Advertisement

Optimal Stair Climbing Pattern Generation for Humanoids Using Virtual Slope and Distributed Mass Model

  • Ahmadreza Shahrokhshahi
  • Aghil Yousefi-KomaEmail author
  • Majid Khadiv
  • Saeed Mansouri
  • Seyed Saeid Mohtasebi
Article
  • 12 Downloads

Abstract

This study addresses optimal walking pattern generation for SURENA III humanoid robot in a stair-climbing scenario. To this end, the kinematic configuration of the 31-DOF humanoid robot is studied. Integrating the detailed dynamic properties of the robot, a comprehensive and precise dynamic model is developed for its lower-limb. In order to generate the optimal walking pattern for the considered humanoid robot, trajectories for feet and pelvis are first designed, and then joint angles are derived by means of inverse kinematics. Such a complete model provides the designer with the necessary tools to optimize the trajectory generation. Using two different types of objective functions, namely joints maximum torque and overall energy consumption, several optimization processes have been carried out to account for different stair-climbing speeds as well as different stair heights. Subsequently, the optimal walking patterns are obtained by applying the Genetic Algorithm (GA). The simulation results are verified experimentally by implementing the proposed walking patterns on SURENA III, a humanoid robot designed and fabricated in CAST (Center of Advanced Systems and Technologies). This paper provides insight into how an optimized gait for climbing stairs can be realized for a human-size humanoid robot from two different viewpoints and at several walking speeds and stair heights by assuming each stair as a virtual slope.

Keywords

Humanoid robot Distributed mass model Stair Trajectory generation Virtual slope Zero-Moment Point (ZMP) 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgements

The authors would like to thank CAST members who provided insight and expertise that greatly assisted this research and Iran National Science Foundation (INSF) for their financial support.

