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Legged Robots

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Springer Handbook of Robotics

Abstract

In this chapter, we introduce legged robots. After introducing the history of legged robot research in Sect. 16.1, we start to discuss hopping robots and analyze a simple passive walker as a typical cycling walking robot in Sect. 16.2; the Poincaré map is one of the most important tools to analyze its dynamics and stability. In Sect. 16.3, the dynamics and control of general biped robots are discussed. The key is the forward dynamics subject to the unilateral constraint between the feet and the ground. Its formal treatment leads to walking trajectory generation and various control methods. As a practical scheme to control biped robots, we discuss the zero-moment point (ZMP) in Sect. 16.4, including its definition, physical meaning, measurement, calculation, and usage. In Sect. 16.5, we move to multilegged robots. In this field, the most important subject is the relationship between gaits and stability. We also introduce the landmark robots in this field. In Sect. 16.6, we overview the divergence of the legged robots. We see leg–wheel hybrid robots, leg–arm hybrid robots, tethered walking robots, and wall-climbing robots. To compare these legged robots with different configurations, we use some useful performance indices such as the Froude number and the specific resistance, which are introduced in Sect. 16.7. We conclude the chapter and address future trends in Sect. 16.8.

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Abbreviations

ASV:

adaptive suspension vehicle

CG:

center of gravity

CPG:

central pattern generators

DOF:

degree of freedom

FRI:

foot rotating indicator

FSW:

feasible solution of wrench

MPC:

model predictive control

NASA:

National Aeronautics and Space Agency

PD:

proportional-derivative

PID:

proportional–integral–derivative

QRIO:

quest for curiosity

VI:

value iteration

ZMP:

zero-moment point

References

  1. M. Wisse, L. Schwab, F.L.T. Van der Helm: Passive walking dynamic model with upper body, Robotica 22(6), 681–688 (2004)

    Article  Google Scholar 

  2. C. Chevallereau, G. Abba, Y. Aoustin, F. Plestan, E.R. Westervelt, C. Canudas-de-Wit, J.W. Grizzle: RABBIT: a testbed for advanced control theory, IEEE Contr. Syst. Mag. 23(5), 57–79 (2003)

    Article  Google Scholar 

  3. M. Vukobratović, B. Borovac: Zero-moment point – Thirty five years of its life, Int. J. Humanoid Robot. 1(1), 157–173 (2004)

    Article  Google Scholar 

  4. T. McGeer: Passive dynamic walking, Int. J. Robot. Res. 9(2), 62–82 (1990)

    Article  Google Scholar 

  5. M.H. Raibert: Legged Robots That Balance (MIT Press, Cambridge 1986)

    Google Scholar 

  6. M. Coleman, A. Ruina: An uncontrolled walking toy that cannot stand still, Phys. Rev. Lett. 80(16), 3658–3661 (1998)

    Article  Google Scholar 

  7. A. Goswami, B. Thuilot, B. Espiau: A study of a compass-like biped robot: symmetry and chaos, Int. J. Robot. Res. 17(12), 1282–1301 (1998)

    Article  Google Scholar 

  8. C. Azevedo, B. Amblard, B. Espiau, C. Assaiante: A synthesis of bipedal locomotion in human and robots, Res. Rep. 5450, INRIA https://hal.inria.fr/inria-00070557 (December 2004)

  9. C. Azevedo, B. Espiau, B. Amblard, C. Assaiante: Bipedal locomotion: toward unified concepts in robotics and neurosciences, Biol. Cybern. 96(2), 209–228 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. P.B. Wieber: Constrained stability and parameterized control in biped walking, Int. Symp. Math. Theory Netw. Syst. (2000)

    Google Scholar 

  11. P.B. Wieber: On the stability of walking systems, Int. Workshop Humanoids Human Friendly Robot. (2002)

    Google Scholar 

  12. F. Pfeiffer, C. Glocker: Multibody Dynamics with Unilateral Contacts (Wiley, New York 1996)

    Book  MATH  Google Scholar 

  13. L. Righetti, A.J. Ijspeert: Programmable central pattern generators: an application to biped locomotion control, IEEE Int. Conf. Robot. Autom. (Orlando,USA May 2006)

    Google Scholar 

  14. K. Matsuoka: Sustained oscillations generated by mutually inhibiting neurons with adaptation, Biol. Cybern. 52, 345–353 (1985)

