This paper describes the design and implementation of a novel adaptive control method to track a set of bioinspired reference trajectories. These references define anthropomorphic movements for an exoskeleton robot. The proposed controller implemented the adjustment laws for the variable gains of a state feedback (Proportional-Derivative type) structure. The method to adjust the adaptive gains was determined using a controlled Lyapunov function. The adaptation laws use velocity estimation based on a robust exact differentiator (RED) implemented as a variation of a distributed Super-Twisting algorithm. The adaptive gain controller was evaluated on a simulated exoskeleton structure. The set of simulations considered the presence of external disturbances and modeling uncertainties. The controller proved efficient in rejecting external perturbations/uncertainties affecting the exoskeleton. The proposed controller’s performance was superior to the one obtained if the standard fixed-gain proportional derivative controller was evaluated. As an additional benefit of the adaptive PD controller implementation, a controller power reduction of at least 14 concerning the non-adaptive version of the feedback controller was attained. An experimental evaluation of the proposed controller confirmed the benefits of the proposed controller with adaptive gains. The successful tracking of nine different biomechanically inspired reference trajectories justified the exoskeleton application, which could be used as a potential tool for rehabilitation purposes.
VanderborghtBVerrelstBVan HamRet al. Dynamic control of a bipedal walking robot actuated with pneumatic artificial muscles. In Proceedings of the 2005 IEEE International Conference on Robotics and Automation. IEEE, pp. 1–6.
2.
KangJH and Wang. Adaptive robust control of 5 dof upper-limb exoskeleton robot. Int J Control, Autom Syst2015; 13: 733–741.
3.
ZossABKazerooniHChuA. Biomechanical design of the berkeley lower extremity exoskeleton. IEEE ASME Trans Mechatron2006; 11: 128–138.
4.
JezernikSWassinkRGVKellerT. Sliding mode closed-loop control of fes: controlling the shank movement. IEEE Trans Biomed Eng2004; 51: 263–272.
5.
ZossABKazerooniHChuA. Biomechanical design of the berkeley lower extremity exoskeleton (bleex). IEEE ASME Trans Mechatron2006; 11: 128–138.
6.
ChuAKazerooniHZossA. On the biomimetic design of the berkeley lower extremity exoskeleton (bleex). In Proceedings of the IEEE International Conference on Robotics and Automation. Citeseer, pp. 4345–4352.
7.
SankaiY. Hal: Hybrid assistive limb based on cybernics. In Kaneko M and Nakamura Y (eds.) Robotics Research. Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 978-3-642-14743-2, pp. 25–34.
LowK. Robot-assisted gait rehabilitation: From exoskeletons to gait systems. In Defense Science Research Conference and Expo (DSR). IEEE, pp. 1–10.
10.
FaieghiMJalaliA. Robust adaptive cruise control of high speed trains. ISA Trans2014; 53: 533–541.
11.
YuWRosenJ. A novel linear pid controller for an upper limb exoskeleton. In 49th IEEE Conference on Decision and Control (CDC). IEEE, pp. 3548–3553.
12.
ZohdyMZaherA. Robust control of biped robots. In Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No. 00CH36334), volume 3. IEEE, pp. 1473–1477.
13.
KazerooniHRacineJLHuangLet al. On the control of the berkeley lower extremity exoskeleton (bleex). In Proceedings of the 2005 IEEE international conference on robotics and automation. IEEE, pp. 4353–4360.
14.
AnamKAl-JumailyAA. Active exoskeleton control systems: State of the art. Procedia Eng2012; 41: 988–994.
15.
LetierPMotardEVerschuerenJP. Exostation: Haptic exoskeleton based control station. In 2010 IEEE International Conference on Robotics and Automation. IEEE, pp. 1840–1845.
KashiriNLaffranchiMTsagarakisNGet al. Dynamic modeling and adaptable control of the compactTM arm. In 2013 IEEE International Conference on Mechatronics (ICM). IEEE, pp. 477–482.
18.
Jimenez-FabianRVerlindenO. Review of control algorithms for robotic ankle systems in lower-limb orthoses, prostheses, and exoskeletons. Med Eng Phys2012; 34: 397–408.
19.
FerrisDPLewisCL. Robotic lower limb exoskeletons using proportional myoelectric control. In Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE, pp. 2119–2124.
20.
UgurluBNishimuraMHyodoKet al. A framework for sensorless torque estimation and control in wearable exoskeletons. In 2012 12th IEEE international workshop on advanced motion control (AMC). IEEE, pp. 1–7.
21.
UtkinVGuldnerJShiJ. Sliding mode control in electro-mechanical systems. 2nd ed. Boca Raton: CRC press, Automation and Control Engineering, 2009.
22.
Sira-RamirezH. Dynamic second-order sliding mode control of the hovercraft vessel. IEEE Trans Control Syst Technol2002; 10: 860–865.
23.
QaisarTMahmoodA. Robust control and optimal analysis of a customized robotic arm with h2 and h compensators. In Proceedings of the IEEE 17th International Multi-Topic Conference. IEEE, pp. 428–433.
24.
SlotineJJELiW. On the adaptive control of robot manipulators. Int J Rob Res1987; 6: 49–59.
25.
