Abstract
The statically stable gait control of a mammal-like quadruped robot that provides an adequate or stable manner of traversing over irregular terrain was addressed. The reinforced wave gait which integrates new parameters of the lateral offset and displacements of the center of gravity (COG) based on the profiles of standard wave gait was investigated. The continuous and discontinuous motion trajectory of a robot’s COG in the periodic reinforced wave gait could be realized. The longitudinal and lateral stability margins of a reinforced wave gait were formulated for the gait generation and control of a quadruped robot. Moreover, the effects of the lateral offset on the stability, velocity and the energy efficiency were studied in details. The reinforced wave gait with lateral sway motion adequately improved the stability, and two particular gait patterns that involve the lateral sway motion for a maximal velocity and maximum achievable stability were described. With consideration of a quadruped robot with asymmetric carrying loads on its body, a scheme that relates to the gait parameters of the displacement of a robot’s COG to avoid losing stability was proposed. The simulation and experimental results about the effects of lateral offset added in the reinforced wave gait on the minimum power consumption during a quadruped robot walking on a flat terrain indicated that the reinforced wave gait with a larger lateral offset would generate a better wave gait with a higher velocity and energy efficiency.
Similar content being viewed by others
References
Raibert, M., Blankespoor, K., Nelson, G., Playter, R.: Bigdog, the rough-terrain quadruped robot. In: Proceedings of the 17th World Congress, pp 10823–10825 (2008)
Hutter, M., Gehring, C., Bloesch, M., Hoepflinger, M., Remy, C.D., Siegwart, R.: StarlETH: A compliant quadrupedal robot for fast, efficient, and versatile locomotion. In: 15th International Conference on Climbing and Walking Robot-CLAWAR 2012 (2012)
Bazeille, S., Barasuol, V., Focchi, M., Havoutis, I., Frigerio, M., Buchli, J., Caldwell, D.G., Semini, C.: Quadruped robot trotting over irregular terrain assisted by stereo-vision. Intel. Serv. Robotics 7(2), 67–77 (2014)
Ijspeert, A.J.: Central pattern generators for locomotion control in animals and robots: a review. Neural Netw. 21(4), 642–653 (2008)
Roy, S.S., Pratihar, D.K.: Effects of turning gait parameters on energy consumption and stability of a six-legged walking robot. Robot. Auton. Syst. 60(1), 72–82 (2012)
Kar, D., Kurien Issac, K., Jayarajan, K.: Minimum energy force distribution for a walking robot. J. Robot. Syst. 18(2), 47–54 (2001)
McGhee, R.B., Frank, A.A.: On the stability properties of quadruped creeping gaits. Math. Biosci. 3, 331–351 (1968)
Song, S.-M., Waldron, K.J.: An analytical approach for gait study and its applications on wave gaits. Int. J. Robot. Res. 6(2), 60–71 (1987)
Song, S.-M., Choi, B.S.: The optimally stable ranges of 2 < e1 > n < /e1 > -legged wave gaits. IEEE Trans. Syst. Man Cybern. 20(4), 888–902 (1990)
Jeong, K.-M., Oh, J.-H.: An aperiodic z type spinning gait planning method for a quadruped walking robot. Auton. Robot. 2(2), 163–173 (1995)
Zhang, C.-D., Song, S.-M.: Turning gaits of a quadrupedal walking machine. Adv. Robot. 7(2), 121–157 (1992)
Hirose, S., Kikuchi, H., Umetani, Y.: The standard circular gait of a quadruped walking vehicle. Adv. Robot. 1(2), 143–164 (1986)
Jiménez, M.A, de Santos, P.G., Tabera, J.: An omnidirectional control algorithm for walking machines based on a wave-crab gait. In: Advances in Intelligent Autonomous Systems, pp 355–380. Springer (1999)
Song, S.-M., Soo Choi, B.: A study on continuous follow-the-leader (FTL) gaits: an effective walking algorithm over rough terrain. Math. Biosci. 97(2), 199–233 (1989)
Hirose, S.: A study of design and control of a quadruped walking vehicle. Int. J. Robot. Res. 3(2), 113–133 (1984)
Bai, S., Low, K.H., Zielinska, T.: Quadruped free gait generation based on the primary/secondary gait. Robotica 17(04), 405–412 (1999)
