Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-25T02:22:17.395Z Has data issue: false hasContentIssue false

Multi-level control of zero-moment point-based humanoid biped robots: a review

Published online by Cambridge University Press:  24 February 2015

Hayder F. N. Al-Shuka*
Affiliation:
Department of Mechanical Engineering, Baghdad University, Baghdad, Iraq Department of Mechanism Theory and Machine Dynamics, RWTH Aachen University, Germany
B. Corves
Affiliation:
Department of Mechanism Theory and Machine Dynamics, RWTH Aachen University, Germany
Wen-Hong Zhu
Affiliation:
Canadian Space Agency, Canada
B. Vanderborght
Affiliation:
Department of Mechanical Engineering, Vrije Universiteit, Brussels, Belgium
*
*Corresponding author. E-mail: [email protected]

Summary

Researchers dream of developing autonomous humanoid robots which behave/walk like a human being. Biped robots, although complex, have the greatest potential for use in human-centred environments such as the home or office. Studying biped robots is also important for understanding human locomotion and improving control strategies for prosthetic and orthotic limbs. Control systems of humans walking in cluttered environments are complex, however, and may involve multiple local controllers and commands from the cerebellum. Although biped robots have been of interest over the last four decades, no unified stability/balance criterion adopted for stabilization of miscellaneous walking/running modes of biped robots has so far been available. The literature is scattered and it is difficult to construct a unified background for the balance strategies of biped motion. The zero-moment point (ZMP) criterion, however, is a conservative indicator of stabilized motion for a class of biped robots. Therefore, we offer a systematic presentation of multi-level balance controllers for stabilization and balance recovery of ZMP-based humanoid robots.

Type
Survey or Review
Copyright
Copyright © Cambridge University Press 2015 

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, (Mar. 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), 17531767 (2012).Google Scholar
3. Bekey, G. A., Autonomous Robots: From Biological Inspiration to Implementation and Control (MIT Press, USA, 2005).Google Scholar
4. Hashimoto, K., Sugahara, Y., Sunazuka, H., Tanaka, C., Ohata, A., Kawase, M., Lim, H.-O. and Takanishi, A., “Biped Landing Pattern Modification Method with Nonlinear Compliance Control,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA 2006), Orlando, FL, pp. 1213–1218 (May, 2006).Google Scholar
5. Hashimoto, K., Hayashi, A., Sawato, T., Yoshimura, Y., Asano, T., Hattori, K., Sugahara, Y., Lim, H.-O. and Takanishi, A., “Terrain-Adaptive Control to Reduce Landing Impact Force for Human-Carrying Biped Robot,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM 2009), Singapore, pp. 174–179 (Jul. 2009).Google Scholar
6. Hashimoto, K., Sawato, T., Hayashi, A., Yoshimura, Y., Asano, T., Hattori, K., Sugahara, Y., Lim, H.-O. and Takanishi, A., “Static and Dynamic Disturbance Compensation Control for a Biped Walking Vehicle,” Proceedings of the 2nd Biennial IEEE RAS/EMBS International Conference on Biomedical Robotics and Biomechatronics, AZ, USA, pp. 457–462 (Oct. 2008).Google Scholar
7. Hashimoto, K., Sugahara, Y., Tanaka, C., Ohta, A., Hattori, K., Sawato, T., Hayashi, A., Lim, H.-O. and Takanishi, A., “Unknown Disturbance Compensation Control for a Biped Walking Vehicle,” Proceedings of the 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, USA, pp. 2204–2209 (2007).CrossRefGoogle Scholar
8. Sugahara, Y., Hashimoto, K., Endo, N., Sawato, T., Kawase, M., Ohta, A., Tanaka, C., Hayashi, A., Lim, H.-O. and Takanishi, A., “Development of a Biped Locomotor with the Double Stage Linear Actuator,” Proceedings of the 2007 IEEE International Conference on Robotics and Automation, Roma, Italy, pp. 1850–1855 (Apr. 2007).Google Scholar
9. Hashimoto, K., Sugahara, Y., Hayashi, A., Kawase, M., Sawato, T., Endo, N., Ohta, A., Tanaka, C., Lim, H.-O. and Takanishi, A., “New Foot System Adaptable to Convex and Concave Surface,” Proceedings of the 2007 IEEE International Conference on Robotics and Automation, Roma, Italy, pp. 1869–1874 (2007).Google Scholar
10. Sugahara, Y., Endo, T., Lim, H.-O. and Takanishi, A., “Design of a Battery-Powered Multi-Purpose Bipedal Locomotor with Parallel Mechanism,” Proceedings of the 2002 IEEE/RSJ International Conference on Intelligent Robots and Systems, Lausanne, Switzerland, pp. 2658–2663 (Oct. 2002).Google Scholar
11. Lim, H.-O., Sugahara, Y. and Takanishi, A., “Development of a Biped Locomotor Applicable to Medical and Welfare Fields,” Proceedings of the 2003 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 950–955 (2003).Google Scholar
12. Vaughan, C. L., “Theories of bipedal walking: An odyssey,” J. Biomech. 36 (4), 513523 (2003).Google Scholar
13. Raibert, M. H., Legged Robots that Balance (MIT Press, USA, 1986).CrossRefGoogle Scholar
14. Vukobratovic, M. and Borovac, B., “Zero-moment point-thirty five years of its life,” Int. J. Humanoid Robot. 1 (1), 157173 (2004).Google Scholar
15. Vanderborght, B., Van Ham, R., Verrelst, B., Van Damme, M. and Lefeber, D., “Overview of the Lucy project: Dynamic stabilization of a biped powered by pneumatic artificial muscles,” Adv. Robot. 22 (10), 10271051 (2008).Google Scholar
16. 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), (1977) pp. 963972.Google Scholar
17. Kim, D., Seo, S.-J. and Park, G.-T., “Zero-moment point trajectory modelling of a biped walking robot using an adaptive neuro-fuzzy system,” IEE Proc. - Control Theory Appl. 152 (4), 411426 (2005).Google Scholar