    Article  MathSciNet  Google Scholar 

  15. G. Endo, J. Morimoto, J. Nakanishi, G. Cheng: An empirical exploration of a neural oscillator for biped locomotion control, IEEE Int. Conf. Robot. Autom. (New Orleans 2004) pp. 3036–3042

    Google Scholar 

  16. D.C. Witt: A feasibility study on powered lower-limb prosthesis, Univer. Oxford Dep. Eng. Sci. Rep. (1970)

    Google Scholar 

  17. F. Gubina, H. Hemami, R.B. McGhee: On the dynamic stability of biped locomotion, IEEE Trans. Biomed. Eng. BME-21(2), 102–108 (1974)

    Article  Google Scholar 

  18. H. Miura, I. Shimoyama: Dynamic walk of a biped, The Int. J. Robot. Res. 3(2), 60–74 (1984)

    Article  Google Scholar 

  19. J. Furusho, M. Masubuchi: A theoretically motivated reduced order model for the control of dynamic biped locomotion, J. Dyn. Syst. Meas. Contr. 109, 155–163 (1987)

    Article  MATH  Google Scholar 

  20. S. Kawamura, F. Miyazaki, S. Arimoto: Realization of robot motion based on a learning method, IEEE Trans. Syst. Man Cybern. 18(1), 126–134 (1988)

    Article  Google Scholar 

  21. S. Kajita, T. Yamaura, A. Kobayashi: Dynamic walking control of a biped robot along a potential energy conserving orbit, IEEE Trans. Robot. Autom. 8(4), 431–438 (1992)

    Article  Google Scholar 

  22. J. Pratt, C.-M. Chew, A. Torres, P. Dilworth, G. Pratt: An intuitive approach for bipedal locomotion, Int. J. Robot. Res. 20(2), 129–143 (2001)

    Article  Google Scholar 

  23. E.R. Westervelt, J.W. Grizzle, D.E. Koditschek: Hybrid zero dynamics of planar biped walkers, IEEE Trans. Autom. Contr. 48(1), 42–56 (2003)

    Article  MathSciNet  Google Scholar 

  24. S. Lohmeier, K. Löffler, M. Gienger, H. Ulbrich, F. Pfeiffer: Computer system and control of biped Johnnie, IEEE Int. Conf. Robot. Autom. (New-Orleans 2004) pp. 4222–4227

    Google Scholar 

  25. J.H. Kim, J.H. Oh: Walking control of the humanoid platform KHR-1 based on torque feedback control, IEEE Int. Conf. Robot. Autom. (2004) pp. 623–628

    Google Scholar 

  26. P.B. Wieber, C. Chevallereau: Online adaptation of reference trajectories for the control of walking systems, Robot. Auton. Syst. 54(7), 559–566 (2006)

    Article  Google Scholar 

  27. F. Allgöwer, T.A. Badgwell, J.B. Rawlings, S.J. Wright: Nonlinear predictive control and moving horizon estimation an overview., Eur. Contr. Conf. (Karlsruhe 1999) pp. 392–449

    Google Scholar 

  28. C. Azevedo, P. Poignet, B. Espiau: Artificial locomotion control: from human to robots, Robot. Auton. Syst. 47(4), 203–223 (2004)

    Article  Google Scholar 

  29. P.B. Wieber: Trajectory-free linear model predictive control for stable walking in the presence of strong perturbations, IEEE-RAS Int. Conf. Humanoid Robots (Genoa 2006)

    Google Scholar 

  30. A. Takanishi, M. Ishida, Y. Yamazaki, I. Kato: The realization of dynamic walking by the biped walking robot WL-10RD, Int. Conf. Adv. Robot. (ICARʼ85) (1985) pp. 459–466

    Google Scholar 

  31. M. Hirose, Y. Haikawa, T. Takenaka, K. Hirai: Development of humanoid robot ASIMO, IEEE/RSJ Int. Conf. Intell. Robots Syst. – Workshop 2 (2001)

    Google Scholar 

  32. M. Gienger, K. Löffler, F. Pfeiffer: Towards the design of a biped jogging robot, IEEE Int. Conf. Robot. Autom. (2001) pp. 4140–4145

    Google Scholar 

  33. K. Kaneko, S. Kajita, F. Kanehiro, K. Yokoi, K. Fujiwara, H. Hirukawa, T. Kawasaki, M. Hirata, T. Isozumi: Design of advanced leg module for humanoid robotics project of METI, IEEE Int. Conf. Robot. Autom. (2002) pp. 38–45