Estremera, J: de Santos, P.G.: Generating continuous free crab gaits for quadruped robots on irregular terrain. IEEE Trans. Robot. 21(6), 1067–1076 (2005)
Erden, M.S., Leblebicioğlu, K.: Analysis of wave gaits for energy efficiency. Auton. Robot. 23 (3), 213–230 (2007)
Inagaki, S., Yuasa, H., Suzuki, T., Arai, T.: Wave CPG model for autonomous decentralized multi-legged robot: Gait generation and walking speed control. Robot. Auton. Syst. 54(2), 118–126 (2006)
Hung, M.H., Cheng, F.T., Lee, H.L., Orin, D.E.: Increasing the stability margin of multilegged vehicles through body sway. J. Chin. Inst. Eng. 28(1), 39–54 (2005)
Tsukagoshi, H., Hirose, S., Yoneda, K.: Maneuvering operations of a quadruped walking robot on a slope. Adv. Robot. 11(4), 359–375 (1996)
Hirose, S., Kunieda, O.: Generalized standard foot trajectory for a quadruped walking vehicle. Int. J. Robot. Res. 10(1), 3–12 (1991)
Santos, P.G.D., Jimenez, M.A.: Generation of discontinuous gaits for quadruped walking vehicles. J. Robot. Syst. 12(9), 599–611 (1995)
Lu, D., Dong, E., Liu, C., Xu, M., Yang, J.: Design and development of a leg-wheel hybrid robot “HyTRo-I”. In: 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp 6031–6036. IEEE (2013)
Lu, D., Dong, E., Liu, C., Wang, Z., Zhang, X., Xu, M., Yang, J.: Mechanical system and stable gait transformation of a leg-wheel hybrid transformable robot. In: 2013 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp 530–535. IEEE (2013)
Alexander, R.M.: Principles of animal locomotion. Princeton University Press (2003)
Dickinson, M.H., Farley, C.T., Full, R.J., Koehl, M., Kram, R., Lehman, S.: How animals move: an integrative view. Science 288(5463), 100–106 (2000)
Bottaro, A., Casadio, M., Morasso, P.G., Sanguineti, V.: Body sway during quiet standing: is it the residual chattering of an intermittent stabilization process Hum. Mov. Sci. 24(4), 588–615 (2005)
Donelan, J.M., Shipman, D.W., Kram, R., Kuo, A.D.: Mechanical and metabolic requirements for active lateral stabilization in human walking. J. Biomech. 37(6), 827–835 (2004)
Zhang, C.-D., Song, S.-M.: Stability analysis of wave-crab gaits of a quadruped. J. Robot. Syst. 7(2), 243–276 (1990)
Zhang, C.-D., Song, S.-M.: A study of the stability of generalized wave gaits. Math. Biosci. 115 (1), 1–32 (1993)
Zhang, C.D., Song, S.M.: Stability analysis of wavecrab gaits of a quadruped. J. Robot. Syst. 7 (2), 243–276 (1990)
de Santos, P.G., Garcia, E., Ponticelli, R., Armada, M.: Minimizing energy consumption in hexapod robots. Adv. Robot. 23(6), 681–704 (2009)
Garcia, E., Galvez, J.A., De Santos, P.G.: On finding the relevant dynamics for model-based controlling walking robots. J. Intell. Robot. Syst. 37(4), 375–398 (2003)
Roy, S.S., Pratihar, D.K.: Kinematics, dynamics and power consumption analyses for turning motion of a six-legged robot. J. Intell. Robot. Syst. 74(3-4), 663–688 (2014)
Jin, B., Chen, C., Li, W.: Power Consumption Optimization for a Hexapod Walking Robot. J. Intell. Robot. Syst. 71(2), 195–209 (2013)
Roy, S.S., Singh, A.K., Pratihar, D.K.: Estimation of optimal feet forces and joint torques for on-line control of six-legged robot. Robot. Comput. Integr. Manuf. 27(5), 910–917 (2011)
Roy, S.S., Pratihar, D.K.: Dynamic modeling, stability and energy consumption analysis of a realistic six-legged walking robot. Robot. Comput. Integr. Manuf. 29(2), 400–416 (2013)
Lin, B.S., Song, S.M.: Dynamic modeling, stability, and energy efficiency of a quadrupedal walking machine. J. Robot. Syst. 18(11), 657–670 (2001)
Gregorio, P., Ahmadi, M., Buehler, M.: Design, control, and energetics of an electrically actuated legged robot. IEEE Trans. Syst. Man Cybern. B Cybern. 27(4), 626–634 (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, D., Dong, E., Liu, C. et al. Generation and Analyses of the Reinforced Wave Gait for a Mammal-Like Quadruped Robot. J Intell Robot Syst 82, 51–68 (2016). https://doi.org/10.1007/s10846-015-0265-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10846-015-0265-4