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Optimal gait planning for humanoids with 3D structure walking on slippery surfaces

Published online by Cambridge University Press:  01 September 2015

Majid Khadiv*
Affiliation:
Center of Excellence in Robotics and Control, Advanced Robotics & Automated Systems (ARAS) Lab, Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
S. Ali A. Moosavian
Affiliation:
Center of Excellence in Robotics and Control, Advanced Robotics & Automated Systems (ARAS) Lab, Department of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
Aghil Yousefi-Koma
Affiliation:
Center of Advanced Systems and Technologies (CAST), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Majid Sadedel
Affiliation:
Center of Advanced Systems and Technologies (CAST), School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
Saeed Mansouri
Affiliation:
Department of Mechanical Engineering, Sharif University of Technology, Tehran, Iran
*
*Corresponding author. E-mail: [email protected]

Summary

In this study, a gait optimization routine is developed to generate walking patterns which demand the lowest friction forces for implementation. The aim of this research is to fully address the question “which walking pattern demands the lowest coefficient of friction amongst all feasible patterns?”. To this end, first, the kinematic structure of the considered 31 DOF (Degrees of Freedom) humanoid robot is investigated and a closed-form dynamics model for its lower-body is developed. Then, the medium through which the walking pattern generation is conducted is presented. In this medium, after designing trajectories for the feet and the pelvis, the joint space variables are obtained, using the inverse kinematics. Finally, by employing a genetic algorithm (GA), an optimization process is conducted to generate walking patterns with the minimum Required Coefficient Of Friction (RCOF). Six parameters are adopted to parameterize the pelvis trajectory and are exploited as the design variables in this optimization procedure. Also, a parametrical study is accomplished to address the effects of some other variables on RCOF. For comparison purposes, a tip-over Stability Margin (SM) is defined, and an optimization procedure is conducted to maximize this margin. Finally, the proposed gait planning procedure is implemented on SURENA III, a humanoid robot designed and fabricated in CAST, to validate the developed simulation procedure. The obtained results reveal merits of the proposed optimal gait planning procedure in terms of RCOF.

