Soil searching by an artificial root. (English) Zbl 1525.35215
Summary: We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a “breakdown configuration” is reached. Some numerical simulations are performed to test the effectiveness of our feedback control algorithm.
MSC:
| 35Q70 | PDEs in connection with mechanics of particles and systems of particles |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 70B15 | Kinematics of mechanisms and robots |
| 92C80 | Plant biology |
| 35R09 | Integro-partial differential equations |
| 49M41 | PDE constrained optimization (numerical aspects) |
Keywords:
evolution equations; integro-differential equations; one-sided constraints; optimality conditions; biological inspiration; plant-inspired robotReferences:
| [1] | F. Ancona, A. Bressan, O. Glass, and W. Shen, Feedback stabilization of stem growth, J. Dyn. Differential Equations, 31 (2017), pp. 1079-1106, https://doi.org/10.1007/s10884-017-9633-z. · Zbl 1420.35036 |
| [2] | N. Bessonov and V. Volpert, On a model of plant growth, in Patterns and Waves, A. Abramian, S. Vakulenko, and V. Volpert, eds., AkademPrint, St. Petersburg, 2003, pp. 323-337. |
| [3] | N. Bessonov and V. Volpert, Dynamic models of plant growth, in Mathematics and Mathematical Modelling, Publibook, Paris, 2006. · Zbl 1151.92021 |
| [4] | G. Bianchi, A. Agoni, and S. Cinquemani, Design of a pneumatic growing robot inspired to plants’ roots, Proceedings of the ASME 2021 Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2021, V001T01A006, https://doi.org/10.1115/SMASIS2021-67686. |
| [5] | L. H. Blumenschein, M. M. Coad, D. A. Haggerty, A. M. Okamura, and E. W. Hawkes, Design, modeling, control, and application of everting vine robots, Front. Robotics and AI, 7 (2020), p. 153, https://doi.org/10.3389/frobt.2020.548266. |
| [6] | A. Bressan and M. Palladino, Well-posedness of a model for the growth of tree stems and vines, Discrete Contin. Dyn. Syst., 38 (2018), pp. 2047-2064, https://doi.org/10.3934/dcds.2018083. · Zbl 1397.49028 |
| [7] | A. Bressan, M. Palladino, and W. Shen, Growth models for tree stems and vines, J. Differential Equations, 263 (2017), pp. 2280-2316, https://doi.org/10.1016/j.jde.2017.03.047. · Zbl 1372.35305 |
| [8] | J. Burgner-Kahrs, D. C. Rucker, and H. Choset, Continuum robots for medical applications: A survey, IEEE Trans. Robotics, 31 (2015), pp. 1261-1280. |
| [9] | G. Dal Maso, An Introduction to \(\Gamma \)-Convergence, Progress in Nonlinear Differential Equations and their Applications, vol. 8, Birkhäuser, Boston, 1993, https://doi.org/10.1007/978-1-4612-0327-8. · Zbl 0816.49001 |
| [10] | G. Dal Maso, A. DeSimone, and M. G. Mora, Quasistatic evolution problems for linearly elastic-perfectly plastic materials, Arch. Ration. Mech. Anal., 180 (2006), pp. 237-291, https://doi.org/10.1007/s00205-005-0407-0. · Zbl 1093.74007 |
| [11] | E. Del Dottore, A. Mondini, A. Sadeghi, V. Mattioli, and B. Mazzolai, An efficient soil penetration strategy for explorative robots inspired by plant root circumnutation movements, Bioinspir. Biomim., 13 (2018), 015003, https://doi.org/10.1088/1748-3190/aa9998. |
| [12] | A. R. Dexter, Mechanics of root growth, Plant and Soil, 98 (1987), pp. 303-312, https://doi.org/10.1007/BF02378351. |
