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Variable walking trajectory generation method for biped robots based on redundancy analysis

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Abstract

This paper proposes a variable walking trajectory generation method for biped robots based on redundancy analysis. In designing a bipedal trajectory for locomotion, maintaining locomotion stability without falling down and natural patterns of the locomotion are important. First, the positions and orientations of the feet and body of a robot are chosen as the reference factors, whose trajectories are predetermined. The augmented Jacobian method is used at the acceleration level with differential equation of the reference factors and the ZMP equation to secure stable walking motions. A virtual spring-damper system is implemented as an additional task in the null-space of the augmented Jacobian to make a balanced cyclic configuration of the robot. For a more stable trajectory generation, the condition to avoid kinematic singularity is also used. Computer simulations were conducted for various situations, for example, with locomotion speed changes or an asymmetrical mass distribution, which showed that the proposed trajectory generation method was very effective in generating various walking motions for biped robots.

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References

  1. C. Zhu, Y. Tomizawa, X. Luo and A. Kawamura, Biped walking with variable ZMP, frictional constraint, and inverted pendulum model, Proc. of IEEE International Conference on Robotics and Biomimetics (2004) 425–430.

    Google Scholar 

  2. S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi and H. Hirukawa, Biped walking pattern generation by a simple three-dimensional inverted pendulum model, Advanced Robotics, 17 (2) (2003) 131–147.

    Article  Google Scholar 

  3. P. N. Mousavi, C. Nataraj, A. Bagheri and M. A. Entezari, Mathematical simulation of combined trajectory paths of a seven link biped robot, Applied Mathematical Modelling, 32 (2008) 1445–1462.

    Article  MATH  MathSciNet  Google Scholar 

  4. C. Chevallereau, D. Djoudi and J. W. Grizzle, Stable bipedal walking with foot rotation through direct regulation of the zero moment point, IEEE Transactions on Robotics, 24 (2) (2008) 390–401.

    Article  Google Scholar 

  5. J. S. Yeon, O. Kwon and J. H. Park, Trajectory generation and dynamic control of planar biped robot with curved soles, Journal of Mechanical Science and Technology, 20 (5) (2006) 602–611.

    Article  Google Scholar 

  6. K. Hirai, M. Hirose, Y. Haikawa and T. Takenake, The development of honda humanoid robot, Proc. of IEEE International Conference on Robotics and Automation (1998) 1321–1326.

    Google Scholar 

  7. S. Kajita, M. Morisawa, K. Harada, K. Kaneko, F. Kanehiro, K. Fujiwara and H. Hirukawa, Biped walking pattern generator allowing auxiliary ZMP control, Proc. of IEEE/RSJ International Conference on Intelligent Robots and Systems (2006) 2993–2999.

    Google Scholar 

  8. S. Kajita and K. Tani, Study of dynamic biped locomotion on rugged terrain: Derivation and application of the linear inverted pendulum mode, Proc. of IEEE International Conference on Robotics and Automation (1991) 1405–1411.

    Google Scholar 

  9. J. H. Park and K. D. Kim, Biped robot walking using gravity- compensated inverted pendulum mode and computed torque control, Proc. Of IEEE International Conf. on Robotics & Automation (1998) 3528–3533.

    Google Scholar 

  10. J. S. Yeon and J. H. Park, Redundancy trajectory generation for biped robot manipulators, KSME-A, 33 (10) (2009) 1014–1022.

    Google Scholar 

  11. Y. Ogura, H. Aikawa, K. Shimomura, H. Kondo, A. Morishima, H.-O. Lim and A. Takanishi, Development of a New Humanoid Robot WARIAN-2, Proc. of IEEE International Conference on Robotics and Automation (2006) 76–81.

    Google Scholar 

  12. N. Sonoda, T. Murakami and K. Ohnishi, An approach to biped robot control utilized redundancy in double support phase, Proc. of Industrial Electronics Conference (1997) 1332–1336.

    Google Scholar 

  13. R. Shima, M. Haishi and M. Shibata, Gait control for redundant legged biped robot at constant velocity and constant height of the waist, Electrical Engineering in Japan, 156 (4) (2006) 51–59.

    Article  Google Scholar 

  14. D. Yoo, B. R. So, J. Y. Choi and B.-J. Yi, Study on redundancy resolution algorithm of humanoid, Proc. Of International Conference on Control, Automation and Systems (2003) 2759–2764.

    Google Scholar 

  15. D. Yoo, B. R. So, B.-J. Yi and W. Kim, Motion planning algorithms for kinematically redundant manipulator not fixed to the ground, Journal of Control, Automation and Systems Engineering, 10 (10) (2004) 869–877.

    Article  Google Scholar 

  16. B. R. So, J. Y. Choi and B.-J. Yi, A new ZMP constraint equation with application to motion planning of humanoid using kinematic redundancy, Proc. Of IEEE/RSJ International Conference on Intelligent Robots and Systems (2005) 1794–1800.

    Google Scholar 

  17. Y. Nakamura, Advanced robotics: Redundancy and optimization, Addison-Wesley Publishing Company, Inc. (1991).

    Google Scholar 

  18. R. V. Patel and F. Shadpey, Control of redundant robot manipulators, Springer (2005).

    MATH  Google Scholar 

  19. C. W. Wampler, Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods, IEEE Transactions on Systems, Man, and Cybernetics, 16 (1) (1986) 93–101.

    Article  MATH  Google Scholar 

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Correspondence to Jong Hyeon Park.

Additional information

This paper was presented at the ISR-2013, KINTEX, Seoul, Korea, October 24–26, 2013. Recommended by Guest Editor Byung Kyu Kim

Jesung Yeon received the B.S. degree in Mechanical Engineering from Chungbuk National University, Korea, in 2002 and his M.S. and Ph.D. degrees from Hanyang University in 2004 and 2014, respectively. His research interests include biped robots, quadruped robots, industrial robots, and robot dynamics and control.

Jong Hyeon Park (M’96) received the B.S. degree in Mechanical Engineering from Seoul National University, Seoul, Korea, in 1981 and the S.M. and Ph.D. degrees from the Massachusetts Institute of Technology (MIT), Cambridge, in 1983 and 1991, respectively. Since 1992, he has been with the School of Mechanical Engineering at Hanyang University, Seoul, Korea, where he is currently a Professor. His research interests include biped robots, robot dynamics and control, haptics, and bio-robots.

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Yeon, J.S., Park, J.H. Variable walking trajectory generation method for biped robots based on redundancy analysis. J Mech Sci Technol 28, 4397–4405 (2014). https://doi.org/10.1007/s12206-014-1007-4

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  • DOI: https://doi.org/10.1007/s12206-014-1007-4

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