18. Chevallereau, C., Bessonnet, G., Abba, G. and Aoustin, Y., Bipedal Robots, Modeling, Design and Building Walking Robots (John Wiley and Sons Inc, USA, 2009).Google Scholar
19. Raibert, M., Tzafestas, S. and Tzafestas, C., “Comparative Simulation Study of three Control Techniques Applied to a Biped Robot,” Proceedings of the International Conference on Systems, Man & Cybernetics System Engineering in the Service of Humans, Le Touquet, France, vol. 1, pp. 494–502 (1993).Google Scholar
20. Zhu, W.-H., Virtual Decomposition Control: Towards Hyper Degrees of Freedom (Springer, Berlin 2010).Google Scholar
21. 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),” IEEE-RAS International Conference on Humanoid Robots, Genova, pp. 398–403 (Dec. 2006).Google Scholar
22. Pratt, J., “Exploiting Inherent and Natural Dynamics in the Control of Bipedal Walking Robots,” Ph.D. Dissertation, (Massachusetts Institute of Technology, USA, 2000).Google Scholar
23. Al-Shuka, H. F. N., Allmendinger, F., Corves, B. and Zhu, W.-H., “Modeling, stability and walking pattern generators of biped robots: A review,” Robotica 32 (6), 907934 (2014).CrossRefGoogle Scholar
24. Ozyurt, G., “3-D Humanoid Gait Simulation using an Optimal Predictive Control,” MSc. Thesis, (Turkey: Middle East Technical University, 2005).Google Scholar
25. Whittle, M. W., Gait Analysis: An Introduction, 4th ed. (Edinburgh, Butterworth-Heinemann, USA, 2007).Google Scholar
26. Huang, Q., Kajita, S., Koyachi, N., Kaneko, K., Yokoi, K., Arai, H., Komoriya, K. and Tane, K., “A High Stability, Smooth Walking Pattern for a Biped Robot,” Proceedings of the 1999 IEEE International conference on Robotics and Automation, vol. 1, Detroit, MI, pp. 65–71 (May, 1999).Google Scholar
27. Huang, Q., Yokoi, K., Kajita, S., Kaneko, K., Arai, H., Koyachi, N. and Tanie, K., “Planning walking patterns for a biped robot,” IEEE Trans. Robot. Autom. 17 (3), 280289 (2001).Google Scholar
28. Handharu, N., Yoon, J. and Kim, G., “Gait Pattern Generation with Knee Stretch Motion for Biped Robot using Toe and Heel Joints,” IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea, pp. 265–270 (Dec. 2008).Google Scholar
29. Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523533 (1999).Google Scholar
30. van Zutven, P., Kostic, D. and Nijmeijer, H., On the Stability of Bipedal Walking, (Ando, N. et al. eds.) (SIMPAR 2010, LNAI 6472), pp. 521532 (Springer-Verlag, Heidelberg, Berlin, 2010).Google Scholar
31. Nicholls, E., “Bipedal Dynamic Walking in Robotics,” Honors Thesis, (The University of Western Australia Department of Electrical and Electronic Engineering, Australia, 1998).Google Scholar
32. Pratt, J. and Tedrake, R., “Velocity-Based Stability Margins for Fast Bipedal Walking,” Fast Motions in Biomechanics & Robotics, Lecture Notes in Control and Information Sciences, vol. 340, pp. 299324 (2006).Google Scholar
33. Pratt, J., Carff, J., Drakunov, S. and Goswami, A., “Capture Point: A Step Toward Humanoid Push Recovery,” IEEE-RAS International Conference on Humanoid Robot, Genova, pp. 200–207 (Dec. 2006).Google Scholar
34. Wight, D. L., Kubica, E. G. and Wang, D. W. L., “Introduction to the foot placement estimator: A dynamic measure of balance for bipedal robotics,” J. Comput. Nonlinear Dyn. 3, 19 (2008).Google Scholar
35. Vukobratovic, M. and Stepanenko, J., “On the stability of anthropomorphic systems,” Math. Biosci. 15 (1–2), 137 (1972).Google Scholar
36. Kajita, S. and Espiau, B., “Legged Robots,” In: Springer Handbook of Robotics (Siciliano, B. and Khatib, O., eds.) (Springer, Berlin, 2008).Google Scholar
37. Alba, A. G. and Zielinska, T., “Postural equilibrium criteria concerning feet properties for biped robots,” J. Autom. Mobile Robot. Intell. Syst. 6 (1), 2227, 2012.Google Scholar
38. Pop, C., Khajepour, A., Huissoon, J. P. and Patla, A. E., “Experimental/analytical analysis of human locomotion using bondgraphs,” J. Biomech. Eng. 125 (4), 490498 (2003).Google Scholar
39. Hobbelen, D. G. E. and Wisse, M., “Limit Cycle Walking,” Humanoid Robots: Human-like Machines (Hackel, M. ed.) (I-Tech, Vienna, Australia, 2007) pp. 277294.Google Scholar
40. Hyon, S.-H., Hale, J. G. and Cheng, G., “Full-body compliant human-humanoid interaction: Balancing in the presence of unknown external forces,” IEEE Trans. Robot. 23 (5), 884898 (Oct. 2007).CrossRefGoogle Scholar
41. Ott, C., Roa, M. A. and Hirzinger, G., “Posture and Balance Control for Biped Robots based on Contact Force Optimization,” 11th IEEE-RAS International Conference on Humanoid Robots (Humanoids), Bled, Solvenia, pp. 26–33 (Oct. 2011).Google Scholar
42. Or, J. and Takanishi, A., “A Biologically Inspired CPG-ZMP Control System for the Real-Time Balance of a Single-Legged Belly Dancing Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, vol. 1, pp. 931–936 (Oct. 2004).Google Scholar
43. Park, J. H. and Kim, K. D., “Biped Robot Walking using Gravity-Compensated Inverted Pendulum mode and Computed Torque Control,” Proceedings of the 1998 IEEE International conference of Robotics & Automation, Leuven, Belgium, vol. 4, pp. 3528–3533 (May 1998).Google Scholar
44. Huang, Q. and Ono, K., “Energy-Efficient Walking for Biped Robot using Self-Excited Mechanism and Optimal Trajectory Planning,” Humanoid Robots, New Developments (de Pina Filho, A. Carlos ed.) (I-Tech, Vienna, Austria, 2007) pp. 321342.Google Scholar
45. Takanishi, A., Ishida, M., Yamazaki, Y. and Kato, I., “Realization of Dynamic Walking by the Biped Walking Robot WL-10RD;Journal of the Robotics Society of Japan 3 (4), 325336 (1985).Google Scholar
46. Harada, K., Kajita, S., Kaneko, K. and Hirukawa, H., “Pushing Manipulation by Humanoid Considering Two-kinds of ZMPs,” Proceedings of the 2003 IEEE International Conference on Robotics and Automation, Taipei, Taiwan, vol. 2, pp. 1627–1632 (Sept. 2003).Google Scholar
