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

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New Robot Constructed 2012: It's name is MARLO. The robot was built in collaboration with Jonathan Hurst. The robot is 3D (does not need a boom for support) and has onboard power. See the robot in action on our YouTube Channel: DynamicLegLocomotion Channel. Robot Constructed 2007: It's name is MABEL . The robot was built in collaboration with Jonathan Hurst when he was at the Robotics Institute of Carnegie Mellon. A model of the robot is available on IEEE-Xplore, Here is the first page, and in pre-print form: Identification of a Bipedal Robot With a Compliant Drivetrain: Parameter Estimation for Control Design, Control Systems Magazine, Vol 31, No. 2, April, 2011 . See the robot in action on our YouTube Channel: DynamicLegLocomotion Channel. 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:

Papers on Bipedal Robots and Robotics: In Review or Recent or Planar or Compliance or Observers and Event-Based Control or Rehabilitation

In Review

1. Brian G. Buss, Kaveh Akbari Hamed, Brent A. Griffin, Jessy W. Grizzle, Experimental Results for 3D Bipedal Robot Walking Based On Systematic Optimization of Virtual Constraints,, Preprint--Submitted September 28, 2015 American Control Conference, Boston, 2016.

   More Recent (Mostly 3D Bipeds but not Exclusively)

2. Brent Griffin and Jessy Grizzle, Nonholonomic Virtual Constraints for Dynamic Walking, Dec. 2015, 54th IEEE Conference of Decision and Control (CDC 2015). [Animation ]
3. K. Akbari Hamed and J.W. Grizzle, Iterative Robust Stabilization Algorithm for Periodic Orbits of Hybrid Dynamical Systems: Application to Bipedal Running, ADHS --Analysis and Design of Hybrid Systems, October 14-16, 2015.
4. K. Akbari Hamed, B.G. Buss and J.W. Grizzle, Exponentially Stabilizing Continuous-Time Controllers for Periodic Orbits of Hybrid Systems: Application to Bipedal Locomotion with Ground Height Variations, The International Journal of Robotics Research. ( August 2015 ) [Animation 1], [Animation 2].
5. Kevin Galloway, Koushil Sreenath, Aaron D. Ames, and J. W. Grizzle, Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs, Reprint, IEEE Access, Vol. 3, April 2015, pp. 323 - 332Remark] While the result is illustrated here for a 2D robot, it applies to 3D compliant robots as well. Only depends on HZD. [Supplemental Material] Video on YouTube Other robotics video are here: Dynamic Leg Locomotion.
6. Brent Griffin and Jessy Grizzle, Walking Gait Optimization for Accommodation of Unknown Terrain Height Variations, American Control Conference, July 2015. [YouTube video]
7. A. D. Ames, P. Tabuada, B. Schuermann, W. Ma, S. Kolathaya, M. Rungger and J. W. Grizzle, First Steps toward Formal Controller Synthesis for Bipedal Robots., Published Hybrid Systems: Computation and Control (HSCC), 2015.
8. J.W.~Grizzle, Christine Chevallereau, Aaron D. Ames, and Ryan W. Sinnet, Models, Feedback Control, and Open Problems of 3D Bipedal Robotic Walking , (Survey Paper) reprint Automatica, Volume 50, Issue 8, August 2014, Pages 1955 -- 1988
9. K. Akbari Hamed, B. G. Buss, and J. W. Grizzle, Continuous-Time Controllers for Stabilizing Periodic Orbits of Hybrid Systems: Application to an Underactuated 3D Bipedal Robot 53rd IEEE Conference of Decision and Control (CDC 2014), Final version, December 2014. Supplement: Proofs
