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Analysis of wave gaits for energy efficiency

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Abstract

In this paper an energy efficiency analysis of wave gaits is performed for a six-legged walking robot. A simulation model of the robot is used to obtain the data demonstrating the energy consumption while walking in different modes and with varying parameters. Based on the analysis of this data some strategies are derived in order to minimize the search effort for determining the parameters of the gaits for an energy efficient walk. Then, similar data is obtained from an actual experimental setup, in which the Robot-EA308 is used as the walking machine. The strategies are justified based on this realistic data. The analysis concludes the following: a phase modified version of wave gaits is more efficient than the (conventional) wave gaits, using the possible minimum protraction time results in more energy efficient gaits and higher velocity results in less energy consumption per traveled distance. A stability analysis is performed for the phase modification of the wave gaits, and the stability loss due to the modification is calculated. It is concluded that the loss in stability is insignificant.

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References

  • Altendorfer, R., Moore, N., Komsuoglu, H., Buehler, M., Brown, H. B., Jr., McMordie, D., Saranli, U., Full, R., & Koditschek, D. E. (2001). RHex: A biologically inspired hexapod runner. Autonomous Robots, 11, 207–213.

    Article  MATH  Google Scholar 

  • Bekey, G. A. (2005). Autonomous robots, from biological inspiration to implementation and control (pp. 156–165). Cambridge: MIT.

    Google Scholar 

  • Bobrow, J. E., Martin, B., Sohl, G., Wang, E. C., Park, F. C, & Kim, K. (2001). Optimal robot motions for physical criteria. Journal of Robotic Systems, 18(12), 785–792.

    Article  MATH  Google Scholar 

  • Brambilla, G., Buchli, J., & Ijspeert, J. (2006). Adaptive four legged locomotion control based on nonlinear dynamical systems. In Lecture Notes in Computer Science : Vol. 4095. From animals to animats—proceedings of the ninth international conference on the simulation of adaptive behavior (SAB’06). Berlin: Springer.

    Google Scholar 

  • Cruse, H. (1990). What mechanisms coordinate leg movement in walking arthropods? Trends in Neurosciences, 13, 15–21.

    Article  Google Scholar 

  • Cruse, H., Dürr, V., Schmitz, J., & Schneider, A. (2006). Control of hexapod walking in biological systems. In Adaptive motion of animals and machines (pp. 17–29). Tokyo: Springer.

    Chapter  Google Scholar 

  • Dickinson, M. H., Farley, C. T., Full, R. J., Koehl, M. A. R., Kram, R., & Lehman, S. (2000). How animals move: an integrative view. Science, 288, 100–106.

    Article  Google Scholar 

  • Donner, M. D. (1987). Real time control of walking. Birkhäuser: Boston.

    Google Scholar 

  • Erden, M. S. (2006). Six-legged walking machine: the Robot-EA308. PhD thesis, Middle East Technical university, Department of Electrical and Electronics Engineering, July.

  • Erden, M. S., & Leblebicioğlu, K. (2005). Multi legged walking in robotics and dynamic gait pattern generation for a six-legged robot with reinforcement learning. In Mobile robots: new research, New York: Nova. ISBN: 1-59454-359-3.

    Google Scholar 

  • Erden, M. S., & Leblebicioğlu, K. (2006a). Free gait generation with reinforcement learning for a six-legged robot. In Proceedings of the 9th international conference on climbing and walking robots—CLAWAR 2006 (pp. 413–424). Brussels, Belgium, September 2006.

  • Erden, M. S., & Leblebicioğlu, K. (2006b). Protraction of a three joint robot reg: trajectory optimization and controller design. Under Review.

  • Erden, M. S., & Leblebicioğlu, K. (2007). Torque distribution in a six-legged robot. IEEE Transactions on Robotics, 23(1), 179–186.

    Article  Google Scholar 

  • Ferrell, C. (1995). A comparison of three insect-inspired locomotion controllers. Robotics and Autonomous Systems, 16, 135–159.

