Modeling and Control of Legged Robots

  • Pierre-Brice Wieber
  • Russ Tedrake
  • Scott Kuindersma

Abstract

The promise of legged robots over wheeled robots is to provide improved mobility over rough terrain. Unfortunately, this promise comes at the cost of a significant increase in complexity. We now have a good understanding of how to make legged robots walk and run dynamically, but further research is still necessary to make them walk and run efficiently in terms of energy, speed, reactivity, versatility, and robustness. In this chapter, we will discuss how legged robots are usually modeled, how their stability analysis is approached, how dynamic motions are generated and controlled, and finally summarize the current trends in trying to improve their performance. The main problem is avoiding to fall. This can prove difficult since legged robots have to rely entirely on available contact forces to do so. The temporality of leg motions appears to be a key aspect in this respect, as current control solutions include continuous anticipation of future motion (using some form of model predictive control), or focusing more specifically on limit cycles and orbital stability.

2-D

two-dimensional

3-D

three-dimensional

CMU

Carnegie Mellon University

COM

center of mass

COP

center of pressure

CP

capture point

CPG

central pattern generator

DLR

Deutsches Zentrum für Luft- und Raumfahrt

FRI

foot rotation indicator

KAIST

Korea Advanced Institute of Science and Technology

LCP

linear complementarity problem

LP

linear program

LQR

linear quadratic regulator

MIT

Massachusetts Institute of Technology

MPC

model predictive control

ODE

ordinary differential equation

ODI

ordinary differential inclusion

PD

proportional–derivative

QP

quadratic programming

XCOM

extrapolated center of mass

ZMP

zero moment point

References

  1. 48.1
    K.J. Waldron, R.B. McGhee: The adaptive suspension vehicle, IEEE Control Syst. Mag. 6, 7–12 (1986)CrossRefGoogle Scholar
  2. 48.2
    K. Hirai, M. Hirose, Y. Haikawa, T. Takenaka: The development of honda humanoid robot, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1998) pp. 1321–1326Google Scholar
  3. 48.3
    H. Lim, A. Takanishi: Biped walking robots created at waseda university: WL and WABIAN family, Philos. Trans. Royal Soc. A 365(1850), 49–64 (2007)CrossRefGoogle Scholar
  4. 48.4
    H. Miura, I. Shimoyama: Dynamic walk of a biped, Int. J. Robotics Res. 3(2), 60–74 (1984)CrossRefGoogle Scholar
  5. 48.5
    M. Raibert: Legged Robots that Balance (MIT Press, Cambridge 1986)MATHGoogle Scholar
  6. 48.6
    T. McGeer: Passive Dynamic Walking, Simon Fraser University Tech. Rep., (Simon Fraser Univ., Burnaby 1988) Google Scholar
  7. 48.7
    M. Raibert, K. Blankespoor, G. Nelson, R. Playter, the BigDog Team: BigDog, the rough-terrain quadruped robot, Proc. 17th World Cong. Int. Fed. Autom. Control. (2008)Google Scholar
  8. 48.8
    P.-B. Wieber: Holonomy and nonholonomy in the dynamics of articulated motion, Proc. Ruperto Carola Symp. Fast Motion Biomech. Robotics (2005)Google Scholar
  9. 48.9
    R.M. Murray, Z. Li, S.S. Sastry: A Mathematical Introduction to Robotic Manipulation (CRC, Boca Raton 1994)MATHGoogle Scholar
  10. 48.10
    M.K. Vukobratović: Contribution to the study of anthropomorphic systems, Kybernetika 8(5), 404–418 (1972)MATHGoogle Scholar
  11. 48.11
    P. Sardain, G. Bessonnet: Forces acting on a biped robot. center of pressure—zero moment point, IEEE Trans. Syst. Man. Cybern. A 34(5), 630–637 (2004)CrossRefGoogle Scholar
  12. 48.12
    K. Harada, S. Kajita, K. Kaneko, H. Hirukawa: ZMP analysis for arm/leg coordination, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2003) pp. 75–81Google Scholar
  13. 48.13
    K. Harada, H. Hirukawa, F. Kanehiro, K. Fujiwara, K. Kaneko, S. Kajita, M. Nakamura: Dynamical balance of a humanoid robot grasping an environment, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2004) pp. 1167–1173Google Scholar
  14. 48.14
    Y. Or, E. Rimon: Analytic characterization of a class of 3-contact frictional equilibrium postures in 3D gravitational environments, Int. J. Robotics Res. 29(1), 3–22 (2010)CrossRefGoogle Scholar
  15. 48.15
    P.-B. Wieber: On the stability of walking systems, Proc. Int. Workshop Humanoids Hum. Friendly Robots (2002)Google Scholar
  16. 48.16
    T. Saida, Y. Yokokoji, T. Yoshikawa: FSW (feasible solution of wrench) for multi-legged robots, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003)Google Scholar
  17. 48.17
    H. Hirukawa, S. Hattori, K. Harada, S. Kajita, K. Kaneko, F. Kanehiro, K. Fujiwara, M. Morisawa: A universal stability criterion of the foot contact of legged robots -- adios ZMP, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006) pp. 1976–1983Google Scholar
  18. 48.18
    T. Bretl, S. Lall: Testing static equilibrium for legged robots, IEEE Trans. Robotics 24(4), 794–807 (2008)CrossRefGoogle Scholar
  19. 48.19
    S. Barthélemy, P. Bidaud: Stability measure of postural dynamic equilibrium based on residual radius, Proc. Int. Symp. Adv. Robot Kinemat. (2008)Google Scholar
  20. 48.20
