This paper develops feedback controllers for walking in 3D, on level ground, with energy efficiency as the performance objective. Assume The Robot Is A Sphere (ATRIAS) 2.1 is a new robot that has been designed for the study of 3D bipedal locomotion, with the aim of combining energy efficiency, speed, and robustness with respect to natural terrain variations in a single platform. The robot is highly underactuated, having 6 actuators and, in single support, 13 degrees of freedom. Its sagittal plane dynamics are designed to embody the spring loaded inverted pendulum (SLIP), which has been shown to provide a dynamic model of the body center of mass during steady running gaits of a wide diversity of terrestrial animals. A detailed dynamic model is used to optimize walking gaits with respect to the cost of mechanical transport (CMT), a dimensionless measure of energetic efficiency, for walking speeds ranging from 0.5 to 1.4 . A feedback controller is designed that stabilizes the 3D walking gaits, despite the high degree of underactuation of the robot. The 3D results are illustrated in simulation. In experiments on a planarized (2D) version of the robot, the controller yielded stable walking.
Issue Section:
Research Papers
References
1.
Grimes
, J. A.
, and Hurst
, J. W.
, 2012
, “The Design of ATRIAS 1.0 a Unique Monoped, Hopping Robot
,” Proceedings of the 2012 International Conference on Climbing and Walking Robots and the Support Technologies for Mobile Machines
, pp. 548
–554
.2.
Collins
, S. H.
, Ruina
, A.
, Tedrake
, R.
, and Wisse
, M.
, 2005
, “Efficient Bipedal Robots Based on Passive-Dynamic Walkers
,” Science
, 307
, pp. 1082
–1085
.10.1126/science.11077993.
Grizzle
, J.
, 2012
, “ATRIAS 2.1 First Steps,” http://www.youtube.com/watch? v=uVkQ5ytOg54&list=UUMfDV8rkQqWhUwnTAYAq0tQ&index=2& feature=plpp_video4.
Blickhan
, R.
, 1989
, “The Spring Mass Model for Running and Hopping
,” J. Biomech.
, 22
(11–12
), pp. 1217
–1227
.10.1016/0021-9290(89)90224-85.
McMahon
, T. A.
, and Cheng
, G. C.
, 1990
, “The Mechanics of Running: How Does Stiffness Couple With Speed?
,” J. Biomech.
, 23
, pp. 65
–78
.10.1016/0021-9290(90)90042-26.
Farley
, C. T.
, Glasheen
, J.
, and McMahon
, T. A.
, 1993
, “Running Springs: Speed and Animal Size
,” J. Exp. Biol.
, 185
,, pp. 71
–86
.7.
Full
, R. J.
, and Farley
, C. T.
, 2000
, “Musculoskeletal Dynamics in Rhythmic Systems—A Comparative Approach to Legged Locomotion
,” Biomechanics and Neural Control of Posture and Movement
, J. M.
Winters
and P. E.
Crago
, eds. Springer-Verlag
, New York
.8.
Seyfarth
, A.
, Geyer
, H.
, Gunther
, M.
, and Blickhan
, R.
, 2001
, “A Movement Criterion for Running
,” J. Biomech.
, 35
, pp. 649
–655
.10.1016/S0021-9290(01)00245-79.
Raibert
, M.
, 1986
, Legged Robots that Balance
, MIT Press
, Cambridge, MA
.10.
Zeglin
, G.
, and Brown
, H. B.
, 1998
, “Control of a Bow Leg Hopping Robot
,” IEEE International Conference on Robotics and Automation
.11.
Ahmadi
, M.
, and Buehler
, M.
, 2006
, “Controlled Passive Dynamic Running Experiment With the ARL Monopod II
,” IEEE Trans. Robotics
, 22
, pp. 974
–986
.10.1109/TRO.2006.87893512.
Sreenath
, K.
, Park
, H.-W.
, Poulakakis
, I.
, and Grizzle
, J. W.
, 2011
, “Compliant Hybrid Zero Dynamics Controller for Achieving Stable, Efficient and Fast Bipedal Walking on MABEL
,” Int. J. Robot. Res.