References

  1. 1.
    Vukobratovic, M.: Contribution to the study of anthropomorphic systems. Kybernetika 8(5), 404–418 (1972)zbMATHGoogle Scholar
  2. 2.
    Goswami, A.: Postural stability of biped robots and the foot-rotation indicator (FRI) point. Int. J. Rob. Res. 18(6), 523–533 (1999)CrossRefGoogle Scholar
  3. 3.
    Hirukawa, H., et al.: A universal stability criterion of the foot contact of legged robots - Adios ZMP. Proc IEEE Int. Conf. Robot. Autom. 2006, 1976–1983 (2006)Google Scholar
  4. 4.
    Loffler, K., Gienger, M., Pfeiffer, F.: Sensor and control design of a dynamically stable biped robot,” 2003. IEEE Int. Conf. Robot. Autom. (Cat. No.03CH37422) 1, 484–490 (2003)CrossRefGoogle Scholar
  5. 5.
    Kuffner, J.J., Kagami, S., Nishiwaki, K., Inaba, M., Inoue, H.: Dynamically-stable motion planning for humanoid robots. Auton. Robot. 12(1), 105–118 (2002)CrossRefGoogle Scholar
  6. 6.
    Liu, J., Urbann, O.: Bipedal walking with dynamic balance that involves three-dimensional upper body motion. Rob. Auton. Syst. 77, 39–54 (2016)CrossRefGoogle Scholar
  7. 7.
    Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Yokoi, K., Hirukawa, H.: Biped walking pattern generation by a simple three-dimensional inverted pendulum model. Adv. Robot. 17(2), 131–147 (2003)CrossRefGoogle Scholar
  8. 8.
    Kuo, A.D., Donelan, J.M., Ruina, A.: Energetic consequences of walking like an inverted pendulum: step-to-step transitions. Exerc. Sport Sci. Rev. 33(2), 88–97 (2005)CrossRefGoogle Scholar
  9. 9.
    Kajita, S., Kanehiro, F., Kaneko, K., Yokoi, K., Hirukawa, H.: The 3D linear inverted pendulum model: a simple modeling for biped walking pattern generation. In: Proc. 2001 IEEE/RSJ Int. Conf. Intell. Robot. Syst., 2016, pp. 239–246 (2011)Google Scholar
  10. 10.
    Kobayashi, T., Hasegawa, Y., Sekiyama, K., Aoyama, T., Fukuda, T.: Unified bipedal gait for walking and running by dynamics-based virtual holonomic constraint in PDAC. In: Proceedings IEEE Int. Conf. Robot. Autom., pp. 1769–1775 (2016)Google Scholar
  11. 11.
    Park, J.H.: Fuzzy-logic zero-moment-point trajectory generation for reduced trunk motions of biped robots. Fuzzy Sets Syst. 134(1), 189–203 (2003)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Takanishi, A., Kato, I.: A biped walking robot having a ZMP measurement system using universal force-moment sensors. In: Proc. IROS ’91IEEE/RSJ Int. Work. Intell. Robot. Syst. ’91, issue 91, pp. 1568–1573 (1991)Google Scholar
  13. 13.
    Erbatur, K., Okazaki, A., Obiya, K., Takahashi, T, Kawamura, A: A study on the zero moment point measurement for biped walking robots. In: 2002 7th International Workshop on Advanced Motion Control, pp. 431–436 (2002)Google Scholar
  14. 14.
    Harada, K., Kajita, S., Kaneko, K., Hirukawa, H.: An analytical method for ral-time gait planning for a humanoid robot. Int. J. Humanoid Robot. 03(01), 1–19 (2006)CrossRefGoogle Scholar
  15. 15.
    Sato, T., Sakaino, S., Ohnishi, K.: Real-time walking trajectory generation method at constant body height in single support phase for three-dimensional biped robot. In: Proceedings of the IEEE International Conference on Industrial Technology (2009)Google Scholar
  16. 16.
    Hopkins, S.H., Pham, D.T.: Derivation of optimal walking motions for a bipedal walking robot. Robotica 10(2), 165–172 (1992)CrossRefGoogle Scholar
  17. 17.
    Chevallereau, C., Aoustin, Y.: Optimal reference trajectories for walking and running of a biped robot. Robotica 19(05), 557–569 (Sep. 2001)CrossRefGoogle Scholar
  18. 18.
    Dau, V.-H., Chew, C.-M., Poo, A.-N.: Achieving energy-efficient bipedal walking trajectory through ga-based optimization of key parameters. Int. J. Humanoid Robot. 06(04), 609–629 (2009)CrossRefGoogle Scholar
  19. 19.
    Rostami, M., Bessonnet, G.: Sagittal gait of a biped robot during the single support phase. Part 2: Optimal motion. Robotica 19(3), 241–253 (2001)CrossRefGoogle Scholar
  20. 20.
    Bessonnet, G.: A parametric optimization approach to walking pattern synthesis. Int. J. Rob. Res. 24(7), 523–536 (2005)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Löffler, K., Gienger, M., Pfeiffer, F., Ulbrich, H.: Sensors and control concept of a biped robot. IEEE Trans. Ind. Electron. 51(5), 972–980 (2004)CrossRefGoogle Scholar