10. Brian G. Buss, Alireza Ramezani, Kaveh Akbari Hamed, Brent A. Griffin, Kevin S. Galloway, Jessy W. Grizzle, Preliminary Walking Experiments with Underactuated 3D Bipedal Robot MARLO,, Final version IROS, Chicago, IL, September, 2014.
11. Kaveh Akbari Hamed and J.W.~Grizzle, Event-based Stabilization of Periodic Orbits for Underactuated 3D Bipedal Robots with Left-Right Symmetry, Re-print IEEE Transaction of Robotics, Vol. 30, No. 2, pp. 365 - 381, April 2014. [Animation 1], [Animation 2], [Animation 3], [Animation 4].
12. Aaron D. Ames, Kevin Galloway, J.W. Grizzle, and Koushil Sreenath Rapidly Exponentially Stabilizing Control Lyapunov Functions and Hybrid Zero Dynamics, reprint 2 IEEE TAC, Vol. 59, NO. 4, April 2014, pp 876-891. [Supplemental Material] Video on YouTube Other robotics video are here: Dynamic Leg Locomotion.
13. Alireza Ramezani, Jonathan Hurst, Kaveh Akbari Hamed and J.W.~Grizzle, Performance Analysis and Feedback Control of ATRIAS, A 3D Bipedal Robot, Re-print ASME J. Dynamic Systems Measurement and Control,Volume 136, Issue 2, March 2014. On-line prepublication version
14. A.R. Teel, R. Goebel, B. Morris, A.D. Ames, J.W. Grizzle, A stabilization result with application to bipedal locomotion,, IEEE Conf. on Decision and Control, Florence, Italy, Dec., 2013.
15. Kaveh Akbari Hamed and J.W.~Grizzle, Robust Event-based Stabilization of Periodic Orbits for Hybrid Systems: Application to an Underactuated 3D Bipedal Robot, Reprint American Control Conference, Washington DC, June 2013.
16. Aaron D. Ames, Kevin Galloway, and J.W. Grizzle, Control Lyapunov Functions and Hybrid Zero Dynamics, Reprint 2012-CDC, Hawaii, USA, December, 2012. [Supplemental Material] The proofs could not be included in the final 6 page submission, so they are given here: Proofs for CLF and HZD [Remark] While the result is illustrated here for a 2D rigid robot, it applies to 3D compliant robots as well. Only depends on HZD.
17. Ching-Long Shih, J. W. Grizzle and Christine Chevallereau, From Stable Walking to Steering of a 3D Bipedal Robot with Passive Point Feet, Reprint Robotica, Volume 30, Issue 07, December 2012, pp 1119-1130. Zip File of Simulation Videos [Right Click and Save].
18. Christine Chevallereau, J.W.~Grizzle, and Ching-Long Shih, Steering of a 3D Bipedal Robot with an Underactuated Ankle, Reprint IROS, Taipei, Taiwan, October 2010.
19. J.W.~Grizzle, Christine Chevallereau, Aaron D. Ames, and Ryan W. Sinnet, 3D Bipedal Robotic Walking: Models, Feedback Control, and Open Problems , Reprint NOLCOS, Bologna, Italy, September 2010.
20. Christine Chevallereau, J. W. Grizzle and Ching-Long Shih, Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot, Published IEEE Transactions on Robotics, Vol. 25, No. 1, February 2009, pp. 37-50. [Supplemental Material].
21. J. W. Grizzle, Christine Chevallereau and Ching-Long Shih, HZD-Based Control of a Five-Link Underactuated 3D Bipedal Robot, Published IEEE Conf. on Decision and Control, December 2008.
22. Ching-Long Shih, J. W. Grizzle and Christine Chevallereau, Asymptotically Stable Walking of a Simple Underactuated 3D Bipedal Robot, Published 33rd Annual Conference of IEEE Industrial Electronics (IECON 2007), Taipei, Taiwan, November 5-8, 2007.

    Legged Robots with Compliance (Back to Top of Papers)

