@article{03dc7f8786ac4c24a3f83c0b51af7b55,
title = "Extremum Seeking Control for Power Tracking via Functional Electrical Stimulation",
abstract = "Motorized Functional Electrical Stimulation (FES)-cycling is a promising rehabilitative strategy for people possessing movement disorders as a result of neurological conditions. Cadence and torque (power) tracking objectives have been previously prescribed in FES-cycling to exploit the functional benefits of neuromuscular electric stimulation and produce intensive active therapy with motorized assistance. However, predetermined desired trajectories for either objective may yield sub-optimal training performance since the movement capacity of a person recovering from injury is unknown and time-varying. Hence, online adaptation is well-motivated to determine optimal cadence and torque trajectories. In this paper, an extremum seeking control (ESC) algorithm is implemented in real-time to compute the optimal cadence and torque trajectory (i.e., the peak torque demand) to maximize power output in an FES-cycling protocol. The uncertain, nonlinear FES-cycle system is an autonomous, state-dependent switched system to activate lower-limb muscles and an electric motor. Torque tracking is achieved by electrically stimulating the muscles via a learning controller and cadence tracking by engaging an electric motor. A passivity-based approach is utilized to analyze the stability of both tracking objectives.",
keywords = "Extremum Seeking Control (ESC), Functional Electrical Stimulation (FES) Cycling, Passivity-Based Control, Repetitive Learning Control (RLC)",
author = "Duenas, {Victor H.} and Cousin, {Christian A.} and Rouse, {Courtney A.} and Dixon, {Warren E.}",
note = "Funding Information: viduals with spinal cord injuries Sadowsky et al. (2013); Motorized ˚ES-cycles have the capability to regulate ca-viduals with spinal cord injuries Sadowsky et al. (2013); Mooutsoirnizeetd{\aa}l.E(S2-0c1y7c)l;esBhelalvmeatnh(e2c0a1p5a).bility to regulate ca-˚errante et al. (2008); Bo et al. (2017). Rehabilitation deontcoeriazned v{\aa}EryS-tchyeclreessihstaive tlohaedctaopaebvoilkiteyttoorqrueegufrloamte tchae-˚errante et al. (2008); Bo et al. (2017). Rehabilitation dence and vary the resistive load to evoke torque from the protocols that involve motorized cycles with ˚ES have riedonetcroe.riaHzneodwveavEreyrS,-tcthyhecelreeusssihestaiovvfeatlrohbaeidtcrtaaopryaebvcoilakidteyetntocoreqruaeengudfrloatmtoerqtchuaee-protocols that involve motorized cycles with ˚ES have rider. However, the use of arbitrary cadence and torque provided means to exercise lower-limb muscles and achieve rriedanejcere.ctaHonrodiwesveavuresyru,atthllheyerdeuessmiestoionvfestalrroabatidetrtlaiomryeivtceoadkdeeetfnfoecrceqtuiavenedfnreotsmosrdqthuueee provided means to exercise lower-limb muscles and achieve trajectories usually demonstrate limited effectiveness due consistent, repetitive movements with the assistance of an tridaejterh.cetHolroaiwecskevueosrfu,astlulhyfefidcuieesmnetoonfksntarorawbtielterdlaigmreyitcaeabddoeeufntfeccetthiavenednheutsmosradqnuu{\textquoteright}ees consistent, repetitive movements with the assistance of an to the lack of sufficient knowledge about the human{\textquoteright}s electric motor. Closed-loop control strategies have been moaotjteohcretoclaraipecaskbuiolsifutyasluldyfufirdciienemgntornekhsntarobawitlelietdalitgmieointae.bdPoeaufrtfteicctthuivelaernhlyeu,smssaidnnuc{\textquoteright}ees electric motor. Closed-loop control strategies have been motor capability during rehabilitation. Particularly, since implemented for cadence tracking, utilizing feedback con-toeottpohlree cwlaapictakhbiomliftoysvuedfmufirceiinnetgntdreikshonarobdwielliretsdatgpieoonsas.ebPsosaurtdtiicftfhueelraernhltyu,mlseaivnnecl{\textquoteright}ess implemented