Type
Articles
Copyright
Copyright © Cambridge University Press 2015 

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References

1. Channon, P., Hopkins, S. and Pham, D., “Derivation of optimal walking motions for a bipedal walking robot,” Robotica 10 (02), 165172 (1992).Google Scholar
2. Chevallereau, C. and Aoustin, Y., “Optimal reference trajectories for walking and running of a biped robot,” Robotica 19 (05), 557569 (2001).CrossRefGoogle Scholar
3. Rostami, M. and Bessonnet, G., “Sagittal gait of a biped robot during the single support phase. Part 2: Optimal motion,” Robotica 19 (03), 241253 (2001).CrossRefGoogle Scholar
4. Bessonnet, G., Seguin, P. and Sardain, P., “A parametric optimization approach to walking pattern synthesis,” Int. J. Robot. Res. 24 (7), 523536 (2005).Google Scholar
5. Sadigh, M. J. and Mansouri, S., “Application of phase-plane method in generating minimum time solution for stable walking of biped robot with specified pattern of Motion,” Robotica 31 (06), 837851 (2013).Google Scholar
6. Goswami, A., “Postural stability of biped robots and the foot-rotation indicator (FRI) point,” Int. J. Robot. Res. 18 (6), 523533 (1999).Google Scholar
7. Popovic, M. B., Goswami, A. and Herr, H., “Ground reference points in legged locomotion: Definitions, biological trajectories and control implications,” Int. J. Robot. Res. 24 (12), 10131032 (2005).Google Scholar
8. Vukobratović, M. and Stepanenko, J., “Mathematical models of general anthropomorphic systems,” Math. Biosci. 17 (3), 191242 (1973).CrossRefGoogle Scholar
9. Vukobratović, M. and Borovac, B., “Zero-moment point––thirty five years of its life,” Int. J. Humanoid Robot. 1 (01), 157173 (2004).Google Scholar
10. 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 ICRA'03, IEEE International Conference on. Robotics and Automation, (IEEE, 2003) pp. 1620–1626.Google Scholar
11. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Yokoi, K. and Hirukawa, H., “Biped walking pattern generation by a simple three-dimensional inverted pendulum model,” Adv. Robot. 17 (2), 131147 (2003).CrossRefGoogle Scholar
12. Kagami, S., Kitagawa, T., Nishiwaki, K., Sugihara, T., Inaba, M. and Inoue, H., “A fast dynamically equilibrated walking trajectory generation method of humanoid robot,” Auton. Robots 12 (1), 7182 (2002).Google Scholar
13. 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).CrossRefGoogle Scholar
14. Dau, V.-H., Chew, C.-M. and Poo, A.-N., “Achieving energy-efficient bipedal walking trajectory through GA-based optimization of key parameters,” Int. J. Humanoid Robot. 6 (04), 609629 (2009).Google Scholar
15. Capi, G., Nasu, Y., Barolli, L., Mitobe, K. and Takeda, K., “Application of genetic algorithms for biped robot gait synthesis optimization during walking and going up-stairs,” Adv. Robot. 15 (6), 675694 (2001).Google Scholar
16. Park, J. H. and Choi, M., “Generation of an optimal gait trajectory for biped robots using a genetic algorithm,” JSME Int. J. Ser. C 47 (2), 715721 (2004).Google Scholar
17. Chambers, A. J., Perera, S. and Cham, R., “Changes in walking characteristics of young and older adults when anticipating slippery floors,” IIE Trans. Occup. Ergon. Hum. Factors 1 (3), 166175 (2013).Google Scholar
18. Oates, A. R., Frank, J. S. and Patla, A. E., “Control of dynamic stability during adaptation to gait termination on a slippery surface,” Exp. Brain Res. 201 (1), 4757 (2010).Google Scholar
19. Fong, D. T.-P., Hong, Y. and Li, J.-X., “Human walks carefully when the ground dynamic coefficient of friction drops below 0.41,” Saf. Sci. 47 (10), 14291433 (2009).Google Scholar
20. Cooper, R. C., Prebeau-Menezes, L. M., Butcher, M. T. and Bertram, J. E., “Step length and required friction in walking,” Gait & Posture 27 (4), 547551 (2008).CrossRefGoogle ScholarPubMed
21. Nagano, H., Sparrow, W. and Begg, R. K., “Biomechanical characteristics of slipping during unconstrained walking, turning, gait initiation and termination,” Ergonomics 56 (6), 10381048 (2013).Google Scholar
22. Chang, W.-R., Lesch, M. F., Chang, C.-C. and Matz, S., “Contribution of gait parameters and available coefficient of friction to perceptions of slipperiness,” Gait & Posture 41 (1), 288290 (2015).CrossRefGoogle ScholarPubMed
23. Chang, W.-R., Chang, C.-C. and Matz, S., “Comparison of different methods to extract the required coefficient of friction for level walking,” Ergonomics 55 (3), 308315 (2012).Google Scholar
24. Yamamoto, H. and Ohnishi, K., “An Approach to Stable Walking on unknown Slippery Floor for Biped Robot,” The 27th Annual Conference of the IEEE. Industrial Electronics Society, (IEEE, 2001) pp. 1728–1733.Google Scholar
25. Kaneko, K., Kanehiro, F., Kajita, S., Morisawa, M., Fujiwara, K., Harada, K. and Hirukawa, H., “Slip Observer for Walking on a Low Friction Floor,” IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, 2005) pp. 634–640.Google Scholar
26. Hashlamon, I. and Erbatur, K., “Ground Reaction Force Sensor Fault Detection and Recovery Method based on Virtual Force Sensor for walking Biped Robots,” 9th Asian. Control Conference (ASCC), (IEEE, 2013) pp. 1–6.Google Scholar
27. Roosen, S., “Ground-Contact Friction Estimation and Slip Prevention in Bipedal Robots,” Master Thesis, (University of Melbourne, Department of Mechanical Engineering, 2012).Google Scholar
28. Bliman, P. and Sorine, M., “Easy-to-use Realistic Dry Friction Models for Automatic Control,” Proceedings of 3rd European Control Conference, Rome, Italy, (1995) pp. 3788–3794.Google Scholar
29. Zhou, X., Guan, Y., Jiang, L., Zhu, H., Cai, C., Wu, W. and Zhang, H., “Stability of biped robotic walking with frictional constraints,” Robotica 31 (04), 573588 (2013).Google Scholar
30. Hirabayashi, T., Ugurlu, B., Kawamura, A. and Zhu, C., “Yaw Moment Compensation of Biped Fast Walking using 3D Inverted Pendulum,” AMC'08. 10th IEEE International Workshop on. Advanced Motion Control (IEEE, 2008) pp. 296–300.Google Scholar
31. Ugurlu, B., Saglia, J. A., Tsagarakis, N. G. and Caldwell, D. G., “Yaw moment compensation for bipedal robots via intrinsic angular momentum constraint,” Int. J. Humanoid Robot. 9 (04), (2012).CrossRefGoogle Scholar
32. Kajita, S., Kaneko, K., Harada, K., Kanehiro, F., Fujiwara, K. and Hirukawa, H., “Biped walking on a Low Friction Floor,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, (IEEE, 2004) pp. 3546–3552.Google Scholar
33. Brandao, M., Hashimoto, K., Santos-Victor, J. and Takanishi, A., “Gait planning for biped locomotion on slippery terrain,” In: 14th IEEE-RAS International Conference on, Humanoid Robots (IEEE, 2014), pp. 303–308.Google Scholar
34. Boone, G. N. and Hodgins, J. K., “Slipping and tripping reflexes for bipedal robots,” Auton. Robots 4 (3), 259271 (1997).Google Scholar
35. Kwon, O. and Park, J. H., “Reflex control of bipedal locomotion on a slippery surface,” Adv. Robot. 16 (8), 721734 (2002).Google Scholar
36. Khadiv, M., Ali, S., Moosavian, A. and Sadedel, M., “Dynamics Modeling of Fully-Actuated Humanoids with General Robot-Environment Interaction,” International Conference on Robotics and Mechatronics (ICROM), Tehran, Iran (IEEE, 2014).Google Scholar
37. Park, H. A., Ali, M. A. and Lee, C. G., “Closed-form inverse kinematic position solution for humanoid robots,” Int. J. Humanoid Robot. 9 (03), (2012).Google Scholar
38. Khadiv, M. and Ali, S., Moosavian, A., “A low friction demanding approach in gait planning for humanoid robots during 3D manoeuvres,” J. Appl. Mech. 45 (1), 4760 (2014).Google Scholar