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Volumn 54, Issue 8, 2009, Pages 1779-1793

The spring loaded inverted pendulum as the hybrid zero dynamics of an asymmetric hopper

Author keywords

Dynamic running; Hybrid Zero Dynamics (HZD); Legged robots; Spring Loaded Inverted Pendulum (SLIP)

Indexed keywords

CENTER-OF-MASS; CLOSED-LOOP; CLOSED-LOOP SYSTEM; CONTROL LAWS; DYNAMIC RUNNING; EVENT-BASED CONTROL; GROUND FORCES; HOLONOMIC CONSTRAINTS; HYBRID CONTROLLER; HYBRID ZERO DYNAMICS; HYBRID ZERO DYNAMICS (HZD); INVARIANT SURFACES; LEGGED ROBOTS; PERIODIC ORBITS; PERIODIC SOLUTION; SECOND LEVEL; SLIP DYNAMICS; SPRING LOADED INVERTED PENDULUM (SLIP); SPRING LOADED INVERTED PENDULUMS; STEADY-STATE BEHAVIORS; TRANSIENT CONDITIONS; TWO-DEGREE-OF-FREEDOM;

EID: 68949196206     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2024565     Document Type: Article
Times cited : (256)

References (54)
  • 1
    • 0031077241 scopus 로고    scopus 로고
    • Stable control of a simulated one-legged running robot with hip and leg compliance
    • Feb
    • M. Ahmadi and M. Buehler, "Stable control of a simulated one-legged running robot with hip and leg compliance," IEEE Trans. Robot. Automat., vol. 13, no. 2, pp. 96-104, Feb. 1997.
    • (1997) IEEE Trans. Robot. Automat , vol.13 , Issue.2 , pp. 96-104
    • Ahmadi, M.1    Buehler, M.2
  • 2
    • 33750206792 scopus 로고    scopus 로고
    • Controlled passive dynamic running experiment with the ARL monopod II
    • Oct
    • M. Ahmadi and M. Buehler, "Controlled passive dynamic running experiment with the ARL monopod II," IEEE Trans. Robotics, vol. 22, no. 10, pp. 974-986, Oct. 2006.
    • (2006) IEEE Trans. Robotics , vol.22 , Issue.10 , pp. 974-986
    • Ahmadi, M.1    Buehler, M.2
  • 3
    • 6344258820 scopus 로고    scopus 로고
    • Stability analysis of legged locomotion models by symmetry-factored return maps
    • Oct
    • R. Altendorfer, D. E. Koditschek, and P. Holmes, "Stability analysis of legged locomotion models by symmetry-factored return maps," in Int. J. Robot. Res., vol. 23, no. 10-11, pp. 979-999, Oct. 2004.
    • (2004) Int. J. Robot. Res , vol.23 , Issue.10-11 , pp. 979-999
    • Altendorfer, R.1    Koditschek, D.E.2    Holmes, P.3
  • 4
    • 46449123101 scopus 로고    scopus 로고
    • Stably extending two-dimensional bipedal walking to three dimensions
    • New York, NY, Jul
    • A. D. Ames and R. D. Gregg, "Stably extending two-dimensional bipedal walking to three dimensions," in Proc. Amer. Control Conf., New York, NY, Jul. 2007, pp. 2848-2854.
    • (2007) Proc. Amer. Control Conf , pp. 2848-2854
    • Ames, A.D.1    Gregg, R.D.2
  • 6
    • 0024909217 scopus 로고
    • The spring-mass model for running and hopping
    • R. Blickhan, "The spring-mass model for running and hopping," J. Biomech., vol. 22, no. 11-12, pp. 1217-1227, 1989.
    • (1989) J. Biomech , vol.22 , Issue.11-12 , pp. 1217-1227
    • Blickhan, R.1
  • 7
    • 0000308710 scopus 로고
    • Similarity in multi-legged locomotion: Bouncing like a monopode
    • R. Blickhan and R. J. Full, "Similarity in multi-legged locomotion: Bouncing like a monopode," J. Comparative Physiol. A, vol. 173, pp. 509-517, 1993.
    • (1993) J. Comparative Physiol. A , vol.173 , pp. 509-517
    • Blickhan, R.1    Full, R.J.2
  • 9
    • 0025383315 scopus 로고
    • A family of robot control strategies for intermittent dynamical environments
    • Feb
    • M. Bühler, D. Koditschek, and P. Kindlmann, "A family of robot control strategies for intermittent dynamical environments," IEEE Control Syst. Mag., vol. 10, no. 2, pp. 16-22, Feb. 1990.
