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Bio-Inspired Modular Relative Jacobian for Holistically Controlled Four-Arm Manipulators Using Opposite and Adjacent Dual-Arm Pairs

  • Research Article-Computer Engineering and Computer Science
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A Correction to this article was published on 16 November 2021

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Abstract

This work presents a holistic approach to control a robot with four arms as a single manipulator (with a single end-effector) using a modular relative Jacobian. The proposed method uses dual-arm pairing using opposite, adjacent, and counter-lateral pairs, in an attempt to interpret biological holistic movements through leg pairing in insects, as well as in large four-legged animals. A modular expression of the relative Jacobian for four arms is derived using an analogous principle of derivation used for the relative Jacobian for dual arms. The proposed approach pairs two arms as a single dual-arm manipulator and then pairs the two dual arms into a single four-arm manipulator. In this paper, the dual-arm pairing is performed to mimic the pacing and trotting movement of a large four-legged animal. A purely kinematic simulation in Gazebo is shown to demonstrate a holistically controlled four-arm manipulator.

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References

  1. Agarwal, A.; Shah, S.; Bandyopadhyay, S.; Saha, S.: Dynamics of serial kinematic chains with large number of degrees-of-freedom. Multibody Syst. Dyn. 32(3), 273–298 (2014)

    Article  Google Scholar 

  2. Ahmadizadeh, M.; Shafei, A.; Fooladi, M.: A recursive algorithm for dynamics of multiple frictionless impact-contacts in open-loop robotic mechanisms. Mech. Mach. Theory 146, 103745 (2020)

    Article  Google Scholar 

  3. Ahmadizadeh, M.; Shafei, A.; Fooladi, M.: Dynamic analysis of multiple inclined and frictional impact-contacts in multi-branch robotic systems. Appl. Math. Model. 91, 24–42 (2021)

    Article  MathSciNet  Google Scholar 

  4. Beer, R.D.; Quinn, R.D.; Chiel, H.J.; Ritzmann, R.E.: Biologically inspired approaches to robotics: What can we learn from insects? Commun. ACM 40(3), 30–38 (1997)

    Article  Google Scholar 

  5. Biancardi, C.M.; Fabrica, C.G.; Polero, P.; Loss, J.F.; Minetti, A.E.: Biomechanics of octopedal locomotion: kinematic and kinetic analysis of the spider grammostola mollicoma. J. Exp. Biol. 214(20), 3433–3442 (2011)

    Article  Google Scholar 

  6. Clune, J.; Beckmann, B.E.; Ofria, C.; Pennock, R.T.: Evolving coordinated quadruped gaits with the HyperNEAT generative encoding. In: 2009 IEEE Congress on Evolutionary Computation, pp. 2764–2771. IEEE (2009)

  7. Cruse, H.; Warnecke, H.: Coordination of the legs of a slow-walking cat. Exp. Brain Res. 89(1), 147–156 (1992)

    Article  Google Scholar 

  8. Dabelow, S.: Zur Biologie der Leimschleuderspinne Scytodes thoracica (Latreille). Zool. Jb. Syst. 86, 85–126 (1958)

  9. Delcomyn, F.; Nelson, M.E.: Architectures for a biomimetic hexapod robot. Robot. Auton. Syst. 30(1), 5–15 (2000)

    Article  Google Scholar 

  10. Eberhard, W.G.: Behavioral characters for the higher classification of orb-weaving spiders. Evolution. 36(5), 1067–1095 (1982)

  11. Fuchs, A.; Goldner, B.; Nolte, I.; Schilling, N.: Ground reaction force adaptations to tripedal locomotion in dogs. Vet. J. 201(3), 307–315 (2014)

    Article  Google Scholar 

  12. Goldner, B.; Fuchs, A.; Nolte, I.; Schilling, N.: Kinematic adaptations to tripedal locomotion in dogs. Vet. J. 204(2), 192–200 (2015)

    Article  Google Scholar 

  13. Grabowska, M.; Godlewska, E.; Schmidt, J.; Daun-Gruhn, S.: Quadrupedal gaits in hexapod animals-inter-leg coordination in free-walking adult stick insects. J. Exp. Biol. 215(24), 4255–4266 (2012)

    Google Scholar 

  14. He, W., Gao, H., Zhou, C., Yang, C., Li, Z.: Reinforcement learning control of a flexible two-link manipulator: an experimental investigation. IEEE Trans. Syst. Man Cybern. Syst. 1–11 (2020)