47. Sardain, P. and Bessonnet, G., “Zero-moment point-Measurements from a human walker wearing robot feet as shoes,” IEEE Trans. Syst. Man Cybern.- A: Syst. Humans 34 (5), 638648 (2004).Google Scholar
48. Yuksel, B., Zhou, C. and and Leblebicioglu, K., “Ground Reaction Force Analysis of Biped Locomotion,” Proceedings of the 2004 IEEE Conference on Robotics, Automation and Mechatronics, Singapore, vol. 1, pp. 330–335 (Dec. 2004).Google Scholar
49. Takanishi, A., Takeya, T., Karaki, H. and Kato, I., “A control method for dynamic biped walking under unknown external force,” IEEE International Workshop on Intelligent Robots and Systems, IROS'90, Ibaraki, vol. 2, pp. 795–801 (Jul. 1990).Google Scholar
50. Sardain, P. and Bessonnet, G., “Force acting on a biped robot. Center of pressure-zero moment point,” IEEE Trans. Syst. Man Cybern.-A: Syst. Humans 34 (5), 630637 (2004).Google Scholar
51. Tsuji, T. and Ohnishi, K., “A Control of Biped Robot which Applies Inverted Pendulum Mode with Virtual Supporting Point,” Proceedings of Advanced Motion Control, 7th Int. Workshop, Maribor, Solvenia, pp. 478–483 (2002).Google Scholar
52. Waki, N., Matsumoto, K. and Kawamura, A., “Lateral Sway Motion Generation for Biped Robots using Virtual Supporting Point,” The 11th IEEE Int. workshop on Advanced Motion Control, Nagaoka, Japan, pp. 124–128 (Mar. 2010).Google Scholar
53. Herr, H. and Popovic, M., “Angular momentum in human walking,” J. Exp. Biol. 211, 467481 (2008).Google Scholar
54. 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.) (InTech, Germany, 2006) pp. 79104.Google Scholar
55. Goswami, A. and Kallem, V., “Rate of Change of Angular Momentum and Balance Maintenance of Biped Robots,” Proceedings of the 2004 IEEE International Conference on Robotics and Automation, New Orleans, LA, vol. 4, pp. 3785–3790 (2004).Google Scholar
56. Sano, A. and Furusho, J., “Realization of Natural Dynamic Walking using the Angular Momentum Information,” IEEE International Conference on Robotics and Automation, Cincinnati, OH, vol. 3, pp. 1476–1481 (May 1990).Google Scholar
57. Sano, A. and Furusho, J., “Control of Torque Distribution for the BLR-G2 Biped Robot,” 5th International Conference on Advanced Robotics, Pisa, Italy, vol. 1, pp. 729–734 (Jun. 1991).Google Scholar
58. Popovic, M., Hofmann, A. and Herr, H., “Angular Momentum Regulation during Human Walking: Biomechanics and Control,” IEEE International Conference on Robotics and Automation, New Orleans, LA, USA, vol. 3, pp. 2405–2411 (2004).Google Scholar
59. Popovic, M., Englehart, A. and Herr, H., “Angular Momentum Primitives for Human Walking: Biomechanics and Control,” Proceedings of te 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, vol. 2, pp. 1685–1691 (2004).Google Scholar
60. Popovic, M., Hofmann, A. and Herr, H., “Zero Spin Angular Momentum Control: Definition and Applicability,” IEEE-RAS/RSJ International Conference on Humanoid Robots, Los Angeles, CA, vol. 1, pp. 478–493 (2004).Google Scholar
61. Popovic, M. and Herr, H., “Global Motion Control and Support base Planning,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Alberta, Canada, pp. 3877–3884 (2005).Google Scholar
62. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K. and Hirukawa, H., “Resolved Momentum Control: Humanoid Motion Planning based on the Linear and Angular Momentum,” Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), vol. 2, pp. 1644–1650 (2003).Google Scholar
63. Sian, N. E., Yokoi, K., Kajita, S., Kanchiro, F. and Tanie, K., “Whole Body Teleoperation of a Humanoid Robot-A Method of Integrating Operator's Intention and Robot's Autonomy-,” Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, Taiwan, vol. 2, pp. 1613–1619 (Sept. 2003).Google Scholar
64. Pratt, J. and Pratt, G., “Intuitive Control of a Planar Bipedal Walking Robot,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), vol. 3, pp. 2014–2021 (1998).Google Scholar
65. Al-Shuka, H. F. N., Corves, B., Vanderborght, B. and Zhu, W.-H., “Finite difference-based suboptimal walking pattern generators of biped robot with continuous dynamic response,” Int. J. Model. Optim. 3 (4), 337343 (2013).Google Scholar
66. Rebula, J., Canas, I., Pratt, J. and Goswami, A., “Learning Capture Points for Humanoid Push Recovery,” IEEE/RAS International Conference on Humanoid Robots, Pittsburgh, PA, pp. 65–72 (Nov. 2007).Google Scholar
67. Azevedo, C., Espiau, B., Amblard, B. and Assaiante, C., “Bipedal locomotion: Toward unified concepts in robotics and neuroscience,” Biol. Cybern. 96 (2), 209228 (2007).Google Scholar
68. Huxham, F. E., Goldie, P. A. and Patla, A. E., “Theoretical considerations in balance assessment,” Aust. J. Physiotherapy 47 (2), 89100 (2001).Google Scholar
69. Bessonnet, G., Chesse, S. and Sardain, P., “Generating Optimal Gait of a Human-Sized Biped Robot,” 5th International Conference on Climbing Walking Robots, Paris, pp. 241–253 (2002).Google Scholar
70. Al-Shuka, H. F. N., Corves, B. and Zhu, W.-H., “On the dynamic optimization of biped robot,” Lecture Notes Softw. Eng. 1 (3), 237243 (2013).Google Scholar
71. Kajita, S. and Tani, K., “Experimental Study of Biped Dynamic Walking in the Linear Inverted Pendulum Mode,” Proceedings of the IEEE Conference on Robotics and Automation, vol. 3, pp. 2885–2891 (1995).Google Scholar
72. Tang, Z., Zhou, C. and Sun, Z., “Trajectory Planning for Smooth Transition of a Biped Robot,” Proceedings of the IEEE International Conference on Robotics and Automations, vol. 2, pp. 2455–2460 (2003).Google Scholar
73. Wang, L., Yu, Z., He, F. and Jiao, Y., “Research on Biped Robot Gait in Double-Support Phase,” IEEE International Conference on Mechatronics and Automation, pp. 1553–1558 (2007).CrossRefGoogle Scholar
