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Optimal Protraction of a Biologically Inspired Robot Leg

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Abstract

In this paper, protraction movement, namely forward stepping, of a biologically inspired three-joint robot leg is optimized for minimum energy consumption. Trajectory optimization is performed for various initial-final tip point positions of protraction. A modified version of gradient descent based optimal control algorithm is used. The objective function is modified in steps to jump over many unfeasible and inefficient local optima. The optimized trajectories are used to construct a radial basis function neural network (RBFNN) to interpolate for the untrained regions. The results of optimization are compared with the observations of protraction of stick insects. It is concluded that a direct biological imitation of protraction is not energy efficient. A sample protraction of a leg of the Robot-EA308 is demonstrated in guidance of the optimized trajectory. Energy optimal protraction of a robot leg necessitates flexion of the leg, rather than extension as observed in the stick insects.

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References

  1. Preumont, A., Alexandre, P., Doroftei, I., Goffin, F.: A conceptual walking vehicle for planetory exploration. Mechatronics 7(3), 287–296 (1997)

    Article  Google Scholar 

  2. Huang, Q.J., Nomani, K.: Humanitarian mine detecting six-legged walking robot and hybrid neuro walking control with position/force control. Mechatronics 13, 773–790 (2003)

    Article  Google Scholar 

  3. Galvez, J.A., Gonzalez de Santos, P., Pfeiffer, F.: Intrinsic tactile sensing for the optimization of force distribution in a pipe crawling robot. IEEE/ASMA Trans. Mechatron. 6(1), 26–35 (2001)

    Article  Google Scholar 

  4. Erden, M.S., Leblebicioğlu, K.: Free gait generation with reinforcement learning for a six-legged robot. Robot. Auton. Syst. 56, 199–212 (2008). doi:10.1016/j.robot.2007.08.001

    Article  Google Scholar 

  5. Erden, M.S., Leblebicioğlu, K.: Analysis of wave gaits for energy efficiency. Auton. Robots. 23(3), 213–230 (2007). doi:10.1007/s10514-007-9041-z

    Article  Google Scholar 

  6. Erden, M.S., Leblebicioğlu, K.: Torque distribution in a six-legged robot. IEEE Trans. Robot. 23(1), 179–186 (2007)

    Article  Google Scholar 

  7. Erden, M.S., Leblebicioğlu, K.: Multi legged walking in robotics and dynamic gait pattern generation for a six-legged robot with reinforcement learning. Book chapter in Mobile Robots: New Research. Nova Publishers, New York (2006). (ISBN: 1-59454-359-3)

  8. Delcomyn, F., Nelson, M.E.: Architectures for a biomimetic hexapod robot. Robot. Auton. Syst. 30, 5–15 (2000)

    Article  Google Scholar 

  9. Fielding, M., Damaren, C.J., Dunlop, R.: Hamlet: force/position controlled hexapod walker – design and dydtems. In: Proc. of IEEE Int. Conf. on Control Applications, pp. 984–989, Mexico City, Mexico (2001)

  10. Soyguder, S., Alli, H.: Design and prototype of a six-legged walking insect robot. Ind. Rob. 34(5), 412–422 (2007)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  12. Inagaki, S., Yuasa, H., Tamio, A.: CPG model for autonomous decentralized multi-legged robot system—generation and transition of oscillation patterns and dynamics of oscillators. Robot. Auton. Syst. 44, 171–179 (2003)

    Article  Google Scholar 

  13. Porta, J.M., Celaya, E.: Reactive free gait generation to follow arbitrary trajectories with a hexapod robot. Robot. Auton. Syst. 47, 187–201 (2004)

    Article  Google Scholar 

  14. Svinin, M.M., Yamada, K., Ueda, K.: Emergent synthesis of motion patterns for locomotion robots. Artif. Intell. Eng. 15, 353–363 (2001)

    Article  Google Scholar 

  15. Cruse, H., Kindermann, T., Schumm, M., Dean, J., Schmitz, J.: Walknet-a biologically inspired network to control six legged walking. Neural Netw. 11, 1435–1447 (1998)

    Article  Google Scholar 

  16. Dürr, V., Schmitz, J., Cruse, H.: Behaviour-based modeling of hexapod locomotion: linking biology and technical application. Arthropod Struct. Develop. 33, 237–250 (2004)