  22. 22.
    Channon, P.H., Hopkins, S.H., Pham, D.T.: A variational approach to the optimization of gait for a bipedal robot. In: Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci., vol. 2, pp. 210 (1996)Google Scholar
  23. 23.
    Escande, A., Kheddar, A.: Contact planning for acyclic motion with tasks constraints. In: 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2009, pp. 435–440 (2009)Google Scholar
  24. 24.
    Lengagne, S., Mathieu, P., Kheddar, A., Yoshida, E.: Generation of dynamic motions under continuous constraints: Efficient computation using B-splines and taylor polynomials. In: IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems, IROS 2010 - Conference Proceedings, pp. 698–703 (2010)Google Scholar
  25. 25.
    Jeon, K.S., Kwon, O., Park, J.H.: Optimal trajectory generation for a biped robot walking a staircase based on genetic algorithms. Intell. Robot. Syst. 2004. (IROS 2004). Proceedings. 2004 IEEE/RSJ Int. Conf. 3(1), 2837–2842 (2004)Google Scholar
  26. 26.
    Kajita, S., et al.: Biped walking pattern generation by using preview control of zero-moment point. In: 2003 IEEE Int. Conf. Robot. Autom. (Cat. No.03CH37422), pp. 1620–1626 (2003)Google Scholar
  27. 27.
    Wieber, P.-B.: Trajectory free linear model predictive control for stable walking in the presence of strong perturbations. IEEE-RAS Int. Conf. Humanoid. Robot (2006)Google Scholar
  28. 28.
    Brasseur, C., Sherikov, A., Collette, C., Dimitrov, D., Wieber, P.B.: A Robust linear MPC approach to online generation of 3D biped walking motion. IEEE-RAS Int. Conf. Humanoid Robot. 595–601 (2015)Google Scholar
  29. 29.
    Morisawa, M., et al.: Pattern generation of biped walking constrained on parametric surface. Proc. IEEE Int. Conf. Robot. Autom. 2005, 2405–2410 (2005)Google Scholar
  30. 30.
    Fu, C., Chen, K.: Gait synthesis and sensory control of stair climbing for a humanoid robot. IEEE Trans. Ind. Electron. 55(5), 2111–2120 (2008)CrossRefGoogle Scholar
  31. 31.
    Nishiwaki, K., et al.: Online generation of humanoid walking motion based on a fast generation method of motion pattern that follows desired zmp. Intell. Robot. Syst. 3, 2684–2689 (2002)MathSciNetGoogle Scholar
  32. 32.
    Sato, T., Sakaino, S., Ohashi, E., Ohnishi, K.: Walking trajectory planning on stairs using virtual slope for biped robots. IEEE Trans. Ind. Electron. 58(4), 1385–1396 (2011)CrossRefGoogle Scholar
  33. 33.
    Khadiv, M., Moosavian, S.A.A., Sadedel, M: Dynamics modeling of fully-actuated humanoids with general robot-environment interaction. In: 2014 2nd RSI/ISM International Conference on Robotics and Mechatronics, ICRoM 2014, pp 233–238 (2014)Google Scholar
  34. 34.
    Khadiv, M., Moosavian, S.A.A., Yousefi-Koma, A., Sadedel, M., Mansouri, S.: Optimal gait planning for humanoids with 3D structure walking on slippery surfaces. Robotica 35(3), 569–587 (2017)CrossRefGoogle Scholar
  35. 35.
    Ali, M.A., Park, H.A., Lee, C.S.G.: Closed-form inverse kinematic joint solution for humanoid robots. In: IEEE/RSJ 2010 International Conference on Intelligent Robots and Systems, IROS, pp. 704–709 (2010)Google Scholar
  36. 36.
    Khadiv, M., Moosavian, S.A.A., Yousefi-Koma, A., Maleki, H., Sadedel, M.: Online adaptation for humanoids walking on uncertain surfaces. In: Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. (2017)Google Scholar
  37. 37.
    Shahrokhshahi, A., Khalili, M., Yousefi-Koma, A., Mahdavian, M: System identification of a humanoid robot power transmission system. In: 2014 2nd RSI/ISM International Conference on Robotics and Mechatronics, ICRoM 2014, pp. 328–332 (2014)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Ahmadreza Shahrokhshahi
    • 1
  • Aghil Yousefi-Koma
    • 2
    Email author
  • Majid Khadiv
    • 3
  • Saeed Mansouri
    • 4
  • Seyed Saeid Mohtasebi
    • 5
  1. 1.Mechatronic Systems EngineeringSimon Fraser UniversityBritish ColumbiaCanada
  2. 2.Department of Mechanical Engineering, School of EngineeringUniversity of TehranTehranIran
  3. 3.Max Planck Institute for Intelligent SystemsStuttgartGermany
  4. 4.Department of Mechanical EngineeringSharif University of TechnologyTehranIran
  5. 5.Department of Mechanical Engineering of Agricultural MachineryUniversity of TehranAlborzIran

Personalised recommendations