FABRIK-based comparison of the inverse kinematic algorithms operation results for multi-section continuum robots

Flexible bend link robots, also called continuum or soft robots, are an urgent research topic. Various algorithms were developed to solve the inverse problem of the multi-section continuum robot kinematics including those based on the FABRIK (Forward And Backward Reaching Inverse Kinematics) algorithm. This algorithm was originally created to solve the inverse kinematics problem of robots consisting of rigid links connected by spherical joints and could also be used in regard to continuum robots, which are arcs smoothly transiting into each other. To work with the FABRIK algorithm, each bend section is approximated to the virtual rigid link. Two known approaches are known to solve the inverse kinematics problem: the first is based on constructing the tangents (bend section transformation into two tangents), and the second is based on constructing the chords (bend section reduction to a chord). Both approaches demonstrate good results in solving the inverse kinematics problem compared to algorithms based on the Jacobian matrix construction. However, scientific literature misses data on comparing methods that use the FABRIK algorithm. In this regard, two approaches were compared to solve the inverse kinematics problem based on implementing the FABRIK algorithm. Results of numerical experiments with three-, five- and ten-sectional robots are presented. Characteristics of the algorithms and boundaries of their application were determined.

References

[1] Axinte D., Dong X., Palmer D. et al. MiRoR — miniaturized robotic systems for holistic in-situ repair and maintenance works in restrained and hazardous environments. IEEE/ASME Trans. Mechatronics, 2018, vol. 23, no. 2, pp. 978–981, doi: https://doi.org/10.1109/TMECH.2018.2800285

[2] Dong X., Axinte D., Palmer D. et al. Development of a slender continuum robotic system for on-wing inspection/repair of gas turbine engines. Robot. Comput. Integr. Manuf., 2017, vol. 44, pp. 218–229, doi: https://doi.org/10.1016/j.rcim.2016.09.004

[3] Buckingham R., Graham A. Nuclear snake-arm robots. Ind. Rob., 2012, vol. 39, no. 1, pp. 6–11, doi: https://doi.org/10.1108/01439911211192448

[4] Nahar D., Yanik P.M., Walker I.D. Robot tendrils: long, thin continuum robots for inspection in space operations. IEEE Aerosp. Conf., 2017, doi: https://doi.org/10.1109/AERO.2017.7943940

[5] Liljeback P., Mills R. Eelume: a flexible and subsea resident IMR vehicle. OCEANS 2017 — Aberdeen, 2017, doi: https://doi.org/10.1109/OCEANSE.2017.8084826

[6] Burgner-Kahrs J., Rucker D.C., Choset H. Continuum robots for medical applications: a survey. IEEE Trans. Robot., 2015, vol. 31, no. 6, pp. 1261–1280, doi: https://doi.org/10.1109/TRO.2015.2489500

[7] Zhang Y., Lu M. A review of recent advancements in soft and flexible robots for medical applications. Int. J. Med. Robot. Comput. Assist. Surg., 2020, vol. 16, no. 3, art. e2096, doi: https://doi.org/10.1002/rcs.2096

[8] Shchelkunov E.B., Vinogradov S.V., Shchelkunova M.E. Soft robots. Uchenye zapiski Komsomol

[9] Dautov A.M., Kopets E.E., Karimov A.I. et al. [Development of a radio-controlled tentacle robot]. Mezhd. nauch. konf. po problemam upravleniya v tekhnicheskikh sistemakh. T. 1 [Int. Conf. on Problems of Control and Management in Technical Systems. Vol. 1]. Sankt-Petersburg, LETI Publ., 2021, pp. 337–340. (In Russ.).

[10] Lai J., Huang K., Chu H.K. A learning-based inverse kinematics solver for a multi-segment continuum robot in robot-independent mapping. IEEE ROBIO, 2019, pp. 576–582, doi: https://doi.org/10.1109/ROBIO49542.2019.8961669

[11] Melingui A., Merzouki R., Mbede J.B. et al. Neural Networks based approach for inverse kinematic modeling of a Compact Bionic Handling Assistant trunk. IEEE 23rd ISIE, 2014, pp. 1239–1244, doi: https://doi.org/10.1109/ISIE.2014.6864791

[12] Amouri A., Mahfoudi C., Zaatri A. et al. A metaheuristic approach to solve inverse kinematics of continuum manipulators. P. I. Mech. Eng. I-J Sys., 2017, vol. 231, no. 5, pp. 380–394, doi: http://dx.doi.org/10.1177/0959651817700779

[13] Jones B.A., Walker I.D. Kinematics for multisection continuum robots. IEEE Trans. Robot., 2006, vol. 22, no. 1, pp. 43–55, doi: https://doi.org/10.1109/TRO.2005.861458

[14] Mahl T., Hildebrandt A., Sawodny O. A variable curvature continuum kinematics for kinematic control of the bionic handling assistant. IEEE Trans. Robot., 2014, vol. 30, no. 4, pp. 935–949, doi: https://doi.org/10.1109/TRO.2014.2314777

[15] Zhang W., Yang Z., Dong T., Xu K. FABRIKc: an efficient iterative inverse kinematics solver for continuum robots. IEEE/ASME AIM, 2018, pp. 346–352, doi: https://doi.org/10.1109/AIM.2018.8452693

[16] Kolpashchikov D.Yu., Gerget O.M. Comparison of inverse kinematics algorithms for multi-section continuum robots. Mekhatronika, avtomatizatsiya, upravlenie, 2021, vol. 22, no. 8, pp. 420–424, doi: https://doi.org/10.17587/mau.22.420-424 (In Russ.).

[17] Webster R.J., Jones B.A. Design and kinematic modeling of constant curvature continuum robots: a review. Int. J. Rob. Res., 2010, vol. 29, no. 13, pp. 1661–1683, doi: http://dx.doi.org/10.1177/0278364910368147

[18] Aristidou A., Lasenby J. FABRIK: a fast, iterative solver for the Inverse Kinematics problem. Graph. Models, 2011, vol. 73, no. 5, pp. 243–260, doi: https://doi.org/10.1016/j.gmod.2011.05.003