Energy Dissipation Rate Control Via a Semi-Analytical Pattern Generation Approach for Planar Three-Legged Galloping Robot based on the Property of Passive Dynamic Walking

Document Type : Research Paper


1 M.Sc. Student, School of Mechanical Engineering College of Engineering, University of Tehran, Tehran, Iran

2 Associate Professor, School of Mechanical Engineering College of Engineering, University of Tehran, Tehran, Iran


In this paper an Energy Dissipation Rate Control (EDRC) method is introduced, which could provide stable walking or running gaits for legged robots. This method is realized by developing a semi-analytical pattern generation approach for a robot during each Single Support Phase (SSP). As yet, several control methods based on passive dynamic walking have been proposed by researchers to provide an efficient human-like biped walking robot. For most of these passive based controllers the main idea is to shape the robot’s energy level during each SSP to restore the mechanical energy which has been lost in the previous Impact Phases (IP); however, the EDRC method provides stable gaits for legged robots just by controlling the robot’s energy level during each IP. In this paper EDRC is applied to a Six-Link Three-Point Foot (6L3PF) model, to realize an active dynamic galloping gait on level ground. As the point-foot contact assumption for the 6L3PF imposes one degree of under-actuation in the ankle joint, it is not clear how to specify the forward kinematic defining the swing leg position and velocity as a function of actuated joint angles. So, a new strategy for solving the dynamic and kinematic equations of the robot is introduced for deriving suitable joint trajectories during each SSP. Simulation results show that the proposed methods in this paper are effective and the robot exhibits a stable dynamic galloping gait on level ground.


Main Subjects

[1].McGeer, T., 1990, “Passive Dynamic Walking,”
Int. J. Rob. Res., 9(2), pp. 62–82.
[2].McGeer, T., 1990, “Passive walking with
knees,” Robotics and Automation, 1990.
Proceedings., 1990 IEEE International
Conference on, IEEE, pp. 1640–1645.
[3].Kamath, a. K., and Singh, N. M., 2009, “Impact
dynamics based control of compass gait biped,”
2009 Am. Control Conf., (1), pp. 4357–4360.
[4].Farrell, M., “Control of the Compass Biped via
Hip Actuation and Weight Perturbation for
Small Angles and Level Ground Walking,”
[5].Spong, M., 1999, “Passivity based control of the
compass gait biped,” Proc. IFAC World Congr.
Beijing, China, pp. 19–24.
[6].Spong, M. W., and Bhatia, G., 2003, “Further 
results on control of the compass gait biped,” Proc. 2003 IEEE/RSJ Int. Conf. Intell. Robot. Syst. (IROS 2003) (Cat. No.03CH37453), 2. [7].Asano, F., and Yamakita, M., 2001, “Virtual gravity and coupling control for robotic gait synthesis,” IEEE Trans. Syst. Man, Cybern. - Part A Syst. Humans, 31(6), pp. 2–7. [8].Asano, F., Yamakita, M., Kamamichi, N., and Luo, Z.-W., 2004, “A Novel Gait Generation for Biped Walking Robots Based on Mechanical Energy Constraint,” IEEE Trans. Robot. Autom., 20(3), pp. 565–573. [9].Asano, F., and Yamakita, M., 2005, “Biped gait generation and control based on a unified property of passive dynamic walking,” IEEE Trans. Robot., 21(4), pp. 754–762. [10]. Asano, F., and Luo, Z., 2006, “On Energy-Efficient and High-Speed Dynamic Biped Locomotion with Semicircular Feet,” 2006 IEEE/RSJ Int. Conf. Intell. Robot. Syst., pp. 5901–5906. [11]. Harata, Y., Asano, F., Luo, Z.-W., Taji, K., and Uno, Y., 2007, “Biped gait generation based on parametric excitation by knee-joint actuation,” 2007 IEEE/RSJ Int. Conf. Intell. Robot. Syst., pp. 2198–2203.
[12]. Shkolnik, A., and Tedrake, R., 2007, “Inverse Kinematics for a Point-Foot Quadruped Robot with Dynamic Redundancy Resolution,” Proc. 2007 IEEE Int. Conf. Robot. Autom., pp. 4331–4336. [13]. Kuo, A. D., 2007, “The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective,” Hum. Mov. Sci., 26(4), pp. 617–656. [14]. Griffin, T. M., Main, R. P., and Farley, C. T., 2004, “Biomechanics of quadrupedal walking: how do four-legged animals achieve inverted pendulum-like movements?,” J. Exp. Biol., 207(Pt 20), pp. 3545–58. [15]. Mu, X., and Wu, Q., 2006, “On impact dynamics and contact events for biped robots via impact effects.,” IEEE Trans. Syst. Man. Cybern. B. Cybern., 36(6), pp. 1364–1372. [16]. Shah, S., Saha, S., and Dutt, J., 2012, “Modular framework for dynamic modeling and analyses of legged robots,” Mech. Mach. Theory, 49, pp. 234–255.
[17]. Wang, X., Li, M., Wang, P., Guo, W., and Sun, L., 2012, “Bio-Inspired Controller for a Robot Cheetah with a Neural Mechanism Controlling Leg Muscles,” J. Bionic Eng., 9(3), pp. 282–293.
  • Receive Date: 08 July 2014
  • Revise Date: 16 September 2014
  • Accept Date: 20 September 2014