Dynamics modeling and stable gait planning of a quadruped robot in walking over uneven terrains

Document Type : Research Paper


Center of Excellence in Robotics and Control Advanced Robotics and Automated Systems Lab, Dept of Mech Eng, K. N. Toosi Univ of Tech, Tehran, Iran.


Quadruped robots have unique capabilities for motion over uneven natural environments. This article presents a stable gait for a quadruped robot in such motions and discusses the inverse-dynamics control scheme to follow the planned gait. First, an explicit dynamics model will be developed using a novel constraint elimination method for an 18-DOF quadruped robot. Thereafter, an inverse-dynamics control will be introduced using this model. Next, a dynamically stable condition under sufficient friction assumption for the motion of the robot on uneven terrains will be obtained. Satisfaction of this condition assures that the robot does not tip over all the support polygon edges. Based on this stability condition, a constrained optimization problem is defined to compute a stable and smooth center of gravity (COG) path. The main feature of the COG path is that the height of the robot can be adjusted to follow the terrain. Then, a path generation algorithm for tip of the swing legs will be developed. This smooth path is planned so that any collision with the environment is avoided. Finally, the effectiveness of the proposed method will be verified.


Main Subjects

[1]. Raibert, M. 2008, "BigDog, the Rough-Terrain Quadruped Robot," in Proceedings of the 17th
IFAC World Congress, COEX, Korea, South.
[2]. Semini, C. 2010, "HyQ - Design and Development of a Hydraulically Actuated Quadruped Robot," Doctor of Philosophy (Ph.D.), University of Genoa, Italy.
[3]. Hutter, M., Gehring, M., Bloesch, M., Mark, A.H., Remy, C.D. and Siegwart, R.Y. 2013, StarlETH: A compliant quadrupedal robot for fast, efficient, and versatile locomotion: Autonomous Systems Lab, ETH Zurich.
[4]. Moosavian, S.A.A., Alghooneh, M. and Takhmar, A. 2009, "Cartesian approach for gait planning and control of biped robots on irregular surfaces," International Journal of Humanoid Robotics, vol. 6, pp. 675-697.
[5]. Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K. and Hirukawa, H. 2003, "Biped walking pattern generation by using preview control of zero-moment point," in Robotics and Automation, 2003. Proceedings. ICRA '03. IEEE International Conference on, Vol. 2, pp. 1620-1626.
[6]. Sardain P. and Bessonnet, G. 2004, "Forces acting on a biped robot. Center of pressure-zero moment point," Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on, Vol. 34, pp. 630-637.
[7]. Takao, S., Yokokohji, Y. and Yoshikawa, T. 2003, "FSW (feasible solution of wrench) for multi-legged robots," in Robotics and Automation, 2003. Proceedings. ICRA'03. IEEE International Conference on, pp. 3815-3820.
[8]. Ajallooeian, M., Gay, S., Tuleu, A., Sprowitz, A. and Ijspeert, A.J. 2013, "Modular control of limit cycle locomotion over unperceived rough terrain," in Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on, pp. 3390-3397.
[9]. Hirukawa, H., Hattori, S., Harada, K., Kajita, S., Kaneko, Kanehiro, K.F., Fujiwara, K. and Morisawa, M. 2006, "A universal stability criterion of the foot contact of legged robotsadios ZMP," in Robotics and Automation, 2006. ICRA 2006. Proceedings 2006 IEEE International Conference on, pp. 1976-1983.
[10]. Papadopoulos E. and Rey, D.A. 1996, "A new measure of tipover stability margin for mobile manipulators," in Robotics and Automation, 1996. Proceedings., 1996 IEEE International Conference on, pp. 3111-3116.
[11] . Sugihara, T., Nakamura, Y. and Inoue, H. 2002, "Real-time humanoid motion generation through ZMP manipulation based on inverted pendulum control," in Robotics and Automation, 2002. Proceedings. ICRA'02. IEEE International Conference on, pp. 1404-1409.
[12]. Kalakrishnan, M., Buchli, J., Pastor, P., Mistry, M. and Schaal, S. 2011, "Learning, planning, and control for quadruped locomotion over challenging terrain," The International Journal of Robotics Research, Vol. 30, pp. 236- 258.
[13]. Zheng, Y., Lin, M.C., Manocha, D., Adiwahono, A.H. and Chew, C.M. 2010, "A walking pattern generator for biped robots on uneven terrains," in Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on, pp. 4483-4488.
[14]. Alipour K. and Moosavian, S.A.A. 2012, "Effect of terrain traction, suspension stiffness and grasp posture on the tip-over stability of wheeled robots with multiple arms," Advanced Robotics, Vol. 26, pp. 817-842.
[15]. Craig, J.J. 2005, Introduction to robotics : mechanics and control, 3rd ed. Upper Saddle River, N.J.: Pearson/Prentice Hall.
[16]. Featherstone, R. 2008, Rigid body dynamics algorithms, Vol. 49: Springer New York.
[17]. Moosavian S.A.A. and Papadopoulos, E. 2004, "Explicit dynamics of space free-flyers with multiple manipulators via SPACEMAPLE," Advanced Robotics, Vol. 18, pp. 223-244.
[18]. Mistry, M., Buchli, J. and Schaal, S. 2010, "Inverse dynamics control of floating base systems using orthogonal decomposition," in Robotics and Automation (ICRA), 2010 IEEE International Conference on, pp. 3406-3412.
[19]. Aghili, F. 2005, "A unified approach for inverse and direct dynamics of constrained multibody systems based on linear projection operator: applications to control and simulation," Robotics, IEEE Transactions on,  Vol. 21, pp. 834-849.
[20]. Righetti, L., Buchli, J., Mistry, M. and Schaal, S. 2011, "Inverse dynamics control of floating-base robots with external constraints: A unified view," in Robotics and Automation (ICRA), 2011 IEEE International Conference on, pp. 1085-1090.
[21]. Kurazume, R., Hirose, S. and Yoneda, K. 2001, "Feedforward and feedback dynamic trot gait control for a quadruped walking vehicle," in Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, pp. 3172-3180, Vol.3.
[22]. Yoneda, K., Iiyama, H. and Hirose, H. 1996, "Intermittent trot gait of a quadruped walking machine dynamic stability control of an omnidirectional walk," in Robotics and Automation, 1996. Proceedings., 1996 IEEE International Conference on, pp. 3002-3007.
[23] .Song S.M. and Waldron, K.J. 1989, Machines that walk: the adaptive suspension vehicle: MIT press.
[24]. McGhee R.B. and Frank, A.A. 1968, "On the stability properties of quadruped creeping gaits," Mathematical Biosciences, vol. 3, pp. 331-351.
[25]. Hutter, M. 2013, "StarlETH & Co-design and control of legged robots with compliant actuation," Diss., Eidgenössische Technische Hochschule ETH Zürich, Nr. 21073,.
  • Receive Date: 11 July 2015
  • Revise Date: 16 August 2015
  • Accept Date: 16 August 2015