| [13] | M. Fakih, J.-Y. Delenne, F. Radjai, and T. Fourcaud, Root growth and force chains in a granular soil, Phys. Rev. E, 99 (2019), 042903, https://doi.org/10.1103/PhysRevE.99.042903. |
| [14] | A. Goriely, The Mathematics and Mechanics of Biological Growth, Springer, New York, 2017. · Zbl 1398.92003 |
| [15] | J. D. Greer, L. H. Blumenschein, A. M. Okamura, and E. W. Hawkes, Obstacle-aided navigation of a soft growing robot, in Proceedings of the 2018 IEEE International Conference on Robotics and Automation (ICRA), Brisbane, Australia, 2018, pp. 4165-4172, https://doi.org/10.1109/ICRA.2018.8460777. |
| [16] | J. D. Greer, T. K. Morimoto, A. M. Okamura, and E. W. Hawkes, A soft, steerable continuum robot that grows via tip extension, Soft Robotics, 6 (2019), pp. 95-108, https://doi.org/10.1089/soro.2018.0034. |
| [17] | W. E. Heap, N. D. Naclerio, M. M. Coad, S.-G. Jeong, and E. W. Hawkes, Soft retraction device and internal camera mount for everting vine robots, in Proceedings of the 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Prague, Czech Republic, 2021, pp. 4982-4988, https://doi.org/10.1109/IROS51168.2021.9636697. |
| [18] | O. Leyser and S. Day, Mechanisms in Plant Development, Blackwell Publishing, Oxford, 2003. |
| [19] | A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. Partial Differential Equations, 22 (2005), pp. 73-99, https://doi.org/10.1007/s00526-004-0267-8. · Zbl 1161.74387 |
| [20] | R. Pfeifer, M. Lungarella, and F. Iida, Self-organization, embodiment, and biologically inspired robotics, Science, 318 (2007), 10881093. |
| [21] | A. Sadeghi, A. Mondini, and B. Mazzolai, Toward self-growing soft Robots inspired by plant roots and based on additive manufacturing technologies, Soft Robotics, 4 (2017), pp. 211-223, https://doi.org/10.1089/soro.2016.0080. |
| [22] | A. Sadeghi, A. Tonazzini, L. Popova, and B. Mazzolai, A novel growing device inspired by plant root soil penetration behaviors, PLOS ONE, 9 (2014), pp. 1-10, https://doi.org/10.1371/journal.pone.0090139. |
| [23] | F. Tedone, E. Del Dottore, M. Palladino, B. Mazzolai, and P. Marcati, Optimal control of plant root tip dynamics in soil, Bioinspir. Biomim., 15 (2020), 056006, https://doi.org/10.1088/1748-3190/ab99a15. |
| [24] | I. D. Walker, Robot strings: Long, thin continuum robots, in Proceedings of the 2013 IEEE Aerospace Conference, Big Sky, Montana, 2013, pp. 1-12, https://doi.org/10.1109/AERO.2013.6496902. |
| [25] | C. Watson, R. Obregon, and T. K. Morimoto, Closed-loop position control for growing robots via online jacobian corrections, IEEE Robotics and Automat. Lett., 6 (2021), pp. 6820-6827, https://doi.org/10.1109/LRA.2021.3095625. |
| [26] | M. B. Wooten and I. D. Walker, Vine-inspired continuum tendril robots and circumnutations, Robotics, 7 (2018), 58, https://doi.org/10.3390/robotics7030058, https://www.mdpi.com/2218-6581/7/3/58. |
| [27] | T. Yan, S. Teshigawara, and H. H. Asada, Design of a growing robot inspired by plant growth, in Proceedings of the 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Macau, China, 2019, pp. 8006-8011, https://doi.org/10.1109/IROS40897.2019.8968200. |
| [28] | N. Yanagisawa, N. Sugimoto, H. Arata, T. Higashiyama, and Y. Sato, Capability of tip-growing plant cells to penetrate into extremely narrow gaps, Sci. Rep., 7 (2017), 1403. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
