No Access

From a 3D Passive Biped Walker to a 3D Passivity-Based Controlled Robot

Biomechatronics and Cognitive Engineering Research Lab, School of Mechanical Engineering, Iran University of Science and Technology, Tehran 16765-163, Iran

E-mail Address: b_beigzadeh@iust.ac.ir

Search for more papers by this author

Mohammad Reza Sabaapour

Intelligent Medical Robotics Lab, School of Integrated Technology, Gwangju Institute of Science and Technology, Gwangju 61005, South Korea

E-mail Address: sabaapour@ut.ac.ir

Search for more papers by this author

Mohammad Reza Hairi Yazdi

School of Mechanical Engineering, University of Tehran, Tehran 14155-6619, Iran

E-mail Address: myazdi@ut.ac.ir

Search for more papers by this author

, and

Kaamran Raahemifar

http://orcid.org/0000-0002-9835-7897

Electrical and Computer Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada

E-mail Address: kraahemi@ee.ryerson.ca

Search for more papers by this author

https://doi.org/10.1142/S0219843618500093Cited by:11 (Source: Crossref)

Abstract

Asymptotically stable control of biped robots, especially based on reproducing passive periodic motions, have become of interest nowadays. In this paper, firstly, a three-dimensional (3D) stable passive biped walker which is a compass gait one with flat feet, compliant ankles and particular arrangement of moments of inertia has been presented. Then, a passivity-based control of the related biped robot based on elaborating 3D form of potential energy shaping method has been applied. In other words, by adding minimal actuations to the aforementioned passive walker, its passive periodic gait that belongs to a particular slope has been reproduced on any arbitrary surface such as the level ground. Simulation results support the effectiveness of the proposed approach.

Keywords:

References

1. J. W. Grizzle, C. Chevallereau, R. W. Sinnet and A. D. Ames, Models, feedback control, and open problems of 3D bipedal robotic walking, Automatica 50 (8) (2014) 1955–1988. Crossref, Web of Science, Google Scholar
2. F. Farzadpour, M. Danesh and S. M. TorkLarki, Development of multi-phase dynamic equations for a seven-link biped robot with improved foot rotation in the double support phase, Proc. Inst. Mech. Eng. C, J. Mech. Eng. Sci. 229 (1) (2015) 3–17. Crossref, Web of Science, Google Scholar
3. P. Channon, S. Hopkins and D. Pham, A variational approach to the optimization of gait for a bipedal robot, Proc. Inst. Mech. Eng. C, J. Mech. Eng. Sci. 210 (2) (1996) 177–186. Crossref, Web of Science, Google Scholar
4. T. McGeer, Dynamics and control of bipedal locomotion, J. Theor. Biol. 163 (3) (1993) 277–314. Crossref, Web of Science, Google Scholar
5. T. McGeer, Passive dynamic walking, Int. J. Robot. Res. 9 (2) (1990) 62–82. Crossref, Web of Science, Google Scholar
6. M. Vukobratovic and B. Borovac, Zero-moment point-thirty five years of its life, Int. J. Hum. Robot. 1 (1) (2004) 157–173. Link, Google Scholar
7. A. Goswami, B. Espiau and A. Keramane, Limit cycles in a passive compass gait biped and passivity-mimicking control laws, Auton. Robots 4 (3) (1997) 273–286. Crossref, Web of Science, Google Scholar
8. J. W. Grizzle, F. Plestan and G. Abba, Poincaré’s method for systems with impulse effects: Application to mechanical biped locomotion, in Proc. 38th IEEE Conf. Decision and Control (IEEE, Arizona, USA, 1999), pp. 3869–3876. Google Scholar
9. B. Morris and J. Grizzle, A restricted Poincaré map for determining exponentially stable periodic orbits in systems with impulse effects: Application to bipedal robots, in 44th IEEE Conf. Decision and Control, 2005 and 2005 European Control Conf. CDC — ECC’05 (IEEE, Seville, Spain, 2005), pp. 4199–4206. Google Scholar
10. M. Wisse, Three additions to passive dynamic walking: Actuation, an upper body, and 3D stability, Int. J. Hum. Robot. 2 (04) (2005) 459–478. Link, Google Scholar
11. E. Westervelt, J. Grizzle and D. Koditschek, Zero dynamics of underactuated planar biped walkers, IFAC Proc. 35 (1) (2002) 551–556. Crossref, Google Scholar
12. I. R. Manchester and J. Umenberger, Real-time planning with primitives for dynamic walking over uneven terrain, in 2014 IEEE Int. Conf. Robotics and Automation (ICRA) (IEEE, Hong Kong, China, 2014), pp. 4639–4646. Google Scholar
13. T. McGeer, Passive dynamic biped catalogue, in Experimental Robotics II: The 2nd International Symposium (Springer-Verlag, Berlin, 1991), pp. 463–490. Google Scholar
14. A. D. Kuo, Stabilization of lateral motion in passive dynamic walking, Int. J. Robot. Res. 18 (9) (1999) 917–930. Crossref, Web of Science, Google Scholar
15. S. H. Collins, M. Wisse and A. Ruina, A three-dimensional passive-dynamic walking robot with two legs and knees, Int. J. Robot. Res. 20 (7) (2001) 607–615. Crossref, Web of Science, Google Scholar
16. M. J. Coleman, M. Garcia, K. Mombaur and A. Ruina, Prediction of stable walking for a toy that cannot stand, Phys. Rev. E 64 (2) (2001) 022901. Crossref, Web of Science, Google Scholar
17. M. R. Sabaapour, M. R. Hairi Yazdi and B. Beigzadeh, Passive dynamic turning in 3D biped locomotion: An extension to passive dynamic walking, Adv. Robot. 30 (3) (2016) 218–231. Crossref, Web of Science, Google Scholar
18. M. Wisse, D. G. Hobbelen, R. J. Rotteveel, S. O. Anderson and G. J. Zeglin, Ankle springs instead of arc-shaped feet for passive dynamic walkers, in 6th IEEE-RAS Int. Conf. Humanoid Robots (IEEE, Genova, Italy, 2006), pp. 110–116. Google Scholar
19. T. Narukawa, K. Yokoyama, M. Takahashi and K. Yoshida, An experimental study of three-dimensional passive dynamic walking with flat feet and ankle springs, in Cutting Edge Robotics 2010, ed. V. Kordic (INTECH Open Access Publisher, Vukovar, 2010), pp. 131–144. Google Scholar
20. P. Manoonpong, T. Kulvicius, F. Wörgötter, L. Kunze, D. Renjewski and A. Seyfarth, Compliant ankles and flat feet for improved self-stabilization and passive dynamics of the biped robot “RunBot”, in 2011 11th IEEE-RAS Int. Conf. Humanoid Robots (Humanoids) (IEEE, Bled, Slovenia, 2011), pp. 276–281. Google Scholar
21. Q. Wang, L. Wang, Y. Huang, J. Zhu and W. Chen, Three-dimensional quasi-passive dynamic bipedal walking with flat feet and compliant ankles, in Proc. 48th IEEE Conf. Decision and Control, 2009 Held Jointly with the 2009 28th Chinese Control Conf. CDC/CCC 2009 (IEEE, Shanghai, China, 2009), pp. 8200–8205. Google Scholar
