Abstract
Gait generation of a humanoid robot on a deformable terrain is a complex problem as the foot and terrain interaction and terrain deformation have to be included in the dynamics. To simplify the dynamics of walk on deformable terrain, we used a spherical inverted pendulum (SIP) to represent the single support phase, in which the effect of terrain deformation is represented by a spring and damper contact model. The impact model for leg transition is derived from angular momentum conservation. In order to minimize the energy loss due to impact, the double support phase is modeled as a suspended pendulum. Based on the motion of the SIP model, the hip and leg trajectories of a 10-degree-of-freedom (DOF) humanoid robot are generated. The joint trajectories of the robot are obtained from inverse kinematics. The motion of the center of mass is analyzed by inverse dynamics of a floating-base robot. The proposed gait generation method has been experimentally validated using a Kondo KHR-3HV humanoid robot on deformable terrain. The results show that the humanoid can effectively track the trajectories of the SIP model.
Issue Section:
Research Papers
References
1.
Sugihara
, T.
, Nakamura
, Y.
, and Inoue
, H.
, 2002
, “Real-Time Humanoid Motion Generation Through ZMP Manipulation Based on Inverted Pendulum Control
,” Proceedings 2002 IEEE International Conference on Robotics and Automation, Vol. 2
, IEEE
, pp. 1404
–1409
, Cat. No. 02CH37292.2.
Choi
, Y.
, Kim
, D.
, Oh
, Y.
, and You
, B.-J.
, 2007
, “Posture/Walking Control for Humanoid Robot Based on Kinematic Resolution of CoM Jacobian With Embedded Motion
,” IEEE Trans. Rob.
, 23
(6
), pp. 1285
–1293
. 3.
Sarkar
, A.
, and Dutta
, A.
, 2019
, “Optimal Trajectory Generation and Design of an 8-DOF Compliant Biped Robot for Walk on Inclined Ground
,” J. Intell. Rob. Syst.
, 94
(3
), pp. 583
–602
. 4.
Sato
, T.
, Sakaino
, S.
, Ohashi
, E.
, and Ohnishi
, K.
, 2010
, “Walking Trajectory Planning on Stairs Using Virtual Slope for Biped Robots
,” IEEE. Trans. Ind. Electron.
, 58
(4
), pp. 1385
–1396
. 5.
Kuindersma
, S.
, Deits
, R.
, Fallon
, M.
, Valenzuela
, A.
, Dai
, H.
, Permenter
, F.
, Koolen
, T.
, Marion
, P.
, and Tedrake
, R.
, 2016
, “Optimization-Based Locomotion Planning, Estimation, and Control Design for the Atlas Humanoid Robot
,” Auton. Rob.
, 40
(3
), pp. 429
–455
. 6.
Sygulla
, F.
, and Rixen
, D.
, 2020
, “A Force-Control Scheme for Biped Robots to Walk Over Uneven Terrain Including Partial Footholds
,” Int. J. Adv. Rob. Syst.
, 17
(1
), p. 1729881419897472
. 7.
Gong
, Y.
, and Grizzle
, J. W.
, 2022
, “Zero Dynamics, Pendulum Models, and Angular Momentum in Feedback Control of Bipedal Locomotion
,” ASME J. Dyn. Syst. Meas. Control.
, 144
(12
), p. 121006
. 8.
Zheng
, Y. F.
, Wang
, H.
, Li
, S.
, Liu
, Y.
, Orin
, D.
, Sohn
, K.
, Jun
, Y.
, and Oh
, P.
, 2013
, “Humanoid Robots Walking on Grass, Sands and Rocks
,” IEEE Conference on Technologies for Practical Robot Applications (TePRA)
, Woburn, MA
, Apr. 22–23
, IEEE, pp. 1
–6
.9.
Kolvenbach
, H.
, Bellicoso
, D.
, Jenelten
, F.
, Wellhausen
, L.
, and Hutter
, M.
, 2018
, “Efficient Gait Selection for Quadrupedal Robots on the Moon and Mars
,” 14th International Symposium on Artificial Intelligence, Robotics and Automation in Space (i-SAIRAS 2018)
, Madrid, Spain
, June 4–6
.10.
Hashimoto
, K.
, Kang
, H.-j.
, Nakamura
, M.
, Falotico
, E.
, Lim
, H.-o.
, Takanishi
, A.
, Laschi
, C.
, Dario
, P.
, and Berthoz
, A.
, 2012
, “Realization of Biped Walking on Soft Ground With Stabilization Control Based on Gait Analysis
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, Vilamoura-Algarve, Portugal
, Oct. 7–12
, IEEE, pp. 2064
–2069
.11.
Mesesan
, G.
, Englsberger
, J.
, Garofalo
, G.
, Ott
, C.
, and Albu-Schäffer
, A.
, 2019
, “Dynamic Walking on Compliant and Uneven Terrain Using DCM and Passivity-Based Whole-Body Control
,” IEEE-RAS 19th International Conference on Humanoid Robots (Humanoids)
, Toronto, ON, Canada
, Oct. 15–17
, IEEE, pp. 25
–32
.12.
