Dynamic Analysis of Lower Limb Exoskeleton Motion and Control Using Differential Transform Method

Abstract:

In this study, the nonlinear dynamic analysis of the motion and control of the lower limb exoskeleton using differential transform method is presented. Devices for medical processes are continuously undergoing improvement such as enhancing and assisting automatic therapies with flexible and configurable programs for treating people with partial disability in lower limbs as applied in lower-limb exoskeleton. The configurable programs in this exoskeleton can be applied to observe and control the motion of the exoskeleton for effective physiotherapy and reduced rehabilitation time for patients with such disability. Hence, a two degree of freedom nonlinear dynamic model for the motion and control of the lower limb exoskeletons was developed for two links. The nonlinear dynamic models are solved by applying the differential transform method (DTM) and verified with the forth order Runge-Kutta numerical method (RK4). The effects of the applied torque on the two links are investigated and it is observed that Link 1 has large negative deflection amplitude that drives link 2 towards the opposite positive direction. An increase in the applied torque resulted in increase in the amplitude of the system for all initial condition considered. This in turns increases the nonlinear dynamic behavior of link 2 due to its lower mass value. The speed of both links dampens out over the history due to the presence of damping term. At equilibrium, both links are in phase and have the same amplitude over the time history. This study provides an analytical tool for observing and controlling the motions of the lower limb exoskeleton and for improving the designs of the medical device.

• Periodical: Journal of Biomimetics, Biomaterials and Biomedical Engineering (Volume 51)
• Pages: 77-94
• DOI: https://doi.org/10.4028/www.scientific.net/JBBBE.51.77
• Online since: June 2021
• Authors: Olurotimi A. Adeleye*, Tamunomiete S. Ekine, Ahmed A. Yinusa
• Keywords: Control, Differential Transform Method, Dynamic Model, Lower Limbs Exoskeleton, Motion, Runge-Kutta Method

References

[1] X. Jin, and S. K. Agrawal, Exploring Laparoscopic Surgery Training with Cable-Driven ARm Exoskeleton (CAREX-M), in IEEE International Conference on Rehabilitation Robotics (ICORR). 2015: Singapore.

DOI: 10.1109/icorr.2015.7281247

[2] B. Misgeld, T. Schauer, O. Simanski, M. Hessinger, R. Müller, R. Werthschützky, and P.P. Pott, Tool Position Control of an Upper Limb Exoskeleton for Robot-Assisted Surgery. IFAC-PapersOnLine 2015. 48: p.195–200.

DOI: 10.1016/j.ifacol.2015.10.138

[3] S. K. Banala, S. K. Agrawal, and J. P. Scholz, Active Leg Exoskeleton (ALEX) for Gait Rehabilitation of Motor-Impaired Patients, in IEEE 10th International Conference on Rehabilitation Robotics (ICORR 2007). 2007: Noordwijk, The Netherlands.

DOI: 10.1109/icorr.2007.4428456

[4] A. Crema, M. Mancuso, A. Frisoli, F. Salsedo, F. Raschella, and S. Micera, A Hybrid NMES-Exoskeleton for Real Objects Interaction, in 7th International IEEE/EMBS Conference on Neural Engineering (NER). 2015: Montpellier, France.

DOI: 10.1109/ner.2015.7146710

[5] H. Kim, L. M. Miller, I. Fedulow, M. Simkins, G. M. Abrams, N. Byl, and J. Rosen, Kinematic Data Analysis for Post-Stroke Patients Following Bilateral versus Unilateral Rehabilitation with an Upper Limb Wearable Robotic System. IEEE Trans. Neural Syst. Rehabil. Eng, 2013. 21: p.153–164.

DOI: 10.1109/tnsre.2012.2207462

[6] H. Cao, Z. Ling, J. Zhu, Y. Wang, and W. Wang, Design Frame of a Leg Exoskeleton for Load-Carrying Augmentation, in IEEE International Conference on Robotics and Biomimetics (ROBIO). 2009: Guilin, China.

