Abstract
This chapter introduces reduced-order models that have been used in various studies of humanoid motion synthesis and control, particularly for balancing and locomotion. The models may be categorized into two groups. The first group derives physically explicit representations of the simplified system based on the centroidal dynamics embedded in the equation of motion. This category includes a number of successful models, which are intuitively easy to understand. The second group applies systematic order reduction techniques to the full-body dynamics. They make it easy to generalize the reduced-order model to different robot poses or tasks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
D.C. Witt, A feasibility study on automatically-controlled powered lower-limb prostheses, 1970
M. Vukobratović, J. Stepanenko, On the stability of anthropomorphic systems. Math. Biosci. 15(1), 1–37 (1972)
S. Kajita, K. Tani, Experimental study of biped dynamic walking in the linear inverted pendulum mode, in Proceeding of the IEEE International Conference on Robotics and Automation, 1995, pp. 2885–2819
R. Blickhan, The spring-mass model for running and hopping. J. Biomech. 22(11), 1217–1227 (1989)
M. Vukobratović, A.A. Frank, D. Juričić, On the stability of biped locomotion. IEEE Trans. Biomed. Eng. BME 17(1), 25–36 (1970)
C.K. Chow, D.H. Jacobson, Further studies of human locomotion: postural stability and control. Math. Biosci. 15(1), 93–108 (1972)
T. Yamashita, M. Yamada, H. Inotani, A fundamental study of walking (in Japanese). Biomechanics 1, 226–234 (1972)
F. Gubina, H. Hemami, R.B. McGhee, On the dynamic stability of biped locomotion. IEEE Trans. Biomed. Eng. BME 21(2), 102–108 (1974)
F. Miyazaki, S. Arimoto, A control theoretic study on dynamical biped locomotion. Trans. ASME J. Dyn. Syst. Measur. Control 102, 233–239 (1980)
J. Furusho, M. Masubuchi, Control of a dynamical biped locomotion system for steady walking. Trans. ASME J. Dyn. Syst. Measur. Control 108, 111–118 (1986)
M.H. Raibert, Legged Robots That Balance (MIT Press, Cambridge, 1986)
Y. Fujimoto, A. Kawamura, Simulation of an autonomous biped walking robot including environmental force interaction. IEEE Robot. Autom. Mag. 5(2), 33–41 (1998)
D.E. Orin, A. Goswami, S.-H. Lee, Centroidal dynamics of a humanoid robot. Auton. Robot. 35, 161–176 (2013)
R. Boulic, R. Mas, D. Thalmann, Inverse kinetics for center of mass position control and posture optimization, in Proceeding of the European Workshop on Combined Real and Synthetic Image Processing for Broadcast and Video Production, 1994
T. Sugihara, A Study of the realtime generation of legged motions on a whole-body humanoid robot (in Japanese). Masters thesis, The University of Tokyo, 2001
T. Sugihara, Y. Nakamura, H. Inoue, Realtime humanoid motion generation through ZMP manipulation based on inverted pendulum control, in Proceeding of the IEEE International Conference on Robotics and Automation, 2002, pp. 1404–1409
S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa, Resolved momentum control: humanoid motion planning based on the linear and angular momentum, in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2003, pp. 1644–1650
K. Mitobe, G. Capi, Y. Nasu, Control of walking robots based on manipulation of the zero moment point. Robotica 18, 651–657 (2000)
M. Popovic, A. Goswami, H.M. Herr, Ground reference points in legged locomotion: definitions, biological trajectories and control implications. Int. J. Robot, Res. 24(12), 1013–1032 (2005)
K. Nagasaka, The whole body motion generation of humanoid robot using dynamics filter (in Japanese). Ph.D. thesis, 2000
S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa, Biped walking pattern generation by using preview control of zero-moment point, in Proceeding of the IEEE International Conference on Robotics and Automation, 2003, pp. 1620–1626
R.M. Alexander, Mechanics of bipedal locomotion, in Perspectives in Experimental Biology, vol. 1, ed. by P.S. Davies (Pergamon, Oxford, 1976), pp. 493–504
R. Kato, M. Mori, Control method of biped locomotion giving asymptotic stability of trajectory. Automatica 20(4), 405–414 (1984)
A. Goswami, B. Espiau, A. Keramane, Limit cycles and their stability in a passive bipedal gait, in Proceeding of the IEEE International Conference on Robotics and Automation, 1996, pp. 273–286
M. Garcia, A. Chatterjee, A. Ruina, M. Coleman, The simplest walking model: stability, complexity, and scaling. ASME J. Biomech. Eng. 120(2), 281–288 (1998)
T. McGeer, Passive dynamic walking. Int. J. Robot. Res. 9(2), 62–82 (1990)