    Article  Google Scholar 

  17. Dean, J., Kindermann, T., Schmitz, J., Schum, M., Cruse, H.: Control of walking in the stick insect: from behavior and physiology to modeling. Auton. Robots 7, 271–288 (1999)

    Article  Google Scholar 

  18. Ilg, W., Bernes, K.: A learning architecture based on reinforcement learning for adaptive control of the walking machine LAURON. Robot. Auton. Syst. 15, 321–334 (1995)

    Article  Google Scholar 

  19. Ilg, W., Bernes, K., Mühlfriedel, T., Dillman, R.: Hybrid learning concepts based on self-organizing neural networks for adaptive control of walking machines. Robot. Auton. Syst. 22, 317–327 (1997)

    Article  Google Scholar 

  20. Kirchner, F.: Q-learning of complex behaviours on a six-legged walking machine. Robot. Auton. Syst. 25, 253–262 (1998)

    Article  MathSciNet  Google Scholar 

  21. Espenschied, K.S., Quinn, R.D., Beer, R.D., Chiel, H.J.: Biologically based distributed control and local reflexes improve rough terrain locomotion in a hexapod robot. Robot. Auton. Syst. 18, 59–64 (1996)

    Article  Google Scholar 

  22. Erden, M.S., Leblebicioğlu, K.: Fuzzy controller design for a three-joint robot leg in protraction phase - an optimal behavior inspired fuzzy controller design. In: Proceedings of the First International Conference on Informatics in Control, Automation And Robotics, vol. 2, pp. 302–306, Setúbal, Portugal (2004)

  23. Erden, M.S., Leblebicioğlu, K.: Optimal protraction of a three-joint robot leg. In: Proc. of 17th IFAC World Congress, July 6–11, pp. 1703–1710, Seoul, South Korea (2008)

  24. Cruse, H., Bartling, C.: Movement of joint angles in the legs of a walking insect. J. Insect Physiol. 41(9), 761–771 (1995)

    Article  Google Scholar 

  25. Frantsevich, L., Cruse, H.: The stick insect, obrimus asperrimus (phasmida, bacillidae) walking on different surfaces. J. Insect Physiol. 43(5), 447–455 (1997)

    Article  Google Scholar 

  26. Bassler, U., Buschges, A.: Pattern generation of stick insect walking movements – multisensory control of a locomotor program. Brain Res. Rev. 27, 65–88 (1998)

    Article  Google Scholar 

  27. Schumm, M., Cruse, H.: Control of swing movement: influences of differently shaped substrate. J. Comp. Physiol. A-Neuroethol. Sensory Neural Behav. Physiol. 192, 1147–1164 (2006)

    Article  Google Scholar 

  28. Ekeberg, O., Blumen, M., Buschges, A.: Dynamic simulation of insect walking. Arthropod Struct. Develop. 33, 287–300 (2004)

    Article  Google Scholar 

  29. Ferrell, C.A.: Comparison of three insect-inspired locomotion controllers. Robot. Auton. Syst. 16, 135–159 (1995)

    Article  Google Scholar 

  30. Klaassen, B., Linnemann, R., Spenneberg, D., Kirchner, F.: Biomimetic walking robot SCORPION: control and modeling. Robot. Auton. Syst. 41, 69–76 (2002)

    Article  Google Scholar 

  31. Koo, I.M., Trong, T.D., Kang, T.H., Vo, G.L., Song, Y.K., Lee, C.M., Choi, H.Y.: Control of a quadruped walking robot based on biologically inspired approach. In: Proc. Of the 2007 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, Oct. 29 – Nov. 2, pp. 2969–2974, San Diego, CA, USA (2007)

  32. Dasgupta, A., Nakamura, Y.: Making feasible walking motion of humanoid robots from human motion capture data. In: Proc. Of the 1999 IEEE Int. Conf. on Robotics and Automation, pp. 1044–1049, Detroit, Michigan (1999)

  33. Khatib, O., Demircan, E., De Sapio, V., Sentis, L., Besier, T., Delp, S.: Robotics-based synthesis of human motion. J. Physiol. – Paris. 103, 211–219 (2009)