DOI: 10.1109/robio.2009.5420684

[7] B. S. Rupal, S. Rafique, A. Singla, E. Singla, M. Isaksson, and G. S. Virk, Lower-limb exoskeletons: Research trends and regulatory guidelines in medical and non-medical applications. International Journal of Advanced Robotic Systems, 2017. November-December 2017: pp.1-27.

DOI: 10.1177/1729881417743554

[8] H. Lee, J. Kim, and T. Kim, A Robot Teaching Framework for a Redundant Dual Arm Manipulator with Teleoperation from Exoskeleton Motion Data, in IEEE-RAS International Conference on Humanoid Robots. 2014: Madrid, Spain.

DOI: 10.1109/humanoids.2014.7041495

[9] G. Schultz, and K. Mombaur, Modeling and Optimal Control of Human-Like Running. IEEE/ASME Trans. Mechatron, 2010. 15(5): p.783–792.

DOI: 10.1109/tmech.2009.2035112

[10] K. B. Bellenfant, G. L. Robbins, R. R. Rogers, T. J. Kopec, and C. G. Ballmann, Effects of Dominant and Nondominant Limb Immobilization on Muscle Activation and Physical Demand during Ambulation with Axillary Crutches. J Funct Morphol Kinesiol. 2021; 6(16): pp.1-12.

DOI: 10.3390/jfmk6010016

[11] B. Zhang, S. Li, and Y. Zhang, Evaluation of Dynamic Posture Control when Wearing High-Heeled Shoes Using Star Ecursion Balance Test, Physical Activity and Health, 2017. 1(1): pp.1-7.

DOI: 10.5334/paah.1

[12] W. Tsang, K. Singh, and E. Fiume, Helping hand: an anatomically accurate inverse dynamics solution for unconstrained hand motion, in ACM SIGGRAPH/Eurographics symposium on Computer animation. 2005. pp.319-328.

DOI: 10.1145/1073368.1073414

[13] I. Albrecht, J. Haber, and H. Seidel, Construction and animation of anatomically based human hand models, in ACM SIGGRAPH/Eurographics symposium on Computer animation (SCA'03). 2003. pp.98-109.

[14] F. Dong, G. J. Clapworthy, and M. A. Krokos, J. Yao, An Anatomy Based Approach to Hum a Muscle Modeling and Deformation. IEEE Transaction Visualization and Computer Graphics, 2002. 8(2): pp.154-170.

DOI: 10.1109/2945.998668

[15] C. Antfolk, M. D'Alonzo, B. Rosén, G. Lundborg, F. Sebelius, and C. Cipriani, Sensory Feedback in Upper Limb Prosthetics. Expert Review of Medical Devices, 2013. 10(1): pp.45-54.

DOI: 10.1586/erd.12.68

[16] F. C. Anderson, and M. G. Pandy, Dynamic Optimization of Human Walking. ASME J. Biomech. Eng., 2001. 123(5): p.381–390.

[17] R. D. Crowninshield, and R. Brand, A Physiologically Based Criterion of Muscle Force Prediction in Locomotion. J. Biomech., 1981. 14(11): p.793–801.

DOI: 10.1016/0021-9290(81)90035-x

[18] D. Farina, and O. Aszmann, Bionic limbs: clinical reality and academic promises. Sci. Transl. Med, (2014).

DOI: 10.1126/scitranslmed.3010453

[19] S. Safavi, and A. S. Ghafari, A. Meghdari, Design of an Optimum Torque Actuator for Augmenting Lower Extremity Exoskeletons in Biomechanical Framework, in IEEE International Conference on Robotics and Biomimetics (ROBIO). 2011: Karon Beach, Phuket, Thailand.

DOI: 10.1109/robio.2011.6181581

[20] P. Surachai, Design and simulation of leg-exoskeleton suit for rehabilitation. Glob. J. Med. Res, 2012. 12: pp.1-8.

[21] E. K. Chadwick, D. Blana, A. J. van den Bogert, and R. F. Kirsch, A Real-Time, 3-D Musculoskeletal Model for Dynamic Simulation of Arm Movement. Biomedical Engineering IEEE Transactions, 2009. 56(4): pp.941-948.

