Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Input Decoupling of Lagrangian Systems via Coordinate Transformation: General Characterization and its Application to Soft Robotics (2306.07258v2)

Published 12 Jun 2023 in cs.RO, cs.SY, eess.SY, and physics.class-ph

Abstract: Suitable representations of dynamical systems can simplify their analysis and control. On this line of thought, this paper aims to answer the following question: Can a transformation of the generalized coordinates under which the actuators directly perform work on a subset of the configuration variables be found? Not only we show that the answer to this question is yes, but we also provide necessary and sufficient conditions. More specifically, we look for a representation of the configuration space such that the right-hand side of the dynamics in Euler-Lagrange form becomes $[\boldsymbol{I} \; \boldsymbol{O}]{T}\boldsymbol{u}$, being $u$ the system input. We identify a class of systems, called collocated, for which this problem is solvable. Under mild conditions on the input matrix, a simple test is presented to verify whether a system is collocated or not. By exploiting power invariance, we provide necessary and sufficient conditions that a change of coordinates decouples the input channels if and only if the dynamics is collocated. In addition, we use the collocated form to derive novel controllers for damped underactuated mechanical systems. To demonstrate the theoretical findings, we consider several Lagrangian systems with a focus on continuum soft robots.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (36)
  1. G. Chen and F. L. Lewis, “Distributed adaptive tracking control for synchronization of unknown networked Lagrangian systems,” IEEE Trans. on Systems, Man, and Cybernetics, vol. 41, no. 3, pp. 805–816, 2010.
  2. A. Loría, “Observers are unnecessary for output-feedback control of Lagrangian systems,” IEEE Trans. on Automatic Control, vol. 61, no. 4, pp. 905–920, 2015.
  3. M.-F. Ge, Z.-W. Liu, G. Wen, X. Yu, and T. Huang, “Hierarchical controller-estimator for coordination of networked Euler–Lagrange systems,” IEEE Trans. on Cybernetics, vol. 50, no. 6, pp. 2450–2461, 2019.
  4. Y. Sun, D. Dong, H. Qin, and W. Wang, “Distributed tracking control for multiple Euler–Lagrange systems with communication delays and input saturation,” ISA Trans., vol. 96, pp. 245–254, 2020.
  5. A. M. Giordano, C. Ott, and A. Albu-Schäffer, “Coordinated control of spacecraft’s attitude and end-effector for space robots,” IEEE Robotics and Automation Lett., vol. 4, no. 2, pp. 2108–2115, 2019.
  6. B. Yi, R. Ortega, I. R. Manchester, and H. Siguerdidjane, “Path following of a class of underactuated mechanical systems via immersion and invariance-based orbital stabilization,” Int. J. of Robust and Nonlinear Control, vol. 30, no. 18, pp. 8521–8544, 2020.
  7. R. Mengacci, F. Angelini, M. G. Catalano, G. Grioli, A. Bicchi, and M. Garabini, “On the motion/stiffness decoupling property of articulated soft robots with application to model-free torque iterative learning control,” Int. J. of Robotics Research, vol. 40, no. 1, pp. 348–374, 2021.
  8. M. Keppler, C. Ott, and A. Albu-Schäffer, “From underactuation to quasi-full actuation: Aiming at a unifying control framework for articulated soft robots,” Int. J. of Robust and Nonlinear Control, vol. 32, no. 9, pp. 5453–5484, 2022.
  9. P. Borja, A. Dabiri, and C. Della Santina, “Energy-based shape regulation of soft robots with unactuated dynamics dominated by elasticity,” in Proc. 5th IEEE Int. Conf. on Soft Robotics, 2022, pp. 396–402.
  10. W. Zhang, Y. Wang, Y. Liu, and W. Zhang, “Multivariable disturbance observer-based H2subscript𝐻2{H}_{2}italic_H start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT analytical decoupling control design for multivariable systems,” Int. J. of Systems Science, vol. 47, no. 1, pp. 179–193, 2016.
  11. A. J. Krener, “On the equivalence of control systems and the linearization of nonlinear systems,” SIAM J. on Control, vol. 11, no. 4, pp. 670–676, 1973.
  12. R. W. Brockett, “Feedback invariants for nonlinear systems,” IFAC Proceedings, vol. 11, no. 1, pp. 1115–1120, 1978.
  13. A. Isidori, A. Krener, C. Gori-Giorgi, and S. Monaco, “Nonlinear decoupling via feedback: A differential geometric approach,” IEEE Trans. on Automatic Control, vol. 26, no. 2, pp. 331–345, 1981.
  14. J. Wu and Y. Lu, “Adaptive backstepping sliding mode control for boost converter with constant power load,” IEEE Access, vol. 7, pp. 50 797–50 807, 2019.
  15. A. Lazrak and A. Abbou, “An improved control strategy for DFIG wind turbine to ride-through voltage dips,” in Proc. 6th Int. Renewable and Sustainable Energy Conf., 2018, pp. 1–6.