74. Shih, C.-L., “Gait synthesis for a biped robot,” Robotica 15 (6), 599607 (1997).Google Scholar
75. Mu, X. and Wu, Q., “Synthesis of a complete sagittal gait cycle for a five-link biped robot,” Robotica 21 (5), 581587 (2003).Google Scholar
76. Takanishi, A., Lim, H.-O., Tsuda, M. and Kato, I., “Realization of dynamic biped walking stabilized by trunk motion on a sagittally uneven surface,” IEEE Int. Workshop Intell. Robot. Syst. 1 323–330 (1990).Google Scholar
77. Harada, K., Kajita, S., Kanehiro, F., Fujiwara, K., Kaneko, K., Yokoi, K. and Hirukawa, H.Real-time planning of humanoid robot's gait for force-controlled manipulation,” IEEE/ASME Trans. Mechatronics 12 (1), 5362 (2007).Google Scholar
78. Park, I.-W., Kim, J.-Y. and Oh, J.-H., “Online walking pattern generation and its application to a biped humanoid robot-KHR-3 (HUBO),” Adv. Robot. 22 (2–3), 159190 (2008).Google Scholar
79. 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,” Proceedings of the IEEE/RSJ International conference on Intelligent Robots and Systems (IROS), Las Vegas, Nevada, vol. 2, pp. 1394–1399 (Oct. 2003).Google Scholar
80. Kuffner, J., Nishiwaki, K., Kagami, S., Kuniyoshi, Y., Inaba, M. and Inoue, H., “Self-Collision Detection and Prevention for Humanoid Robots,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, vol. 3, pp. 2265–2270 (May 2002).Google Scholar
81. Mirtich, B., “V-Clip: Fast and robust polyhedral collision detection,” ACM Trans. Graph. (TOG) 17 (3), 177208 (1998).Google Scholar
82. Sugiura, H., Gienger, M., Janssen, H. and Goerick, C., “Real-Time Collision Avoidance with Whole Body Motion Control for Humanoid Robots,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, San Diego, CA, pp. 2053–2058 (Oct. 2007).CrossRefGoogle Scholar
83. Stasse, O., Escande, A., Mansard, N., Miossec, S., Ervrard, P. and Kheddar, A., “Real-Time (Self)-Collision Avoidance Task on a HRP-2 Humanoid Robot,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, USA, pp. 3200–3205 (May 2008).Google Scholar
84. Safonova, A. Pollard, N. and Hodgins, J. K., “Optimizing Human Motion for the Control of a Humanoid Robot,” 2nd International Symposium on Adaptive Motion and Animals and Machines (AMAM) (Mar. 2003).Google Scholar
85. Kuffner, J., Kagami, S., Nishiwaki, K., Inaba, M. and Inoue, H., “Online Footstep Planning for Humanoid Robots,” Proceedings of the IEEE International Conference on Robotics and Automation, Taipei, Taiwan, vol. 1, pp. 932–937 (Sept. 2003).Google Scholar
86. Faverjon, B. and Tournassoud, P., “A Local based Approach for Path Planning of Manipulators with a High Number of Degrees of Freedom,” IEEE International Conference on Robotics and automation, Raleigh, NC, USA, vol. 4, pp. 1152–1159 (Mar. 1987).Google Scholar
87. Kanehiro, F., Lamiraux, O. Kanoun, Yoshida, E. and Laumond, J.-P., “A local Collision Avoidance Method for Non-Strictly Convex Polyhedra,” Proceedings of: Science and Systems, pp. 151–158 (2009).Google Scholar
88. Escande, A., Miossec, S. and Kheddar, A., “Continuous Gradient Proximity Distance for Humanoids Free-Collision Optimized-Postures,” 7th IEEE-RAS International Conference on Humanoid Robots, Pittsburgh, PA, pp. 188–195 (2007).Google Scholar
89. Nakaoka, S., Nakazawa, A., Kanehiro, F., Kaneko, K., Morisawa, M. and Ikeuchi, K., “Task Model of Lower Body Motion for a Biped Humanoid Robot to Imitate Human Dances,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Canada, pp. 3157–3162 (Aug. 2005).Google Scholar
90. Kajita, S. and Tani, K., “Experimental study of biped dynamic walking,” IEEE, Control Syst. 16 (1), 1319 (1996).Google Scholar
91. Miyazaki, F. and Arimoto, S., “A control theoretic study on dynamical biped locomotion,” J. Dyn. Syst. Meas. Control 102, 233239 (1980).Google Scholar
92. Cannon, R. C., Dynamics of Physical Systems (New York, McGraw-Hill, 1967).Google Scholar
93. Schaefer, J., “On the Bounded Control of some Unstable Mechanical Systems,” Dept. of Aeronautics and Astronautics (Stanford University, SUDAR Rep. 233, Apr. 1965).Google Scholar
94. Witt, D. C., “A feasibility study of powered-limb prosthesis,” Proc. Inst. Mech. Eng. 183 (10), 1825 (1968).Google Scholar
95. 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), 658661 (1973).Google Scholar
96. Gubina, F., Hemami, H. and McGhee, R. B., “On the dynamic stability of biped locomotion,” IEEE Transactions on Biomedical Engineering, BME–21 (2), 102108 (1974).CrossRefGoogle Scholar
97. Miura, H. and Shimoyama, I., “Dynamic walk of a biped,” Int. J. Robot. Res. 3 (2), 6074 (1984).Google Scholar
98. Kajita, S., Yamaura, T. and Kobayashi, A., “Dynamic walking control of a biped robot along a potential energy conserving orbit,” IEEE Trans. Robot. Autom. 8 (4), 431438 (1992).Google Scholar
99. Pratt, J. E. and Drakunov, S. V., “Derivation and Application of a Conserved Orbital Energy for the Inverted Pendulum Bipedal Walking Model,” IEEE International Conference on Robotics and Automation, Roma, pp. 4653–4660 (2007).Google Scholar
100. Shibuya, M., Suzuki, T. and Ohnishi, K., “Trajectory Planning of Biped Robot using Linear Pendulum mode for Double Support Phase,” Proceedings of the IECON 2006–32nd Annual Conference on IEEE Industrial Electronics, Paris, pp. 4094–4099 (2006).Google Scholar
101. Kudoh, S. and Komura, T., “C2 Continuous Gait-Pattern Generation for Biped Robots,” Proceedings of the 2003 IEEE/RSJ Intelligent Robots and Systems, Las Vegas, Nevada, vol. 2, pp. 1135–1140 (2003).Google Scholar
102. Al-Shuka, H. F. N., Corves, B., Zhu, W.-H. and Vanderborght, B., “A simple algorithm for generating stable biped walking patterns,” Int. J. Intell. Comput. Appl. 101 (4), 2933 (2014).Google Scholar