    • (1990) IEEE Control Syst. Mag , vol.10 , Issue.2 , pp. 16-22
    • Bühler, M.1    Koditschek, D.2    Kindlmann, P.3
  • 10
    • 78651510909 scopus 로고    scopus 로고
    • Single actuator control analysis of a planar 3DOF hopping robot
    • S. Thrun, G. Sukhatme, and S. Schaal, Eds. Cambridge, MA: MIT Press
    • N. Cherouvim and E. Papadopoulos, "Single actuator control analysis of a planar 3DOF hopping robot," in Robot.: Sci. Syst. I, S. Thrun, G. Sukhatme, and S. Schaal, Eds. Cambridge, MA: MIT Press, 2005, pp. 145-152.
    • (2005) Robot.: Sci. Syst. I , pp. 145-152
    • Cherouvim, N.1    Papadopoulos, E.2
  • 12
    • 19344369521 scopus 로고    scopus 로고
    • Asymptotically stable running for a five-link, four-actuator, planar bipedal robot
    • Jun
    • C. Chevallereau, E. R. Westervelt, and J. W. Grizzle, "Asymptotically stable running for a five-link, four-actuator, planar bipedal robot," in Int. J. Robot. Res., vol. 24, no. 6, pp. 431-464, Jun. 2005.
    • (2005) Int. J. Robot. Res , vol.24 , Issue.6 , pp. 431-464
    • Chevallereau, C.1    Westervelt, E.R.2    Grizzle, J.W.3
  • 13
    • 0028060978 scopus 로고    scopus 로고
    • C. Fran&ois and C. Samson, Running with constant energy, in Proc. IEEE Int. Conf. Robot. Automat., San Diego, CA, May 1994, 1, pp. 131-136.
    • C. Fran&ois and C. Samson, "Running with constant energy," in Proc. IEEE Int. Conf. Robot. Automat., San Diego, CA, May 1994, vol. 1, pp. 131-136.
  • 14
    • 0032205067 scopus 로고    scopus 로고
    • A new approach to the control of the planar one-legged hopper
    • Jan
    • C. François and C. Samson, "A new approach to the control of the planar one-legged hopper," in Int. J. Robot. Res., vol. 17, no. 11, pp. 1150-1166, Jan. 1998.
    • (1998) Int. J. Robot. Res , vol.17 , Issue.11 , pp. 1150-1166
    • François, C.1    Samson, C.2
  • 15
    • 0033372952 scopus 로고    scopus 로고
    • Templates and anchors: Neuromechanical hypotheses of legged locomotion on land
    • Dec
    • R. Full and D. E. Koditschek, "Templates and anchors: Neuromechanical hypotheses of legged locomotion on land," J. Exper. Biol., vol. 202, pp. 3325-3332, Dec. 1999.
    • (1999) J. Exper. Biol , vol.202 , pp. 3325-3332
    • Full, R.1    Koditschek, D.E.2
  • 17
    • 0031209812 scopus 로고    scopus 로고
    • Design, control, and energetics of an electrically actuated legged robot
    • Aug
    • P. Gregorio, M. Ahmadi, and M. Buehler, "Design, control, and energetics of an electrically actuated legged robot," IEEE Trans. Syst., Man Cybern., vol. 27, pp. 626-634, Aug. 1997.
    • (1997) IEEE Trans. Syst., Man Cybern , vol.27 , pp. 626-634
    • Gregorio, P.1    Ahmadi, M.2    Buehler, M.3
  • 18
    • 68949178601 scopus 로고    scopus 로고
    • Dec. 2, 2008 [Online, Available
    • J. W. Grizzle, Papers on Biped Robots Dec. 2, 2008 [Online]. Available: http://www.eecs.umich.edu/~grizzle/papers/robotics.html
    • Papers on Biped Robots
    • Grizzle, J.W.1
  • 19
    • 0035119101 scopus 로고    scopus 로고
    • Asymptotically stable walking for biped robots: Analysis via systems with impulse effects
    • Jan
    • J. W. Grizzle, G. Abba, and F. Plestan, "Asymptotically stable walking for biped robots: Analysis via systems with impulse effects," IEEE Trans. Automat. Control, vol. 46, no. 1, pp. 51-64, Jan. 2001.
    • (2001) IEEE Trans. Automat. Control , vol.46 , Issue.1 , pp. 51-64
    • Grizzle, J.W.1    Abba, G.2    Plestan, F.3
  • 21
    • 33744929666 scopus 로고    scopus 로고
    • The dynamics of legged locomotion: Models, analyses, and challenges
    • May
    • P. Holmes, R. J. Full, D. Koditschek, and J. Guckenheimer, "The dynamics of legged locomotion: Models, analyses, and challenges," SIAM Rev., vol. 48, no. 2, pp. 207-304, May 2006.