    Z. Qiu, A. Escande, A. Micaelli, T. Robert: Human motions analysis and simulation based on a general criterion of stability, Proc. Int. Symp. Digit. Hum. Model. (2011)Google Scholar
  21. 48.21
    Z. Qiu, A. Escande, A. Micaelli, T. Robert: A hierarchical framework for realizing dynamically-stable motions of humanoid robot in obstacle-cluttered environments, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  22. 48.22
    E. Rimon, R. Mason, J.W. Burdick, Y. Or: A general stance stability test based on stratified morse theory with application to quasi-static locomotion planning, IEEE Trans. Robotics 24(3), 626–641 (2008)CrossRefGoogle Scholar
  23. 48.23
    Q. Huang, S. Sugano, K. Tanie: Stability compensation of a mobile manipulator by manipulator motion: Feasibility and planning, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (1997) pp. 1285–1292Google Scholar
  24. 48.24
    J. Kim, W.K. Chung, Y. Youm, B.H. Lee: Real-time ZMP compensation method using null motion for mobile manipulators, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2002) pp. 1967–1972Google Scholar
  25. 48.25
    B. Brogliato: Nonsmooth Mechanics, Communications and Control Engineering (Springer, London 1999)MATHCrossRefGoogle Scholar
  26. 48.26
    F. Pfeiffer, C. Glocker: Multibody Dynamics with Unilateral Contacts (Wiley, New York 1996)MATHCrossRefGoogle Scholar
  27. 48.27
    S. Chareyron, P.-B. Wieber: Stability and Regulation of Nonsmooth Dynamical Systems INRIA Res. Rep. RR-5408 (INRIA, Montbonnot Saint-Ismier 2004)Google Scholar
  28. 48.28
    C. Liu, Z. Zhao, B. Brogliato: Frictionless multiple impacts in multibody systems. I. Theoretical framework, Proc. R. Soc. A 464, 3193–3211 (2008)MathSciNetMATHCrossRefGoogle Scholar
  29. 48.29
    Y.-B. Jia, M. Mason, M. Erdmann: Multiple impacts: A state transition diagram approach, Int. J. Robotics Res. 32(1), 84–114 (2013)CrossRefGoogle Scholar
  30. 48.30
    J.-M. Bourgeot, C. Canudas de Wit, B. Brogliato: Impact shaping for double support walk: From the rocking block to the biped robot, Proc. Int. Conf. Climb. Walk. Robots (2005)Google Scholar
  31. 48.31
    B. Gamus, Y. Or: Analysis of dynamic bipedal robot locomotion with stick-slip transitions, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2013) pp. 3348–3355Google Scholar
  32. 48.32
    S. Kajita, K. Miura, M. Morisawa, K. Kaneko, F. Kanehiro, K. Yokoi: Evaluation of a stabilizer for biped walk with toe support phase, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  33. 48.33
    V. Acary, B. Brogliato: Numerical Methods for Nonsmooth Dynamical Systems, Lect. Notes Appl. Comput. Mech., Vol. 35 (Springer, Berlin, Heidelberg 2008)MATHGoogle Scholar
  34. 48.34
    R.I. Leine, N. van de Wouw: Stability and Convergence of Mechanical Systems with Unilateral Constraints, Lect. Notes Appl. Comput. Mech., Vol. 36 (Springer, Berlin, Heidelberg 2008)MATHGoogle Scholar
  35. 48.35
    Y. Or, A.D. Ames: Stability and completion of zeno equilibria in lagrangian hybrid systems, IEEE Trans. Autom. Control 56(6), 1322–1336 (2011)MathSciNetCrossRefGoogle Scholar
  36. 48.36
    D.E. Stewart, J.C. Trinkle: An implicit time-stepping scheme for rigid body dynamics with inelastic collisions and coulomb friction, Int. J. Numer. Methods Eng. 39(15), 2673–2691 (1996)MathSciNetMATHCrossRefGoogle Scholar
  37. 48.37
    M. Posa, C. Cantu, R. Tedrake: A direct method for trajectory optimization of rigid bodies through contact, Int. J. Robotics Res. 33(1), 69–81 (2014)CrossRefGoogle Scholar
  38. 48.38
    E.R. Westervelt, J.W. Grizzle, C. Chevallereau, J.H. Choi, B. Morris: Feedback Control of Dynamic Bipedal Robot Locomotion (CRC, Boca Raton 2007)CrossRefGoogle Scholar
  39. 48.39
    M. Wisse: Essentials of Dynamic Walking: Analysis and Design of Two-Legged Robots, Dissertation (Technische Universiteit, Delft 2004)Google Scholar
  40. 48.40
    R. Tedrake, I.R. Manchester, M.M. Tobenkin, J.W. Roberts: LQR-Trees: Feedback motion planning via sums of squares verification, Int. J. Robotics Res. 29, 1038–1052 (2010)CrossRefGoogle Scholar
  41. 48.41
    M. Posa, M. Tobenkin, R. Tedrake: Lyapunov analysis of rigid body systems with impacts and friction via sums-of-squares, Proc. Int. Conf. Hybrid Syst. Comput. Control (2013) pp. 63–72Google Scholar
  42. 48.42
    S. Cotton, I. Olaru, M. Bellman, T. van der Ven, J. Godowski, J. Pratt: Fastrunner: A fast, efficient and robust bipedal robot. concept and planar simulation, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2012)Google Scholar
  43. 48.43
    M. Srinivasan, A. Ruina: Computer optimization of a minimal biped model discovers walking and running, Nature 439, 72–75 (2006)CrossRefGoogle Scholar
  44. 48.44
    K. Mombaur, H.G. Bock, J.P. Schloder, R.W. Longman: Open-loop stable solutions of periodic optimal control problems in robotics, Z. Angew. Math. Mech. 85(7), 499–515 (2005)MathSciNetMATHCrossRefGoogle Scholar
  45. 48.45
    J. Hauser, C.C. Chung: Converse Lyapunov functions for exponentially stable periodic orbits, Syst. Control Lett. 23(1), 27–34 (1994)MathSciNetMATHCrossRefGoogle Scholar
  46. 48.46
    J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, Heidelberg 1983)MATHCrossRefGoogle Scholar
  47. 48.47