103. Kim, M.-S., Kim, I., Park, S. and Oh, J. H., “Realization of Stretch-Legged Walking of the Humanoid Robot,” 8th IEEE-RAS International Conference on Humanoid Robots, Daejeon, Korea, pp. 118–124 (Dec. 2008).Google Scholar
104. Ogura, Y., Kataoka, T., Aikawa, H., Shimomura, K., Lim, H.-O. and Takanishi, A., “Evaluation of Various Walking Patterns of Biped Humanoid Robot,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 603–608 (Apr. 2005).Google Scholar
105. Kurazume, R., Tanaka, S., Yamashita, M., Hasegawa, T. and Yoneda, K., “Straight Legged Walking of a Biped Robot,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Canada, pp. 3095–3101 (2005).Google Scholar
106. Albert, A. and Gerth, W., “Analytic path planning algorithms for bipedal robots without a trunk,” J. Intell. Robot. Syst. 36 (2), 109127 (2003).Google Scholar
107. Takanishi, A., Tochizawa, M., Karaki, H. and Kato, I., “Dynamic Biped Walking Stabilized with Optimal Trunk and Waist Motion,” IEEE/RSJ International Workshop on Intelligent Robots and Systems, Tsukuba, Japan, pp. 187–192 (Sept. 1989).Google Scholar
108. Ha, T. and Choi, C.-H., “An effective trajectory generation method for bipedal walking,” Robot. Auton. Syst. 55 (10), 795810 (2007).Google Scholar
109. Sugihara, T., Nakamura, Y. and Inoue, H., “Realtime Humanoid Motion Generation Through ZMP Manipulation based on Inverted Pendulum Control,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, vol. 2, pp. 1404–1409 (May 2002).Google Scholar
110. Choi, Y., You, B.-J. and Oh, S.-R., “On the Stability of Indirect ZMP Controller for Biped Robot Systems,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, vol. 2, pp. 1966–1971 (Oct. 2004).Google Scholar
111. Napoleon, S. Nakaura, Sampei, M., “Balance Control Analysis of Humanoid Robot Based on ZMP Feedback Control,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 3, pp. 2437–2442 (2002).Google Scholar
112. Hong, S., Oh, Y., Chang, Y.-H. and You, B.-J., “Walking Pattern Generation for Humanoid Robots with LQR and Feedforward Control Method,” 34th Annual Conference of IEEE on Industrial Electronics, Orlando, FL, pp. 1698–1703 (Nov. 2008).Google Scholar
113. 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,” Proceedings of the IEEE International Conference on Robotics and Automation, vol. 2, pp. 1620–1626 (Sept. 2003).Google Scholar
114. Takenaka, T., Matsumoto, T. and Yoshiike, T., “Real Time Motion Generation and Control for Biped Robot-1st Report: Walking Gait Pattern Generation,” IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, pp. 1084–1091 (Oct. 2009).Google Scholar
115. Kajita, S., Morisawa, M., Harada, K., Kaneko, K., Kanehiro, F., Fujiwara, K. and Hirukawa, H., “Biped Walking Pattern Generator Allowing Auxiliary ZMP Control,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, pp. 2993–2999 (Oct. 2006).Google Scholar
116. Shimmyo, S. and Ohnishi, K., “Nested Preview Control by Utilizing Virtual Plane for Biped Walking Pattern Generation Including COG up-down Motion,” 36th Annual Conference on IEEE Industrial Electronics Society, Glendale, AZ, pp. 1571–1576 (Nov. 2010).Google Scholar
117. Czarnetzki, S., Korner, S. and Urbann, O., “Observer-based dynamic walking control for biped robots,” Robot. Auton. Syst. 57 (8), 839845 (2009).Google Scholar
118. Wieber, P.-B., “Trajectory Free Linear Model Predictive Control for Stable Walking in the Presence of Strong Perturbations,” 6th IEEE-RAS International Conference on Humanoid Robots, Genova, pp. 137–142 (Dec. 2006).Google Scholar
119. Dimitrov, D., Wieber, P.-B., Ferreau, H. J. and Diehl, M., “On the Implementation of Model Predictive Control for On-line Walking Pattern Generation,” IEEE International Conference on Robotics and Automation (ICRA), Pasadena, CA, pp. 2685–2690 (May 2008).Google Scholar
120. Wright, S., “Applying New Optimization Algorithms to Model Predictive Control,” 5th International Conference on Chemical Process Control-CPC-V (1996).Google Scholar
121. Bartlett, R. A., Wächter, A. and Biegler, L. T., “Active set vs. Interior Point Strategies for Model Predictive Control,” Proceedings of the American Control Conference, Chicago, IL, vol. 6, pp. 4229–4233 (2000).Google Scholar
122. Arbulu, M., Kaynov, 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, 2010).Google Scholar
123. Lee, B.-J., Stonier, D., Kim, Y.-D., Yoo, J.-K., Yoo, J.-K. and Kim, J.-H., “Modifiable walking pattern of a humanoid robot by using allowable ZMP variation,” IEEE Trans. Robot. 24 (4), 917925 (2008).Google Scholar
124. Hong, S., Oh, Y., Chang, Y.-H. and You, B.-J., “A Walking Pattern Generation Method for Humanoid Robots using Least Square Method and Quartic Polynomial,” In: Humnoid Robots (Choi, B. ed.) (InTech, 2009). ISBN: 978-953-7619-44-2.Google Scholar
125. Harada, K., Kajita, S., Kaneko, K. and Hirukawa, H., “An Analytical Method on Real-Time Gait Planning for a Humanoid Robot,” IEEE/RAS International Conference on Humanoid Robots, vol. 2, pp. 640–655 (2004).Google Scholar
126. Morisawa, M., Harada, K., Kajita, S., Kaneko, K., Kanehiro, F., Fujiwara, K., Nakaoka, S. and Hirukawa, H., “A Biped Pattern Generation Allowing Immediate Modification of Foot Placement in Real-Time,” 6th IEEE-RAS International Conference on Humanoid Robots, Genova, pp. 581–586 (2006).Google Scholar
127. Morisawa, M., Harada, K., Kajita, S., Kaneko, K., Sola, J., Yoshida, E., Mansard, N., Yokoi, K. and Laumond, J.-P., “Reactive Stepping to Prevent Falling for Humanoids,” 9th IEEE-RAS International Conference on Humanoid Robots, Paris, France, pp. 528–534 (2009).Google Scholar
