From Passive Dynamic Walking to Passive Turning of Biped walker

Document Type : Research Paper


1 School of Mechanical Engineering, University of Tehran, Iran.

2 School of Mechanical Engineering, Iran University of Science and Technology, Iran.


Dynamically stable biped robots mimicking human locomotion have received significant attention over the last few decades. Formerly, the existence of stable periodic gaits for straight walking of passive biped walkers was well known and investigated as the notion of passive dynamic walking. This study is aimed to elaborate this notion in the case of three dimensional (3D) walking and extend it for other maneuvers, specifically curved walking or turning. For this purpose, the motion of a general 3D compass gait model on a ramp has been analyzed theoretically in detail. A comprehensive dynamic modeling with respect to the vertical fixed frame is used based on Lagrangian and augmented methods. In addition to 3D passive straight walking, the results confirm the existence of some passive turning motions for the biped walker towards the steepest decent of the ramp. It was shown that the value of passive turning is strictly concerned to the value of initial perturbed condition of the walker, especially to the value of heading angle. A parameter analysis was also accompanied to examine the change in the characteristics of such passive motions caused by the change in model parameters.


Main Subjects

[1]   F. Farzadpour, M. Danesh, S. M. TorkLarki, Development of multi-phase dynamic equations for a seven-link biped robot with improved foot rotation in the double support phase, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol. 229, No. 1, pp. 3-17, 2015.
[2]   T. McGeer, Passive dynamic walking, The International Journal of Robotics Research, Vol. 9, No. 2, pp. 62-82, 1990.
[3]   T. McGeer, Passive dynamic biped catalogue, in Proceeding of Experimental Robotics II: The 2nd International Symposium, Springer-Verlag, pp. 463-490, 1991.
[4]   M. J. Coleman, M. Garcia, K. Mombaur, A. Ruina, Prediction of stable walking for a toy that cannot stand, Physical Review E, Vol. 64, No. 2, pp. 022901, 2001.
[5]   A. Goswami, B. Thuilot, B. Espiau, Compass-like biped robot part I: Stability and bifurcation of passive gaits, 1996.
[6]   M. W. Spong, Passivity based control of the compass gait biped, in Proceeding of IFAC World Congress, Citeseer, pp. 19-24, 1999.
[7]   M. S. Orendurff, A. D. Segal, J. S. Berge, K. C. Flick, D. Spanier, G. K. Klute, The kinematics and kinetics of turning: limb asymmetries associated with walking a circular path, Gait & Posture, Vol. 23, No. 1, pp. 106-111, 2006.
[8]   R. D. Gregg IV, Geometric control and motion planning for three-dimensional bipedal locomotion, Ph.D. Thesis, Electrical & Computer Engr, University of Illinois at Urbana-Champaign, 2011.
[9]   R. D. Gregg, A. K. Tilton, S. Candido, T. Bretl, M. W. Spong, Control and Planning of 3D Dynamic Walking with Asymptotically Stable Gait Primitives, 2012.
[10] C. Shih, J. Grizzle, C. Chevallereau, Asymptotically stable walking and steering of a 3D bipedal robot with passive point feet, IEEE Transactions on Robotics, 2009.
[11] S. Lim, Y. I. Son, Discrete-Time Circular Walking Pattern for Biped Robots, Journal of Electric Engineering Technology, Vol. 2, No. 2, pp. 2, 2016.
[12] Y. Cao, S. Suzuki, Turn Control of a Three-Dimensional Quasi-Passive Walking Robot by Utilizing a Mechanical Oscillator, Engineering, Vol. 6, pp. 93-99, 2014.
[13] F. Ikeda, S. Toyama, A proposal of right and left turning mechanism for quasi-passive walking robot, in Proceeding of International Conference on Advanced Robotics and Intelligent Systems (ARIS) 2015, 1-5, 2015.
[14] M. R. Sabaapour, M. R. Hairi-Yazdi, B. Beigzadeh, Towards Passive Turning in Biped Walkers, Procedia Technology, Vol. 12, No. 0, pp. 98-104, 2014.
[15] M. R. Sabaapour, M. R. Hairi-Yazdi, B. Beigzadeh, Passive Turning Motion of 3D Rimless Wheel: Novel Periodic Gaits for Bipedal Curved Walking, Advanced Robotics, 2015.
[16] M. Wisse, Three additions to passive dynamic walking; actuation, an upper body, and 3D stability, in Proceeding of 2004 4th IEEE/RAS International Conference on Humanoid Robots, IEEE, pp. 113-132, 2004.
[17] M. Wisse, R. Q. van der Linde, 2007, Delft pneumatic bipeds, Springer Berlin Heidelberg, Germany
[18]      J. W. Grizzle, G. Abba, F. Plestan, Asymptotically stable walking for biped robots: Analysis via systems with impulse effects, Automatic Control, IEEE Transactions on, Vol. 46, No. 1, pp. 51-64, 2001.
Volume 47, Issue 1
June 2016
Pages 24-34
  • Receive Date: 01 January 2016
  • Revise Date: 18 March 2016
  • Accept Date: 02 April 2016