    I.R. Manchester, M.M. Tobenkin, M. Levashov, R. Tedrake: Regions of attraction for hybrid limit cycles of walking robots, Proc. 21st World Cong. Int. Fed. Autom. Control (2011)Google Scholar
  48. 48.48
    E.R. Westervelt, G. Buche, J.W. Grizzle: Experimental validation of a framework for the design of controllers that induce stable walking in planar bipeds, Int. J. Robotics Res. 23(6), 559–582 (2004)CrossRefGoogle Scholar
  49. 48.49
    A.S. Shiriaev, L.B. Freidovich, I.R. Manchester: Can we make a robot ballerina perform a pirouette? Orbital stabilization of periodic motions of underactuated mechanical systems, Annu. Rev. Control 32(2), 200–211 (2008)CrossRefGoogle Scholar
  50. 48.50
    I.R. Manchester, U. Mettin, F. Iida, R. Tedrake: Stable dynamic walking over uneven terrain, Int. J. Robotics Res. 30(3), 265–279 (2011)MATHCrossRefGoogle Scholar
  51. 48.51
    J.-P. Aubin: Viability Theory (Birkhäuser, Basel 1991)MATHGoogle Scholar
  52. 48.52
    P.-B. Wieber: Constrained dynamics and parametrized control in biped walking, Proc. Int. Symp. Math. Theory Networks Syst. (2000)Google Scholar
  53. 48.53
    P.-B. Wieber: Viability and predictive control for safe locomotion, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2008)Google Scholar
  54. 48.54
    K. Ogata: Modern Control Engineering, 3rd edn. (Prentice Hall, Upper Saddle River 1996)MATHGoogle Scholar
  55. 48.55
    J. Pratt, R. Tedrake: Velocity based stability margins for fast bipedal walking, Proc. Ruperto Carola Symp. Fast Motion Biomech. Robotics (2005)Google Scholar
  56. 48.56
    A.L. Hof, M.G.J. Gazendam, W.E. Sinke: The condition for dynamic stability, J. Biomech. 38, 1–8 (2005)CrossRefGoogle Scholar
  57. 48.57
    J. Pratt, J. Carff, S. Drakunov, A. Goswami: Capture point: A step toward humanoid push recovery, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2006)Google Scholar
  58. 48.58
    T. Takenaka, T. Matsumoto, T. Yoshiike: Real time motion generation and control for biped robot -- 1st report: Walking gait pattern generation, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2009)Google Scholar
  59. 48.59
    J. Englsberger, C. Ott, M.A. Roa, A. Albu-Schäffer, G. Hirzinger: Bipedal walking control based on capture point dynamics, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2011)Google Scholar
  60. 48.60
    T. Koolen, T. de Boer, J. Rebula, A. Goswami, J. Pratt: Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models, Int. J. Robotics Res. 31(9), 1094–1113 (2012)CrossRefGoogle Scholar
  61. 48.61
    A. Papachristodoulou, S. Prajna: Robust stability analysis of nonlinear hybrid systems, IEEE Trans. Autom. Control 54(5), 1035–1041 (2009)MathSciNetCrossRefGoogle Scholar
  62. 48.62
    P. Hanggi, P. Talkner, M. Borkovec: Reaction-rate theory: Fifty years after Kramers, Rev. Mod. Phys. 62(2), 251–342 (1990)MathSciNetCrossRefGoogle Scholar
  63. 48.63
    K. Byl: Metastable Legged-Robot Locomotion, Dissertation (MIT, Cambridge 2008)Google Scholar
  64. 48.64
    J. Steinhardt, R. Tedrake: Finite-time regional verification of stochastic nonlinear systems, Int. J. Robotics Res. 31(7), 901–923 (2012)CrossRefGoogle Scholar
  65. 48.65
    D.G.E. Hobbelen, M. Wisse: A disturbance rejection measure for limit cycle walkers: The gait sensitivity norm, IEEE Trans. Robotics 23(6), 1213–1224 (2007)CrossRefGoogle Scholar
  66. 48.66
    C. Ebenbauer: Polynomial Control Systems: Analysis and Design via Dissipation Inequalities and Sum of Squares, Dissertation (Univ. Stuttgart, Stuttgart 2005)Google Scholar
  67. 48.67
    H. Dai, R. Tedrake: L2-gain optimization for robust bipedal walking on unknown terrain, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2013)Google Scholar
  68. 48.68
    E. Garcia, J. Estremera, P. Gonzalez de Santos: A classification of stability margins for walking robots, Proc. Int. Conf. Climb. Walk. Robots (2002)Google Scholar
  69. 48.69
    A. Goswami: Postural stability of biped robots and the foot rotation indicator (FRI) point, Int. J. Robotics Res. 18(6), 523–533 (1999)CrossRefGoogle Scholar
  70. 48.70
    C.K. Chow, D.H. Jacobson: Studies of human locomotion via optimal programming, Tech. Rep. No. 617 (Harvard Univ., Cambridge 1970)MATHGoogle Scholar
  71. 48.71
    P.H. Channon, S.H. Hopkins, D.T. Phan: Derivation of optimal walking motions for a biped walking robot, Robotica 10(2), 165–172 (1992)CrossRefGoogle Scholar
  72. 48.72
    G. Cabodevilla, N. Chaillet, G. Abba: Energy-minimized gait for a biped robot, Proc. Auton. Mob. Syst. (1995)Google Scholar
  73. 48.73
    C. Chevallereau, A. Formal'sky, B. Perrin: Low energy cost reference trajectories for a biped robot, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1998)Google Scholar
  74. 48.74
    M. Rostami, G. Bessonnet: Impactless sagittal gait of a biped robot during the single support phase, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1998)Google Scholar
  75. 48.75
    L. Roussel, C. Canudas de Wit, A. Goswami: Generation of energy optimal complete gait cycles for biped robots, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1998)Google Scholar
  76. 48.76
