
193. Kaneko, K., Kanehiro, F., Kajita, S., Hirukawa, H., Kawasaki, T., Hirata, M., Akachi, K. and Isozumi, T., “Humanoid Robot HRP-2,” In: IEEE International Conference on Robotics and Automation, New Orleans, Vol. 2 (May 2004) pp. 1083–1090.Google Scholar
194. Kanchira, N., Kawasaki, T., Ohta, S., Ismumi, T., Kawada, T., Kanehiro, F., Kajita, S. and Kaneko, K., “Design and Experiments of Advanced Leg Module (HRP-2L) for Humanoid Robot (HRP-2) Development,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, Vol. 3 (Oct. 2002) pp. 2455–2460.Google Scholar
195. Kanehiro, F., Kaneko, K., Fujiwara, K., Kajita, S., Yokoi, K., Hirukawa, H., Akachi, K. and Isozumi, T., “The First Humanoid Robot that Has the Same Size as a Human and that Can Lie Down and Get Up,” In: IEEE International Conference on Robotics and Automation, Taipei, Taiwan, Vol. 2 (Sep. 2003) pp. 1633–1639.Google Scholar
196. Kaneko, K., Harada, K., Kanehiro, F., Miyamori, G. and Akachi, K., “Humanoid Robot HRP-3,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France (Sep. 2008) pp. 2471–2478.Google Scholar
197. Kaneko, K., Kanehiro, F., Morisawa, M., Akachi, K., Miyamori, G., Hayashi, A. and Kanehira, N., “Humanoid Robot HRP-4-Humanoid Robotics Platform with Lightweight and Slim Body,” In: IEEE/RSJ International Conference on IROS, San Francisco, CA (Sep. 2011) pp. 4400–4407.Google Scholar
198. Sugahara, Y., Endo, T., Lim, H. and Takanishi, A., “Design of a Battery-Powered Multi-Purpose Bipedal Locomotor with Parallel Mechanism,” In: Proceedings IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland (Oct. 2002) pp. 2658–2663.Google Scholar
199. Sugahara, Y., Hosobata, H., Mikuriya, Y. and Takanishi, A., “Control and Experiments of a Multi-Purpose Bipedal Locomotor with Parallel Mechanism,” In: Proceedings of IEEE International Conference on Robotics and Automation, Taipei, Taiwan (Sep. 2003) pp. 4342–4347.Google Scholar
200. Garcia, M., Chatterjee, A., Ruina, A. and Coleman, M. J., “The simplest walking model: Stability, complexity, and scaling,” ASME J. Biomech. Eng. 120 (2), 281–288 (April 1998).Google Scholar
201. Wisse, M. and van Frankenhuyzen, J., “Design and construction of MIKE; 2D autonomous biped based on passive dynamic walking,” In: Adaptive Motion of Animals and Machines (Kimura, H. and Tsuchiya, K., eds.) (Springer-Verlag, Tokyo, 2006) pp. 143–154.Google Scholar
202. Tedrake, R., Zhang, T. W., Fong, Ming-Fai and Seung, H. S., “Actuating a Simple 3D Passive Dynamic Walker,” In: IEEE International Conference on Robotics and Automation, New Orleans, LA, Vol. 5 (Apr. 2004) pp. 4656–4661.Google Scholar
203. Tedrake, R., Zhang, T. W. and Seung, H. S., “Stochastic Policy Gradient Reinforcement Learning on a Simple 3D Biped,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, Vol. 3 (Sep. 2004) pp. 2849–2854.Google Scholar
204. Anderson, S. O., Wisse, M., Atkeson, C. G., Hodgins, J. K., Zeglin, G. J. and Moyer, B., “Powered Bipeds Based on Passive Dynamic Principles,” In: IEEE-RAS International Conference on Humanoid Robots (2005) pp. 110–116.Google Scholar
205. Wisse, M., “Three Additions to Passive Dynamic Walking; Actuation, an Upper Body, and 3D Stability,” In: IEEE International Conference on Humanoid Robots, Vol. 1 (Nov. 2004) pp. 113–132.Google Scholar
206. Kim, J.-H and Oh, J.-H, “Realization of dynamic walking for the humanoid robot platform KHR-1,” Adv. Robot. 18 (2004) pp.749–768.Google Scholar
207. Kim, J.-H and Oh, J.-H, “Walking Control of the Humanoid Platform KHR-1 Based on Torque Feedback Control,” In: IEEE International Conference on Robotics and Automation, New Orleans (Apr. 2004) pp. 623–628.Google Scholar
208. Kim, J.-Y, Park, I.-W and Oh, J.-H, “Design and Walking Control of the Humanoid Robot, KHR-2 (KAIST Humanoid Robot-2),” In: Proceedings of International Conference on Control, Automation and Systems (Nov. 2004) pp. 1540–1543.Google Scholar
209. Kim, J.-Y., Park, I.-W., Lee, J., Kim, M.-S, Cho, B.-K and Oh, J.-H, “System Design and Dynamic Walking of Humanoid Robot KHR-2,” In: Proceedings of IEEE International Conference on Robotics and Automation, Barcelona, Spain (Apr. 2005) pp. 1431–1436.Google Scholar
