Abstract
In our previous work, we have presented results on Virtual Slope Walking, that is when a robot walks on level ground down a virtual slope by leg length modulation, based on the potential energy restoration in Passive Dynamic Walking. In this paper, we introduce the model of Virtual Slope Walking with Trajectory Leg Extension (TLE) and equivalent Instantaneous Leg Extension (ILE) under the Equivalent Definition. The analytic solution of the model’s fixed point is obtained to analyze the essence of Virtual Slope Walking. We systematically investigate the characteristics and illustrate the effect of model parameters: the length-shortening ratio β, the equivalent extension angle \(\theta^{*}_{\mathrm{II}}\), and the inter-leg angle ϕ 0. We examine the energy efficiency and walking speed to demonstrate that Virtual Slope Walking is effective in generating high speed and energy-efficient walking. The high energy efficiency of the proposed model is theoretically confirmed. And the fast walking is validated by the experiments of a planar biped robot Stepper-2D, which achieves a sufficiently fast relative speed of 4.48 leg/s.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- m :
-
the mass of the body;
- r :
-
the length of the stance leg;
- rs,re:
-
the length of the stance leg before and after leg extension;
- θ :
-
the clockwise angle of the stance leg with respect to the vertical line;
- ω :
-
the angular velocity of the stance leg;
- ϕ :
-
the inter-leg angle;
- g :
-
gravitational acceleration;
- E c :
-
the complementary energy in one step;
- E d :
-
the dissipated energy in one step;
- E T :
-
the total mechanical energy;
- T :
-
step period;
- Ts,Te:
-
the start and end time of stance leg extension, respectively.
References
Aoi, S., & Tsuchiya, K. (2005). Locomotion control of a biped robot using nonlinear oscillators. Autonomous Robots, 19(3), 219–232.
Asano, F., & Luo, Z.-W. (2008). Energy-efficient and high-speed dynamic biped locomotion based on principle of parametric excitation. IEEE Transactions on Robot, 24(6), 1289–1301.
Asano, F., Yamakita, M., Kamamichi, N., & Luo, Z.-W. (2004). A novel gait generation for biped walking robots based on mechanical energy constraint. IEEE Transactions on Robotics and Automation, 20(3), 565–573.
Asano, F., Luo, Z.-W., & Yamakita, M. (2005). Biped gait generation and control based on a unified property of passive dynamic walking. IEEE Transactions on Robot, 21(4), 754–762.
Chevallereau, C., Abba, G., Aoustin, Y., Plestan, F., Westervelt, E. R., Canudas-De-Wit, C., & Grizzle, J. W. (2003). RABBIT: a testbed for advanced control theory. IEEE Control Systems Magazine, 23(5), 57–79.
Coleman, M. J. (1998). A stability study of three dimensional passive dynamic model of human gait. Ph.D. Thesis, Cornell University.
Collins, S.H. & Ruina, A. (2005). A bipedal walking robot with efficient and human-like gait. In Proc. IEEE international conference on robotics and automation, 18–22 April, pp. 1983–1988.
Collins, S., Ruina, A., Tedrake, R. et al. (2005). Efficient bipedal passive-dynamic walkers. Science, 307(5712), 1082–1085.
Dong, H., Zhao, M., Zhang, J., & Zhang, N. (2009). Hardware design and gait generation of humanoid soccer robot Stepper-3D. Robotics and Autonomous Systems, 57, 828–838.
Garcia, M., Chatterjee, A., Ruina, A., & Coleman, M. (1998). The simplest walking model: stability, complexity, and scaling. ASME Journal of Biomechanical Engineering, 281–288.
Geng, T., Porr, B., & Wörgötter, F. (2006). Fast biped walking with a sensor driven neuronal controller and real time online learning. International Journal of Robotics Research, 25(3), 243–259.
Goswami, A., Espiau, B., & Keramane, A. (1997). Limit cycles in a passive compass gait biped and passivity-mimicking control laws. Autonomous Robots, 4(3), 273–286.
Goswami, A., Thuilot, B., & Espiau, B. (1998). A study of the passive gait of a compass-like biped robot: symmetry and chaos. The International Journal of Robotics Research, 1282–1301.
Harata, Y., Asano, F., Taji, K., & Uno, Y. (2009). Parametric excitation walking for four-linked bipedal robot. In Proceedings of the 9th international IFAC symposium on robot control (SYROCO) (pp. 589–594).
Hobbelen, D., & Wisse, M. (2007). In Humanoid robots: human-like machines. Limit cycle walking (p. 642). Vienna: I-Tech Education and Publishing, Chap. 14.
Hobbelen, D. G. E., & Wisse, M. (2008). Ankle actuation for limit cycle walkers. International Journal of Robotics Research, 27(6), 709–735.
Honjo, T., Luo, Z.-W. & Nagano, A. (2008). Parametric excitation of a biped robot as an inverted pendulum. In Proceedings of IEEE/RSJ 2008 international conference on intelligent robots and systems (pp. 3408–3413).
Hurmuzlu, Y., & Moskowitz, G. (1986). The role of impact in the stability of bipedal locomotion. Dynamics and Stability of Systems, 1, 217–234.
Ikemata, Y., Sano, A., & Fujimoto, H. (2006). A physical principle of gait generation and its stabilization derived from mechanism of fixed point. In Proc. of the 2006 IEEE int. conf. on robotics and automation (pp. 836–841).
Kajita, S., & Tani, K. (1997). Adaptive gait control of a biped robot based on realtime sensing of the ground profile. Autonomous Robots, 4(3), 297–305.
McGeer, T. (1988). Stability and control of two-dimensional biped walking (Technical Report). CSS-IS TR 88-01, Simon Fraser University.
McGeer, T. (1990). Passive dynamic walking. International Journal of Robotics Research, 9(2), 62–82.
Pratt, J., Chew, C.-M., Torres, A., Dilworth, P., & Pratt, G. (2001). Virtual model control: an intuitive approach for bipedal locomotion. The International Journal of Robotics Research, 20(2), 129–143.
Spong, M. W. (1999). Passivity-based control of the compass gait biped. In Proc. of the IFAC world congress (pp. 19–23).
Vanderborght, B., Verrelst, B., Van Ham, R., Van Damme, M., Beyl, P., & Lefeber, D. (2008). Development of a compliance controller to reduce energy consumption for bipedal robots. Autonomous Robots, 24(4), 419–434.
Verrelst, B., Van Ham, R., Vanderborght, B., Daerden, F., Lefeber, D., & Vermeulen, J. (2005). The pneumatic biped “Lucy” actuated with pleated pneumatic artificial muscles. Autonomous Robots, 18(2), 201–213.
Wisse, M. (2004). Three additions to passive dynamic walking: actuation, an upper body, and 3d stability. In Proc. int. conf. on humanoid robots, Los Angeles, USA, IEEE.
Zhao, M., Zhang, J., Dong, H., Liu, Y., Li, L., & Su, X. (2008). Humanoid robot gait generation based on limit cycle stability. In The proceedings of the RoboCup symposium, China, JUL 15–18.
Zhao, M., Dong, H., & Zhang, N. (2009). The instantaneous leg extension model of Virtual Slope Walking. In Proceedings of the IEEE/RSJ international conference on intelligent robots and systems (IROS 2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dong, H., Zhao, M. & Zhang, N. High-speed and energy-efficient biped locomotion based on Virtual Slope Walking. Auton Robot 30, 199–216 (2011). https://doi.org/10.1007/s10514-010-9201-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10514-010-9201-4