    J. Denk, G. Schmidt: Synthesis of a walking primitive database for a humanoid robot using optimal control techniques, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2001)Google Scholar
  77. 48.77
    T. Buschmann, S. Lohmeier, H. Ulbrich, F. Pfeiffer: Optimization based gait pattern generation for a biped robot, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2005)Google Scholar
  78. 48.78
    K. Mombaur: Using optimization to create self-stable human-like running, Robotica 27(3), 321–330 (2009)CrossRefGoogle Scholar
  79. 48.79
    J. Denk, G. Schmidt: Synthesis of walking primitive databases for biped robots in 3D-environments, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003)Google Scholar
  80. 48.80
    S.A. Setiawan, S.H. Hyon, J. Yamaguchi, A. Takanishi: Quasi real-time walking control of a bipedal humanoid robot based on walking pattern synthesis, Proc. Int. Symp. Exp. Robotics (1999)Google Scholar
  81. 48.81
    P.-B. Wieber, C. Chevallereau: Online adaptation of reference trajectories for the control of walking systems, Robotics Auton. Syst. 54(7), 559–566 (2006)CrossRefGoogle Scholar
  82. 48.82
    C. Liu, C.G. Atkeson: Standing balance control using a trajectory library, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2009) pp. 3031–3036Google Scholar
  83. 48.83
    J. Yamaguchi, A. Takanishi, I. Kato: Development of biped walking robot compensating for three-axis moment by trunk motion, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (1993)Google Scholar
  84. 48.84
    Q. Huang, K. Yokoi, S. Kajita, K. Kaneko, H. Arai, N. Koyachi, K. Tanie: Planning walking patterns for a biped robot, IEEE Trans. Robotics Autom. 17(3), 280–289 (2001)CrossRefGoogle Scholar
  85. 48.85
    P.-B. Wieber: Trajectory free linear model predictive control for stable walking in the presence of strong perturbations, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2006)Google Scholar
  86. 48.86
    T. de Boer: Foot placement in robotic bipedal locomotion, Dissertation (Technische Univ. Delft, Dleft 2012)Google Scholar
  87. 48.87
    R.J. Full, D.E. Koditschek: Templates and anchors: Neuromechanical hypotheses of legged locomotion on land, J. Exp. Biol. 202, 3325–3332 (1999)Google Scholar
  88. 48.88
    R.M. Alexander: Mechanics of bipedal locomotion, Persp. Exp. Biol. 1, 493–504 (1976)Google Scholar
  89. 48.89
    R.M. Alexander: Simple models of human movement, ASME Appl. Mech. Rev. 48(8), 461–470 (1995)CrossRefGoogle Scholar
  90. 48.90
    S.S. Keerthi, E.G. Gilbert: Optimal infinite-horizon feedback laws for a general class of constrained discrete-time systems: Stability and moving-horizon approximations, J. Optim. Theory Appl. 57(2), 265–293 (1988)MathSciNetMATHCrossRefGoogle Scholar
  91. 48.91
    D.Q. Mayne, J.B. Rawlings, C.V. Rao, P.O.M. Scokaert: Constrained model predictive control: Stability and optimality, Automatica 26(6), 789–814 (2000)MathSciNetMATHCrossRefGoogle Scholar
  92. 48.92
    M. Alamir, N. Marchand: Numerical stabilisation of non-linear systems: Exact theory and approximate numerical implementation, Eur. J. Control 5(1), 87–97 (1999)MATHCrossRefGoogle Scholar
  93. 48.93
    M. Alamir, G. Bornard: Stability of a truncated infinite constrained receding horizon scheme: The general discrete nonlinear case, Automatica 31(9), 1353–1356 (1995)MathSciNetMATHCrossRefGoogle Scholar
  94. 48.94
    A. Takanishi, M. Tochizawa, H. Karaki, I. Kato: Dynamic biped walking stabilized with optimal trunk and waist motion, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (1989)Google Scholar
  95. 48.95
    H. Lim, Y. Kaneshima, A. Takanishi: Online walking pattern generation for biped humanoid robot with trunk, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2002)Google Scholar
  96. 48.96
    T. Buschmann, S. Lohmeier, M. Bachmayer, H. Ulbrich, F. Pfeiffer: A collocation method for real-time walking pattern generation, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2007)Google Scholar
  97. 48.97
    K. Nishiwaki, S. Kagami, Y. Kuniyoshi, M. Inaba, H. Inoue: Online generation of humanoid walking motion based on a fast generation method of motion pattern that follows desired ZMP, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2002)Google Scholar
  98. 48.98
    R. Tajima, D. Honda, K. Suga: Fast running experiments involving a humanoid robot, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2009)Google Scholar
  99. 48.99
    K. Nagasaka, Y. Kuroki, S. Suzuki, Y. Itoh, J. Yamaguchi: Integrated motion control for walking, jumping and running on a small bipedal entertainment robot, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004)Google Scholar
  100. 48.100
    M. Morisawa, K. Harada, S. Kajita, K. Kaneko, F. Kanehiro, K. Fujiwara, S. Nakaoka, H. Hirukawa: A biped pattern generation allowing immediate modification of foot placement in real-time, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2006)Google Scholar
  101. 48.101
    S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa: Biped walking pattern generation by using preview control of zero moment point, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003) pp. 1620–1626Google Scholar
  102. 48.102