  15. Hollerbach, J.M.: A recursive lagrangian formulation of maniputator dynamics and a comparative study of dynamics formulation complexity. IEEE Trans. Syst. Man Cybern. 10(11), 730–736 (1980)

    Article  Google Scholar 

  16. Hosoda, K.; Sakaguchi, Y.; Takayama, H.; Takuma, T.: Pneumatic-driven jumping robot with anthropomorphic muscular skeleton structure. Auton. Robot. 28(3), 307–316 (2010)

    Article  Google Scholar 

  17. Ijspeert, A.J.: Biorobotics: using robots to emulate and investigate agile locomotion. Science 346(6206), 196–203 (2014)

    Article  Google Scholar 

  18. Jamisola, R.S.; Chang, P.H.; Lee, J.: Guaranteeing task prioritization for redundant robots given maximum number of tasks and singularities. In: TENCON 2012 IEEE Region 10 Conference, Manila, Philippines, pp. 1–6. IEEE (2012)

  19. Jamisola Jr, R.S.; Kormushev, P.; Caldwell, D.G.; Ibikunle, F.: Modular relative jacobian for dual-arms and the wrench transformation matrix. In: 2015 IEEE 7th IEEE International Conference on Cybernetics and Intelligent Systems (CIS) and IEEE Conference on Robotics, Automation and Mechatronics (RAM), Angkor Wat, Cambodia, pp. 181–186. IEEE (2015)

  20. Jamisola, R.S., Jr.; Roberts, R.G.: A more compact expression of relative Jacobian based on individual manipulator Jacobians. Robot. Auton. Syst. 63, 158–164 (2015)

    Article  Google Scholar 

  21. Kaston, B.J.: Some little known aspects of spider behavior. The American Midland Naturalist. 73(2), 336–356 (1965)

  22. Khatib, O.: Inertial properties in robotic manipulation: an object-level framework. Int. J. Robot. Res. 14(1), 19–36 (1995)

    Article  Google Scholar 

  23. Kirpensteijn, J.; Van den Bos, R.; Van den Brom, W.; Hazewinkel, H.: Ground reaction force analysis of large breed dogs when walking after the amputation of a limb. Vet. Rec. 146(6), 155–159 (2000)

    Article  Google Scholar 

  24. Korayem, M.; Dehkordi, S.: Derivation of motion equation for mobile manipulator with viscoelastic links and revolute-prismatic flexible joints via recursive gibbs-appell formulations. Robot. Auton. Syst. 103, 175–198 (2018)

    Article  Google Scholar 

  25. Korayem, M.; Shafei, A.; Dehkordi, S.: Systematic modeling of a chain of n-flexible link manipulators connected by revolute-prismatic joints using recursive gibbs-appell formulation. Arch. Appl. Mech. 84(2), 187–206 (2014)

    Article  Google Scholar 

  26. Lacquaniti, F.; Ivanenko, Y.; Zago, M.: Kinematic control of walking. Arch. Ital. Biol. 140(4), 263–272 (2002)

    Google Scholar 

  27. Lauder, G.V.; Anderson, E.J.; Tangorra, J.; Madden, P.G.: Fish biorobotics: kinematics and hydrodynamics of self-propulsion. J. Exp. Biol. 210(16), 2767–2780 (2007)

    Article  Google Scholar 

  28. Lee, J.; Chang, P.; Jamisola, R.S.: Relative impedance control for dual-arm robots performing asymmetric bimanual tasks. Ind. Electron. IEEE Trans. 61(7), 3786–3796 (2014). https://doi.org/10.1109/TIE.2013.2266079.

    Article  Google Scholar 

  29. Lee, J.; Chang, P.H.; Jamisola, R.S.: Relative impedance control for dual-arm robots performing asymmetric bimanual tasks. Ind. Electron. IEEE Trans. 61(7), 3786–3796 (2014)

    Article  Google Scholar 

  30. Lewis, C.: Trajectory generation for two robots cooperating to perform a task. In: Robotics and Automation, IEEE International Conference on, pp. 1626–1631. IEEE (1996)

  31. Lewis, C.; Maciejewski, A.: Trajectory generation for cooperating robots. In: Systems Engineering, IEEE International Conference on, pp. 300–303. IEEE (1990)

  32. Liu, C.; Chen, Q.; Wang, D.: CPG-inspired workspace trajectory generation and adaptive locomotion control for quadruped robots. Syst. Man Cybern. Part B Cybern. IEEE Trans. 41(3), 867–880 (2011)

