Abstract
Human limbs from kinematic point of view can be considered as simple robots’ manipulators. The first part is dedicated to kinematics of human arm modeled as three-link planar manipulation system. For dynamics we propose simple 2-DOF nonlinear model with use of fractional calculus. According to the latest research fractional systems have “natural” damping. This means that even simple model may be able to show some additional properties of the object. Moreover, in presented paper we study the impact of approximation method on solving the inverse kinematics for 3-DOF human limb as well as some parameters of compared methods. This part of research may have some value from visualization point of view. Solving the Inverse Kinematics is the first step in getting full information about the system. The second part of research may be of use in simplifying models. Creating ideologically simple model may let us understand the nature of the world.
The research presented here was supported by Polish Ministry for Science and Higher Education for Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland under internal grant BKM-508/RAU1/2017 (M.N.). Moreover, the research was done as parts of the project funded by the National Science Centre in Poland granted according to decisions DEC-2015/19/D/ST7/03679 (P.J.), DEC-2017/25/B/ST7/02888 (A.Ł.).
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References
Aoun, M., Malti, R., Levron, F., Oustaloup, A.: Numerical simulations of fractional systems: an overview of existing methods and improvements. Nonlinear Dyn. 38(1), 117–131 (2004)
Babiarz, A.: On mathematical modelling of the human arm using switched linear system. In: AIP Conference Proceedings, vol. 1637, pp. 47–54 (2014)
Babiarz, A., Czornik, A., Niezabitowski, M., Zawiski, R.: Mathematical model of a human leg: the switched linear system approach. In: 2015 International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS), pp. 1–8. IEEE (2015)
Babiarz, A., Klamka, J., Zawiski, R., Niezabitowski, M.: An approach to observability analysis and estimation of human arm model. In: 11th IEEE International Conference on Control & Automation (ICCA), pp. 947–952. IEEE (2014)
Barbosa, R.S., Machado, J.A.T.: Implementation of discrete-time fractional-order controllers based on LS approximations. Acta Polytech. Hung. 3(4), 5–22 (2006)
Biess, A., Flash, T., Liebermann, D.G.: Riemannian geometric approach to human arm dynamics, movement optimization, and invariance. Phys. Rev. E 83(3), 031927 (2011)
Cao, J.Y., Cao, B.G.: Design of fractional order controllers based on particle swarm optimization. In: 2006 1ST IEEE Conference on Industrial Electronics and Application, pp. 1–6, May 2006
Cruse, H., Brüwer, M.: The human arm as a redundant manipulator: the control of path and joint angles. Biol. Cybern. 57(1), 137–144 (1987)
David, S., Balthazar, J.M., Julio, B., Oliveira, C.: The fractional-nonlinear robotic manipulator: modeling and dynamic simulations. In: AIP Conference Proceedings, pp. 298–305 (2012)
David, S.A., Valentim, C.A.: Fractional Euler-Lagrange equations applied to oscillatory systems. Mathematics 3(2), 258–272 (2015)
Duarte, F.B.M., Machado, J.A.T.: Pseudoinverse trajectory control of redundant manipulators: a fractional calculus perspective. In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation, ICRA 2002, Washington, DC, USA, 11–15 May 2002, pp. 2406–2411 (2002)
Frolov, A.A., Prokopenko, R., Dufosse, M., Ouezdou, F.B.: Adjustment of the human arm viscoelastic properties to the direction of reaching. Biol. Cybern. 94(2), 97–109 (2006)
Garrappa, R.: A Grünwald-Letnikov scheme for fractional operators of Havriliak-Negami type. Recent Adv. Appl. Model. Simul. 34, 70–76 (2014)
Gomi, H., Osu, R.: Task-dependent viscoelasticity of human multijoint arm and its spatial characteristics for interaction with environments. J. Neurosci. 18(21), 8965–8978 (1998)
da Graça Marcos, M., Duarte, F.B., Machado, J.T.: Fractional dynamics in the trajectory control of redundant manipulators. Commun. Nonlinear Sci. Numer. Simul. 13(9), 1836–1844 (2008)
Van der Helm, F.C., Schouten, A.C., de Vlugt, E., Brouwn, G.G.: Identification of intrinsic and reflexive components of human arm dynamics during postural control. J. Neurosci. Methods 119(1), 1–14 (2002)
Kubo, K., Kanehisa, H., Kawakami, Y., Fukunaga, T.: Influence of static stretching on viscoelastic properties of human tendon structures in vivo. J. Appl. Physiol. 90(2), 520–527 (2001)
Łȩgowski, A.: The global inverse kinematics solution in the adept six 300 manipulator with singularities robustness. In: 2015 20th International Conference on Control Systems and Computer Science, pp. 90–97, May 2015
Mackowski, M., Grzejszczak, T., Łȩgowski, A.: An approach to control of human leg switched dynamics. In: 2015 20th International Conference on Control Systems and Computer Science (CSCS), pp. 133–140, May 2015
Mobasser, F., Hashtrudi-Zaad, K.: A method for online estimation of human arm dynamics. In: 28th Annual International Conference of the IEEE 2006 Engineering in Medicine and Biology Society, EMBS 2006, pp. 2412–2416. IEEE (2006)
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and some of Their Applications, vol. 198. Academic press (1998)
Rosen, J., Perry, J.C., Manning, N., Burns, S., Hannaford, B.: The human arm kinematics and dynamics during daily activities-toward a 7 DOF upper limb powered exoskeleton. In: 2005 Proceedings of 12th International Conference on Advanced Robotics, ICAR 2005, pp. 532–539. IEEE (2005)
Ross, B.: A brief history and exposition of the fundamental theory of fractional calculus. In: Ross, B. (ed.) Fractional Calculus and Its Applications. LNM, vol. 457, pp. 1–36. Springer, Heidelberg (1975). https://doi.org/10.1007/BFb0067096
Sabatier, J., Aoun, M., Oustaloup, A., Grégoire, G., Ragot, F., Roy, P.: Fractional system identification for lead acid battery state of charge estimation. Sign. Process. 86(10), 2645–2657 (2006)
Vinagre, B., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fractional Calc. Appl. Anal. 3(3), 231–248 (2000)
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Grzejszczak, T., Jurgaś, P., Łȩgowski, A., Niezabitowski, M., Orwat, J. (2019). Fractional Calculus in Human Arm Modeling. In: Nguyen, N., Gaol, F., Hong, TP., Trawiński, B. (eds) Intelligent Information and Database Systems. ACIIDS 2019. Lecture Notes in Computer Science(), vol 11432. Springer, Cham. https://doi.org/10.1007/978-3-030-14802-7_54
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