    Google Scholar 

  34. Y. Sugahara, M. Kawase, Y. Mikuriya, T. Hosobata, H. Sunazuka, K. Hashimoto, H. Lim, A. Takanishi: Support torque reduction mechanism for biped locomotor with parallel mechanism, IEEE/RSJ Int. Conf. Intell. Robots Syst. (2004) pp. 3213–3218

    Google Scholar 

  35. I.W. Park, J.Y. Kim, J. Lee, J.H. Oh: Online free walking trajectory generation for biped humanoid robot KHR-3(HUBO), IEEE Int. Conf. Robot. Autom. (Orlando 2006) pp. 1231–1236

    Google Scholar 

  36. M. Vukobratović, J. Stepanenko: On the stability of anthropomorphic systems, Math. Biosci. 15, 1–37 (1972)

    Article  MATH  Google Scholar 

  37. 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, IEEE Int. Conf. Robot. Autom. (2003) pp. 1620–1626

    Google Scholar 

  38. A. Takanishi, Y. Egusa, M. Tochizawa, T. Takeya, I. Kato: Realization of dynamic biped walking stabilized with trunk motion, ROMANSY 7 (1988) pp. 68–79

    Google Scholar 

  39. A. Takanishi, H. Lim, M. Tsuda, I. Kato: Realization of dynamic biped walking stabilized by trunk motion on a sagittally uneven surface, IEEE Int. Workshop Intell. Robots Syst. (1990) pp. 323–330

    Google Scholar 

  40. S. Kagami, K. Nishiwaki, T. Kitagawa, T. Sugihiara, M. Inaba, H. Inoue: A fast generation method of a dynamically stable humanoid robot trajectory with enhanced ZMP constraint, IEEE Int. Conf. Humanoid Robot. (2000)

    Google Scholar 

  41. Q. Huang, K. Yokoi, S. Kajita, K. Kaneko, H. Arai, N. Koyachi, K. Tanie: Planning walking patterns for a biped robot, IEEE Trans. Robot. Autom. 17(3), 280–289 (2001)

    Article  Google Scholar 

  42. T. Sugihara, Y. Nakamura, H. Inoue: Realtime humanoid motion generation through ZMP manipulation based on inverted pendulum control, IEEE Int. Conf. Robot. Autom. (2002) pp. 1404–1409

    Google Scholar 

  43. K. Nagasaka, K. Kuroki, S. Suzuki, Y. Itoh, J. Yamaguchi: Integrated motion control for walking, jumping and running on a small bipedal entertainment robot, IEEE Int. Conf. Robot. Autom. (2004) pp. 3189–3194

    Google Scholar 

  44. K. Harada, S. Kajita, F. Kanehiro, K. Fujiwara, K. Kaneko, K. Yokoi, H. Hirukawa: Real-time planning of humanoid robotʼs gait for force controlled manipulation, IEEE Int. Conf. Robot. Autom. (2004) pp. 616–622

    Google Scholar 

  45. M. Tomizuka, D.E. Rosenthal: On the optimal digital state vector feedback controller with integral and preview actions, Trans. the ASME J. Dyn. Syst. Meas. Contr. 101, 172–178 (1979)

    Article  Google Scholar 

  46. T. Katayama, T. Ohki, T. Inoue, T. Kato: Design of an optimal controller for a discrete time system subject to previewable demand, Int. J. Contr. 41(3), 677–699 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  47. J. Yamaguchi, A. Takanishi, I. Kato: Experimental development of a foot mechanism with shock absorbing material for acquisition of landing surface position information and stabilization of dynamic biped walking, IEEE Int. Conf. Robot. Autom. (1995) pp. 2892–2899

    Google Scholar 

  48. K. Hirai, M. Hirose, Y. Haikawa, T. Takenaka: The development of honda humanoid robot, IEEE Int. Conf. Robot. Autom. (1998) pp. 1321–1326

    Google Scholar 

  49. K. Yokoi, F. Kanehiro, K. Kaneko, S. Kajita, K. Fujiwara, H. Hirukawa: Experimental study of humanoid robot HRP-1S, Int. J. Robot. Res. 23(4-5), 351–362 (2004)

    Article  Google Scholar 

  50. K. Hashimoto, Y. Sugahara, H. Sunazuka, C. Tanaka, A. Ohta, M. Kawase, H. Lim, A. Takanishi: Biped landing pattern modification method with nonlinear compliance control, IEEE Int. Conf. Robot. Autom. (Orlando 2006) pp. 1213–1218

