Numerous experiments using the theoretical work reported here have been carried out. See VIDEOS

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New Robot Constructed: It's name is MABEL . The robot was built in collaboration with Jonathan Hurst at the Robotics Institute of Carnegie Mellon. Recent Book on Control of Bipeds: Feedback Control of Dynamic Bipedal Robot Locomotion , Taylor & Francis, CRC Press, June 2007, 503 pages. Treats advanced issues and covers all the basics too! Professionals and graduate students alike will find the book accessible and useful. Quick introduction: If you're looking to understand the basic ideas of our control designs, see the paper RABBIT: A Testbed for Advanced Control Theory, (This paper emphasizes the ideas and down plays the mathematics; the other papers are quite mathematical). We made the cover of the special issue of Control Systems Magazine in which the article appeared! Workshop: 2003 CDC Workshop A half-day workshop we did with Eric Westervelt, Mark Spong, Carlos Canudas de Wit, and Anton Shiriaev.

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Papers on Bipedal Robots and Robotics: Planar or Compliance or 3D or Rehabilitation or Observers and Event-Based Control

3D Legged Robots (Back to Top of Papers)

1. Ching-Long Shih, J. W. Grizzle and Christine Chevallereau, Asymptotically Stable Walking and Steering of a 3D Bipedal Robot with Passive Point Feet, Pre-print IEEE Transactions on Robotics, Submitted June 6, 2009. Zip File of Simulation Videos [Right Click and Save].
2. Christine Chevallereau, J. W. Grizzle and Ching-Long Shih, Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot, Reprint IEEE Transactions on Robotics, Vol. 25, No. 1, February 2009, pp. 37-50. [Supplemental Material].
3. J. W. Grizzle, Christine Chevallereau and Ching-Long Shih, HZD-Based Control of a Five-Link Underactuated 3D Bipedal Robot, Reprint IEEE Conf. on Decision and Control, December 2008.
4. Ching-Long Shih, J. W. Grizzle and Christine Chevallereau, Asymptotically Stable Walking of a Simple Underactuated 3D Bipedal Robot, Reprint 33rd Annual Conference of IEEE Industrial Electronics (IECON 2007), Taipei, Taiwan, November 5-8, 2007.

   Legged Robots with Compliance (Back to Top of Papers)

5. J.W. Grizzle Jonathan Hurst, Benjamin Morris, Hae-Won Park, and Koushil Sreenath, MABEL, A New Robotic Bipedal Walker and Runner, Re-print, American Control Conference'', St. Louis, MO, June 2009. A ZIP file detailing the powertrain model of the robot is available here. [Right Click and Save]
6. Ioannis Poulakakis and J. W. Grizzle, Modeling and Control of the Monopedal Robot Thumper, Pre-print, ICRA, Kobe, Japan, May 12-17, 2009; submitted Sept. 2008.
7. Ioannis Poulakakis and J. W. Grizzle, The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper, Preprint IEEE Transaction on Automatic Control, Accepted.
8. B. Morris and J.W. Grizzle, Hybrid Invariant Manifolds in Systems with Impulse Effects with Application to Periodic Locomotion in Bipedal Robots, Pre-print IEEE Transaction on Automatic Control, Submitted February 2007; accepted December 2007 (to appear).
9. Ioannis Poulakakis and J. W. Grizzle, Monopedal Running Control: SLIP Embedding and Virtual Constraint Controllers, Reprint 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, October 29--Nov. 2 2007; [Supplemental Material].
10. Ioannis Poulakakis and J. W. Grizzle, Formal Embedding of the Spring Loaded Inverted Pendulum in an Asymmetric Hopper, Reprint European Control Conference (2007-ECC), Kos, Greece, July 2007.
11. B. Morris and J.W. Grizzle, Hybrid Invariance in Bipedal Robots with Series Compliant Actuators , Reprint 2006-CDC, San Diego, California, December, 2006.