23. Hae-Won Park, Alireza Ramezani, and Jessy W. Grizzle, A Finite-state Machine for Accommodating Unexpected Large Ground Height Variations in Bipedal Robot Walking, Reprint IEEE Trans. on Robotics, Vol. 29, Issue 2, April 2013, pp. 331 - 345. [YouTube video]
24. Koushil Sreenath, Hae-Won Park, Ioannis Poulakakis, and Jessy W. Grizzle, Embedding Active Force Control within the Compliant Hybrid Zero Dynamics to Achieve Stable, Fast Running on MABEL, The International Journal of Robotics Research, Vol. 33, June 2014, pp. 988-1005. [Supplemental Material]
25. Hae-Won Park, Koushil Sreenath, Alireza Ramezani, and J. W. Grizzle, Switching Control Design for Accommodating Large Step-down Disturbances in Bipedal Robot Walking, Published Int. Conf. on Robotics and Automation (ICRA), 2012. [Video]
26. Koushil Sreenath, Hae-Won Park, and Jessy W. Grizzle, Design and Experimental Implementation of a Compliant Hybrid Zero Dynamics Controller with Active Force Control for Running on MABEL, Published Int. Conf. on Robotics and Automation (ICRA), May 2012. [Video]
27. Koushil Sreenath, Hae-Won Park, Ioannis Poulakakis, and Jessy W. Grizzle, A Compliant Hybrid Zero Dynamics Controller for Stable, Efficient and Fast Bipedal Walking on MABEL, Published Int. J. Robotics Research (IJRR), 30(9):1170–1193, August 2011. (on-line version published 17 Sept 2010) [Supplemental Material] (such as videos).
28. Koushil Sreenath, Hae-Won Park, Ioannis Poulakakis, and Jessy W. Grizzle, "Design and experimental implementation of a compliant hybrid zero dynamics controller for walking on MABEL, Published IEEE Conference on Decision and Control, pages 280–287, Atlanta, GA, USA, December 2010
29. Hae Won Park, Koushil Sreenath, Jonathan W. Hurst and J.W. Grizzle, Identification of a Bipedal Robot With a Compliant Drivetrain: Parameter Estimation for Control Design, Control Systems Magazine, Vol 31, No. 2, April, 2011 . [Supplemental Material] The full article is available on IEEE-Xplore. Here is the first page, MABEL was on the cover here.
30. Hae Won Park, Koushil Sreenath, Jonathan W. Hurst and J.W. Grizzle, Identification and Dynamic Model of a Bipedal Robot With a Cable-Differential-Based Compliant Drivetrain, Control Group Report, No. CGR 10-06 ; 16 March 2010 . [Supplemental Material]. A longer version of the report is available here.
31. Ioannis Poulakakis and J. W. Grizzle, The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper, Published IEEE Transaction on Automatic Control, Volume 54, Issue 8, Aug. 2009 Page(s):1779 - 1793.
32. B. Morris and J.W. Grizzle, Hybrid Invariant Manifolds in Systems with Impulse Effects with Application to Periodic Locomotion in Bipedal Robots, Published IEEE Transaction on Automatic Control, Volume 54, Issue 8, Aug. 2009 Page(s):1751 - 1764
33. J.W. Grizzle Jonathan Hurst, Benjamin Morris, Hae-Won Park, and Koushil Sreenath, MABEL, A New Robotic Bipedal Walker and Runner, Published, 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]
34. Ioannis Poulakakis and J. W. Grizzle, Modeling and Control of the Monopedal Robot Thumper, Published, ICRA, Kobe, Japan, May 12-17, 2009; submitted Sept. 2008.
35. Ioannis Poulakakis and J. W. Grizzle, Monopedal Running Control: SLIP Embedding and Virtual Constraint Controllers, Published 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems, October 29--Nov. 2 2007; [Supplemental Material].
36. Ioannis Poulakakis and J. W. Grizzle, Formal Embedding of the Spring Loaded Inverted Pendulum in an Asymmetric Hopper, Published European Control Conference (2007-ECC), Kos, Greece, July 2007.
37. B. Morris and J.W. Grizzle, Hybrid Invariance in Bipedal Robots with Series Compliant Actuators , Published 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)

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

    Rehabilitation Robotics (Back to Top of Papers)

42. 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)