22. Q. Wang, Y. Huang and L. Wang, Passive dynamic walking with flat feet and ankle compliance, Robotica 28 (3) (2010) 413–425. Crossref, Web of Science, Google Scholar
23. S. Collins, A. Ruina, R. Tedrake and M. Wisse, Efficient bipedal robots based on passive-dynamic walkers, Science 307 (5712) (2005) 1082–1085. Crossref, Web of Science, Google Scholar
24. C. Chevallereau, J. W. Grizzle and C.-L. Shih, Asymptotically stable walking of a five-link underactuated 3D bipedal robot, IEEE Trans. Robot. 25 (1) (2009) 37–50. Crossref, Web of Science, Google Scholar
25. C. Shih, J. Grizzle and C. Chevallereau, From stable walking to steering of a 3D bipedal robot with passive point feet, Robotica 30(7) (2012) 1119–1130. Crossref, Web of Science, Google Scholar
26. S. Guobiao and M. Zefran, Underactuated dynamic three-dimensional bipedal walking, in IEEE Int. Conf. Robotics and Automation (ICRA) (IEEE, Orlando, USA, 2006), pp. 854–859. Google Scholar
27. M. W. Spong, Passivity-based control of the compass gait biped, in IFAC World Congress (Citeseer, Beijing, China, 1999), pp. 19–24. Google Scholar
28. M. W. Spong and G. Bhatia, Further results on control of the compass gait biped, in Proc. 2003 IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 2003 (IROS 2003) (IEEE, Las Vegas, USA, 2003), pp. 1933–1938. Google Scholar
29. F. Asano, Z. W. Luo and M. Yamakita, Biped gait generation and control based on a unified property of passive dynamic walking, IEEE Trans. Robot. 21 (4) (2005) 754–762. Crossref, Web of Science, Google Scholar
30. J. K. Holm and M. W. Spong, Kinetic energy shaping for gait regulation of underactuated bipeds, in IEEE Int. Conf. Control Applications, 2008 (CCA 2008) (IEEE, 2008), pp. 1232–1238. Google Scholar
31. A. M. Bloch, D. E. Chang, N. E. Leonard and J. E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping, IEEE Trans. Autom. Control 46 (10) (2001) 1556–1571. Crossref, Web of Science, Google Scholar
32. A. M. Bloch, N. E. Leonard and J. E. Marsden, Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem, IEEE Trans. Autom. Control 45 (12) (2000) 2253–2270. Crossref, Web of Science, Google Scholar
33. M. W. Spong and F. Bullo, Controlled symmetries and passive walking, IEEE Trans. Autom. Control 50 (7) (2005) 1025–1031. Crossref, Web of Science, Google Scholar
34. M. W. Spong and F. Bullo, Controlled symmetries and passive walking, in 15th Triennial World Congress (IFAC, Barcelona, Spain, 2002), pp. 557–562. Google Scholar
35. R. D. Gregg and M. W. Spong, Reduction-based control of three-dimensional bipedal walking robots, Int. J. Robot. Res. 29 (6) (2010) 680–702. Crossref, Web of Science, Google Scholar
36. R. D. Gregg and M. W. Spong, Bringing the compass-gait bipedal walker to three dimensions, in IEEE/RSJ Int. Conf. Intelligent Robots and Systems, 2009 (IROS 2009) (IEEE, Michigan, USA, 2009), pp. 4469–4474. Google Scholar
37. Y. Ayaz, K. Munawar, M. B. Malik, A. Konno and M. Uchiyama, Human-like approach to footstep planning among obstacles for humanoid robots, Int. J. Hum. Robot. 4 (01) (2007) 125–149. Link, Web of Science, Google Scholar
38. Z. Jiwen, L. Li and C. Ken, Footstep planning for rapid path following in humanoid robots, Int. J. Hum. Robot. 13(4) (2016) 1650013. Link, Web of Science, Google Scholar
39. F. Gómez-Bravo, G. Carbone and J. Fortes, Collision free trajectory planning for hybrid manipulators, Mechatronics 22 (6) (2012) 836–851. Crossref, Web of Science, Google Scholar
40. Y. Harada, J. Takahashi, D. Nenchev and D. Sato, Limit cycle based walk of a powered 7DOF 3D biped with flat feet, in 2010 IEEE/RSJ Int. Conf. Intelligent Robots and Systems (IROS) (IEEE, Taipei, Taiwan, 2010), pp. 3623–3628. Google Scholar
41. J. Kim, C.-H. Choi and M. W. Spong, Passive dynamic walking with symmetric fixed flat feet, in IEEE Int. Conf. Control and Automation, 2007 (ICCA 2007) (IEEE, Guangzhou, China, 2007), pp. 24–30. Google Scholar
42. K. Farrell, C. Chevallereau and E. Westervelt, Energetic effects of adding springs at the passive ankles of a walking biped robot, in IEEE Int. Conf. Robotics and Automation (IEEE, 2007), pp. 3591–3596. Google Scholar
43. J. W. Grizzle, G. Abba and F. Plestan, Asymptotically stable walking for biped robots: Analysis via systems with impulse effects, IEEE Trans. Autom. Control 46 (1) (2001) 51–64. Crossref, Web of Science, Google Scholar
44. B. Beigzadeh, A. Meghdari and S. Sohrabpour, Passive dynamic object manipulation: A framework for passive walking systems, Proc. Inst. Mech. Eng. K, J. Multi-Body Dyn. 227 (2) (2013) 185–198. Google Scholar