Abstract
In this paper, we intend to show the basis of a general legged locomotion controller with the ability to integrate both posture and rhythmic motion controls and shift continuously from one control method to the other according to the walking speed. The rhythmic motion of each leg in the sagittal plane is generated by a single leg controller which controls the swing-to-stance and stance-to-swing phase transitions using respectively leg loading and unloading information. Since rolling motion induced by inverted pendulum motion during the two-legged stance phases results in the transfer of the load between the contralateral legs, leg loading/unloading involves posture information in the frontal plane. As a result of the phase modulations based on leg loading/unloading, rhythmic motion of each leg is achieved and inter-leg coordination (resulting in a gait) emerges, even without explicit coordination amongst the leg controllers, allowing to realize dynamic walking in the low- to medium-speed range. We show that the proposed method has resistance ability against lateral perturbations to some extent, but that an additional ascending coordination mechanism between ipsilateral legs is necessary to withstand perturbations decreasing the rolling motion amplitude. Even without stepping reflex using vestibular information, our control system, relying on phase modulations based on leg loading/unloading and the ascending coordination mechanism between ipsilateral legs, enables low speed dynamic walking on uneven terrain with long cyclic period, which was not realized in our former studies. Details of trajectory generation, movies of simulations and movies of preliminary experiments using a real robot are available at: http://robotics.mech.kit.ac.jp/kotetsu/.
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References
Akay, T., McVea, D. A., Tachibana, A., & Pearson, K. G. (2006). Coordination of fore and hind leg stepping in cats on a transversely-split treadmill. Experimental Brain Research, 175, 211–222.
Alexander, R. M. (1984). The gaits of bipedal and quadrupedal animals. International Journal of Robotics Research, 6(3), 49–59.
Alexander, R. M. (1992). Exploring biomechanics. New York: Freeman.
Aoi, S., & Tsuchiya, K. (2005). Locomotion control of a biped robot using nonlinear oscillators. Autonomous Robots, 19(3), 219–232.
Aoi, S., & Tsuchiya, K. (2006). Stability analysis of a simple walking model driven by an oscillator with a phase reset using sensory feedback. IEEE Transactions on Robotics, 22(2), 391–397.
Berns, K., Ilg, W., Deck, M., Albiez, J., & Dillmann, R. (1999). Mechanical construction and computer architecture of the four legged walking machine BISAM. IEEE/ASM Transactions on Mechatronics, 4(1), 32–38.
Boston Dynamics (2005). BigDog project. http://www.bdi.com/content/sec.php?section=BigDog.
Buchli, J., & Ijspeert, A. J. (2008). Self-organized adaptive legged locomotion in a compliant quadruped robot. Autonomous Robots, 25(4), 331–347.
Cruse, H. (2002). The functional sense of central oscillations in walking. Biological Cybernetics, 86, 271–280.
Deliagina, T., & Orlovsky, G. (2002). Comparative neurobiology of postural control. Current Opinion in Neurobiology, 12, 652–657.
Duysens, J., & Pearson, K. G. (1980). Inhibition of flexor burst generation by loading ankle extensor muscles in walking cats. Brain Research, 187, 321–332.
Ekeberg, O., & Pearson, K. (2005). Computer simulation of stepping in the hind legs of the cat: an examination of mechanisms regulating the stance-to-swing transition. Journal of Neurophysiology, 94(6), 4256–4268.
Fukuoka, Y., Kimura, H., & Cohen, A. H. (2003). Adaptive dynamic walking of a quadruped robot on irregular terrain based on biological concepts. International Journal of Robotics Research, 22(3–4), 187–202.
Grillner, S. (1981). Control of locomotion in bipeds, tetrapods and fish. In Handbook of physiology II (pp. 1179–1236). Bethesda: Am. Physiol. Soc.
Hildebrand, M. (1968). Symmetrical gaits of dogs in relation to body build. Journal of Morphology, 124, 353–359.
Hirai, K., Hirose, M., Haikawa, Y., & Takenaka, T. (1998). The development of Honda humanoid robot. In Proc. of ICRA 1998 (pp. 1321–1326).
Hobbelen, D. G., & Wisse, M. (2008). Controlling the walking speed in limit cycle walking. International Journal of Robotics Research, 27(9), 989–1005.
Ijspeert, A. J. (2001). A connectionist central pattern generator for the aquatic and terrestrial gaits of a simulated salamander. Biological Cybernetics, 84(5), 331–348.
Ijspeert, A. J. Crespi, A., Ryczko, D., & Cabelguen, J. M. (2007). From swimming to walking with a salamander robot driven by a spinal cord model. Science, 315(5817), 1416–1420.
Jindrich, D. L., & Full, R. J. (2002). Dynamic stabilization of rapid hexapedal locomotion. Journal of Experimental Biology, 205, 2803–2823.