    • (2006) SIAM Rev , vol.48 , Issue.2 , pp. 207-304
    • Holmes, P.1    Full, R.J.2    Koditschek, D.3    Guckenheimer, J.4
  • 22
    • 68949190941 scopus 로고    scopus 로고
    • The Role and Implementation of Compliance in Legged Locomotion,
    • Ph.D. dissertation, The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA
    • J. W. Hurst, "The Role and Implementation of Compliance in Legged Locomotion," Ph.D. dissertation, The Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, 2008.
    • (2008)
    • Hurst, J.W.1
  • 23
    • 36348968280 scopus 로고    scopus 로고
    • Design and philosophy of the BiMASC, a higly dynamic biped
    • Roma, Italy, Apr
    • J. W. Hurst, J. E. Chestnutt, and A. A. Rizzi, "Design and philosophy of the BiMASC, a higly dynamic biped," in Proc. IEEE Int. Conf. Robot. Automat., Roma, Italy, Apr. 2007, pp. 1863-1868.
    • (2007) Proc. IEEE Int. Conf. Robot. Automat , pp. 1863-1868
    • Hurst, J.W.1    Chestnutt, J.E.2    Rizzi, A.A.3
  • 24
    • 52949148182 scopus 로고    scopus 로고
    • Series compliance for an efficient running gait
    • Sep
    • J. W. Hurst and A. Rizzi, "Series compliance for an efficient running gait," IEEE Robot. Automat. Mag., vol. 15, no. 3, pp. 42-51, Sep. 2008.
    • (2008) IEEE Robot. Automat. Mag , vol.15 , Issue.3 , pp. 42-51
    • Hurst, J.W.1    Rizzi, A.2
  • 25
    • 0036058540 scopus 로고    scopus 로고
    • Development of a biologically inspired hopping robot - Kenken
    • Washington, DC
    • S. H. Hyon and T. Mita, "Development of a biologically inspired hopping robot - Kenken," in Proc. IEEE Int. Conf. Robot. Automat., Washington, DC, 2002, pp. 3984-3991.
    • (2002) Proc. IEEE Int. Conf. Robot. Automat , pp. 3984-3991
    • Hyon, S.H.1    Mita, T.2
  • 26
    • 33846133265 scopus 로고    scopus 로고
    • Symmetric walking control: Invariance and global stability
    • Barcelona, Spain
    • S.-H. Hyon and T. Emura, "Symmetric walking control: Invariance and global stability," in Proc. IEEE Int. Conf. Robot. Automat., Barcelona, Spain, 2005, pp. 1455-1462.
    • (2005) Proc. IEEE Int. Conf. Robot. Automat , pp. 1455-1462
    • Hyon, S.-H.1    Emura, T.2
  • 27
    • 2342486084 scopus 로고    scopus 로고
    • Energy-preserving control of a passive one-legged running robot
    • May
    • S.-H. Hyon and T. Emura, "Energy-preserving control of a passive one-legged running robot," Adv. Robot., vol. 18, no. 4, pp. 357-381, May 2004.
    • (2004) Adv. Robot , vol.18 , Issue.4 , pp. 357-381
    • Hyon, S.-H.1    Emura, T.2
  • 29
    • 0004178386 scopus 로고    scopus 로고
    • 3 ed. Upper Saddle River, NJ: Prentice Hall
    • H. K. Khalil, Nonlinear Systems, 3 ed. Upper Saddle River, NJ: Prentice Hall, 2002.
    • (2002) Nonlinear Systems
    • Khalil, H.K.1
  • 30
    • 0026372031 scopus 로고
    • Analysis of a simplified hopping robot
    • Dec
    • D. E. Koditschek and M. Bühler, "Analysis of a simplified hopping robot," in Int. J. Robot. Res., vol. 10, no. 6, pp. 587-605, Dec. 1991.
    • (1991) Int. J. Robot. Res , vol.10 , Issue.6 , pp. 587-605
    • Koditschek, D.E.1    Bühler, M.2
  • 31
    • 0025416905 scopus 로고
    • Passive dynamic walking
    • Apr
    • T. McGeer, "Passive dynamic walking," in Int. J. Robot. Res., vol. 9, no. 2, pp. 62-82, Apr. 1990.
