Hostname: page-component-74656f9884-rdgjk Total loading time: 0 Render date: 2026-11-07T20:38:30.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Using optimization to create self-stable human-like running

Published online by Cambridge University Press:  01 May 2009

Katja Mombaur
Katja Mombaur*
Affiliation:
Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, Germany. E-mail: kmombaur@uni-hd.de
Rights & Permissions [Opens in a new window]

Summary

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

This paper demonstrates how numerical optimization techniques can efficiently be used to create self-stable running motions for a human-like robot model. Exploitation of self-stability is considered to be a crucial factor for biological running and might be the key for success to make bipedal and humanoid robots run in the future. We investigate a two-dimensional simulation model of running with nine bodies (trunk, thighs, shanks, feet, and arms) powered by external moments at all internal joints. Using efficient optimal control techniques and stability optimization, we were able to determine model parameters and actuator inputs that lead to fully open-loop stable running motions.

Keywords

BipedsControl of robotic systemsDesignRobot dynamicsBiomimetic robots

Information

Type
Article
Information
Robotica , Volume 27 , Issue 3 , May 2009 , pp. 321 - 330
Copyright
Copyright © Cambridge University Press 2008

References

1.Bock, H. G., “Randwertproblemmethoden zur Parameteridentifizierung in Systemen nichtlinearer Differentialgleichungen,” In: Bonner Mathematische Schriften 183 (Universität Bonn, 1987).Google Scholar
2.Bock, H. G. and Plitt, K.-J., “A Multiple Shooting Algorithm for Direct Solution of Optimal Control Problems,” Proceedings of the 9th IFAC World Congress, Budapest, International Federation of Automatic Control (1984) pp. 242–247.Google Scholar
3.Brown, I. E. and Loeb, G. E., Neuro-control of posture and movement, chapter A reductionist approach to creating and using neuromusculoskeletal models (Springer-Verlag, New York, 2000).Google Scholar
4.Buehler, M., “Dynamic locomotion with one, four and six-legged robots,” J. Rob. Soc. Jpn. 20 (3), 15–20 (Apr. 2002).Google Scholar
5.Cheng, M.-Y. and Lin, C.-S., “Measurement of robustness for biped locomotion using a linearized Poincaré map,” Robotica 14, 253–259 (1996).CrossRefGoogle Scholar
6.Coleman, M. J., A Stability Study of a Three-Dimensional Passive-Dynamic Model of Human Gait. Ph.D. Thesis (Cornell University, Feb. 1998).Google Scholar
7.Coleman, M. J., Garcia, M., Mombaur, K. D. and Ruina, A., “Prediction of stable walking for a toy that cannot stand,” Phys. Rev. E 2 022901 1–3 (2001).Google Scholar
8.Collins, S. H., Ruina, A. L., Tedrake, R. and Wisse, M., “Efficient bipedal robots based on passive-dynamic walkers,” Science 307, 1082–1085 (2005).CrossRefGoogle ScholarPubMed
9.Cronin, J., Differential Equations—Introduction and Qualitative Theory (Marcel Dekker, New York, 1994).Google Scholar
10.de Leva, P., “Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters,” J. Biomech. 9, 1223–1230 (1996).CrossRefGoogle Scholar
11.Gienger, M., Löffler, K. and Pfeiffer, F., “Design and realization of Jogging Johnnie,” CISM Courses and Lectures (2002) pp. 445–452.Google Scholar
12.Goswami, A., “Postural stability of biped robots and the foot rotation indicator (FRI) point,” Int. J. Rob. Res. 18 (6), 523–533 (1999).CrossRefGoogle Scholar
13.Goswami, A., Espiau, B. and Keramane, A., “Limit Cycles and Their Stability in a Passive Bipedal Gait,” Proceedings of IEEE International Conference on Robotics and Automation, Minneapolis (1996) pp. 246–251.Google Scholar
14.Wagner, H. and Blickhan, R., “Stabilizing function of sceletal muscles: An analytical investigation,” J. Theor. Biol. 199 (2), 163–179 (1999).Google Scholar
15.Honda. Honda robots webpage, http://www.honda-robots.com (2007).Google Scholar
16.Hsu, J. C. and Meyer, A. U., Modern Control Principles and Applications (McGraw-Hill, New York, 1968).Google Scholar
17.Hurmuzlu, Y., “Dynamics of bipedal gait: Part II – Stability analysis of a planar five-link biped,” J. Appl. Mech. 60, 337–343 (June 1993).CrossRefGoogle Scholar
18.Kaneko, K., Kanehiro, F., Kajita, S., Hirukawa, H., Kawasaki, T., Hirata, M., Akachi, K. and Isozumi, T., “Humanoid Robot hrp-2,” Proceedings of ICRA 04, IEEE RAS (May 2004) pp. 1083–1090.Google Scholar
19.Leineweber, D. B., Bauer, I., Bock, H. G. and Schlöder, J. P., “An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization—Part I: Theoretical aspects,” Comput. Chem. Eng. 27, 157–166 (2003).Google Scholar
20.Leineweber, D. B., Schäfer, A., Bock, H. G. and Schlöder, J. P., “An efficient multiple shooting based reduced SQP strategy for large-scale dynamic process optimization—Part II: Software aspects and applications,” Comput. Chem. Eng. 27, 167–174 (2003).CrossRefGoogle Scholar