    K. Nishiwaki, S. Kagami: Online walking control systems for humanoids with short cycle pattern generation, Int. J. Robotics Res. 28(6), 729–742 (2009)CrossRefGoogle Scholar
  103. 48.103
    J. Park, Y. Youm: General ZMP preview control for bipedal walking, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2007)Google Scholar
  104. 48.104
    D. Gouaillier, C. Collette, C. Kilner: Omni-directional closed-loop walk for NAO, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2010)Google Scholar
  105. 48.105
    M. Krause, J. Englsberger, P.-B. Wieber, C. Ott: Stabilization of the capture point dynamics for bipedal walking based on model predictive control, Proc. IFAC Symp. Robot Control (2012)Google Scholar
  106. 48.106
    M. van de Panne: From footprints to animation, Comput. Graph. 16(4), 211–223 (1997)Google Scholar
  107. 48.107
    A. Herdt, H. Diedam, P.-B. Wieber, D. Dimitrov, K. Mombaur, M. Diehl: Online walking motion generation with automatic foot step placement, Adv. Robotics 24(5-6), 719–737 (2010)CrossRefGoogle Scholar
  108. 48.108
    A. Herdt, N. Perrin, P.-B. Wieber: LMPC based online generation of more efficient walking motions, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  109. 48.109
    Z. Aftab, T. Robert, P.-B. Wieber: Ankle, hip and stepping strategies for humanoid balance recovery with a single model predictive control scheme, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  110. 48.110
    J. Urata, K. Nishiwaki, Y. Nakanishi, K. Okada, S. Kagami, M. Inaba: Online decision of foot placement using singular LQ preview regulation, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2011)Google Scholar
  111. 48.111
    J. Kuffner, S. Kagami, K. Nishiwaki, M. Inaba, H. Inoue: Dynamically-stable motion planning for humanoid robots, Auton. Robots 12, 105–118 (2002)MATHCrossRefGoogle Scholar
  112. 48.112
    S. Dalibard, A. El Khoury, F. Lamiraux, M. Taix, J.-P. Laumond: Small-space controllability of a walking humanoid robot, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2011)Google Scholar
  113. 48.113
    K. Kaneko, F. Kanehiro, S. Kajita, H. Hirukawa, T. Kawasaki, M. Hirata, K. Akachi, T. Isozumi: Humanoid robot HRP-2, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004) pp. 1083–1090Google Scholar
  114. 48.114
    E. Yoshida, C. Esteves, I. Belousov, J.-P. Laumond, T. Sakaguchi, K. Yokoi: Planning 3-D collision-free dynamic robotic motion through iterative reshaping, IEEE Trans. Robotics 24(5), 1186–1198 (2008)CrossRefGoogle Scholar
  115. 48.115
    J.-D. Boissonnat, O. Devillers, S. Lazard: Motion planning of legged robots, SIAM J. Comput. 30(1), 218–246 (2000)MathSciNetMATHCrossRefGoogle Scholar
  116. 48.116
    N. Perrin, O. Stasse, F. Lamiraux, E. Yoshida: Weakly collision-free paths for continuous humanoid footstep planning, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2011)Google Scholar
  117. 48.117
    N. Perrin: From discrete to continuous motion planning, Proc. Int. Workshop Algorithm. Found. Robotics (2012)Google Scholar
  118. 48.118
    J. Kuffner, S. Kagami, K. Nishiwaki, M. Inaba, H. Inoue: Online footstep planning for humanoid robots, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2003)Google Scholar
  119. 48.119
    J. Chestnutt, J. Kuffner: A tiered planning strategy for biped navigation, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2004)Google Scholar
  120. 48.120
    P. Michel, J. Chestnutt, J. Kuffner, T. Kanade: Vision-Guided Humanoid Footstep Planning for Dynamic Environments. In: Proc. IEEE/RAS Int. Conf. Humanoid Robots 2005)Google Scholar
  121. 48.121
    J. Chestnutt, P. Michel, J. Kuffner, T. Kanade: Locomotion among dynamic obstacles for the honda asimo, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2007)Google Scholar
  122. 48.122
    J.-M. Bourgeot, N. Cislo, B. Espiau: Path-planning and tracking in a 3D complex environment for an anthropomorphic biped robot, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2002)Google Scholar
  123. 48.123
    J. Chestnutt, J. Kuffner, K. Nishiwaki, S. Kagami: Planning biped navigation strategies in complex environments, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2003)Google Scholar
  124. 48.124
    M. Zucker, J.A. Bagnell, C. Atkeson, J. Kuffner: An optimization approach to rough terrain locomotion, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2010)Google Scholar
  125. 48.125
    J. Chestnutt, Y. Takaoka, K. Suga, K. Nishiwaki, J. Kuffner, S. Kagami: Biped navigation in rough environments using on-board sensing, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2009)Google Scholar
  126. 48.126
    N. Perrin, O. Stasse, F. Lamiraux, Y. Kim, D. Manocha: Real-time footstep planning for humanoid robots among 3D obstacles using a hybrid bounding box, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2012)Google Scholar
  127. 48.127
    N. Perrin, O. Stasse, L. Baudoin, F. Lamiraux, E. Yoshida: Fast humanoid robot collision-free footstep planning using swept volume approximations, IEEE Trans. Robotics 28(2), 427–439 (2012)CrossRefGoogle Scholar
  128. 48.128
    R.L.H. Deits, R. Tedrake: Computing large convex regions of obstacle-free space through semidefinite programming, Proc. Int. Workshop Algorithmic Found. Robotics (2014)Google Scholar