    • (1990) Int. J. Robot. Res , vol.9 , Issue.2 , pp. 62-82
    • McGeer, T.1
  • 32
    • 0000319505 scopus 로고
    • Periodic motions of a hopping robot with vertical and forward motion
    • Jun
    • R. M'Closkey and J. Burdick, "Periodic motions of a hopping robot with vertical and forward motion," in Int. J. Robot. Res., vol. 12, no. 3, pp. 197-218, Jun. 1993.
    • (1993) Int. J. Robot. Res , vol.12 , Issue.3 , pp. 197-218
    • M'Closkey, R.1    Burdick, J.2
  • 34
    • 33847229812 scopus 로고    scopus 로고
    • A restricted Poincaré map for determining exponentially stable periodic orbits in systems with impulse effects: Application to bipedal robots
    • Seville, Spain, Dec
    • B. Morris and J. W. Grizzle, "A restricted Poincaré map for determining exponentially stable periodic orbits in systems with impulse effects: Application to bipedal robots," in Proc. IEEE Int. Conf. Decision Control, Seville, Spain, Dec. 2005, pp. 4199-4206.
    • (2005) Proc. IEEE Int. Conf. Decision Control , pp. 4199-4206
    • Morris, B.1    Grizzle, J.W.2
  • 35
    • 39649109481 scopus 로고    scopus 로고
    • Hybrid invariance in bipedal robots with series compliant actuators
    • San Diego, CA, Dec
    • B. Morris and J. W. Grizzle, "Hybrid invariance in bipedal robots with series compliant actuators," in Proc. IEEE Int. Conf. Decision Control, San Diego, CA, Dec. 2006, pp. 4793-4800.
    • (2006) Proc. IEEE Int. Conf. Decision Control , pp. 4793-4800
    • Morris, B.1    Grizzle, J.W.2
  • 37
    • 68949196238 scopus 로고    scopus 로고
    • Stabilizing Monopedal Robot Running: Reduction-by-Feedback and Compliant Hybrid Zero Dynamics,
    • Ph.D. dissertation, Dept. Elect. Eng. Comput. Sci, University of Michigan, Ann Arbor
    • I. Poulakakis, "Stabilizing Monopedal Robot Running: Reduction-by-Feedback and Compliant Hybrid Zero Dynamics," Ph.D. dissertation, Dept. Elect. Eng. Comput. Sci., University of Michigan, Ann Arbor, 2009.
    • (2009)
    • Poulakakis, I.1
  • 38
    • 84927728845 scopus 로고    scopus 로고
    • Formal embedding of the spring loaded inverted pendulum in an asymmetric hopper
    • Kos, Greece, Jul, CD ROM
    • I. Poulakakis and J. W. Grizzle, "Formal embedding of the spring loaded inverted pendulum in an asymmetric hopper," in Proc. Eur. Control Conf., Kos, Greece, Jul. 2007, [CD ROM].
    • (2007) Proc. Eur. Control Conf
    • Poulakakis, I.1    Grizzle, J.W.2
  • 39
    • 51349154197 scopus 로고    scopus 로고
    • Monopedal running control: SLIP embedding and virtual constraint controllers
    • San Diego, CA, Oct
    • I. Poulakakis and J. W. Grizzle, "Monopedal running control: SLIP embedding and virtual constraint controllers," in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., San Diego, CA, Oct. 2007, pp. 323-330.
    • (2007) Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst , pp. 323-330
    • Poulakakis, I.1    Grizzle, J.W.2
  • 40
    • 84876252172 scopus 로고    scopus 로고
    • Modeling and control of the monopedal running robot Thumper
    • Kobe, Japan, CD ROM
    • I. Poulakakis and J. W. Grizzle, "Modeling and control of the monopedal running robot Thumper," in Proc. IEEE Int. Conf. Robot. Automat., Kobe, Japan, 2009, [CD ROM].
    • (2009) Proc. IEEE Int. Conf. Robot. Automat
    • Poulakakis, I.1    Grizzle, J.W.2
  • 42
    • 0345307585 scopus 로고    scopus 로고
    • Template based control of hexapedal running
    • Taipei, Taiwan, Sep
    • U. Saranli and D. Koditschek, "Template based control of hexapedal running," in Proc. IEEE Int. Conf. Robot. Automat., Taipei, Taiwan, Sep. 2003, vol. 1, pp. 1374-1379.
    • (2003) Proc. IEEE Int. Conf. Robot. Automat , vol.1 , pp. 1374-1379
    • Saranli, U.1    Koditschek, D.2
  • 43
    • 0031625960 scopus 로고    scopus 로고
    • Toward the control of a multi-jointed, monoped runner
    • Leuven, Belgium, May
    • U. Saranli, W. Schwind, and D. E. Koditschek, "Toward the control of a multi-jointed, monoped runner," in Proc. IEEE Int. Conf. Robot. Automat., Leuven, Belgium, May 1998, vol. 3, pp. 2676-2682.