    Observers and Event-Based Stabilization for Systems with Impulse Effects (i.e., Hybrid)(Back to Top of Papers)

12. J.W. Grizzle, Jun-Ho Choi, Hassan Hammouri and B. Morris, On Observer-Based Feedback Stabilization of Periodic Orbits in Bipedal Locomotion, Reprint, Methods and Models in Automation and Robotics (MMAR 2007), 27 - 30 August 2007, Szczecin, Poland. Plenary Talk
13. J.W. Grizzle, ``Remarks on Event-Based Stabilization of Periodic Orbits in Systems with Impulse Effects," Reprint, Second International Symposium on Communications, Control and Signal Processing, March 2006, Marrakech, Morocco.
14. J.W. Grizzle, E.R. Westervelt, and C. Canudas-de-Wit Event-based PI Control of an Underactuated Biped Walker, Reprint, IEEE Conference on Decision and Control, December 2003. [Supplemental Material].
15. E.R. Westervelt, J.W. Grizzle, and C. Canudas de Wit Switching and PI Control for Planar Biped Walkers, Reprint, IEEE Transactions on Automatic Control;Vol. 48, N0. 2, February 2003, pp. 308-312. [Supplemental Material].

    Rehabilitation Robotics (Back to Top of Papers)

16. Kari A. Danek, R. Brent Gillespie, J. Wayne Aldridge, D.P. Ferris, and J.W. Grizzle, A Dual Input Device for Self-Assisted Control of a Virtual Pendulum, 9Th International Conference On Rehabilitation Robotics (ICORR) , Chicago, IL, June 28 - July 1, 2005.

    Planar Rigid Robots, RABBIT, and Hybrid Zero Dynamics (HZD)(Back to Top of Papers)