    Article  Google Scholar 

  • Full, R. J., & Tu, M. S. (1989). Mechanics of six-legged runners. Journal of Experimental Biology, 148, 129–146.

    Google Scholar 

  • Full, R. J., & Tu, M. S. (1990). Mechanics of a rapid running insect: two-, four- and six-legged locomotion. Journal of Experimental Biology, 156, 215–231.

    Google Scholar 

  • Garg, D. P., & Kumar, M. (2002). Optimization techniques applied to multiple manipulators for path planning and torque minimization. Engineering Applications of Intelligence, 15, 241–252.

    Article  Google Scholar 

  • Hirose, S., Tsukagoshi, H., & Yoneda, K. (2001). Normalized energy stability margin and its contour of walking vehicles on rough terrain. In Proceedings of the 2001 IEEE international conference on robotics and automation (pp. 181–186), Seoul, Korea, 21–26 May 2001.

  • Huber, M., & Grupen, R. A. (1997). A feedback control structure for online-learning tasks. Robotics and Autonomous Systems, 22, 303–315.

    Article  Google Scholar 

  • Inagaki, K. (1997). Gait study for hexapod walking with disabled leg. In Proceedings of the 1997 IEEE/RSJ—international conference on intelligent robots and systems (IROS’97) (Vol. 1, pp. 408–413).

  • Inagaki, K., & Kobayashi, H. (1994). Adaptive wave gait for hexapod synchronized walking. In Proceedings of 1994 IEEE international conference on robotics and automation (Vol. 2, pp. 1326–1331).

  • Kar, D. C., Issac, K. K., & Jayarajan, K. (2001). Minimum energy force distribution for a walking robot. Journal of Robotic Systems, 18(2), 47–54.

    Article  MATH  Google Scholar 

  • Kar, D. C., Issac, K. K., & Jayarajan, K. (2003). Gaits and energetics in terrestrial legged locomotion. Mechanisms and Machine Theory, 38(2), 355–366.

    Article  MATH  Google Scholar 

  • Karalarli, E., Erkmen, A. M., & Erkmen, I. (2004). Intelligent gait synthesizer for hexapod walking rescue robots. In Proceedings of the 2004 IEEE international conference on robotics and automation (pp. 2177–2182), New Orleans, LA, April 2004.

  • Kim, S., Clark, J. E., & Cutkosky, M. R. (2006). iSprawl: Design and tuning for high-speed autonomous open-loop running. The International Journal of Robotics Research, 25(9), 903–912.

    Article  Google Scholar 

  • Kimura, H., Yamashita, T., & Kobayashi, S. (2001). Reinforcement learning of walking behavior for a four-legged robot. In Proceedings of the 40th IEEE conference on decisions and control, Oriando, Florida USA, December 2001.

  • Koditschek, D. E., Full, R. J., & Buehler, M. (2004). Mechanical aspects of legged locomotion control. Arthropod Structure and Development, 33, 251–272.

    Article  Google Scholar 

  • Lewis, M. A., Fagg, A. H., & Bekey, G. A. (1994). Genetic algorithms for gait synthesis in a hexapod robot. In E. Zheng (Ed.), Recent trends in mobile robots, New Jersey: World Scientific.

    Google Scholar 

  • Lin, B. S., & Song, S. M. (2001). Dynamic modeling, stability and energy efficiency of a quadrupedal walking machine. Journal of Robotic Systems, 18(11), 657–670.

    Article  MATH  Google Scholar 

  • Liu, J. F., & Abdel-Malek, K. (2000). Robust control of planar dual-arm cooperative manipulators. Robotics and Computer-Integrated Manufacturing, 16(2–3), 109–120.

    Article  Google Scholar 

  • Marhefka, D. W., & Orin, D. E. (1997). Gait planning for energy efficiency in walking machines. In Proceedings of the 1997 IEEE international conference on robotics and automation, Albuquerque, NM, April 1997.

  • Marhefka, D. W., & Orin, D. E. (1998). Quadratic optimization of force distribution in walking machines, In Proceedings of the 1998 IEEE international conference on robotics and automation (pp. 477–483), Lueven, Belgium, May 1998.

