Abstract
This paper proposes a stabilization method for dynamic walking of a bipedal robot with real-time optimization of capture point trajectories. We used the capture point trajectories to generate the control input, which is the desired zero moment point (ZMP) with a sliding-mode ZMP controller to follow the desired ZMP. This method enables the robot to implement various dynamic walking commands, such as forward stride, lateral stride, walking direction, single support time, and double support time. We also adopted enhanced dynamics with the three mass linear inverted pendulum model (3M-LIPM). First, the compensated ZMP is calculated by both walking commands and kinematic configuration of the robot in closed form. Then, the walking pattern is obtained by using initial and boundary conditions of the 3M-LIPM, which satisfies the walking commands. The capture point (CP) trajectory is optimized in real time to control the walking stability and a capture point tracking controller is used for tracking the optimized CP trajectory, which generates an optimal control input that is near the center of the support polygon. The performance of the proposed stabilization method was verified by a dynamics simulator, Webots, and comparison with the original capture point controller-based walking algorithm is presented.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Vukobratovic, M., Borovac, B.: Zero-moment point-thirty five years of its life. Int. J. Humanoid Robot. 1 (1), 157–173 (2004)
Kajita, S., Osamu, M., Muneharu, S.: Real-time 3D walking pattern generation for a biped robot with telescopic legs. In: Proc. IEEE Int. Conf. Robot. Autom., vol. 3, pp. 2299–2306 (2001)
Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Yokoi, K., Hirukawa, H.: A realtime pattern generator for biped walking. In: Proc. IEEE Int. Conf. Robot. Autom., vol. 1, pp. 31–37 (2002)
Kajita, S., Kanehiro, F., Kaneko, K., Fujiwara, K., Harada, K., Yokoi, K., Hirukawa, H.: Biped walking pattern generation by using preview control of zero-moment point. In: Proc. IEEE Int. Conf. Robot. Autom., vol. 2, pp. 1620–1626 (2003)
Morisawa, M., Kajita, S., Kaneko, K., Harada, K., Kanehiro, F., Fujiwara, K., Hirukawa, H.: Pattern generation of biped walking constrained on parametric surface. In: Proc. IEEE Int. Conf. Robot. Autom., pp. 2405–2410 (2005)
Nishiwaki, K., Kagami, S., Kuniyoshi, Y., Inaba, M., Inoue, H.: Online generation of humanoid walking motion based on fast generation method of motion pattern that follows desired ZMP. In: Proc. IEEE Int. Conf. Intell. Robots Syst., pp. 2684–2689 (2002)
Erbatur, K., Kurt, O.: Natural ZMP trajectories for biped robot reference generation. IEEE Trans. Ind. Electron. 56(3), 835–845 (2009)
Hong, Y.-D., Lee, B.-J., Kim, J.-H.: Command state-based modifiable walking pattern generation on an inclined plane in pitch and roll directions for humanoid robots. IEEE/ASME Trans. Mechatron. 16(4), 783–789 (2011)
Hong, Y.-D., Kim, J.-H.: 3-D command state-based modifiable bipedal walking on uneven terrain. IEEE/ASME Trans. Mechatron. 18(2), 657–663 (2013)
Hong, Y.-D., Lee, B.-J.: Experimental study on modifiable walking pattern generation for handling infeasible navigational commands. J. Elect. Eng. Technol. 10(6), 2368–2375 (2015)
Nishiwaki, K., Kagami, S.: Simultaneous planning of CoM and ZMP based on the preview control method for online walking control. In: Proc.IEEE-RAS Int. Conf. Humanoid Robots, pp. 745–751 (2011)
Park, J.H., Kim, K.D.: Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control. In: Proc. IEEE Int. Conf. Robotics Automation, Leuven, Belgium, pp. 3528–3533 (1998)
Sato, T., Sakaino, S., Ohnishi, K.: Real-time walking trajectory generation method with three-mass models at constant body height for three dimensional biped robots. IEEE Trans. Ind. Electron. 58(2), 376–383 (2011)
Kajita, S., Morisawa, M., Miura, K., Nakaoka, S., Harada, K., Kaneko, K., Kanehiro, F., Yokoi, K.: Biped walking stabilization based on linear inverted pendulum tracking. In: Proc. on IEEE Int. Conf. on Intelligent Robots and Systems, pp. 4489–4496 (2010)
Campos-Macias, L., et al.: Stabilization method for dynamic gait in bipedal walking robots. In: IEEE Int. Conf. on Humanoid Robots (Humanoids), pp. 1276–1281 (2016)
Hu, K., Ott, C., Lee, D.: Learning and generalization of compensative zero-moment point trajectory for biped walking. IEEE Trans. Robot 32(3), 717725 (2016)
Pratt, J., Carff, J., Drakunov, S., Goswami, A.: Capture point: A step toward humanoid push recovery. In: Proceedings of the international conference on humanoid robots. IEEE, pp. 200–207 (2006)
Hof, A.L.: The extrapolated center of mass concept suggests a simple control of balance in walking. Human Movement Sci. 27, 112–125 (2008)
Englsberger, J., Ott, C., Roa, M.A., Albu-Schäffer, A., Hirzinger, G.: Bipedal walking control based on capture point dynamics. In: IEEE/RSJ int. conference on intelligent robots and systems, pp. 4420–4427 (2011)
Englsberger, J., Ott, C.: Integration of vertical com motion and angular momentum in an extended capture point tracking controller for bipedal walking. In: 2012 12th IEEE-RAS international conference on humanoid robots (Humanoids), pp. 183–189 (2012)
Morisawa, M., Kajita, S., Kanehiro, F., Kaneko, K., Miura, K., Yokoi, K.: Balance control based on capture point error compensation for biped walking on uneven terrain. In: IEEE-RAS Int. Conf. on Humanoid Robots, pp. 734–740 (2012)
Krause, M., Englsberger, J., Wieber, P.-B., Ott, C.: Stabilization of the capture point dynamics for bipedal walking based on model predictive control. IFAC Pro. 45, 22 (2012)
Lanari, L., Hutchinson, S., Marchionni, L.: Boundedness issues in planning of locomotion trajectories for biped robots. In: Proc. of the IEEE/RSJ Int. Conf. on Humanoid Robots, pp. 951–958 (2014)
Lanari, L., Hutchinson, S.: Planning desired center of mass and zero moment point trajectories for bipedal locomotion. In: Proc. of the IEEE-RAS Int. Conf. on Humanoid Robots, pp. 637–642 (2015)
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B1006691).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kim, IS., Han, YJ. & Hong, YD. Stability Control for Dynamic Walking of Bipedal Robot with Real-time Capture Point Trajectory Optimization. J Intell Robot Syst 96, 345–361 (2019). https://doi.org/10.1007/s10846-018-0965-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10846-018-0965-7