Karayannidou, A., Zelenin, P. V., Orlovsky, G. N., Sirota, M. G., Beloozerova, I. N., & Deliagina, T. G. (2009). Maintenance of lateral stability during standing and walking in the cat. Journal of Neurophysiology, 101, 8–19.
Kimura, H., Shimoyama, I., & Miura, H. (1990). Dynamics in the dynamic walk of a quadruped robot. Advanced Robotics, 4(3), 283–301.
Kimura, H., Akiyama, S., & Sakurama, K. (1999). Realization of dynamic walking and running of the quadruped using neural oscillator. Autonomous Robots, 7(3), 247–258.
Kimura, H., & Fukuoka, Y. (2004). Biologically inspired adaptive dynamic walking in outdoor environment using a self-contained quadruped robot: ‘Tekken2’. In Proc. IROS 2004 (pp. 986–991).
Kimura, H., Fukuoka, Y., & Cohen, A. H. (2007). Adaptive dynamic walking of a quadruped robot on natural ground based on biological concepts. International Journal of Robotics Research, 26(5), 475–490.
Maufroy, C., Kimura, H., & Takase, K. (2008). Towards a general neural controller for quadrupedal locomotion. Neural Networks, 21(4), 667–681.
Maufroy, C. (2009a). Generation and stabilization of quadrupedal dynamic walk using phase modulations based on leg loading information. Ph.D. dissertation, University of Electro-Communications (available at: http://robotics.mech.kit.ac.jp/kotetsu/Maufroy-phd-dissertation.pdf).
Maufroy, C., Kimura, H., & Takase, K. (2009b). Stable dynamic walking of a quadruped via phase modulations against small disturbances. In Proc. of ICRA 2009 (pp. 4201–4206).
Maufroy, C., Nishikawa, T., & Kimura, H. (2010). Stable dynamic walking of a quadruped robot “Kotetsu” using phase modulations based on leg loading/unloading. In Proc. of ICRA 2009 (accepted).
Misiaszek, J. (2006). Control of frontal plane motion of the hindlimbs in the unrestrained walking cat. Journal Neurophysiology, 96, 1816–1828.
Miura, H., & Shimoyama, I. (1984). Dynamical walk of biped locomotion. International Journal of Robotics Research, 3(2), 60–74.
Orlovsky, G. N., Deliagina, T. G. & Grillner, S. (1999). Neural control of locomotion. London: Oxford University Press.
Raibert, M. H. (1986). Legged robots that balance. Cambridge: MIT Press.
Righetti, L., & Ijspeert, A. (2008). Pattern generators with sensory feedback for the control of quadruped locomotion. In Proc. of ICRA 2008 (pp. 819–824).
Rossignol, S. (1996) Neural control of stereoscopic leg movements. In L. B. Rowell & J. T. Sheperd (Eds.), Handbook of physiology—exercise regulation and integration of multiple systems (pp. 173–216). London: Oxford University Press.
Taga, G., Yamaguchi, Y., & Shimizu, H. (1991). Self-organized control of bipedal locomotion by neural oscillators. Biological Cybernetics, 65, 147–159.
Taga, G. (1995). A model of the neuro-musculo-skeletal system for human locomotion II. Real-time adaptability under various constraints. Biological Cybernetics, 73, 113–121.
Takanishi, A., Takeya, T., Karaki, H., & Kato, I. (1990). A control method for dynamic biped walking under unknown external force. In Proc. of IROS 1990 (pp. 795–801).
Tomita, M. (1967). A study on the movement pattern of four limbs in walking. Journal Anthropological Society of Nippon, 75, 120–146 171–194.
Tomita, N., & Yano, M. (2003). A model of learning free bipedal walking in indefinite environment—constraints self-emergence/self-satisfaction paradigm. In Prof. SICE Annual Conf. (pp. 3176–3181).
Tsujita, K., Tsuchiya, K., & Onat, A. (2001). Adaptive gait pattern control of a quadruped locomotion Robot. In Proc. of IROS2001 (pp. 2318–2325).
Vukobratović, M., & Borovac, B. (2004). Zero-moment point—thirty five years of its life. International Journal of Humanoid Robotics, 1(1), 157–173.
Yoneda, K., Iiyama, H., & Hirose, S. (1994). Sky-hook suspension control of a quadruped walking vehicle. In Proc. of ICRA 1994 (pp. 999–1004).
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Maufroy, C., Kimura, H. & Takase, K. Integration of posture and rhythmic motion controls in quadrupedal dynamic walking using phase modulations based on leg loading/unloading. Auton Robot 28, 331–353 (2010). https://doi.org/10.1007/s10514-009-9172-5
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DOI: https://doi.org/10.1007/s10514-009-9172-5