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Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Articulated Soft Robots

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Experimental Robotics (ISER 2020)

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Abstract

Thanks to their body elasticity, articulated soft robots promise to produce effective and robust oscillations with low energy consumption. This in turn is an important feature which can be exploited in the execution of many tasks, as for example locomotion. Yet, an established theory and general techniques allowing to excite and sustain these nonlinear oscillations are still lacking. A possible solution to this problem comes from nonlinear modal theory, which defines curved extensions of linear Eigenspaces called Eigenmanifolds. Stabilizing these surfaces is equivalent to exciting regular hyper-efficient oscillations in the robotic system. This paper proposes a first experimental validation of the Eigenmanifold stabilization technique. It also proposes a simple yet effective means of injecting energy into the system, so to sustain the oscillations in presence of damping. We consider as experimental setups a single robotic leg, and a full soft quadruped. Preliminary locomotion results are provided with both systems.

This work is supported by the European Union ERC project 835284 M-Runners.

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Notes

  1. 1.

    Different choices of the physical parameters (e.g. the spring stiffnesses) could have produced a convex oscillation.

References

  1. Albu-Schaeffer, A., Della Santina, C.: A review on nonlinear modes in conservative mechanical systems. Annu. Rev. Control 50, 49–71 (2020)

    Article  MathSciNet  Google Scholar 

  2. Albu-Schaeffer, A., Eiberger, O., Grebenstein, M., Haddadin, S., Ott, C., Wimboeck, T., Wolf, S., Hirzinger, G.: Soft robotics. IEEE Robot. Autom. Mag. 15(3), 20–30 (2008)

    Article  Google Scholar 

  3. Albu-Schaeffer, A., Lakatos, D., Stramigioli, S.: One-dimensional solution families of nonlinear systems characterized by scalar functions on Riemannian manifolds. arXiv preprint arXiv:1911.01882 (2019)

  4. Åström, K.J., Furuta, K.: Swinging up a pendulum by energy control. Automatica 36(2), 287–295 (2000)

    Article  MathSciNet  Google Scholar 

  5. Buondonno, G., De Luca, A.: A recursive Newton-Euler algorithm for robots with elastic joints and its application to control. In: 2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 5526–5532. IEEE (2015)

    Google Scholar 

  6. Calzolari, D., Della Santina, C., Albu-Schäffer, A.: PD-like regulation of mechanical systems with prescribed bounds of exponential stability: the point-to-point case. IEEE Control Syst. Lett., 1 (2021). https://doi.org/10.1109/LCSYS.2020.3046538

  7. Della Santina, C., Albu Schaeffer, A.: Exciting efficient oscillations in nonlinear mechanical systems through Eigenmanifold stabilization. IEEE Control Syst. Lett. 5(6), 1916–1921 (2021). https://doi.org/10.1109/LCSYS.2020.3048228

  8. Della Santina, C., Bianchi, M., Grioli, G., Angelini, F., Catalano, M.G., Garabini, M., Bicchi, A.: Controlling soft robots: balancing feedback and feedforward elements. IEEE Robot. Autom. Mag. 24, 75–83 (2017)

    Article  Google Scholar 

  9. Della Santina, C., Catalano, M.G., Bicchi, A.: Soft Robots, pp. 1–14. Springer, Heidelberg (2020). https://doi.org/10.1007/978-3-642-41610-1_146-1

  10. Garofalo, G., Ott, C.: Passive energy-based control via energy tanks and release valve for limit cycle and compliance control. IFAC-PapersOnLine 51(22), 73–78 (2018)

    Article  Google Scholar 

  11. Hutter, M., Remy, C.D., Höpflinger, M.A., Siegwart, R.: Slip running with an articulated robotic leg. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4934–4939. IEEE (2010)

    Google Scholar 

  12. Lakatos, D., Friedl, W., Albu-Schäffer, A.: Eigenmodes of nonlinear dynamics: definition, existence, and embodiment into legged robots with elastic elements. IEEE Robot. Autom. Lett. 2(2), 1062–1069 (2017)

    Google Scholar 

  13. Seidel, D., Hermann, M., Gumpert, T., Loeffl, F.C., Albu-Schäffer, A.: Using elastically actuated legged robots in rough terrain: experiments with DLR quadruped bert. In: 2020 IEEE Aerospace Conference, pp. 1–8. IEEE (2020)

    Google Scholar 

  14. Zhakatayev, A., Rubagotti, M., Varol, H.A.: Time-optimal control of variable-stiffness-actuated systems. IEEE/ASME Trans. Mechatron. 22(3), 1247–1258 (2017)

    Article  Google Scholar 

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Della Santina, C., Lakatos, D., Bicchi, A., Albu-Schaeffer, A. (2021). Using Nonlinear Normal Modes for Execution of Efficient Cyclic Motions in Articulated Soft Robots. In: Siciliano, B., Laschi, C., Khatib, O. (eds) Experimental Robotics. ISER 2020. Springer Proceedings in Advanced Robotics, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-71151-1_50

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