210. Park, I.-W., Kim, J.-Y, Park, S.-W and Oh, J.-H, “Development of Humanoid Robot Platform KHR-2 (KAIST Humanoid Robot 2),” In: IEEE/RAS International Conference Humanoid Robots, Vol. 1 (Nov. 2004) pp. 292–310.Google Scholar
211. Kim, J.-Y, Lee, J. and J.-H Oh, “Experimental realization of dynamic walking for a human-riding biped robot, HUBO FX-1,” Adv. Robot. 21 (3), 461–482 (2007).Google Scholar
212. Park, I.-W, Kim, J.-Y, Lee, J. and Oh, J.-H, “Mechanical Design of Humanoid Robot Platform KHR-3 (KAIST Humanoid Robot-3: HUBO),” In: IEEE-RAS International Conference on Humanoid Robots, Tsukuba, Japan (Dec. 2005) pp. 321–326.Google Scholar
213. Park, I.-W, Kim, J.-Y., Lee, J. and Oh, J.-H, “Online Free Walking Trajectory Generation for Biped Humanoid Robot KHR-3 (HUBO),” In: Proceedings of IEEE International Conference on Robotics and Automation, Orlando, FL (May 2006) pp. 1231–1236.Google Scholar
214. Lee, J., Kim, J.-Y., Park, I.-W., Cho, B.-K., Kim, M.-S., Kim, I. and Oh, J.-H., “Development of a Humanoid Robot Platform HUBO FX-1,” In: SICE-ICASE International Joint Conference, Busan, Korea (Oct. 2006) pp. 1190–1194.Google Scholar
215. Peng, Z., Huang, Q., Chen, X., Zhao, W., Xiao, T. and Li, K., “Online Trajectory Generation Based on Off-Line Trajectory for Biped Humanoid,” In: IEEE International Conference on Robotics and Biomimetics, Shenyang, China (Aug. 2009) pp. 752–756.Google Scholar
216. Xiao, T., Huang, Q., Li, J., Zhang, W. and Li, K., “Trajectory Calculation and Gait Change Online for Humanoid Teleoperation,” In: IEEE International Conference on Mechatronics and Automation, Luoyang, China (Jun 2006) pp. 1614–1619.Google Scholar
217. Lohmeier, S., Buschmann, T., Ulbrich, H. and Pfeiffer, F., “Modular Joint Design for Performance Enhanced Humanoid Robot LOLA,” In: IEEE International Conference on Robotics and Automation (ICRA 2006), Orlando, FL (May 2004) pp. 88–93.Google Scholar
218. Monje, C. A., Pierro, P. and Balaguer, C., “Pose Control of the Humanoid Robot RH-1 for Mobile Manipulation,” In: IEEE International Conference on Advanced Robotics (ICAR), Munich, Germany (Jun 2009) pp. 1–6.Google Scholar
219. Arbulu, M., Kaynor, D. and Balaguer, C., “The Rh-1 full-size humanoid robot: Control system design and walking pattern generation,” In: Climbing and Walking Robots (Miripour, B., ed.) (InTech, Rijeka, Croatia, 2010), Chap. 26, pp. 446–508.Google Scholar
220. Arbulu, M. and Balaguer, C., “Real-Time Gait Planning for Rh-1 Humanoid Robot Using Local Axis Gait Algorithm,” In: IEEE-RAS International Conference on Humanoid Robots, Pittsburgh, PA (Nov. 2007) pp. 563–568.Google Scholar
221. Sardain, P., Rostami, M. and Bessonnet, G., “An anthropomorphic biped robot, dynamic concepts and technological design,” IEEE Trans. Syst. Man Cybern. 28 (6), 823–838 (1998).Google Scholar
222. Espiau, B. and the BIP Team, “BIP: A Joint Project for the Development of an Anthropomorphic Biped Robot,” In: IEEE International Conference on Advanced Robotics, Monterey, CA (Jul. 1997) pp. 267–272.Google Scholar
223. Sardain, P., Rostami, M., Thomas, E. and Bessonnet, G., “Biped robots: Correlation between technological design and dynamic behavior,” Control Eng. Pract. 7 (3) (1999) pp. 401–411.Google Scholar
224. Azevedo, C., Poignet, P. and Espiau, B., “Artificial locomotion control: From human to robots,” Robot. Auton. Syst. 47 (4), 203–223 (2004).Google Scholar
225. Azedvedo, C., Andreff, N., Arias, S. and Espiau, B., “Experimental BIPedal walking,” In: Experimental Robotics VIII, Springer Tracts in Advanced Robotics, Vol. 5 (Siciliano, B. and Dario, P., eds.) (Springer, New York, NY, 2003) pp. 582–591.Google Scholar
226. Azevedo, C. and the BIP Team, “Control Architecture and Algorithms of the Anthropomorphic Biped Robot Bip2000,” In: Proceedings International Conference of Climbing and Walking Robots (2000) pp. 285–293.Google Scholar
