Optimal Sliding Mode Controller for Knee Flexion During Walking
Authors: Gabriel Sitler, Yousef Sardahi, Asad Salem
Abstract:
This paper presents an optimal and robust sliding mode controller (SMC) to regulate the position of the knee joint angle for patients suffering from knee injuries. The controller imitates the role of active orthoses that produce the joint torques required to overcome gravity and loading forces and regain natural human movements. To this end, a mathematical model of the shank, the lower part of the leg, is derived first and then used for the control system design and computer simulations. The design of the controller is carried out in optimal and multi-objective settings. Four objectives are considered: minimization of the control effort and tracking error; and maximization of the control signal smoothness and closed-loop system’s speed of response. Optimal solutions in terms of the Pareto set and its image, the Pareto front, are obtained. The results show that there are trade-offs among the design objectives and many optimal solutions from which the decision-maker can choose to implement. Also, computer simulations conducted at different points from the Pareto set and assuming knee squat movement demonstrate competing relationships among the design goals. In addition, the proposed control algorithm shows robustness in tracking a standard gait signal when accounting for uncertainty in the shank’s parameters.
Keywords: Optimal control, multi-objective optimization, sliding mode control, wearable knee exoskeletons.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 202References:
[1] P. K. Sancheti, M. Razi, E. B. Ramanathan, and P. S.-H. Yung, “Injuries around the knee – symposium,” British Journal of Sports Medicine, vol. 44, pp. i1 – i1, 2010.
[2] D. Miranda-Linares, G. Alrezage, and M. Tokhi, “Control of lower limb exoskeleton for elderly assistance on basic mobility tasks,” in 2015 19th International Conference on System Theory, Control and Computing (ICSTCC). IEEE, 2015, pp. 441–446.
[3] A. Chevalier, C. M. Ionescu, and R. De Keyser, “Model-based vs auto-tuning design of pid controller for knee flexion during gait,” in 2014 IEEE International Conference on Systems, Man, and Cybernetics (SMC). IEEE, 2014, pp. 3878–3883.
[4] W. Huo, S. Mohammed, and Y. Amirat, “Impedance reduction control of a knee joint human-exoskeleton system,” IEEE Transactions on Control Systems Technology, vol. 27, no. 6, pp. 2541–2556, 2018.
[5] K. Seo, K. Kim, Y. J. Park, J.-K. Cho, J. Lee, B. Choi, B. Lim, Y. Lee, and Y. Shim, “Adaptive oscillator-based control for active lower-limb exoskeleton and its metabolic impact,” in 2018 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2018, pp. 6752–6758.
[6] T. Erfani and S. V. Utyuzhnikov, “Directed search domain: a method for even generation of the pareto frontier in multiobjective optimization,” Engineering Optimization, vol. 43, no. 5, pp. 467–484, 2011.
[7] O. M. Shir, S. Chen, D. Amid, D. Boaz, A. Anaby-Tavor, and D. Moor, “Pareto optimization and tradeoff analysis applied to meta-learning of multiple simulation criteria,” in 2013 Winter Simulations Conference (WSC). IEEE, 2013, pp. 89–100.
[8] G. Reinelt, The traveling salesman: computational solutions for TSP applications. Springer-Verlag, 1994.
[9] C. M. M. D. Fonseca, “Multiobjective genetic algorithms with application to control engineering problems.” Ph.D. dissertation, University of Sheffield, 1995.
[10] J. Moore and R. Chapman, “Application of particle swarm to multiobjective optimization,” Department of Computer Science and Software Engineering, Auburn University, vol. 32, 1999.
[11] E. Zitzler, M. Laumanns, and L. Thiele, “SPEA2: Improving the strength pareto evolutionary algorithm,” TIK-report, vol. 103, 2001.
[12] M. Erickson, A. Mayer, and J. Horn, “The niched Pareto genetic algorithm 2 applied to the design of groundwater remediation systems,” in International Conference on Evolutionary Multi-Criterion Optimization. Springer, 2001, pp. 681–695.
[13] Y. Sardahi and A. Boker, “Multi-objective optimal design of four-parameter PID controls,” in ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018, pp. V001T01A001–V001T01A001.
[14] X. Xu, Y. Sardahi, and C. Zheng, “Multi-objective optimal design of passive suspension system with inerter damper,” in ASME 2018 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2018, pp. V003T40A006–V003T40A006.
[15] B. Gadhvi, V. Savsani, and V. Patel, “Multi-objective optimization of vehicle passive suspension system using NSGA-II, SPEA2 and PESA-II,” Procedia Technology, vol. 23, pp. 361–368, 2016.
[16] M. Ashmi, M. Anila, and K. Sivanandan, “Comparison of SMC and PID controllers for pneumatically powered knee orthosis,” Journal of Control, Automation and Electrical Systems, vol. 32, no. 5, pp. 1153–1163, 2021.
[17] J. Cao, S. Q. Xie, and R. Das, “Mimo sliding mode controller for gait exoskeleton driven by pneumatic muscles,” IEEE Transactions on Control Systems Technology, vol. 26, no. 1, pp. 274–281, 2017.
[18] X. Xu, Y. Sardahi, and A. Boker, “Multi-objective optimal design of a PID sliding mode controller with three different reaching laws,” in Dynamic Systems and Control Conference, vol. 59155. American Society of Mechanical Engineers, 2019, p. V002T25A002.
[19] B. Janardhanan and S. Spurgeon, “Advances in sliding mode control: Concept, theory and implementation,” 2013.
[20] J. Liu and X. Wang, Advanced sliding mode control for mechanical systems: design, analysis and MATLAB simulation. Springer Science & Business Media, 2012.
[21] V. Pareto, Manual of Political Economy. London: The MacMillan Press, 1971 (original edition in French in 1927).
[22] K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms. New York: Wiley, 2001.
[23] Y. Liu, K. Lu, S. Yan, M. Sun, D. K. Lester, and K. Zhang, “Gait phase varies over velocities,” Gait & posture, vol. 39, no. 2, pp. 756–760, 2014.
[24] M. Al-Fandi, M. A. K. Jaradat, and Y. Sardahi, “Optimal PI-fuzzy logic controller of glucose concentration using genetic algorithm,” International Journal of Knowledge-based and Intelligent Engineering Systems, vol. 15, no. 2, pp. 99–117, 2011.