  129. 48.129
    T. Bretl, S. Lall, J.-C. Latombe, S. Rock: Multi-step motion planning for free-climbing robots, Proc. Int. Workshop Algorithmic Found. Robotics (2004)Google Scholar
  130. 48.130
    K. Hauser, T. Bretl, J.-C. Latombe: Non-gaited humanoid locomotion planning, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2005)Google Scholar
  131. 48.131
    K. Hauser, T. Bretl, J.-C. Latombe, K. Harada, B. Wilcox: Motion planning for legged robots on varied terrain, Int. J. Robotics Res. 27(11/12), 1325–1349 (2008)CrossRefGoogle Scholar
  132. 48.132
    A. Escande, A. Kheddar, S. Miossec: Planning support contact-points for humanoid robots and experiments on HRP-2, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2006)Google Scholar
  133. 48.133
    A. Escande, A. Kheddar, S. Miossec, S. Garsault: Planning support contact-points for acyclic motions and experiments on HRP-2, Proc. Int. Symp. Exp. Robotics (2008)Google Scholar
  134. 48.134
    K. Bouyarmane, J. Vaillant, F. Keith, A. Kheddar: Exploring humanoid robots locomotion capabilities in virtual disaster response scenarios, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  135. 48.135
    S. Lengagne, J. Vaillant, E. Yoshida, A. Kheddar: Generation of whole-body optimal dynamic multi-contact motions, Int. J. Robotics Res. 32(9/10), 1104–1119 (2013)CrossRefGoogle Scholar
  136. 48.136
    K. Harada, E. Yoshida, K. Yokoi: Motion Planning for Humanoid Robots (Springer, Berlin, Heidelberg 2010)MATHCrossRefGoogle Scholar
  137. 48.137
    R.B. McGhee, A.A. Frank: On the stability properties of quadruped creeping gaits, Math. Biosci. 3, 331–351 (1968)MATHCrossRefGoogle Scholar
  138. 48.138
    G.C. Haynes, A.A. Rizzi: Gaits and gait transitions for legged robots, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006) pp. 1117–1122Google Scholar
  139. 48.139
    Y. Fujimoto, A. Kawamura: Proposal of biped walking control based on robust hybrid position/force control, Proc. IEEE Int. Conf. Robotics Autom. (ICRA), Minneap. (1996) pp. 2724–2730CrossRefGoogle Scholar
  140. 48.140
    S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Yokoi, H. Hirukawa: A realtime pattern generator for biped walking, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2002) pp. 31–37Google Scholar
  141. 48.141
    K. Yin, K. Loken, M. van de Panne: SIMBICON: Simple Biped Locomotion Control, Proc. ACM SIGGRAPH (2007)Google Scholar
  142. 48.142
    I.-W. Park, J.-Y. Kim, J.-H. Oh: Online biped walking pattern generation for humanoid robot KHR-3(KAIST humanoid robot – 3: HUBO), Proc. IEEE-RAS Int. Conf. Humanoid Robots (2006)Google Scholar
  143. 48.143
    A. Ijspeert, A. Crespi, D. Ryczko, J.-M. Cabelguen: From swimming to walking with a salamander robot driven by a spinal cord model, Science 315(5817), 1416–1420 (2007)CrossRefGoogle Scholar
  144. 48.144
    R. Katoh, M. Mori: Control method of biped locomotion giving asymptotic stability of trajectory, Automatica 20(4), 405–414 (1984)MATHCrossRefGoogle Scholar
  145. 48.145
    L. Righetti, A. Ijspeert: Programmable central pattern generators: An application to biped locomotion control, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006)Google Scholar
  146. 48.146
    K. Matsuoka: Sustained oscillations generated by mutually inhibiting neurons with adaptation, Biol. Cybern. 52, 367–376 (1985)MathSciNetMATHCrossRefGoogle Scholar
  147. 48.147
    G. Endo, J. Morimoto, J. Nakanishi, G. Cheng: An empirical exploration of a neural oscillator for biped locomotion control, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004) pp. 3036–3042Google Scholar
  148. 48.148
    Y. Fukuoka, H. Kimura, A. Cohen: Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts, Int. J. Robotics Res. 22(3-4), 187–202 (2003)CrossRefGoogle Scholar
  149. 48.149
    R. Brooks: Elephants don't play chess, Robotics Auton. Syst. 6, 3–15 (1990)CrossRefGoogle Scholar
  150. 48.150
    R. Brooks: A robot that walks; emergent behaviors from a carefully evolved network, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1989) pp. 292–296Google Scholar
  151. 48.151
    J. Pratt, C.-M. Chew, A. Torres, P. Dilworth, G. Pratt: Virtual model control: An intuitive approach for bipedal locomotion, Int. J. Robotics Res. 20, 129–143 (2001)CrossRefGoogle Scholar
  152. 48.152
    F. Génot, B. Espiau: On the control of the mass center of legged robots under unilateral constraints, Proc. Int. Conf. Climb. Walk. Robots (1998)Google Scholar
  153. 48.153
    L. Saab, O.E. Ramos, F. Keith, N. Mansard, P. Souères, J.-Y. Fourquet: Dynamic whole-body motion generation under rigid contacts and other unilateral constraints, IEEE Trans. Robotics 29(2), 346–362 (2013)CrossRefGoogle Scholar
  154. 48.154
    L. Sentis, J. Park, O. Khatib: Compliant control of multicontact and center-of-mass behaviors in humanoid robots, IEEE Trans. Robotics 26(3), 483–501 (2010)CrossRefGoogle Scholar
  155. 48.155
    R.W. Brockett: Asymptotic stability and feedback stabilization. In: Differential Geometric Control Theory, (Birkhäuser, Boston 1983)Google Scholar
  156. 48.156