    • (1998) Proc. IEEE Int. Conf. Robot. Automat , vol.3 , pp. 2676-2682
    • Saranli, U.1    Schwind, W.2    Koditschek, D.E.3
  • 44
    • 0003875334 scopus 로고    scopus 로고
    • Spring Loaded Inverted Pendulum Running: A Plant Model,
    • Ph.D. dissertation, Dept. Elect. Eng. Comput. Sci, University of Michigan, Ann Arbor
    • W. J. Schwind, "Spring Loaded Inverted Pendulum Running: A Plant Model," Ph.D. dissertation, Dept. Elect. Eng. Comput. Sci., University of Michigan, Ann Arbor, 1998.
    • (1998)
    • Schwind, W.J.1
  • 45
    • 0029182990 scopus 로고
    • Control of forward velocity for a simplified planar hopping robot
    • Nagoya, Japan, May
    • W. J. Schwind and D. E. Koditschek, "Control of forward velocity for a simplified planar hopping robot," in Proc. IEEE Int. Conf. Robot. Automat., Nagoya, Japan, May 1995, vol. 1, pp. 691-696.
    • (1995) Proc. IEEE Int. Conf. Robot. Automat , vol.1 , pp. 691-696
    • Schwind, W.J.1    Koditschek, D.E.2
  • 46
    • 23844558117 scopus 로고    scopus 로고
    • Running in three dimensions: Analysis of a point-mass sprung-leg model
    • Aug
    • J. E. Seipel and P. Holmes, "Running in three dimensions: Analysis of a point-mass sprung-leg model," in Int. J. Robot. Res., vol. 24, no. 8, pp. 657-674, Aug. 2005.
    • (2005) Int. J. Robot. Res , vol.24 , Issue.8 , pp. 657-674
    • Seipel, J.E.1    Holmes, P.2
  • 47
    • 0036214396 scopus 로고    scopus 로고
    • A movement criterion for running
    • May
    • A. Seyfarth, H. Geyer, M. Gunther, and R. Blickhan, "A movement criterion for running," J. Biomech., vol. 35, no. 5, pp. 649-55, May 2002.
    • (2002) J. Biomech , vol.35 , Issue.5 , pp. 649-655
    • Seyfarth, A.1    Geyer, H.2    Gunther, M.3    Blickhan, R.4
  • 48
    • 0041425193 scopus 로고    scopus 로고
    • Swing leg retraction: A simple control model for stable running
    • A. Seyfarth, H. Geyer, and H. Herr, "Swing leg retraction: A simple control model for stable running," J. Exper. Biol., vol. 206, pp. 2547-2555, 2003.
    • (2003) J. Exper. Biol , vol.206 , pp. 2547-2555
    • Seyfarth, A.1    Geyer, H.2    Herr, H.3
  • 50
    • 23144459310 scopus 로고    scopus 로고
    • Controlled symmetries and passive walking
    • Jul
    • M. Spong and F. Bullo, "Controlled symmetries and passive walking," IEEE Trans. Automat. Control, vol. 50, no. 7, pp. 1025-1031, Jul. 2003.
    • (2003) IEEE Trans. Automat. Control , vol.50 , Issue.7 , pp. 1025-1031
    • Spong, M.1    Bullo, F.2
  • 51
    • 0026370797 scopus 로고
    • An interesting strange attractor in the dynamics of a hopping robot
    • Dec
    • A. Vakakis, J. Burdick, and T. Caughey, "An interesting strange attractor in the dynamics of a hopping robot," in Int. J. Robot. Res., vol. 10, no. 6, pp. 606-618, Dec. 1991.
    • (1991) Int. J. Robot. Res , vol.10 , Issue.6 , pp. 606-618
    • Vakakis, A.1    Burdick, J.2    Caughey, T.3
  • 54
    • 0032050689 scopus 로고    scopus 로고
    • Stability theory for hybrid dynamical systems
    • Apr
    • H.Ye,A.N.Michel, and L. Hou, "Stability theory for hybrid dynamical systems," IEEE Trans. Automat. Control, vol. 43, no. 4, pp. 461-474, Apr. 1998.
    • (1998) IEEE Trans. Automat. Control , vol.43 , Issue.4 , pp. 461-474
    • Ye, H.1    Michel, A.N.2    Hou, L.3


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