227. Azevedo, C., Andreff, N. and Arias, S., “BIPedal walking: From gait design to experimental analysis,” Mechatroncis 14 (6), 639–665 (2004).Google Scholar
228. Espiau, B. and Sardain, P., “The Anthropomorphic Biped Robot BIP2000,” In: IEEE International Conference on Robotics and Automation, San Francisco, CA, Vol. 4 (Apr. 2000) pp. 3996–4001.Google Scholar
229. Olaru, I. M. C., Krut, S. and Pierrot, F., “Novel Mechanical Design of Biped Robot SHERPA Using 2 DOF Cable Differential Modular Joints,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO (Oct. 2009) pp. 4463–4468.Google Scholar
230. Gouaillier, D., Hugel, V., Blazevic, P., Kilner, C., Monceaux, J., Lafourcade, P., Marnier, B., Serre, J. and Maisonnier, B., “Mechatronics Design of NAO Humanoid,” In: IEEE International Conference on Robotics and Automation, Kobe, Japan (May 2009) pp. 769–774.Google Scholar
231. Gouaillier, D., Collette, C. and Kilner, C., “Omni-Directional Closed-Loop Walk for NAO,” In: IEEE-RAS International Conference on Humanoid Robots (Humanoids), Nashville, TN (Dec. 2010) pp. 448–454.Google Scholar
232. Hemker, T., Sakamoto, H., Stelzer, M. and von Stryk, O., “Hardware-in-the-Loop Optimization of the Walking Speed of a Humanoid Robot,” 9th International Conference on Climbing and Walking Robots (CLAWAR) (2006).Google Scholar
233. Hemker, T., Stelzer, M., von stryk, O. and Sakamoto, H., “Efficient walking speed optimization of a humanoid robot,” Int. J. Robot. Res. 28 (2), 303–314 (2009).Google Scholar
234. Tawara, T., Okumura, Y., Furuta, T., Shimizu, M., Simomura, M., Endo, K. and Kitano, H., “Morph: A desktop-class humanoid capable of acrobatic behavior,” Int. J. Robot. Res. 23 (10–11), 1097–1103 (2004).Google Scholar
235. Yamasaki, F., Matsui, T., Miyashita, T. and Kitno, H., “PINO the humanoid: A basic architecture,” In: RobotCup 2000 (Stone, P., Balch, T. and Kraetzschmar, K., eds.), LNAI 2019 (Springer-Verlag, Berlin, Germany, 2001) pp. 269–278.Google Scholar
236. Yamasaki, F., Endo, K., Asada, M. and Kitano, H., “A control method for humanoid biped walking with limited torque,” In: RoboCup 2001 (Birk, A., Coradesch, S. and Tadokoro, S., eds) LNAI 2377 (Springer-Verlag, Berlin, Germany, 2002) pp. 60–70.Google Scholar
237. Behnke, S., Mueller, J. and Schreiber, M., “Toni: A soccer playing humanoid robot,” In: RoboCup (Bredenfeld, A. et al., eds.) LNAI 4020 (Springer-Verlag, Berlin, Germany, 2006) pp. 59–70.Google Scholar
238. Behnke, S., “Online Trajectory Generation for Omnidirectional Biped Walking,” In: IEEE International Conference on Robotics and Automation, Orlando, FL (May 2006) pp. 1597–1603.Google Scholar
239. Behnke, S. and Rojas, R., “A hierarchy of reactive behaviors handles complexity,” In: Reactivity and Deliberation in MAS (Hannebauer, M. et al., eds.) LNAI 2103 (Springer-Verlag, Berlin, Germany, 2001) pp. 125–136.Google Scholar
240. Yang, H.-S., Seo, Y.-H, Chae, Y.-N., Jeong, I.-W., Kang, W.-H and Lee, J.-H, “Design and Development of Biped Humanoid Robot AMI2 for Social Interaction with Humans,” In: IEEE-RAS International Conference on Humanoid Robots, Genova, Italy (Dec. 2006) pp. 352–357.Google Scholar
241. Montes, H., Pedraza, L., Armada, M. and Akinfier, T., “Force feedback control implementation for smart nonlinear actuator,” In: Climbing and Walking Robots (Armada, M. A. and de Santos, P. G., eds.) (Springer-Verlag Berlin Heidelberg, 2005) pp. 625–631.Google Scholar
242. Caballero, R., Armada, M. A. and Alarcon, P., “Methodology for zero-moment point experimental modeling in the frequency domain,” J. Vib. Control 12 (2), 1385–1406 (2006).Google Scholar
243. Caballero, R. and Armada, M. A., “Dynamic State Feedback for Zero Moment Point Biped Robot Stabilization,” In: IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, CA (Oct. 2007) pp. 4041–4046.Google Scholar
244. Tellez, R., Ferro, F., Garcia, S., Gomez, E., Jorge, E., Moru, D., Pinyol, D., Oliver, J., Torres, O., Velzquez, J. and Faconti, D., “Reem-B: An Autonomous Light Weight Human-Size Humanoid Robot,” In: IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea (Dec 2008) pp. 462–468.Google Scholar