    Google Scholar 

  51. A. Goswami: Postural stability of biped robots and the foot-rotation indicator(FRI) point, Int. J. Robot. Res. 18(6), 523–533 (1999)

    Article  MathSciNet  Google Scholar 

  52. P. Sardain, G. Bessonnet: Forces acting on a biped robot. center of pressure–zero moment point, IEEE Trans. Syst. Man Cybern. Part A: Syst. Humans 34(5), 630–637 (2004)

    Article  Google Scholar 

  53. T. Saida, Y. Yokokoji, T. Yoshikawa: FSW (feasible solution of wrench) for multi-legged robots, IEEE Int. Conf. Robot. Autom. (2003) pp. 3815–3820

    Google Scholar 

  54. 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, IEEE Int. Conf. Robot. Autom. (Orlando 2006), pp. 1976–1983

    Google Scholar 

  55. R.B. McGhee: Vehicular legged locomotion. In: Advances in Automation and Robotics, ed. by G.N. Saridis (JAI Press, New York 1985) pp. 259–284

    Google Scholar 

  56. S.M. Song, K.J. Waldron: Machines that Walk: the Adaptive Suspension Vehicle (The MIT Press, Cambridge 1989)

    Google Scholar 

  57. R.B. McGhee, A.A. Frank: On the stability properties of quadruped creeping gaits, Math. Biosci. 3, 331–351 (1968)

    Article  MATH  Google Scholar 

  58. K.J. Waldron, R.B. McGhee: The adaptive suspension vehicle, IEEE Contr. Syst. Mag. 6, 7–12 (1986)

    Article  Google Scholar 

  59. S. Hirose, Y. Fukuda, H. Kikuchi: The gait control system of a quadruped walking vehicle, Adv. Robot. 1(4), 289–323 (1986)

    Article  Google Scholar 

  60. S. Hirose, K. Yoneda, R. Furuya, T. Takagi: Dynamic and static fusion control of quadruped walking vehicle, IEEE/RSJ Int. Workshop Intell. Robots Syst. (1989) pp. 199–204

    Google Scholar 

  61. S. Hirose: A study of design and control of a quadruped walking vehicle, Int. J. Robot. Res. 3(2), 113–133 (1984)

    Article  Google Scholar 

  62. Y. Fukuoka, H. Kimura, A.H. Cohen: Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts, Int. J. Robot. Res. 22(3-4), 187–202 (2003)

    Article  Google Scholar 

  63. M. Buehler, R. Playter, M. Raibert: Robots step outside, Int. Symp. Adapt. Motion Animals Mach. (AMAM) (Ilmenau 2005)

    Google Scholar 

  64. R.A. Brooks: A robot that walks; emergent behavior from a carefully evolved network, IEEE Int. Conf. Robot. Autom. (Scottsdale 1989) pp. 292–296

    Google Scholar 

  65. D. Spenneberg, K. McCullough, F. Kirchner: Stability of walking in a multilegged robot suffering leg loss, IEEE Int. Conf. Robot. Autom. (2004) pp. 2159–2164

    Google Scholar 

  66. S. Hirose, K. Yoneda, K. Arai, T. Ibe: Design of prismatic quadruped walking vehicle TITAN VI, 5th Int. Conf. Adv. Robot. (Pisa taly 1991) pp. 723–728

    Google Scholar 

  67. R. McNeill Alexander: The gait of bipedal and quadrupedal animals, Int. J. Robot. Res. 3(2), 49–59 (1984)

    Article  Google Scholar 

  68. H. Kimura, I. Shimoyama, H. Miura: Dynamics in the dynamic walk of a quadruped robot, Adv. Robot. 4(3), 283–301 (1990)

    Article  Google Scholar 

  69. J. Furusho, A. Sano, M. Sakaguchi, E. Koizumi: Realization of bounce gait in a quadruped robot with articular-joint-type legs, IEEE Int. Conf. Robot. Autom. (1995) pp. 697–702

    Google Scholar 

  70. O. Matsumoto, S. Kajita, M. Saigo, K. Tani: Dynamic trajectory control of passing over stairs by a biped type leg-wheeled robot with nominal reference of static gait, IEEE/RSJ Int. Conf. Intell. Robot Syst. (1998) pp. 406–412

    Google Scholar 

  71. S. Hirose, H. Takeuchi: Study on roller-walk (basic characteristics and its control), IEEE Int. Conf. Robot. Autom. (1996) pp. 3265–3270