    Article  Google Scholar 

  34. Fu, K.S., Gonzalez, R.C., Lee, C.S.G.: Robotics. McGraw-Hill, Inc. (1987)

  35. Erden, M.S.: Six-Legged Walking Machine: The Robot-EA308, pp. 148–154. Ph.D. Thesis, Electrical and Electronics Engineering, Middle East Technical University, Ankara, Turkey (2006). http://etd.lib.metu.edu.tr/upload/12607356/index.pdf

  36. Park, J.K.: Convergence properties of gradient-based numeric motion-optimizations for manipulator arms amid static or moving obstacles. Robotica 22, 649–659 (2004)

    Article  Google Scholar 

  37. Bobrow, J.E., Martin, B., Sohl, G., Wang, E.C., Park, F.C., Kim, K.: Optimal robot motions for physical criteria. J. Robot. Syst. 18(12), 785–792 (2001)

    Article  MATH  Google Scholar 

  38. Chettibi, T., Lehtihet, H.E., Haddad, M., Hanchi, S.: Minimum cost trajectory planning for industrial robots. Eur. J. Mech. A/Solids. 23, 703–715 (2004)

    Article  MATH  Google Scholar 

  39. Garg, D.P., Kumar, M.: Optimization techniques applied to multiple manipulators for path planning and torque minimization. Eng. Appl. Intell. 15, 241–252 (2002)

    Article  Google Scholar 

  40. Saramago, S.F.P., Stefen Jr., V.: Optimization of the trajectory planning of robot manipulators taking into account the dynamics of the system. Mech. Mach. Theory 33(7), 883–894 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  41. Khoukhhi, A., Baron, L., Balazinski, M., Demirli, K.: Fuzzy-neuro optimal time-energy control of a three degrees of freedom planar manipulator. In: Proc. of the Annual Meeting of the North American Fuzzy Information Processing Society, pp. 247–252 (2006)

  42. Pires, E.J.S., Oliveira, P.B.M, Machado, J.A.T.: Multi-objective genetic manipulator trajectory planner. In: Raidl, G.R. et al. (eds.) EvoWorkshops, pp. 219–229. Springer-Verlag Berlin Heidelberg (2004)

  43. Buskens, C., Knauer, M.: Higher order real-time approximations in optimal control of multibody-systems for industrial robots. Multibody Syst. Dyn. 15, 85–106 (2006)

    Article  MathSciNet  Google Scholar 

  44. Khoukhi, A., Baron, L., Balazinski, M.: Constrained multi-objective trajectory planning of parallel kinematic machines. Robot. Comput. –Integr. Manuf. 25, 756–769 (2009)

    Article  Google Scholar 

  45. Kirk, D.E.: Optimal control theory – an introduction, pp. 184–209, 236–240, 330–343. Prentice-Hall Inc., Englewood Cliffs, New Jersey (1970)

  46. Frangos, C., Yavin, Y.: Control of a three-link manipulator with inequality constraints on the trajectories of its joints. Comput. Math. Appl. 41, 1562–1574 (2001)

    Article  MathSciNet  Google Scholar 

  47. Liu, J.F., Abdel-Malek, K.: Robust control of planar dual-arm cooperative manipulators. Robot. Comput. –Integr. Manuf. 16(2–3), 109–120 (2000)

    Article  Google Scholar 

  48. Jain, A.K., Mao, J., Mohiuddin, K.M.: Artificial neural networks: a tutorial. Computer 29(3), 31–44 (1996)

    Article  Google Scholar 

  49. Erden, M.S., Leblebicioğlu, K., Halıcı, U.: Multi-agent system based fuzzy controller design with genetic tuning for a service mobile manipulator robot in the hand-over task. J. Intell. Robot. Syst. 38, 287–306 (2004)

    Article  Google Scholar 

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  1. Computer Vision and Intelligent System Research Laboratory, Electrical and Electronics Engineering Department, Middle East Technical University, Ankara, Turkey

    Mustafa Suphi Erden

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Correspondence to Mustafa Suphi Erden.

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Erden, M.S. Optimal Protraction of a Biologically Inspired Robot Leg. J Intell Robot Syst 64, 301–322 (2011). https://doi.org/10.1007/s10846-011-9538-8

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  • DOI: https://doi.org/10.1007/s10846-011-9538-8

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