128. Morisawa, M., Kanehiro, F., Kaneko, K., Mansard, N., Sola, J., Yoshida, E., Yokoi, K. and Laumond, J.-P., “Combining Suppression of the Disturbance and Reactive Stepping for Recovering Balance,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Taipei, pp. 3150–3156 (2010).Google Scholar
129. Tajima, R., Honda, D. and Suga, K., “Fast Running Experiments Involving a Humanoid Robot, “IEEE International Conference on Robotics and Automation, Kobe, Japan, pp. 1571–1576 (May 2009).Google Scholar
130. Komura, T., Leung, H., Kudoh, S. and Kuffner, J., “A Feedback Controller for Biped Humanoids that can Counteract Large Perturbations during Gait,” Proceedings of the IEEE International Conference on Robotics and Automation, Barcelona, Spain, pp. 1989–1995 (Apr. 2005).Google Scholar
131. Horak, F. B. and Nasher, L. M., “Central programming of postural movements: Adaptation to altered support-surface configurations,” J. Neurophysiol. 55 (6), 13691381 (1986).Google Scholar
132. Kuo, A. D., “An optimal control model for analyzing human postural balance,” IEEE Trans. Biomed. Eng. 42 (1), 87101 (1995).Google Scholar
133. Alexandrov, A. V., Frolov, A. A. and Massion, J., “Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling,” Biol. Cybern. 84 (6), 425434 (2001).Google Scholar
134. Runge, C. F., Shupert, C. L., Horak, F. B. and Zajac, F. E., “Ankle and hip postural strategies defined by joint torques,” Gait and Posture 10 (2), 161170 (1999).Google Scholar
135. Nenchev, D. N. and Nishio, A., “Experimental Validation of Ankle and Hip Strategies for Balance Recovery with a Biped Subjected to An Impact,” Proceedings of the IEEE/RSJ International Conference on Robots and Systems, San Diego, CA, pp. 4035–4040 (Nov. 2007).Google Scholar
136. Nishio, A., Takahashi, K. and Nenchev, D. N., “Balance Control of a Humanoid Robot based on the Reaction Null Space Method,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, pp. 1996–2001 (2006).Google Scholar
137. Ono, H., Sato, T. and Ohnishi, K., “Balance Recovery of Ankle Strategy: Using Knee Joint for Biped Robot,” 1st International Symposium on Access Space (ISAS), Yokohama, pp. 236–241 (2011).Google Scholar
138. Park, C.-S., Ha, T., Kim, J. and Choi, C.-H., “Trajectory generation and control for a biped robot walking upstairs,” Int. J. Control Autom. Syst. 8 (2), 339–335 (2010).Google Scholar
139. Prahald, V., Dip, G. and Hwee, C.M.-, “Disturbance rejection by online ZMP compensation,” Robotica 26 (1), 917 (2008).Google Scholar
140. Kajita, S., Yokoi, K., Saigo, M. and Tanie, K., “Balancing a Humanoid Robot using Backdrive Concerned Torque Control and Direct Angular Momentum Feedback,” Proceedings of the IEEE International Conference on Robotics and Automation, Seoul, Korea, vol. 4, pp. 3376–3382 (May 2001).Google Scholar
141. Oda, N. and Ito, M., “Experimental Study of Walking Motion Stabilization for Biped Robot with Flexible Ankle Joints,” 35th Annual Conference of IEEE on Industrial Electronics (IECON'09), Porto, pp. 4197–4202 (Nov. 2009).Google Scholar
142. Sato, T. and Ohnishi, K., “ZMP Disturbance Observer for Walking Stabilization of Biped Robot,” 10th IEEE International Workshop on Advanced Motion Control (AMC'08), Trento, pp. 290–295(Mar. 2008).Google Scholar
143. Takenaka, T., Matsumoto, T. and Yoshiike, T., “Real Time Motion Generation and Control for Biped Robot-3rd Report: Dynamics Error Compensation,” IEEE/RSJ International Conference on Intelligent Robots and Systems, St. Louis, MO, pp. 1594–1600 (Oct. 2009).Google Scholar
144. Takenaka, T., Matsumoto, T., Yoshiike, T., Hasegawa, T., Shirokura, S., Kaneko, H. and Orita, A., “Real Time Motion Generation and Control for Biped Robot-4th Report: Integrated balance Control-,” IEEE/RSJ International Conference on Intelligent robots and Systems, St. Louis, USA, pp. 1601–1608 (Oct. 2009).Google Scholar
145. Sobotka, M., Wollherr, D. and Buss, M., “A Jacobian Method for Online Modification of Precalculated Gait Trajectories,” Proceedings of the 6th International Conference on Climbing and Walking Robots (CLAWAR 2003), Catania, Italy, pp. 435–442 (2003).Google Scholar
146. Wollherr, D. and Buss, M., “Posture Modification for Biped Humanoid Robots based on Jacobian Method,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan, vol. 1, pp. 124–129 (Oct. 2004).Google Scholar
147. Brock, O., Khatib, O. and Viji, S., “Task-Consistent Obstacle Avoidance and Motion behavior for Mobile Manipulation,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'02), Washington, DC, vol. 1, pp. 388–393 (May 2002).Google Scholar
148. Yamane, K. and Nakamur, Y., “Dynamics filter-concept and implementation of online motion generator for human figures,” IEEE Trans. Robot. Autom. 19 (3), 421432 (2003).Google Scholar
149. Tak, S., song, O.-Y. and Ko, H.-S., “Motion balance filtering,” Comput. Graph. Forum 19 (3), 437446 (2000).Google Scholar
150. Nakamura, Y. and Yamane, K., “Dynamics computations of structure-varying kinematic chains and its application to human figures,” IEEE Trans. Robot. Autom. 16 (2), 124134 (Apr. 2000).Google Scholar
151. Silva, P. M. and Machado, J. A. T., “Towards Force Interaction Control of Biped Walking Robots,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2004), Sendai, Japan, vol. 3, pp. 2568–2573 (Oct. 2004).Google Scholar
152. Setiawan, S., Hyon, S., Yamaguchi, J. and Takanishi, A., “Physical Interaction between Human and a Bipedal Humanoid Robot – Realization of Human-Follow Walking,” Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI, vol. 1, pp. 361–367 (May 1999).Google Scholar
153. Hyon, S.-H., Osu, R. and Otaka, Y., “Integration of Multi-Level Postural Balancing on Humanoid Robots,” IEEE International Conference on Robotics and Automation, Kobe International Conference Center, Kobe, Japan, pp. 1549–1556 (May 2009).Google Scholar