17. C. Chevallereau, D. Djoudi, and J.W. Grizzle, Stable Bipedal Walking with Foot Rotation Through Direct Regulation of the Zero Moment Point, Re-print IEEE Transactions on Robotics, Vol. 25, No. 2, April 2008, pp.~390-401.
18. J.W. Grizzle and E.R. Westervelt, ``Hybrid Zero Dynamics of Planar Bipedal Walking,'' Analysis and Design of Nonlinear Control Systems, Springer, Ed., A. Astolfi and L Marconi, pp. 223-237, 2008.
19. D. Djoudi, C. Chevallereau, and J.W. Grizzle, A Path-Following Approach to Stable Bipedal Walking and Zero Moment Point Regulation, Reprint ICRA-07, IEEE International Conference on Robotics and Automation, April 2007, Roma, Italy.
20. B. Morris and J.W. Grizzle, A Restricted Poincare Map for Determining Exponentially Stable Periodic Orbits in Systems with Impulse Effects: Application to Bipedal Robots, Re-print 2005-CDC, Seville, Spain, December, 2005.
21. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Anthropomorphic Foot Action, Internal Report , November 2005.
22. Junho Choi and J.W. Grizzle, Feedback Control of an Underactuated Planar Bipedal Robot with Impulsive Foot Action, Reprint, Robotica, Volume 23, Issue 05, September 2005, pp 567-580.. [Supplemental Material].
23. B. Morris, E.R. Westervelt, C. Chevallereau, G. Buche, and J.W. Grizzle, Achieving Bipedal Running with RABBIT: Six Steps toward Infinity, Reprint Fast Motions in Biomechanics and Robotics Symposium, Heidelberg, September 7 - 9, 2005. Republished as a book chapter in: Fast Motions in Biomechanics and Robotics: Optimization and Feedback Control (Springer Lecture Notes in Control and Information Sciences), pp. 277-297, November 13, 2006. [Supplemental Material].
24. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Foot Rotation, Reprint, American Control Conference'', Portland, OR, June 2005.
25. C. Chevallereau, E.R. Westervelt, and J.W. Grizzle, Asymptotically Stable Running for a Five-Link, Four-Actuator, Planar Bipedal Robot, Re-print, International Journal of Robotics Research, Volume 24, Issue 6, June 2005, pp. 431 - 464. [Supplemental Material].
26. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Foot Rotation, Re-print, ACC, Portland, Oregon, June 2005. JunHo won best presentation of session!
27. J.W. Grizzle, C.H. Moog, and C. Chevallereau, Nonlinear Control of Mechanical Systems with an Unactuated Cyclic Variable. Re-print, IEEE-TAC, Vol. 30, No. 5, May 2005, pp. 559-576. [Supplemental Material].
28. C. Chevallereau, E.R. Westervelt, and J.W. Grizzle, Asymptotic Stabilization of a Five-link, Four-Actuator, Planar Bipedal Runner, Re-print, CDC, December 2004. [Supplemental Material].
29. Junho Choi and J.W. Grizzle, Planar Bipedal Robot with Impulsive Foot Action, Reprint, CDC, December 2004. [Supplemental Material].
30. C. Chevallereau, J.W. Grizzle, and C.H. Moog, Nonlinear Control of Mechanical Systems with one Degree of Underactuation. Re-print, ICRA 2004, New Orleans, April 26 to May 1, 2004. [Supplemental Material].
31. E.R. Westervelt, G. Buche, and J.W. Grizzle Experimental Validation of a Framework for the Design of Controllers that Induce Stable Walking in Planar Bipeds, Reprint, The International Journal of Robotics Research, Vol. 24, No. 6, June 2004, pp. 559-582. [Supplemental Material].
32. C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, E.R. Westervelt, C. Canudas-de-Wit, and J.W. Grizzle RABBIT: A Testbed for Advanced Control Theory, Reprint, IEEE Control Systems Magazine, Vol. 23, No. 5, October, 2003, pp. 57-79. [Supplemental Material].
33. Franck Plestan, J.W. Grizzle, Eric Westervelt and Gabriel Abba, Stable Walking of a 7-DOF Biped Robot. Reprint, IEEE Trans. Robotics and Automation, Vol. 19, No. 4, August 2003, pp. 653-668. [Supplemental Material]
34. E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, Hybrid Zero Dynamics of Planar Biped Walkers. Reprint, IEEE-TAC, Vol. 48, No. 1, January 2003, pp. 42-56. [Supplemental Material].
35. E.R. Westervelt and J.W. Grizzle, Sequential Composition of Walking Motions for a 5-Link Planar Biped Walker, Reprint, WORKSHOP ON FUTURE DIRECTIONS IN NONLINEAR CONTROL OF MECHANICAL SYSTEMS, October 2, 2002,University of Illinois, Urbana-Champaign, IL. [Supplemental Material]. The talk inlcuded results from C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, E.R. Westervelt, C. Canudas-de-Wit, and J.W. Grizzle RABBIT: A Testbed for Advanced Control Theory, Preprint, To appear in IEEE Control Systems Magazine; revised April, 2003; submitted September, 2002. [Supplemental Material].
36. E.R. Westervelt and J.W. Grizzle, Design of Asymptotically Stable Walking for a 5-Link Planar Biped Walker via Optimization. Reprint, ICRA-2002, May 10-17, 2002, Washington, DC.
37. E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, Zero Dynamics of Underactuated Planar Biped Walkers. Reprint, IFAC-2002, Barcelona, Spain, July 21-26, 2002.
38. J.W. Grizzle, An Analytical Approach to Asymptotically Stable Walking in Planar Biped Robots. Reprint, Super Mechano Symposium Conference, November 19-20, 2001, Japan. Two movies are cited in the paper, here they are: Movie_1. and Movie_2..
39. Franck Plestan, J.W. Grizzle, Eric Westervelt and Gabriel Abba, Controlled Periodic Motion in a Nonlinear System with Impulse Effects: Walking of a Biped Robot. Reprint, IFAC NOLCOS-2001, Saint-Petersburg, Russia, July 4-6, 2001.
40. J.W. Grizzle, Gabriel Abba and Franck Plestan, Asymptotically Stable Walking for Biped Robots: Analysis via Systems with Impulse Effects. Reprint, IEEE T-AC, Volume 46, No. 1, January 2001, pp. 51-64. revised version. This paper received the 2002 George S. Axelby Award for the Best Paper in the IEEE Trans. Auto. Control during the years 2000 and 2001.
41. J.W. Grizzle, Gabriel Abba and Franck Plestan, Asymptotic Stability of a Walking Cycle for a Biped Robot with Knees and Torso. Reprint, NATO AVT Fall Symposium, Ankara, Turkey, October 9-13, 2000 .
42. J.W. Grizzle, Franck Plestan and Gabriel Abba Poincaré's Method for Systems with Impulse Effects: Application to Mechanical Biped Locomotion. Reprint, 1999 IEEE-CDC, Phoenix, AZ.
43. J.W. Grizzle, Gabriel Abba and Franck Plestan, Proving Asymptotic Stability of a Walking Cycle for a Five DOF Biped Robot Model. Reprint, CLAWAR 1999.