KhatibO. A unified approach for motion and force control of robot manipulators: The operational space formulation. IEEE J Robot Autom1987; 3: 43–53.
26.
BlayaJAHerrH. Adaptive control of a variable-impedance ankle-foot orthosis to assist drop-foot gait. IEEE Trans Neural Syst Rehabil Eng2004; 12: 24–31.
27.
Marchal-CrespoLReinkensmeyerDJ. Review of control strategies for robotic movement training after neurologic injury. J Neuroeng Rehabil2009; 6: 20.
28.
TomeiP. Adaptive pd controller for robot manipulators. IEEE Trans Rob Autom1991; 7: 565–570.
29.
PomerleauADesbiensAHodouinDet al. Development and evaluation of an auto-tuning and adaptive pid controller. Automatica1996; 32: 71–82.
GaoHLiuCGuoDet al. Fuzzy adaptive pd control for quadrotor helicopter. In Proceedings of the IEEE Cyber Technology in Automation, Control, and Intelligent Systems. IEEE, pp. 281–286.
32.
SiradjuddinIBeheraLMcGinnityTMet al. Image-based visual servoing of a 7-dof robot manipulator using an adaptive distributed fuzzy pd controller. IEEE ASME Trans Mechatron2014; 19: 512–523.
33.
AçıkmeşeBMandićMSpeyerJL. Decentralized observers with consensus filters for distributed discrete-time linear systems. Automatica2014; 50: 1037–1052.
34.
TongSHuoBLiY. Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans Fuzzy Syst2014; 22: 1–15.
35.
EfimovDPolyakovALevantAet al. Convergence acceleration for observers by gain commutation. Int J Control2018; 91: 2009–2018.
36.
WangLAstolfiDMarconiLet al. High-gain observers with limited gain power for systems with observability canonical form. Automatica2017; 75: 16–23.
37.
MorenoJAlvarezJRocha-CozatlEet al. Super-twisting observer-based output feedback control of a class of continuous exothermic chemical reactors. In Proceedings of the 9th International Symposium on Dynamics and Control of Process Systems (DYCOPS). Leuven, Belgium, pp. 727–732.
38.
FridmanLLevantA. Sliding Mode in Control in Engineering, chapter High Order Sliding Modes. 3, Marcel Dekker, 2002. pp. 53–101.
39.
LevantA. Sliding Mode Control in Engineering, chapter High Order Sliding Modes. Marcel Dekker, 2002.
40.
Zhang L, Liu L, Wang Z et al. Continuous finite-time control for uncertain robot manipulators with integral sliding mode. IET Control Theory Applic 2018; 1621–1627.
41.
SalgadoIChairezICamachoOet al. Super-twisting sliding mode differentiation for improving pd controllers performance of second order systems. ISA Trans2014; 53: 1096–1106.
42.
LevantA. Sliding order and sliding accuracy in sliding mode control. Int J Control1993; 58: 1247–1263.
MorenoJ. Lyapunov analysis of non homogeneous super-twisting algorithms. In Proceedings of the 11th International Workshop on Variable Structure Systems. pp. 534–539.
45.
PolyakovAEPoznyakAS. Method of lyapunov functions for systems with higher-order sliding modes. Autom Remote Control2011; 72: 944–965.
46.
PoznyakA. Advanced mathematical tools for automatic control engineers: Volume 1: Deterministic systems. Amsterdam: Elsevier Science, 2008.
47.
AndersonFCPandyMG. Dynamic optimization of human walking. J Biomech Eng2001; 123: 381–390.
48.
AminianKNajafiBBülaCet al. Spatio-temporal parameters of gait measured by an ambulatory system using miniature gyroscopes. J Biomech2002; 35: 689–699.
49.
KhalilHK. Noninear systems. Prentice-Hall, New Jersey1996; 2: 5–1.
50.
DavilaJFridmanLLevantA. Second-order sliding-mode for mechanical system. IEEE Trans Automat Contr2005; 50: 1785–1789.
51.
MorenoJAOsorioM. A lyapunov approach to second-order sliding mode controllers and observers. In Proceedings of the 47th IEEE Conference on Decision and Control.
52.
GaoZ. Active disturbance rejection control: A paradigm shift in feedback control system design. In Proceedings of the American Control Conference. Minneapolis, Minnesota, USA, pp. 2399–2405.
53.
CybenkoG. Approximation by superpositions of a sigmoidal function. Math Control Signals Syst1989; 2: 303–314.
54.
CruzDLuviano-JuarezAChairezI. Output sliding mode controller to regulate the gait of gecko-inspired robot. In Memorias del XVI Congreso Latinoamericano de Control Automatico, CLCA. pp. 558–563.
55.
PolyakovAChairezI. A new homogeneous quasi-continuous second order sliding mode control. In XVI Congreso Latinoamericano de Control Automático.
56.
MorenoAOsorioM. Strict lyapunov funtions for the super-twisting algorithm. IEEE Trans Automat Contr2012; 57: 1035–1040.
57.
DrakunovSUtkinV. Sliding mode observers. tutorial. In Proceedings of the 34th IEEE Conference on Decision and Control, volume 4. IEEE, pp. 3376–3378.
58.
AhrensJHKhalilHK. High-gain observers in the presence of measurement noise: A switched-gain approach. Automatica2009; 45: 936–943.