  • McGhee, R. B., & Frank, A. A. (1968). On the stability properties of quadruped creeping gaits. Mathematical Biosciences, 3, 331–351.

    MATH  Google Scholar 

  • Muraro, A., Chevallereau, C., & Aoustin, Y. (2003). Optimal trajectory for quadruped robot with trot, amble and curvet gaits for two energetic criteria. Multibody System Dynamics, 9, 39–62.

    Article  MATH  Google Scholar 

  • Nishii, J. (1998). Gait pattern and energetic cost in hexapods. In Proceedings of the 20th annual international conference of the IEEE engineering in medicine and biology society (Vol. 20, pp. 2430–2433).

  • Pal, P. K., Mahadev, V., & Jayarajan, K. (1994). Gait generation for six-legged walking machine through graph search. In Proceedings of 1994 IEEE international conference on robotics and automation (Vol. 2, pp. 1332–1337).

  • Pearson, K. G., & Franklin, R. (1984). Characteristics of leg movements and patterns of coordination in locusts walking on rough terrain. The International Journal of Robotics Research, 3(2), 101–112.

    Article  Google Scholar 

  • Porta, J. M., & Celaya, E. (2001). Efficient gait generation using reinforcement learning. In Proceedings of the 4th international conference on climbing and walking robots, clawar (pp. 411–418). Karlsruhe, Germany. Professional Engineering Publishing. ISBN 1-86058-365-2.

  • Porta, J. M., & Celaya, E. (2004). Reactive free gait generation to follow arbitrary trajectories with a hexapod robot. Robotics and Autonomous Systems, 47, 187–201.

    Article  Google Scholar 

  • Pratihar, D. K., Deb, K., & Ghosh, A. (2002). Optimal path and gait generations simultaneously of a six-legged robot using GA-fuzzy approach. Robotics and Autonomous Systems, 41, 1–20.

    Article  Google Scholar 

  • Preumont, A., Alexandre, P., & Ghuys, D. (1991). Gait analysis and implementation of a six leg walking machine. In Proceedings of the fifth international conference on advanced robotics (91 ICAR—IEEE) (Vol. 2, pp. 941–945).

  • Saranli, U., Buehler, M., & Koditschek, D. E. (2001). RHex: A simple and highly mobile hexapod robot. The International Journal of Robotics Research, 20(7), 616–631.

    Article  Google Scholar 

  • Song, S. M., & Choi, B. S. (1990). The optimally stable ranges of 2n-legged wave gaits. IEEE Transactions on System, Man, and Cybernetics, 20(4), 888–902.

    Article  MATH  Google Scholar 

  • Song, S. M., & Waldron, K. J. (1987). An analytical approach for gait study and its applications on wave gaits. The International Journal of Robotics Research, 6(2), 60–71.

    Article  Google Scholar 

  • Svinin, M. M., Yamada, K., & Ueda, K. (2001). Emergent synthesis of motion patterns for locomotion robots. Artificial Intelligence in Engineering, 15, 353–363.

    Article  Google Scholar 

  • Weingarten, J. D., Lopes, G. A. D., Buehler, M., Groff, R. E., & Koditschek, D. E. (2004). Automated gait adaptation for legged robots. In Proceedings of the 2004 IEEE international conference on robotics and automation (pp. 2153–2158), New Orleans, LA, April 2004.

  • Wilson, D. (1966). Insect Walking. Annual Review of Entomology, 11, 103–122.

    Article  Google Scholar 

  • Ye, T. Y. (2003). Gait planning and transitions of walking robots on smooth and rough terrains. PhD thesis, Mechanical Engineering in the Graduate College of the University of Illinois at Chicago.

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Correspondence to Mustafa Suphi Erden.

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This research is partially supported by the research fund of Middle East Technical University as a scientific research project: BAP-2002-03-01-06.

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Suphi Erden, M., Leblebicioğlu, K. Analysis of wave gaits for energy efficiency. Auton Robot 23, 213–230 (2007). https://doi.org/10.1007/s10514-007-9041-z

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