Ding
, L.
, Gao
, H.
, Deng
, Z.
, Song
, J.
, Liu
, Y.
, Liu
, G.
, and Iagnemma
, K.
, 2013
, “Foot–Terrain Interaction Mechanics for Legged Robots: Modeling and Experimental Validation
,” Int. J. Rob. Res.
, 32
(13
), pp. 1585
–1606
. 13.
Gora
, S.
, Gupta
, S. S.
, and Dutta
, A.
, 2021
, “Optimal Gait Generation of an 8-DOF Biped Robot on Deformable Terrain Using Floating-base Dynamics
,” Advances in Robotics-5th International Conference of The Robotics Society, pp. 1
–6
.14.
Xiong
, X.
, Ames
, A. D.
, and Goldman
, D. I.
, 2017
, “A Stability Region Criterion for Flat-Footed Bipedal Walking on Deformable Granular Terrain
,” 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, Canada, Sept. 24–28, IEEE
, pp. 4552
–4559
.15.
Kajita
, S.
, Kanehiro
, F.
, Kaneko
, K.
, Yokoi
, K.
, and Hirukawa
, H.
, 2001
, “The 3d Linear Inverted Pendulum Mode: A Simple Modeling for a Biped Walking Pattern Generation
,” Proceedings 2001 IEEE/RSJ International Conference on Intelligent Robots and Systems. Expanding the Societal Role of Robotics in the the Next Millennium, Vol. 1
, IEEE
, pp. 239
–246
, Cat. No. 01CH37180.16.
Shibuya
, M.
, Suzuki
, T.
, and Ohnishi
, K.
, 2006
, “Trajectory Planning of Biped Robot Using Linear Pendulum Mode for Double Support Phase
,” IECON 2006 – 32nd Annual Conference on IEEE Industrial Electronics
, Paris, France
, Nov. 6–10
, IEEE, pp. 4094
–4099
.17.
Xie
, Z.
, Li
, L.
, and Luo
, X.
, 2021
, “Three-Dimensional Aperiodic Biped Walking Including the Double Support Phase Using Lipm and LPM
,” Rob. Auton. Syst.
, 143
, p. 103831
. 18.
Crews
, S.
, and Travers
, M.
, 2020
, “Energy Management Through Footstep Selection for Bipedal Robots
,” IEEE Rob. Autom. Lett.
, 5
(4
), pp. 5485
–5493
. 19.
Gora
, S.
, Gupta
, S. S.
, and Dutta
, A.
, 2023
, “Energy-based Footstep Planning of Biped on Uneven Deformable Terrain Using Nonlinear Inverted Pendulum
,” ASME J. Mech. Rob.
, 15
(5
), p. 054502
. 20.
McGeer
, T.
, 1990
, “Passive Dynamic Walking
,” Int. J. Rob. Res.
, 9
(2
), pp. 62
–82
. 21.
Shah
, S. V.
, Saha
, S. K.
, and Dutt
, J. K.
, 2013
, Dynamics of Tree-Type Robotic Systems
, S. G.
Tzafestas
, ed., Springer
, Dordrecht, Netherlands
, pp. 73
–88
.22.
Mummolo
, C.
, Peng
, W. Z.
, Gonzalez
, C.
, and Kim
, J. H.
, 2018
, “Contact-Dependent Balance Stability of Biped Robots
,” ASME J. Mech. Rob.
, 10
(2
), p. 021009
. 23.
Gora
, S.
, Gupta
, S. S.
, and Dutta
, A.
, 2023
, “Gait Generation of 6-dof Biped Robot on Inclined Deformable Terrain Using Nonlinear Inverted Pendulum
,” AIR 2023: Advances In Robotics - 6th International Conference of The Robotics Society
, Ropar, India
, July 5–8
, pp. 1
–6
.24.
Tsuji
, T.
, and Ohnishi
, K.
, 2002
, “A Control of Biped Robot Which Applies Inverted Pendulum Mode With Virtual Supporting Point
,” 7th International Workshop on Advanced Motion Control. Proceedings, IEEE
, pp. 478
–483
, Cat. No. 02TH8623.25.
Ge
, C.
, and Rice
, B.
, 2018
, “Impact Damping Ratio of a Nonlinear Viscoelastic Foam
,” Polym. Test.
, 72
, pp. 187
–195
. 26.
Sugihara
, T.
, and Nakamura
, Y.
, 2002
, “Whole-Body Cooperative Balancing of Humanoid Robot Using COG Jacobian
,” IEEE/RSJ International Conference on Intelligent Robots and Systems
, Lausanne, Switzerland
, Sept. 30–Oct. 4
, Vol. 3, IEEE, pp. 2575
–2580
.27.
“Kondo KHR-3HV Humanoid Robot,” https://kondo-robot.com/, Accessed November 1, 2023.
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