Journal of Institute of Control, Robotics and Systems (제어로봇시스템학회논문지)

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지
DOI QR코드

DOI QR Code

Energy-Efficient Reference Walking Trajectory Generation Using Allowable ZMP (Zero Moment Point) Region for Biped Robots

2족 보행 로봇을 위한 허용 ZMP (Zero Moment Point) 영역의 활용을 통한 에너지 효율적인 기준 보행 궤적 생성

  • Received : 2010.12.29
  • Accepted : 2011.08.22
  • Published : 2011.10.01
Download PDF
⟨ Previous Next ⟩

Abstract

An energy-efficient reference walking trajectory generation algorithm is suggested utilizing allowable ZMP (Zero-Moment-Point) region, which maxmizes the energy efficiency for cyclic gaits, based on three-dimensional LIPM (Linear Inverted Pendulum Model) for biped robots. As observed in natural human walking, variable ZMP manipulation is suggested, in which ZMP moves within the allowable region to reduce the joint stress (i.e., rapid acceleration and deceleration of body), and hence to reduce the consumed energy. In addition, opimization of footstep planning is conducted to decide the optimal step-length and body height for a given forward mean velocity to minimize a suitable energy performance - amount of energy required to carry a unit weight a unit distance. In this planning, in order to ensure physically realizable walking trajectory, we also considered geometrical constraints, ZMP stability condition, friction constraint, and yawing moment constraint. Simulations are performed with a 12-DOF 3D biped robot model to verify the effectiveness of the proposed method.

Keywords

References

  1. D. Kuo, "Choosing your steps carefully," IEEE Robotics and Automation Magazine, vol. 14, no. 2, pp. 18-29, 2007.
  2. M. Vukobratovic, B. Borovac, D. Surla, and D. Stokic, Biped Locomotion: Dynamics, Stability and Application, Spring-Verlag, 1990.
  3. S. Kajita, F. Kanehiro, K. Kaneko, K. Yokoi, and H. Hirukawa, "The 3D Linear inverted pendulum mode: A simple modeling for a biped walking pattern generation," Proc. 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems, vol. 1, 29, pp. 239-246, 2001.
  4. S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, and H. Hirukawa, "A real-time pattern generator for biped walking," Proc. IEEE International Conference on Robotics and Automation," vol. 1, pp. 31-37, 2002.
  5. K. Harada, S. Kajita, K. Kaneko, and H. Hirukawa, "An analytical method on real-time gait planning for a humanoid robot," Proc. 4th IEEE/RAS International Conference on Humanoid Robots, vol. 2, pp. 640-655, 10-12 Nov. 2004. https://doi.org/10.1109/ICHR.2004.1442676
  6. J. E. A. Bertram, "Analytic path planning algorithms for bipedal robots without a trunk," Journal of Intelligent and Robotics System, 208, pp. 979-991, 2005.
  7. I. Park and J. Back, "Analytical solution for stable bipedal walking trajectory generation using Fourier series," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 15, no. 12, pp. 1216-1222, 2009. https://doi.org/10.5302/J.ICROS.2009.15.12.1216
  8. N. Naksuk and C. S. G. Lee, "Zero moment point manipulability ellipsoid," Proc. IEEE International Conference on Robotics and Automation, pp. 1970-1975, 2006.
  9. J. H. Park and Y. K. Rhee, "ZMP Trajectory generation for reduced trunk motions of biped robots," Proc. IEEE Int. Conf. on Intelligent Robots and Systems, pp. 90-95, 1998.
  10. M. Choi, O. Kwon, M. Kang, and J. H. Park, "Optimal gait trajectory generation and optimal design for a biped robot using genetic algorithm," Journal of Control, Automation, and System Engineering (in Korean), vol. 10, no. 9, pp. 833-839, 2004. https://doi.org/10.5302/J.ICROS.2004.10.9.833
  11. 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, pp. 425-430, 2004.
  12. E. Taskiran, M. Yilmaz, O. Koca, U. Seven, and K. Erbatur, "Trajectory generation with natural ZMP references for the biped walking robot SURALP," IEEE International Conference on Robotics and Automation, pp. 4237-4242, 2010.
  13. K. Erbatur and U. Seven, "Humanoid gait synthesis with moving single support ZMP trajectories," Proc. on 13th IASTED Int. Conf. on Robotics and Applications and Telematics, pp. 95- 100, 2007.
  14. M. Morisawa, K. Harada, S. Kajita, K. Kaneko, F. Kanehiro, K. Fujiwara, S. Nakaoka, and H. Hirukawa, "A biped pattern generation allowing immediate modification of foot placement in real-time," 6th IEEE-RAS International Conference on Humanoid Robots, pp. 581-586, 2006.
  15. H.-O. Lim and A. Takanishi, "Biped walking robots created at waseda university: WL and WABIAN family," Philosophical Transactions of the Royal Society, vol. 365, no. 1850, pp. 49-64, 2007. https://doi.org/10.1098/rsta.2006.1920
  16. I.-W. Park, J.-Y. Kim, and J.-H. Oh, "Online walking pattern generation and its application to a biped humanoid robot- KHR- 3(HUBO)," Journal of Advanced Robotics, vol. 22, pp. 159-190, 2007.
  17. P. Sardain and G. Bessonnet, "Force acting on a biped robot, center of pressure-zero moment point," IEEE Transaction on Systems, Man and Cybernetics Part A, pp. 630-637, 2004.
  18. T. Hirabayashi, B. Ugurlu, A. Kawamura, and C. Zhu, "Yaw moment compensation of biped fast walking using 3D inverted pendulum," IEEE Int. Workshop on Advanced Motion Control, pp. 296-300, 2008.
  19. J. Nishii, K. Ogawa, and R. Suzuki, "The optimal gait pattern in hexapods based on energetic efficiency," Proc. 3rd International Symposium on Artificial Life and Robotics, Beppu, vol. 1, pp. 106-109 , 1998.
  20. M. Nahon and J. Angeles, "Minimization of power losses in cooperating manipulator," Journal of Dynamics System, Measurement, and Control (Trans. ASME), vol. 114, pp. 213- 219, 1992. https://doi.org/10.1115/1.2896517
  21. S. Ma, Time optimal control of manipulators with limit heat characteristics of actuator, Advanced Robotics 16, pp. 309-324, 2002. https://doi.org/10.1163/15685530260174502
  22. A. Goswami, "Foot rotation indicator (FRI) point: a new gait planning tool to evaluate postural stability of biped robots," Proc. IEEE International Conference on Robotics and Automation, vol. 1, pp. 47-52, 10-15 May 1999.
  23. Maxon EC40 120Watt DC Motor Datasheet - http://www.maxonmotor.com.
  24. J. E. A. Bertram, "Constrained optimization in human walking: cost minimization and gait plasticity," Journal of Experimental Biology 208, pp. 979-991, 2005. https://doi.org/10.1242/jeb.01498
  25. K. Erbatur and O. Kurt, "Natural ZMP trajectories for biped robot reference generation," IEEE Transaction on Industrial Electronics, vol. 56, no. 3, pp. 835-845, 2009. https://doi.org/10.1109/TIE.2008.2005150

Cited by

  1. Fault Tolerant Straight-Line Gaits of a Quadruped Robot with Feet of Flat Shape vol.18, pp.2, 2012, https://doi.org/10.5302/J.ICROS.2012.18.2.141