DOI: 10.1109/tbme.2008.2005946

[22] F. Ferrati, R. Bortoletto, and E. Pagello, Virtual Modelling of a Real Exoskeleton Constrained to a Human Musculoskeletal Model, in Second International Conference Biomimetic and Biohybrid Systems, Living Machines 2013, Springer: London, UK.

DOI: 10.1007/978-3-642-39802-5_9

[23] M. Pan, D. Zhang, and Z. Gao, Novel Design of a Three Degrees of Freedom Hip Exoskeleton Based on Biomimetic Parallel Structure, in IEEE International Conference on Computer Science and Automation Engineering (CSAE). 2011: Shanghai, China.

DOI: 10.1109/csae.2011.5953292

[24] A. Singla, S. Dhand, and G. S. Virk, Mathematical modelling of a hand crank generator for powering lower-limb exoskeletons. Pespect. Sci., 2016. 8: p.561–563.

DOI: 10.1016/j.pisc.2016.06.020

[25] R. Lu, Z. Li, and C-Y. Su, Development and Learning Control of a Human limb with a Rehabilitation Exoskeleton. IEEE Trans. Ind. Electron, 2014. 61: p.3776–3785.

DOI: 10.1109/tie.2013.2275903

[26] C. C. Velandia, D. A. Tibaduiza, and M. A. Vejar, Proposal of Novel Model for a 2 DOF Exoskeleton for Lower-Limb Rehabilitation. Robotic, MDPI, 2017. 6(20): pp.1-25.

DOI: 10.3390/robotics6030020

[27] J. K. Zhou, Differential Transform Method and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan, China, (1986).

[28] M. M. Rashidi, O. A. Bég, and N. Rahimzadeh, A Generalized Differential Transform Method For Combined Free And Forced Convection Flow About Inclined Surfaces In Porous Media. Chemical Engineering Communications, 2012. 199(2): pp.257-282.

DOI: 10.1080/00986445.2011.586757

[29] A. Aziz, M. Torabi, and K. Zhang, Convective–radiative radial fins with convective base heating and convective–radiative tip cooling: Homogeneous and functionally graded materials. Energy Conversion and Management 2013. 74: pp.366-376.

DOI: 10.1016/j.enconman.2013.05.034

[30] Kuo, B., Application of the differential transformation method to the solutions of the free convection problem. Applied Mathematics and Computation 2005. 165(1): pp.63-79.

DOI: 10.1016/j.amc.2004.04.090

[31] M. Ghafarian, and A. Ariaei, Free vibration analysis of a system of elastically interconnected rotating tapered Timoshenko beams using differential transform method. International Journal of Mechanical Sciences, 2016. 107: pp.93-109.

DOI: 10.1016/j.ijmecsci.2015.12.027

[32] S. Ghafoori, M. Motevalli, M. G. Nejad, F. Shakeri, D. D. Ganji, and M. Jalaal, Efficiency of differential transformation method for nonlinear oscillation: Comparison with HPM and VIM. Current Applied Physics 2011. 11(4): pp.965-971.

DOI: 10.1016/j.cap.2010.12.018

[33] O. Adeleye, O. Abdulkareem, A. Yinusa, and G. Sobamowo, Analytical Investigations of Temperature Effects on Creep Strain Relaxation of Biomaterials Using Homotopy Perturbation and Differential Transform Methods. Journal of Computational and Applied Mechanics, 2019. 14(1-2): pp.5-23.

DOI: 10.32973/jcam.2019.001

[34] S. Nourazar, and A. Mirzabeigy, Approximate solution for nonlinear Duffing oscillator with damping effect using the modified differential transform method. Scientia Iranica B 2013. 20(2): p.364–368.

[35] V. S. Erturk, Z.M. Odibat, and S. Momani, The Multi-Step Differential Transform Method And Its Application To Determine The Solutions Of Non-Linear Oscillators. Advances in Applied Mathematics and Mechanics, 2012. 4(4): pp.422-438.

DOI: 10.4208/aamm.10-m1138

[36] E. P. Hanavan, A mathematical model of the human body. AMRL TR 1964: p.1–149.

[37] R. Drillis, and C. Contini, Body Segment Parameters Artificial Limbs. National Academy of Sciences Washington, DC, 1964. 8: pp.44-67.