43. C. Chevallereau, D. Djoudi, and J.W. Grizzle, Stable Bipedal Walking with Foot Rotation Through Direct Regulation of the Zero Moment Point, Published IEEE Transactions on Robotics, Vol. 25, No. 2, April 2008, pp.~390-401.
44. 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.
45. D. Djoudi, C. Chevallereau, and J.W. Grizzle, A Path-Following Approach to Stable Bipedal Walking and Zero Moment Point Regulation, Published ICRA-07, IEEE International Conference on Robotics and Automation, April 2007, Roma, Italy.
46. 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, Published 2005-CDC, Seville, Spain, December, 2005.
47. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Anthropomorphic Foot Action, Internal Report , November 2005.
48. Junho Choi and J.W. Grizzle, Feedback Control of an Underactuated Planar Bipedal Robot with Impulsive Foot Action, Published, Robotica, Volume 23, Issue 05, September 2005, pp 567-580.. [Supplemental Material].
49. B. Morris, E.R. Westervelt, C. Chevallereau, G. Buche, and J.W. Grizzle, Achieving Bipedal Running with RABBIT: Six Steps toward Infinity, Published 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].
50. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Foot Rotation, Published, American Control Conference'', Portland, OR, June 2005.
51. C. Chevallereau, E.R. Westervelt, and J.W. Grizzle, Asymptotically Stable Running for a Five-Link, Four-Actuator, Planar Bipedal Robot, Published, International Journal of Robotics Research, Volume 24, Issue 6, June 2005, pp. 431 - 464. [Supplemental Material].
52. Junho Choi and J.W. Grizzle, Planar Bipedal Walking with Foot Rotation, Published, ACC, Portland, Oregon, June 2005. JunHo won best presentation of session!
53. J.W. Grizzle, C.H. Moog, and C. Chevallereau, Nonlinear Control of Mechanical Systems with an Unactuated Cyclic Variable. Published, IEEE-TAC, Vol. 30, No. 5, May 2005, pp. 559-576. [Supplemental Material].
54. C. Chevallereau, E.R. Westervelt, and J.W. Grizzle, Asymptotic Stabilization of a Five-link, Four-Actuator, Planar Bipedal Runner, Published, CDC, December 2004. [Supplemental Material].
55. Junho Choi and J.W. Grizzle, Planar Bipedal Robot with Impulsive Foot Action, Published, CDC, December 2004. [Supplemental Material].
56. C. Chevallereau, J.W. Grizzle, and C.H. Moog, Nonlinear Control of Mechanical Systems with one Degree of Underactuation. Published, ICRA 2004, New Orleans, April 26 to May 1, 2004. [Supplemental Material].
57. 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, Published, The International Journal of Robotics Research, Vol. 24, No. 6, June 2004, pp. 559-582. [Supplemental Material].
58. 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, Published, IEEE Control Systems Magazine, Vol. 23, No. 5, October, 2003, pp. 57-79. [Supplemental Material].
59. Franck Plestan, J.W. Grizzle, Eric Westervelt and Gabriel Abba, Stable Walking of a 7-DOF Biped Robot. Published, IEEE Trans. Robotics and Automation, Vol. 19, No. 4, August 2003, pp. 653-668. [Supplemental Material]
60. E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, Hybrid Zero Dynamics of Planar Biped Walkers. Published, IEEE-TAC, Vol. 48, No. 1, January 2003, pp. 42-56. [Supplemental Material].
61. E.R. Westervelt and J.W. Grizzle, Sequential Composition of Walking Motions for a 5-Link Planar Biped Walker, Published, 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, Published, To appear in IEEE Control Systems Magazine; revised April, 2003; submitted September, 2002. [Supplemental Material].
62. E.R. Westervelt and J.W. Grizzle, Design of Asymptotically Stable Walking for a 5-Link Planar Biped Walker via Optimization. Published, ICRA-2002, May 10-17, 2002, Washington, DC.
63. E.R. Westervelt, J.W. Grizzle, and D.E. Koditschek, Zero Dynamics of Underactuated Planar Biped Walkers. Published, IFAC-2002, Barcelona, Spain, July 21-26, 2002.
64. J.W. Grizzle, An Analytical Approach to Asymptotically Stable Walking in Planar Biped Robots. Published, Super Mechano Symposium Conference, November 19-20, 2001, Japan. Two movies are cited in the paper, here they are: Movie_1. and Movie_2..
65. 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. Published, IFAC NOLCOS-2001, Saint-Petersburg, Russia, July 4-6, 2001.
66. J.W. Grizzle, Gabriel Abba and Franck Plestan, Asymptotically Stable Walking for Biped Robots: Analysis via Systems with Impulse Effects. Published, 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.
67. J.W. Grizzle, Gabriel Abba and Franck Plestan, Asymptotic Stability of a Walking Cycle for a Biped Robot with Knees and Torso. Published, NATO AVT Fall Symposium, Ankara, Turkey, October 9-13, 2000 .
68. J.W. Grizzle, Franck Plestan and Gabriel Abba Poincaré's Method for Systems with Impulse Effects: Application to Mechanical Biped Locomotion. Published, 1999 IEEE-CDC, Phoenix, AZ.
69. J.W. Grizzle, Gabriel Abba and Franck Plestan, Proving Asymptotic Stability of a Walking Cycle for a Five DOF Biped Robot Model. Published, CLAWAR 1999.

(Back to Top of Papers)

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