    S. Kajita, T. Nagasaki, K. Kaneko, K. Yokoi, K. Tanie: A running controller of humanoid biped HRP-2LR, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2005) pp. 618–624Google Scholar
  157. 48.157
    L. Sentis, O. Khatib: Control of free-floating humanoid robots through task prioritization, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2005) pp. 1730–1735Google Scholar
  158. 48.158
    A. De Luca, G. Oriolo: Modelling and control of nonholonomic mechanical systems, CISM Int. Centre Mech. Sci. 360, 277–342 (1995)MATHCrossRefGoogle Scholar
  159. 48.159
    Y. Nakamura, R. Mukherjee: Exploiting nonholonomic redundancy of free-flying space robots, IEEE Trans. Robotics Autom. 9(4), 499–506 (1993)CrossRefGoogle Scholar
  160. 48.160
    E. Papadopoulos: Nonholonomic behaviour in free-floating space manipulators and its utilization. In: Nonholonomic Motion Planning, ed. by Y. Xu, T. Kanade (Kluwer Academic, Dordrecht 1993)Google Scholar
  161. 48.161
    C. Chevallereau, E.R. Westervelt, J.W. Grizzle: Asymptotically stable running for a five-link, four-actuator, planar bipedal robot, Int. J. Robotics Res. 24(6), 431–464 (2005)CrossRefGoogle Scholar
  162. 48.162
    S. Kajita, F. Kanehiro, K. Kaneko, K. Fujiwara, K. Harada, K. Yokoi, H. Hirukawa: Resolved momentum control: Humanoid motion planning based on the linear and angular momentum, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2003) pp. 1644–1650Google Scholar
  163. 48.163
    M. Popovic, A. Hofmann, H. Herr: Zero spin angular momentum control: definition and applicability, IEEE/RAS Int. Conf. Humanoid Robots (2004)Google Scholar
  164. 48.164
    S.-H. Lee, A. Goswami: Ground reaction force control at each foot: A momentum-based humanoid balance controller for non-level and non-stationary ground, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2010) pp. 3157–3162Google Scholar
  165. 48.165
    C. Ott, M.A. Roa, G. Hirzinger: Posture and balance control for biped robots based on contact force optimization, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2011)Google Scholar
  166. 48.166
    T. Sugihara: Standing stabilizability and stepping maneuver in planar bipedalism based on the best COM-ZMP regulator, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2009)Google Scholar
  167. 48.167
    Y. Choi, D. Kim, B.-J. You: On the walking control for humanoid robot based on the kinematic resolution of CoM jacobian with embedded motion, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2006) pp. 2655–2660Google Scholar
  168. 48.168
    S.-H. Hyon: Compliant terrain adaptation for biped humanoids without measuring ground surface and contact forces, IEEE Trans. Robotics 25(1), 171–178 (2009)CrossRefGoogle Scholar
  169. 48.169
    S. Kajita, K. Yokoi, M. Saigo, K. Tanie: Balancing a humanoid robot using backdrive concerned torque control and direct angular momentum feedback, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2001) pp. 3376–3382Google Scholar
  170. 48.170
    S. Lohmeier, K. Löffler, M. Gienger, H. Ulbrich, F. Pfeiffer: Computer system and control of biped Johnnie, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004) pp. 4222–4227Google Scholar
  171. 48.171
    J.-H. Kim, J.-H. Oh: Walking control of the humanoid platform KHR-1 based on torque feedback control, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004) pp. 623–628Google Scholar
  172. 48.172
    M.-S. Kim, J.-H. Oh: Posture control of a humanoid robot with a compliant ankle joint, Int. J. Humanoid Robotics 7(1), 5–29 (2010)CrossRefGoogle Scholar
  173. 48.173
    T. Buschmann, S. Lohmeier, H. Ulbrich: Biped walking control based on hybrid position/force control, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2009) pp. 3019–3024Google Scholar
  174. 48.174
    S. Kajita, M. Morisawa, K. Miura, S. Nakaoka, K. Harada, K. Kaneko, F. Kanehiro, K. Yokoi: Biped walking stabilization based on linear inverted pendulum tracking, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2010) pp. 4489–4496Google Scholar
  175. 48.175
    M. Morisawa, S. Kajita, F. Kanehiro, K. Kaneko, K. Miura, K. Yokoi: Balance control based on capture point error compensation for biped walking on uneven terrain, Proc. IEEE-RAS Int. Conf. Humanoid Robots (2012)Google Scholar
  176. 48.176
    Y. Fujimoto, A. Kawamura: Simulation of an autonomous biped walking robot including environmental force interaction, IEEE Robotics Autom. Mag. 5(2), 33–41 (1998)CrossRefGoogle Scholar
  177. 48.177
    L. Righetti, J. Buchli, M. Mistry, M. Kalakrishnan, S. Schaal: Optimal distribution of contact forces with inverse dynamics control, Int. J. Robotics Res. 32(3), 280–298 (2013)CrossRefGoogle Scholar
  178. 48.178
    A.D. Ames: Human-inspired control of bipedal robotics via control lyapunov functions and quadratic programs, Proc. Int. Conf. Hybrid Syst. Comput. Control (2013)Google Scholar
  179. 48.179
    S. Kuindersma, F. Permenter, R. Tedrake: An efficiently solvable quadratic program for stabilizing dynamic locomotion, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2014)Google Scholar
  180. 48.180
    S.H. Collins, A. Ruina, R. Tedrake, M. Wisse: Efficient bipedal robots based on passive-dynamic walkers, Science 307, 1082–1085 (2005)CrossRefGoogle Scholar