    Article  Google Scholar 

  33. Pearson, K.; Franklin, R.: Characteristics of leg movements and patterns of coordination in locusts walking on rough terrain. Int. J. Rob. Res. 3(2), 101–112 (1984)

    Article  Google Scholar 

  34. Raibert, M.H.: Trotting, pacing and bounding by a quadruped robot. J. Biomech. 23, 79–98 (1990)

    Article  Google Scholar 

  35. Ritzmann, R.E.; Quinn, R.D.; Watson, J.T.; Zill, S.N.: Insect walking and biorobotics: a relationship with mutual benefits. Bioscience 50(1), 23–33 (2000)

    Article  Google Scholar 

  36. Ryczko, D.; Simon, A.; Ijspeert, A.J.: Walking with salamanders: from molecules to biorobotics. Trends Neurosci. 43(11), 916–930 (2020)

  37. Seipel, J.E.: Analytic-holistic two-segment model of quadruped back-bending in the sagittal plane. In: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Washington, DC, pp. 855–861. ASME (2011)

  38. Semini, C.; Tsagarakis, N.G.; Guglielmino, E.; Focchi, M.; Cannella, F.; Caldwell, D.G.: Design of HyQ -a hydraulically and electrically actuated quadruped robot. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 225(6), 831–849 (2011)

  39. Siciliano, B.; Sciavicco, L.: Robotics: modelling, planning and control. Adv. Textb. Control Signal Process. Springer (2009)

  40. Spong, M.W.; Hutchinson, S.; Vidyasagar, M.: Robot Modeling and Control. Wiley, New York (2006)

    Google Scholar 

  41. Steingrube, S.; Timme, M.; Wörgötter, F.; Manoonpong, P.: Self-organized adaptation of a simple neural circuit enables complex robot behaviour. Nat. Phys. 6(3), 224–230 (2010)

    Article  Google Scholar 

  42. Terzopoulos, D.; Tu, X.; Grzeszczuk, R.: Artificial fishes: autonomous locomotion, perception, behavior, and learning in a simulated physical world. Artif. Life 1(4), 327–351 (1994)

    Article  Google Scholar 

  43. Thomson, T.J.: Three-legged locomotion and the constraints on limb number: why tripeds don‘t have a leg to stand on. BioEssays 41(10), 1900061 (2019)

    Article  Google Scholar 

  44. Tomović, R.; Anastasijević, R.; Vučo, J.; Tepavac, D.: The study of locomotion by finite state models. Biol. Cybern. 63(4), 271–276 (1990)

    Article  Google Scholar 

  45. Tu, X., Terzopoulos, D.: Artificial fishes: physics, locomotion, perception, behavior. In: Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques, pp. 43–50. ACM (1994)

  46. Vereecke, E.E.; D’Août, K.; Aerts, P.: Locomotor versatility in the white-handed gibbon (hylobates lar): a spatiotemporal analysis of the bipedal, tripedal, and quadrupedal gaits. J. Hum. Evol. 50(5), 552–567 (2006)

  47. Vollrath, F.; Krink, T.: Spider webs inspiring soft robotics. J. R. Soc. Interface 17(172), 20200569 (2020)

    Article  Google Scholar 

  48. Wilson, D.M.: Stepping patterns in tarantula spiders. J. Exp. Biol. 47(1), 133–151 (1967)

    Article  Google Scholar 

  49. Yu, X.; He, W.; Li, H.; Sun, J.: Adaptive fuzzy full-state and output-feedback control for uncertain robots with output constraint. IEEE Trans. Syst. Man Cybern. Syst. 1–14 (2020)

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Acknowledgements

The authors would like to thank Carlos Mastalli for his help in the development of the simulation platform.

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Authors and Affiliations

  1. Mechanical, Energy and Industrial Engineering Department, Botswana International University of Science and Technology, Palapye, Botswana

    Rodrigo S. Jamisola Jr.

  2. Electrical and Computer Engineering Department, Florida A&M University - Florida State University, 2525 Pottsdamer Street, Tallahassee, FL, 32310-6046, USA

    Rodney G. Roberts

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Correspondence to Rodrigo S. Jamisola Jr..

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Jamisola, R.S., Roberts, R.G. Bio-Inspired Modular Relative Jacobian for Holistically Controlled Four-Arm Manipulators Using Opposite and Adjacent Dual-Arm Pairs. Arab J Sci Eng 47, 1777–1789 (2022). https://doi.org/10.1007/s13369-021-06046-z

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