154. Hyon, S.-H. and Cheng, G., “Disturbance Rejection for Biped Humanoids,” IEEE International Conference on Robotics and Automation, Roma, Italy, pp. 2668–2675 (Apr. 2007).Google Scholar
155. Hyon, S.-H. and Cheng, G., “Passivity-Based Full-body Force Control for Humanoids and Application to Dynamic Balancing and Locomotion,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Beijing, China, pp. 4915–4922 (Oct. 2006).Google Scholar
156. Azevedo, C., Poignet, P. and Espiau, B., “Moving Horizon Control for Biped Robots without Reference Trajectory,” Proceedings of the IEEE International Conference on Robotics and Automation, Washington, DC, vol. 3, pp. 2762–2767 (May 2002).Google Scholar
157. Camacho, E. F. and Bordons, C., Model Predictive Control (Springer, London, 2007).Google Scholar
158. Wieber, P.-B., “Viability and Predictive Control for Safe Locomotion,” IEEE/RSJ International Conference on Robots and Systems, Nice, France, pp. 1103–1108 (Sept. 2008).Google Scholar
159. Diedam, H., Dimitrov, D., Wieber, P.-B., Mombaur, K. and Diehl, M., “Online Walking Gait Generation with Adaptive Foot Positioning Through Linear Model Predictive Control,” IEEE/RSJ International Conference on Intelligent Robots and Systems, Nice, France, pp. 1121–1126 (Sept. 2008).Google Scholar
160. Azevedo, C., Poignet, P. and Espiau, B., “Artificial locomotion control from human to robots,” Robot. Auton. Syst. 47 (4), 203223 (2004).CrossRefGoogle Scholar
161. Yin, Y. and Hosoe, S., “Mixed Logic Dynamical Modeling and On Line Optimal Control of Biped Robot,” In: Humanoid Robots: Human-like Motion, Book (Hackel, M., ed.) (InTech, Vienna, Austria, Jun. 2007) pp. 315328.Google Scholar
162. Lydoire, F. and Poignet, P., “Nonlinear Predictive Control using Constraint Satisfaction,” 2nd International Workshop on Global Optimization and Constraint Satisfaction (COCOS), Lausanne, Switzerland (Nov. 2003).Google Scholar
163. Parsa, M. and Farrokhi, M., “Robust Nonlinear Model Predictive Trajectory Free Control of Biped Robots based on Nonlinear Disturbance Observer,” 18th Iranian Conference on Electrical Engineering (ICEE), Isfahan, Iran, pp. 617–622 (May 2010).Google Scholar
164. Kalamian, N. and Farrokhi, M., “Stepping of Biped Robots Over Large Obstacles using NMPC Controller,” 2nd International Conference on Control, Instrumentation and Automation (ICCIA), Shiraz, Iran, pp. 917–922 (2011).Google Scholar
165. Katic, D. and Vukobratovic, M., “Survey of intelligent control techniques for humanoid robots,” J. Intell. Robot. Syst. 37 (2), 117141 (2003).Google Scholar
166. Hill, J. and Fahimi, F., “Active disturbance rejection for walking bipedal robots using the acceleration of the upper limbs,” Robotica 33 (2), 264281 (2015).Google Scholar
167. Wieber, P.-B., “Holonomy and Nonholonomy in the Dynamics of Articulated Motion,” In: Fast Motions in Biomechanics and Robotics, Lecture Notes in Control and Information Science (Diehl, M. and Mombaur, K., eds.), vol. 340, pp. 411425 (Springer, Heidelberg, Germany, 2006).Google Scholar
168. Spong, M. W. and Vidyasagar, M., Robot Dynamics and Control (John Wiley and Sons, USA, 1989).Google Scholar
169. Lewis, F. L., Dawson, D. M. and Abdallah, C. T., Robot Manipulator Control: Theory and Practice, (Marcel Dekker, Inc., New York, USA, 2006).Google Scholar
170. Kelly, R., Santibanez, V. and Loria, A., Control of Robot Manipulators in Joint Space, (Springer, London, 2005).Google Scholar
171. Zhu, W.-H., “Dynamics of general constrained robots derived from rigid bodies,” J. Appl. Mech. ASME, 75 (3), 111 (2008).Google Scholar
172. Park, J. H. and Chung, H., “Hybrid Control for Biped Robots using Impedance Control and Computed-Torque Control,” Proceedings of the IEEE International Conference on Robotics and Automation, Detroit, MI, vol. 2, pp. 1365–1370 (1999).Google Scholar
173. Mu, X. and Wu, Q., “Development of a complete dynamic model of a planar five-link biped and sliding mode control of its locomotion during the double support phase,” Int. J. Control 77 (8), 789799 (2004).Google Scholar
174. Moosavian, S. A. A., Takhmar, A. and Alghooneh, M., “Regulating Sliding mode Control of a Biped Robot,” Proceedings of the International Conference on Mechatronics and Automation (ICMA 2007), Harbin, China, pp. 1547–1552 (Aug. 2007).Google Scholar
175. Pournazhdi, A. B., Mirzaei, M. and Ghiasi, A. R., “Dynamic Modeling and Sliding Mode Control for Fast Walking of Seven-Link Biped Robot,” 2nd International Conference on Control, Instrumentation, and Automation (ICCIA), Shiraz, Iran, pp. 1012–1017 (Dec. 2011).Google Scholar
176. Luo, R. C., Tzeng, C.-W., Cheng, P.-Z. and Lee, K.-W., “Trajectory-Tracking of Nonlinear Biped Robot System based on Adaptive Fuzzy Sliding Mode Control,” The 33rd Annual Conference of the IEEE on Industrial Electronics Society (IECON 2007), Tapei, Taiwan, pp. 2789–2794 (Nov. 2007).Google Scholar
177. Hwang, C.-L., “A Trajectory Tracking of Biped Robots using Fuzzy-Model-Based Sliding-Mode Control,” Proceedings of the 41st IEEE Conference on Decision and Control, vol. 1, pp. 203–208 (Dec. 2002).Google Scholar
178. Lee, S. H., Park, J. B. and Choi, Y. H., “Sliding Mode Control based on Self-Recurrent Wavelet Neural Network for Five-Link Biped Robot,” International Joint Conference (SICE-ICASE), Busan, Korea, pp. 726–731 (Oct. 2006).Google Scholar
179. Bartolini, G., Casalino, G. and Aicardi, M., “Learning and variable structure techniques in the control of a mechanical byped,” 28th IEEE Conference on Decision and Control, Tampa, FL, vol. 3, pp. 2621–2628 (Dec. 1989).Google Scholar
180. Kho, J. and Lim, D., “A Learning Controller for Repetitive Gait Control of Biped Walking Robot,” SICE 2004 Annual Conference, Sapporo, vol. 1, pp. 885–889 (Aug. 2004).Google Scholar