  181. 48.181
    S.H. Collins, M. Wisse, A. Ruina: A three-dimensional passive-dynamic walking robot with two legs and knees, Int. J. Robotics Res. 20(7), 607–615 (2001)CrossRefGoogle Scholar
  182. 48.182
    R. Tedrake, T.W. Zhang, H.S. Seung: Stochastic policy gradient reinforcement learning on a simple 3D biped, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2004) pp. 2849–2854Google Scholar
  183. 48.183
    J.E. Wilson: Walking Toy, Patent 0 (1936)Google Scholar
  184. 48.184
    R. Tedrake, T.W. Zhang, M.F. Fong, H.S. Seung: Actuating a simple 3D passive dynamic walker, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (2004) pp. 4656–4661Google Scholar
  185. 48.185
    M. Garcia, A. Chatterjee, A. Ruina: Efficiency, speed, and scaling of two-dimensional passive-dynamic walking, Dyn. Stab. Sytems 15(2), 75–99 (2000)MathSciNetMATHCrossRefGoogle Scholar
  186. 48.186
    A. Goswami, B. Thuilot, B. Espiau: Compass-Like Biped Robot Part I : Stability and Bifurcation of Passive Gaits, INRIA Res. Rep. No. 2996 (INRIA, Les Chesnay Cedex 1996)Google Scholar
  187. 48.187
    M.W. Spong, G. Bhatia: Further results on control of the compass gait biped, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2003) pp. 1933–1938Google Scholar
  188. 48.188
    F. Asano, Z.-W. Luo, M. Yamakita: Biped gait generation and control based on a unified property of passive dynamic walking, IEEE Trans. Robotics 21(4), 754–762 (2005)CrossRefGoogle Scholar
  189. 48.189
    J.T. Betts: Survey of numerical methods for trajectory optimization, J. Guid. Control, Dyn. 21(2), 193–207 (1998)MATHCrossRefGoogle Scholar
  190. 48.190
    C.D. Remy: Optimal Exploitation of Natural Dynamics in Legged Locomotion, Dissertation (ETH, Zurich 2011)Google Scholar
  191. 48.191
    K. Sreenath, H.W. Park, I. Poulakakis, J.W. Grizzle: A compliant hybrid zero dynamics controller for stable, efficient and fast bipedal walking on MABEL, Int. J. Robotics Res. 30(9), 1170–1193 (2011)CrossRefGoogle Scholar
  192. 48.192
    Y. Tassa, T. Erez, E. Todorov: Synthesis and stabilization of complex behaviors through online trajectory optimization, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2012) pp. 4906–4913Google Scholar
  193. 48.193
    S. Hirose, A. Nagakubo, R. Toyama: Machine that can walk and climb on floors, walls and ceilings, Proc. Int. Conf. Adv. Robotics (1991) pp. 753–758Google Scholar
  194. 48.194
    T. Yano, S. Numao, Y. Kitamura: Development of a self-contained wall climbing robot with scanning type suction cups, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (1998) pp. 249–254Google Scholar
  195. 48.195
    S. Kim, A. Asbeck, W. Provancher, M.R. Cutkosky: SpinybotII: Climbing hard walls with compliant microspines, Proc. Int. Conf. Adv. Robotics (2005) pp. 18–20Google Scholar
  196. 48.196
    S. Hirose, K. Yoneda, H. Tsukagoshi: TITAN VII: quadruped walking and manipulating robot on a steep slope, Proc. IEEE Int. Conf. Robotics Autom. (ICRA) (1997) pp. 494–500CrossRefGoogle Scholar
  197. 48.197
    J. Bares, D. Wettergreen: Dante II: technical description, results and lessons learned, Int. J. Robotics Res. 18(7), 621–649 (1999)CrossRefGoogle Scholar
  198. 48.198
    G. Endo, S. Hirose: Study on roller-walker (system integration and basic experiments), IEEE Int. Conf. Robotics Autom. (1999) pp. 2032–2037Google Scholar
  199. 48.199
    R. Siegwart, P. Lamon, T. Estier, M. Lauria, R. Piguet: Innovative design for wheeled locomotion in rough terrain, Robotics Auton. Syst. 40, 151–162 (2002)CrossRefGoogle Scholar
  200. 48.200
    K. Iagnemma, A. Rzepniewski, S. Dubowsky: Control of robotic vehicles with actively articulated suspensions in rough terrain, Auton. Robots 14, 5–16 (2003)MATHCrossRefGoogle Scholar
  201. 48.201
    K. Iagnemma, S. Dubowsky: Traction control of wheeled robotic vehicles in rough terrain with application to planetary rovers, Int. J. Robotics Res. 23(10–11), 1029–1040 (2004)CrossRefGoogle Scholar
  202. 48.202
    C. Grand, F. Ben Amar, F. Plumet, P. Bidaud: Stability and traction optimization of a wheel-legged robot, Int. J. Robotics Res. 23(10–11), 1041–1058 (2004)CrossRefGoogle Scholar
  203. 48.203
    G. Besseron, C. Grand, F. Ben Amar, F. Plumet, P. Bidaud: Locomotion modes of an hybrid wheel-legged robot, Proc. Int. Conf. Climb. Walk. Robots (2004)Google Scholar
  204. 48.204
    U. Saranli, M. Buehler, D.E. Koditschek: Rhex - a simple and highly mobile hexapod robot, Int. J. Robotics Res. 20(7), 616–631 (2001)CrossRefGoogle Scholar
  205. 48.205
    T. Allen, R. Quinn, R. Bachmann, R. Ritzmann: Abstracted biological principles applied with reduced actuation improve mobility of legged vehicles, Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst. (IROS) (2003) pp. 1370–1375Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Pierre-Brice Wieber
    • 1
  • Russ Tedrake
    • 2
  • Scott Kuindersma
    • 3
  1. 1.INRIA Grenoble Rhône-AlpesGrenobleFrance
  2. 2.Computer Science and Artificial Intelligence Laboratory (CSAIL)Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.Harvard UniversityCambridgeUSA

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