J.H. Park, K.D. Kim, Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control, in Proceeding of the IEEE International Conference on Robotics and Automation, 1998, pp. 3528–3533
Napoleon, S. Nakaura, M. Sampei, Balance control analysis of humanoid robot based on ZMP feedback control, in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2002, pp. 2437–2442
J. Pratt, J. Carff, S. Drakunov, A. Goswami, Capture point: a step toward humanoid push recovery, in Proceeding of the IEEE–RAS International Conference on Humanoid Robots, 2006, pp. 200–207
S. Lee, A. Goswami, Reaction mass pendulum (RMP): an explicit model for centroidal angular momentum of humanoid robots, in Proceeding of the IEEE International Conference on Robotics and Automation, 2007, pp. 4667–4672
A. Goswami, Kinematic and dynamic analogies between planar biped robots and the reaction mass pendulum (RMP) model, in Proceeding of the IEEE–RAS International Conference on Humanoid Robots, 2008, pp. 182–188
T. Sugihara, Y. Nakamura, Contact phase invariant control for humanoid robot based on variable impedant inverted pendulum model, in Proceeding of the IEEE International Conference on Robotics and Automation, 2003, pp. 51–56
O. Kwon, J.H. Park, Gait transitions for walking and running of biped robots, in Proceeding of the IEEE International Conference on Robotics and Automation, 2003, pp. 1350–1355
T. Sugihara, Y. Nakamura, Variable impedant inverted pendulum model control for a seamless contact phase transition on humanoid robot, in Proceeding of the IEEE–RAS International Conference on Humanoid Robots, 2003
K. Sadao, T. Hara, R. Yokokawa, Dynamic control of biped locomotion robot for disturbance on lateral plane (in Japanese), 1997, 10.37–10.38
S. Kajita, O. Matsumoto, M. Saigo, Real-time 3D walking pattern generation for a biped robot with telescopic legs, in Proceeding of the IEEE International Conference on Robotics and Automation, 2001, pp. 2299–2036
A.L. Hof, M.G.J. Gazendam, W.E. Sinke, The condition for dynamic stability. J. Biomech. 38, 1–8 (2005)
J.E. Pratt, R. Tedrake, Velocity Based Stability Margins for Fast Bipedal Walking, 2006
T. Takenaka, T. Matsumoto, T. Yoshiike, Real time motion generation and control for biped robot – 1st Report, Walking Gait Pattern Generation, in Proceeding of the IEEE/RSJ International Conference on Intelligent Robots and Systems, 2009, pp. 1084–1091
J. Englsberger, C. Ott, A. Albu-Schäffer, Three-dimensional bipedal walking control based on divergent component of motion. IEEE Trans. Robot. 31(2), 355–368 (2015)
F. Horak, L. Nashner, Central programming of postural movements: adaptation to altered support-surface configurations. J. Neurophys. 55(6), 1369–1381 (1986)
K. Yamane, Systematic derivation of simplified dynamics for humanoid robots, in IEEE-RAS International Conference on Humanoid Robots, 2012, pp. 28–35
D.C. Hyland, D.S. Bernstein, The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton, and Moore. IEEE Trans. Autom. Control AC 30(12), 1201–1211 (1985)
R. Tedrake, LQR-trees: feedback motion planning on sparse randomized trees, in Proceedings of Robotics: Science and Systems, 2009, pp. 17–24
K. Yamane, J.K. Hodgins, Simultaneous tracking and balancing of humanoid robots for imitating human motion capture data, in Proceedings of IEEE/RSJ International Conference on Intelligent Robot Systems, St. Louis, 2009, pp. 2510–2517
U. Nagarajan, K. Yamane, Automatic task-specific model reduction for humanoid robots, IEEE/RSJ International Conference on Intelligent Systems and Robots, 2013, pp. 2578–2585
M.G. Safonov, R.Y. Chiang, A Schur method for balanced model reduction. IEEE Trans. Autom. Control 34(7), 729–733 (1989)
D.G. Meyer, Fractional balanced reduction: model reduction via fractional representation. IEEE Trans. Autom. Control 35(12), 1341–1345 (1990)
K. Glover, All optimal Hankel norm approximation of linear multivariable systems and their L∞-error bounds. Int. J. Control 39(6), 1145–1193 (1984)
M.G. Safonov, R.Y. Chiang, D.J.N. Limebeer, Optimal Hankel model reduction for nonminimal systems. IEEE Trans. Autom. Control 35(4), 496–502 (1990)
W.L. Brogan, Modern Control Theory, 3rd edn. (Prentice Hall, Upper Saddle River, 1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature B.V.
About this entry
Cite this entry
Sugihara, T., Yamane, K. (2019). Reduced-Order Models. In: Goswami, A., Vadakkepat, P. (eds) Humanoid Robotics: A Reference. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6046-2_56
Download citation
DOI: https://doi.org/10.1007/978-94-007-6046-2_56
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-6045-5
Online ISBN: 978-94-007-6046-2
eBook Packages: Intelligent Technologies and RoboticsReference Module Computer Science and Engineering