, 30
(9
), pp. 1170
–1193
.10.1177/027836491037988213.
Sreenath
, K.
, Park
, H.-W.
, and Grizzle
, J.
, 2012
, “Design and Experimental Implementation of a Compliant Hybrid Zero Dynamics Controller With Active Force Control for Running on MABEL
,” International Conference on Robotics and Automation (ICRA)
, pp. 51
–56
.14.
Park
, H.-W.
, Sreenath
, K.
, Ramezani
, A.
, and Grizzle
, J.
, 2012
, “Switching Control Design for Accommodating Large Step-Down Disturbances in Bipedal Robot Walking
,” International Conference on Robotics and Automation (ICRA)
, pp. 3331
–3450
.15.
Park
, H.-W.
, Ramezani
, A.
, and Grizzle
, J.
, 2013
, “A Finite-State Machine for Accommodating Unexpected Large Ground-Height Variations in Bipedal Robot Walking
,” IEEE Trans. Rob. Autom.
, 29
, pp. 45
–50
.10.1109/TRO.2012.223099216.
Geyer
, H.
, Seyfarth
, A.
, and Blickhan
, R.
, 2006
, “Compliant Leg Behaviour Explains the Basic Dynamics of Walking and Running
,” Proc. R. Soc., London, Ser. B
, 273
, pp. 2861
–2867
.10.1098/rspb.2006.363717.
Laboratory
, D. R.
, 2012
, “SolidWorks—Model Parameters for ATRIAS Based on Solidworks,” http://code.google.com/p/atrias/18.
Hodgins
, J. K.
, and Raibert
, M. H.
, 1991
, “Adjusting Step Length for Rough Terrain Locomotion
,” IEEE Trans. Rob. Autom.
, 7
(3
), pp. 289
–298
.10.1109/70.8813819.
Ahmadi
, M.
, and Buehler
, M.
, 1999
, “The ARL Monopod II Running Robot: Control and Energetics
,” IEEE International Conference on Robotics and Automation
, pp. 1689
–1694
.20.
Chevallereau
, C.
, Abba
, G.
, Aoustin
, Y.
, Plestan
, F.
, Westervelt
, E. R.
, Canudas-de-Wit
, C.
, and Grizzle
, J. W.
, 2003
, “RABBIT: A Testbed for Advanced Control Theory
,” IEEE Control Syst. Mag.
, 23
(5
), pp. 57
–79
.10.1109/MCS.2003.123465121.
Corp
., H.
, “Asimo Humanoid Robot,” http://world.honda.com/asimo/22.
McGeer
, T.
, 1988
, “Stability and Control of Two-Dimensional Biped Walking
,” Center for Systems Science
, Simon Fraser University
, Burnaby, B.C., Canada
, Technical Report 1.23.
McGeer
, T.
, 1990
, “Passive Dynamic Walking
,” Int. J. Robot. Res.
, 9
(2
), pp. 62
–82
.10.1177/02783649900090020624.
Collins
, S. H.
, Wisse
, M.
, and Ruina
, A.
, 2001
, “A 3-D Passive Dynamic Walking Robot With Two Legs and Knees
,” Int. J. Robot. Res.
, 20
, pp. 607
–615
.10.1177/0278364012206756125.
Pratt
, J.
, and Pratt
, G.
, 1998
, “Exploiting Natural Dynamics in the Control of a Planar Bipedal Walking Robot
,” Proceedings of the Thirty-Sixth Annual Allerton Conference on Communication, Control, and Computing
.26.
Playter
, R.
, Buehler
, M.
, and Raibert
, M.
, 2006
, “Bigdog
,” Proceedings of SPIE International Society for Optical Engineering
, G. R.
Gerhart
, C. M.
Shoemaker
, and D. W.
Gage
, eds., SPIE
, Vol. 6230
.27.
Robinson
, D. W.
, Pratt
, J. E.
, Paluska
, D. J.
, and Pratt
, G. A.
, 1999
, “Series Elastic Actuator Development for a Biomimetic Walking Robot
,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp. 561
–568
.28.
Boaventura
, T.
, Semini
, C.
, Buchli
, J.
, Frigerio
, M.