    Google Scholar 

  72. U. Saranli, M. Buehler, D.E. Koditschek: RHex: a simple and highly mobile hexapod robot, Int. J. Robot. Res. 20(7), 616–631 (2001)

    Article  Google Scholar 

  73. T.J. Allen, R.D. Quinn, R.J. Bachmann, R.E. Ritzmann: Abstracted biological principles applied with reduced actuation improve mobility of legged vehicles, IEEE Int. Conf. Intell. Robots Syst. (Las Vegas 2003) pp. 1370–1375

    Google Scholar 

  74. N. Koyachi, H. Adachi, M. Izumi, T. Hirose, N. Senjo, R. Murata, T. Arai: Multimodal control of hexapod mobile manipulator MELMANTIS-1, 5th Int. Conf. Climbing Walking Robots (2002) pp. 471–478

    Google Scholar 

  75. Y. Ota, T. Tamaki, K. Yoneda, S. Hirose: Development of walking manipulator with versatile locomotion, IEEE Int. Conf. Robot. Autom. (2003) pp. 477–483

    Google Scholar 

  76. G. Endo, S. Hirose: Study on roller-walker: system integration and basic experiments, IEEE Int. Conf. Robot. Autom. (Detroit 1999) pp. 2032–2037

    Google Scholar 

  77. N. Neville, M. Buehler, I. Sharf: A bipedal running robot with one actuator per leg, IEEE Int. Conf. Robot. Autom. (Orlando 2006) pp. 848–853

    Google Scholar 

  78. J. Bares, D. Wettergreen: Dante II: technical description, results and lessons learned, Int. J. Robot. Res. 18(7), 621–649 (1999)

    Article  Google Scholar 

  79. S. Hirose, A. Nagakubo, R. Toyama: Machine that can walk and climb on floors, walls and ceilings, 5th Int. Conf. Adv. Robot. (Pisa 1991) pp. 753–758

    Google Scholar 

  80. S. Kim, A. Asbeck, W. Provancher, M.R. Cutkosky: SpinybotII: Climbing hard walls with compliant microspines, IEEE ICAR (Seattle 2005) pp. 18–20

    Google Scholar 

  81. S. Hirose, K. Yoneda, H. Tsukagoshi: TITAN VII: quadruped walking and manipulating robot on a steep slope, IEEE Int. Conf. Robot. Autom. (1997)

    Google Scholar 

  82. T. Yano, S. Numao, Y. Kitamura: Development of a self-contained wall climbing robot with scanning type suction cups, IEEE/RSJ Int. Conf. Intell. Robots Syst. (1998) pp. 249–254

    Google Scholar 

  83. A.T. Asbeck, S. Kim, A. McClung, A. Parness, M.R. Cutkosky: Climbing walls with microspines (video), IEEE Int. Conf. Robot. Autom. (Orlando 2006)

    Google Scholar 

  84. P. Gregorio, M. Ahmadi, M. Buehler: Design, control, and energetics of an electrically actuated legged robot, IEEE Trans. Syst. Man Cyber. – Part B: Cyber. 27(4), 626–634 (1997)

    Article  Google Scholar 

  85. D.A. Messuri, C.A. Klein: Automatic body regulation for maintaining stability of a legged vehicle during rough-terrain locomotion, IEEE J. Robot. Autom. RA-1(3), 132–141 (1985)

    Google Scholar 

  86. E. Garcia, P. Gonzalez de Santos: An improved energy stability margin for walking machines subject to dynamic effects, Robotica 23(1), 13–20 (2005)

    Article  Google Scholar 

  87. R. McNeill Alexander: Exploring Biomechanics – Animals in Motion (W.H. Freeman, New York 1992)

    Google Scholar 

  88. G. Gabrielli, T. von Karman: What price speed – specific power required for propulsion of vehicles, Mech. Eng. 72(10), 775–781 (1950)

    Google Scholar 

  89. Y. Umetani, S. Hirose: Biomechanical study of serpentine locomotion (evaluation as a locomotion measure) (in Japanese). In: BIOMECHANISM(2) (Univ. Tokyo Press, Tokyo 1973) pp. 289–297

    Google Scholar 

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Correspondence to Shuuji Kajita Dr. or Bernard Espiau PhD .

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Kajita, S., Espiau, B. (2008). Legged Robots. In: Siciliano, B., Khatib, O. (eds) Springer Handbook of Robotics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30301-5_17

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