181. Wang, L., Liu, Z., Chen, C. L., Zhang, Y., Lee, S. and Chen, X., “Energy-efficient SVM learning control system for biped walking robots,” IEEE Trans. Neural Netw. Lear. Syst. 24 (5), 831837 (2013).Google Scholar
182. Hayder, F. N. Al-Shuka, Corves, B. and Zhu, W.-H., “Function approximation technique-based adaptive virtual decomposition control for a serial chain manipulator,” Robotica 32 (3), 375399 (2014).Google Scholar
183. Lim, H.-O., Setiawan, S. A. and Takanishi, A., “Balance and Impedance Control for Biped Humanoid Robot Locomotion,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Maui, HI, vol. 1, pp. 494–499 (2001).Google Scholar
184. Park, J. H. and Chung, H., “Impedance Control and Modulation for Stable Footing in Locomotion of Biped Robots,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'99), Kyongju, vol. 3, pp. 1786–1791 (1999).Google Scholar
185. Park, J. H., “Impedance control for biped robot locomotion,” IEEE Trans. Robot.Autom. 17 (6), 870882 (2000).Google Scholar
186. Dupree, K., Liang, C.-H., Hu, G. and Dixon, W. E., “Adaptive Lyapunov-based control of a robot and mass-spring system undergoing an impact collision,” IEEE Trans. Syst. Man Cybern., 38 (4), 10501061 (Aug. 2008).Google Scholar
187. Tornambe, A., “Modeling and control of impact in mechanical systems: Theory and experimental results,” IEEE Trans. Autom. Control, 44 (2), 294309 (Feb. 1999).Google Scholar
188. Machado, M., Moreira, P., Flores, P. and Lankarani, H. M., “Compliant contact force models in multibody dynamics: Evolution of the Hertz contact theory,” Mech. Mach. Theory 53, pp. 99–121 (2012).Google Scholar
189. Rengifo, C., Aoustin, Y., Chevallereau, C. and Plestan, F., “A Penalty-Based Approach for Contact Forces Computation in Bipedal Robots,” 9th IEEE-RAS International Conference on Humanoid Robots, Paris, France, pp. 121–127 (2009).Google Scholar
190. Vukobratovic, M., Potkonjak, V. and Matijevic, V., Dynamics of Robots with Contact Tasks, (Kluwer Academic Publishers, the Netherlands, 2003).Google Scholar
191. Bruneau, O. and Ouezdou, F. B., “Compliant Contact of Walking Robot Feet,” Proceedings of the 3rd ECDP International Conference on Advanced Robotics, Intelligent Automation and Active Systems, Bremen, Germany, pp. 1–7 (Sep. 1997).Google Scholar
192. Hwang, Y., Inohira, E., Konno, A. and Uchiyama, M., “An Order n Dynamic Simulator for a Humanoid Robot with a Virtual Spring-Damper Contact Model,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'03), vol. 1, pp. 31–36 (Sep. 2003).Google Scholar
193. Buschmann, T., Lohmeier, S., Ulbrich, H. and Pfeiffer, F., “Dynamics Simulation for a Biped robot: Modeling and Experimental Verification,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'2006), Orlando, FL, pp. 2673–2678 (May 2006).Google Scholar
194. Hirukawa, H., Kanehiro, F., Kajita, S., Fujiwara, K., Yokoi, K., Kaneko, K. and Harada, K., “Experimental Evaluation of the Dynamic Simulation of Biped walking of Humanoid Robots,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA'03), vol. 2, pp. 1640–1645 (Sep. 2003).Google Scholar
195. Blajer, W. and Schiehlen, W. O., “A control scheme for biped walking without impacts,” Lecture Notes in Control and Information Sciences, vol. 187, pp. 311–321 (1993).Google Scholar
196. Blajer, W. and Schiehlen, W., “Walking without impacts as a motion/force control problem,” J. Dyn. Meas. Control 114 (4), 660665 (Dec. 1992).Google Scholar
197. Seguin, P. and Bessonnet, G., “Generating optimal walking cycles using spline-based state-parameterization,” Int. J. Human. Robot. 2 (1) 47–80 (2005).Google Scholar
198. Shibata, M. and Natori, T., “Impact Force Reduction for Biped Robot based on Decoupling COG Control Scheme,” 6th International Workshop on Advanced Motion Control, Nagoya, Japan, pp. 612–617 (Apr. 2000).Google Scholar
199. Liu, Z., Zhang, Y. and Wang, Y., “A Type-2 fuzzy switching control system for biped robots,” IEEE Trans. Syst. Man Cybern. 37 (6), 12021213 (Nov. 2007).Google Scholar
200. Koopman, B., Grootenboer, H. J. and Jongh, H. J., “An inverse dynamics model for the analysis, reconstruction and prediction of bipedal walking,” J. Biomech. 28 (11), 13691376 (1995).Google Scholar
201. Ren, L., Johnes, R. K. and Howard, D., “Whole body inverse dynamics over a complete gait cycle based only on measured kinematics,” J. Biomech. 41 (12), 2750–2759(2008).Google Scholar
202. Dallali, H., Medrano-Corda, G. A. and Brown, M., “A Comparison of Multivariable and Decentralized Control Strategies for Robust Humanoid Walking,” UKACC International Conference on Control (Coventry, UK, Sept. 2010).Google Scholar
203. Blajer, W., Bestle, D. and Schiehlen, W., An orthogonal complement matrix formulation for constrained multibody systems, J. Mech. Des. 116, 423428 (1994).Google Scholar
204. Pennestri, E. and Valentini, P. P., “Coordinate Reduction Strategies in Multibody Dynamics: A review,” Atti Conference on Multibody System Dynamics, (2007).Google Scholar
205. Zeng, G. and Hemami, A., “An overview of robot force control,” Robotica 15 (5), 473482 (1997).Google Scholar
206. Al-Shuka, H. F. N., Corves, B. and Zhu, W.-H., “Dynamic modeling of biped robot using Lagrangian and recursive Newton-Euler formulations,” Int. J. Comput. Appl. 101 (3), 18 (2014).Google Scholar
207. Vukobratovic, M. and Juricic, D., “Contribution to the synthesis of biped gait,” IEEE Trans. Bio-Medical Eng. 16 (1), 16 (1969).Google Scholar
208. Yi, K. Y., “Locomotion of a Biped Robot with Compliant Ankle Joints,” Proceedings of the IEEE International Conference on Robotics and Automation, Albuquerque, NM, vol. 1, pp. 199–204 (Apr. 1997).Google Scholar