, Focchi
, M.
, and Caldwell
, D. G.
, 2012
, “Dynamic Torque Control of a Hydraulic Quadruped Robot
,” IEEE Conference on Robotics and Automation
, pp. 1189
–1894
.29.
30.
Chevallereau
, C.
, Grizzle
, J.
, and Shih
, C.
, 2009
, “Asymptotically Stable Walking of a Five-Link Underactuated 3D Bipedal Robot
,” IEEE Trans. Rob. Autom.
, 25
(1
), pp. 37
–50
.10.1109/TRO.2008.201036631.
Westervelt
, E. R.
, Grizzle
, J. W.
, Chevallereau
, C.
, Choi
, J.
, and Morris
, B.
, 2007
, Feedback Control of Dynamic Bipedal Robot Locomotion. Control and Automation
, CRC Press
, Boca Raton, FL
.32.
Tuttle
, T.
, and Seering
, W.
, 1996
, “A Nonlinear Model of a Harmonic Drive Gear Transmission
,” IEEE Trans. Rob. Autom.
, 12
(3
), pp. 368
–374
.10.1109/70.49981933.
Kennedy
, C.
, and Desai
, J.
, 2005
, “Modeling and Control of the Mitsubishi pa-10 Robot Arm Harmonic Drive System
,” IEEE/ASME Trans. Mechatron.
, 10
(3
), pp. 263
–274
.10.1109/TMECH.2005.84829034.
Hurmuzlu
, Y.
, and Chang
, T.
, 1992
, “Rigid Body Collisions of a Special Class of Planar Kinematic Chains
,” IEEE Trans. Syst. Man Cybern.
, 22
(5
), pp. 964
–971
.10.1109/21.17983635.
Grizzle
, J. W.
, Abba
, G.
, and Plestan
, F.
, 2001
, “Asymptotically Stable Walking for Biped Robots: Analysis Via Systems With Impulse Effects
,” IEEE Trans. Autom. Control
, 46
, pp. 51
–64
.10.1109/9.89869536.
Westervelt
, E.
, Grizzle
, J.
, and Koditschek
, D.
, 2003
, “Hybrid Zero Dynamics of Planar Biped Walkers
,” IEEE Trans. Autom. Control
, 48
(1
), pp. 42
–56
.10.1109/TAC.2002.80665337.
Canudas-de-Wit
, C.
, 2004
, “On the Concept of Virtual Constraints as a Tool for Walking Robot Control and Balancing
,” Annu. Rev. Control
, 28
, pp. 157
–166
.10.1016/j.arcontrol.2004.03.00238.
Isidori
, A.
, 1995
, Nonlinear Control Systems: An Introduction
, 3rd ed., Springer-Verlag
, Berlin, Germany
.39.
Sreenath
, K.
, Park
, H.
, Poulakakis
, I.
, and Grizzle
, J.
, 2011
, “A Compliant Hybrid Zero Dynamics Controller for Stable, Efficient, and Fast Bipedal Walking on MABEL
,” Int. J. Robot. Res.
, 30
, pp. 1170
–1193
.10.1177/027836491037988240.
Morris
, B.
, and Grizzle
, J. W.
, 2009
, “Hybrid Invariant Manifolds in Systems With Impulse Effects With Application to Periodic Locomotion in Bipedal Robots
,” IEEE Trans. Autom. Control
, 54
(8
), pp. 1751
–1764
.10.1109/TAC.2009.202456341.
Piegl
, L.
, and Tiller
, W.
, 1997
, The NURBS Book
, Springer
, New York
.42.
Ruina
, A.
, 2012
, “Cornell Ranger, 2011 4-Legged Bipedal Robot,” Nov. http://ruina.tam.cornell.edu/research/topics/locomotion_and_robotics/ranger/Ranger 2011/index.html43.
Shih
, C.
, Grizzle
, J.
, and Chevallereau
, C.
, 2012
, “From Stable Walking to Steering of a 3D Bipedal Robot With Passive Point Feet
,” Robotica
, 30
, pp. 1119
–1130
.10.1017/S026357471100138XCopyright © 2014 by ASME
You do not currently have access to this content.