21.Loeb, G. E., “Control Implications of Musculosceletal Mechanics,” Annual International Conference IEEE-EMBS, Montreal (1995) Vol. 17, pp. 1393–1394.Google Scholar
22.Lohmeier, S., Löffler, K., Gienger, M., Ulbrich, H. and Pfeiffer, F., “Computer System and Control of Biped Johnnie,” Proceedings of ICRA 04, New Orleans IEEE RAS (2004).Google Scholar
23.McGeer, T., “Passive dynamic walking,” Int. J. Rob. Res. 9, 62–82 (1990).CrossRefGoogle Scholar
24.McGeer, T., “Dynamics and control of bipedal locomotion,” J. Theor. Biol. 163, 277–314 (1993).CrossRefGoogle ScholarPubMed
25.Mombaur, K. D., “Performing Open-Loop Stable Flip-Flops—An Example for Stability Optimization and Robustness Analysis of Fast Periodic Motions,” Fast Motions in Robotics and Biomechanics—Optimization and Feedback Control, Lecture Notes in Control and Information Science (Springer, Heidelberg, 2006).Google Scholar
26.Mombaur, K. D., Bock, H. G., Schlöder, J. P. and Longman, R. W., “Human-Like Actuated Walking that is Asymptotically Stable Without Feedback,” Proceedings of IEEE International Conference on Robotics and Automation, Seoul, Korea (May 2001) pp. 4128–4133.Google Scholar
27.Mombaur, K. D., Bock, H. G., Schlöder, J. P. and Longman, R. W., “Open-loop stable solution of periodic optimal control problems in robotics,” ZAMM—J. Appl. Math. Mech. 85 (7), 499–515 (July 2005).CrossRefGoogle Scholar
28.Mombaur, K. D., Bock, H. G., Schlöder, J. P. and Longman, R. W., “Self-stabilizing somersaults,” IEEE Trans. Rob. 21 (6) (Dec. 2005) pp. 1148–1157.CrossRefGoogle Scholar
29.Mombaur, K. D., Longman, R. W., Bock, H. G. and Schlöder, J. P., “Open-loop stable running,” Robotica 23 (01), 21–33 (Jan. 2005).CrossRefGoogle Scholar
30.Popovic, M., Englehart, A. and Herr, H., “Angular Momentum Primitives for Human Walking: Biomechanics and Control,” Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Sendai, Japan (2004).Google Scholar
31.Pratt, J. and Tedrake, R., “Velocity-based stability margins for fast bipedal walking,” Fast Motions in Robotics and Biomechanics—Optimization and Feedback Control, Lecture Notes in Control and Information Science (Springer, Heidelberg, 2006).Google Scholar
32.Pratt, J. E., Exploiting Inherent Robustness and Natural Dynamics in the Control of Bipedal Walking Robots. Ph.D. Thesis (Massachusetts Institute of Technology, 2000).Google Scholar
33.Sakagami, Y., Watanabe, R., Aoyama, C., Matsunaga, S., Higaki, N. and Fujimura, K., “The Intelligent ASIMO: System Overview and Integration,” Proceedings of IROS, IEEE/RSJ (Dec. 2002) Vol. 3, pp. 2478–2483.Google Scholar
34.Schultz, G., Generation of Optimal Human Running Gaits Master's Thesis (University of Heidelberg, 2007).Google Scholar
35.Schultz, G. and Mombaur, K., “Modeling and optimization of human-like running motions,” submitted.Google Scholar
36.Sony, QRIO—World's first running humanoid robot, press release, http://www.sony.net/SonyInfo/News/Press_Archive/200312/03-060E/ (2003).Google Scholar
37.Toyota, Toyota Partner Robots, http://www.toyota.co.jp/en/special/robot/ (2007).Google Scholar
38.van Soest, A. J. and Bobbert, M. F., “The contribution of muscle properties in the control of explosive movements,” Biol. Cybernet. 69, 195–204 (1993).CrossRefGoogle ScholarPubMed
39.Vukobratovic, M. and Borovac, B., “Zero-moment point—Thirty-five years of its life,” Int. J. Humanoid Rob. 1 (1), 157–173 (2004).CrossRefGoogle Scholar
40.Wieber, P.-B., Modélisation et commande d'un robot marcheur anthropomorphe. Ph.D. Thesis (Ecole des Mines de Paris, 2000).Google Scholar
41.Wieber, P.-B., “Holonomy and nonholonomy in the dynamics of articulated motion,” Fast Motions in Biomechanics and Robotics—Optimization and Feedback Control (Springer, Heidelberg, 2006) pp. 411–425.CrossRefGoogle Scholar
42.Wieber, P.-B., “Viability and Predictive Control for Safe Locomotion,” Proceedings of JNRR 2007 (Journées Nationales de la Recherche en Robotique), Obernai, France (2007).CrossRefGoogle Scholar
43.Wisse, M., “Three Additions to Passive Dynamic Walking: Actuation, an Upper Body and 3D Stability,” Proceedings of IEEE/RAS International Conference on Humanoid Robots, Tsukuba, Japan (2005) pp. 295–300.Google Scholar
44.Wisse, M., Atkeson, C. G. and Kloimwieder, D. K., “Dynamic stability of a simple bipedwalking system with swng leg retraction,” Fast Motions in Robotics and Biomechanics—Optimization and Feedback Control, Lecture Notes in Control and Information Science (Springer, Heidelberg, 2006).Google Scholar
45.Wisse, M. and van Franzenhuyzen, J., “Design and Construction of “Mike”: A 2D Autonomous Biped Based on Passive Dynamic Walking,” Proceedings of International Conference on Adaptive Motion of Animals and Machines (AMAM), Kyoto, Japan (2003).Google Scholar