  16. R. N. Mishra and K. B. Mohanty, “Design and implementation of a feedback linearization controlled IM drive via simplified neuro-fuzzy approach,” IETE J. of Research, vol. 64, no. 2, pp. 209–230, 2018.
  17. X. Ding, J. Liang, S. Lu, F. Kong, and Y. Chen, “Robust back-stepping sliding mode control for LCL-type grid-connected inverters in weak grids,” J. of Power Electronics, vol. 23, pp. 758–768, 2022.
  18. S. Skogestad, C. Zotică, and N. Alsop, “Transformed inputs for linearization, decoupling and feedforward control,” J. of Process Control, vol. 122, pp. 113–133, 2023.
  19. E. Franco and A. Garriga-Casanovas, “Energy-shaping control of soft continuum manipulators with in-plane disturbances,” Int. J. of Robotics Research, vol. 40, no. 1, pp. 236–255, 2021.
  20. B. Caasenbrood, A. Pogromsky, and H. Nijmeijer, “Energy-based control for soft manipulators using Cosserat-beam models,” in Proc. 18th Int. Conf. on Informatics in Control, Automation and Robotics, 2021, pp. 311–319.
  21. P. Pustina, C. Della Santina, and A. De Luca, “Feedback regulation of elastically decoupled underactuated soft robots,” IEEE Robotics and Automation Lett., vol. 7, no. 2, pp. 4512–4519, 2022.
  22. P. Pustina, P. Borja, C. Della Santina, and A. De Luca, “P-satI-D shape regulation of soft robots,” IEEE Robotics and Automation Lett., vol. 8, no. 1, pp. 1–8, 2023.
  23. G. Soleti, J. Prechtl, P. R. Massenio, M. Baltes, and G. Rizzello, “Energy based control of a bi-stable and underactuated soft robotic system based on dielectric elastomer actuators,” in Proc. 22th IFAC World Congr., 2023.
  24. A. De Luca, “Flexible robots,” in Encyclopedia of Systems and Control, 2nd ed., J. Baillieul and T. Samad, Eds.   Springer, 2021, pp. 814–822.
  25. A. Tsolakis and T. Keviczky, “Distributed IDA-PBC for a class of nonholonomic mechanical systems,” IFAC-PapersOnLine, vol. 54, no. 14, pp. 275–280, 2021.
  26. C. Della Santina, A. Bicchi, and D. Rus, “On an improved state parametrization for soft robots with piecewise constant curvature and its use in model based control,” IEEE Robotics and Automation Lett., vol. 5, no. 2, pp. 1001–1008, 2020.
  27. G. Palli, G. Borghesan, and C. Melchiorri, “Modeling, identification, and control of tendon-based actuation systems,” IEEE Trans. on Robotics, vol. 28, no. 2, pp. 277–290, 2011.
  28. F. Renda, C. Armanini, V. Lebastard, F. Candelier, and F. Boyer, “A geometric variable-strain approach for static modeling of soft manipulators with tendon and fluidic actuation,” IEEE Robotics and Automation Lett., vol. 5, no. 3, pp. 4006–4013, 2020.
  29. F. Boyer, V. Lebastard, F. Candelier, and F. Renda, “Dynamics of continuum and soft robots: A strain parameterization based approach,” IEEE Trans. on Robotics, vol. 37, no. 3, pp. 847–863, 2020.
  30. C. Armanini, F. Boyer, A. T. Mathew, C. Duriez, and F. Renda, “Soft robots modeling: A structured overview,” IEEE Trans. on Robotics, vol. 39, no. 3, pp. 1728–1748, 2023.
  31. F. Renda, C. Armanini, A. Mathew, and F. Boyer, “Geometrically-exact inverse kinematic control of soft manipulators with general threadlike actuators’ routing,” IEEE Robotics and Automation Lett., vol. 7, no. 3, pp. 7311–7318, 2022.
  32. B. A. Jones and I. D. Walker, “Kinematics for multisection continuum robots,” IEEE Trans. on Robotics, vol. 22, no. 1, pp. 43–55, 2006.
  33. D. Braganza, D. M. Dawson, I. D. Walker, and N. Nath, “A neural network controller for continuum robots,” IEEE Trans. on Robotics, vol. 23, no. 6, pp. 1270–1277, 2007.
  34. V. Falkenhahn, A. Hildebrandt, R. Neumann, and O. Sawodny, “Dynamic control of the bionic handling assistant,” IEEE/ASME Trans. on Mechatronics, vol. 22, no. 1, pp. 6–17, 2016.
  35. M. Li, R. Kang, S. Geng, and E. Guglielmino, “Design and control of a tendon-driven continuum robot,” Trans. of the Institute of Measurement and Control, vol. 40, no. 11, pp. 3263–3272, 2018.
  36. C. Della Santina, C. Duriez, and D. Rus, “Model based control of soft robots: A survey of the state of the art and open challenges,” IEEE Control Systems Mag., vol. 43, no. 3, pp. 30–65, 2023.
Citations (4)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now