for cadence tracking, utilizing feedback con-people with movement disorders possess different levels trol with identification procedures Hunt et al. (2004), ofeortpeoslreidcuwaapitlahbniemluitoryovledomugriecinnatgl dmreisohotarobdrielcirtsoantptioroonsls.,ePstsharedtiucffsueelraeornflty,plrseeivndeceles-trol with identification procedures Hunt et al. (2004), of residual neurological motor control, the use of prede-robust methods to compensate for the nonlinear, time-peferomrpeislneideuwdaidtlhenseimrueordovletomrgaiejcneatcltodmrisioeotsrodrinecrsocynpctrloiosnlsg,esthshaedsiutffhseeereopnfottpelrenevtdeieals-l robust methods to compensate for the nonlinear, time-termined desired trajectories in cycling has the potential varying rider-cycle dynamics Bellman et al. (2016, 2017), oofrmryeiisenildedudasdul ebnsoeirpuetrdiomltoargalijceaxclteormcriioestesoritnrcaociynnctinrliognlg,pthehraefsorutmhseeanopcfoetper(neetd.iea.-l varying rider-cycle dynamics Bellman et al. (2016, 2017), to yield suboptimal exercise training performance (e.g., repetitive learning control (RLC) to exploit the inherent reerqmuyiiiernilneddgsdiutebesroiarptetidivmetarmal jaeenxcuteoarcrliiesaesdjitunrsatcimyncienlnigntsgpohefraftsohrtemhedaenpscioerteed(net.ciaa.-l repetitive learning control (RLC) to exploit the inherent requiring iterative manual adjustments of the desired ca-periodic nature of cycling Duenas et al. (2016, to appear), roeeqnuyciierilndogrsiuttoberroqaputtieivmetarmal jaeenxcuteoarcrliiesasedjttuorsatimnieanntgcthspoetfrhfteohrepmadarentsiccieriepd(aen.ctga{\textquoteright}.s-, periodic nature of cycling Duenas et al. (2016, to appear), dence or torque trajectories to match the participant{\textquoteright}s and the activation of biarticular muscles Kawai et al. meeoqntucoierrinocgarpitatoecriqtayut)iev.eHtrmeanjaecnceut,oaarlnieasdojntulosintme eaantdctahspottafhtteihonepadsrtetrsiacirtiepedgaynctai{\textquoteright}ss-and the activation of biarticular muscles Kawai et al. motor capacity). Hence, an online adaptation strategy is (to appear). Simultaneous control of cadence and torque motor capacity). Hence, an online adaptation strategy is (to appear). Simultaneous control of cadence and torque well-motivated to determine optimal cadence and torque well-motivated to determine optimal cadence and torque ★★(toThaisppreesaearr)c.hSiismsuupltpaonrteeoduisncpoanrttrboyltohfeNcadtieonncaleSacniedncetoFroquune- trajectories during ˚ES-cycling to accommodate for the ★ This research is supported in part by the National Science Foun-trajectories during ˚ES-cycling to accommodate for the d★aTtihnis rGersaeadrucahteisRsuepsepaorrcthedFienllopwarsthibpyPthroegNraamtiounnaldeSrcieGnrcaenFtoNuno-. rider{\textquoteright}s unique characteristics. dation Graduate Research Fellowship Program under Grant No. rider{\textquoteright}s unique characteristics. d★aGtiEon-13G15ra1d38uaatendRAesFeOarScRh FawelalorwdsnhuipmbPerrogFrAam955u0n-1d8e-r1-G01r0a9n.t ANnoy. Extremum Seeking Control (ESC) is an adaptive control DGE-1315138 and AFOSR award number FA9550-18-1-0109. Any Eidxterre{\textquoteright}smuunmiquSeeeckhinargacCtoenritsrtoicls(.ESC) is an adaptive control DpGinEio-1n3s1,5fi1n3d8inagnsd,aAndFOcoSnRcluaswioanrdsonrurmecboemrmFAen9d5a5t0i-o1n8s-1e-x0p1r0e9s.seAdniny Extremum Seeking Control (ESC) is an adaptive control opinions, findings, and conclusions or recommendations expressed in technique that exploits the existence of an unknown steady opGinEio-1n3s1,5fi1n3d8inagnsd,aAndFOcoSnRcluaswioanrdsonrurmecboemrmFAen9d5a5t0i-o1n8s-1e-x0p1r0e9s.seAdniny techniquethatexploitstheexistenceofanunknownsteady thishesvmaterialieawtesroiafltarehreesthosephoonsesoofrfinthegheaauthor(s)guenthcyo.r(s)anddonotnecessarilyreflect state input-to-output mapping with a local (or global) thpeinvioienws,sfoinfdtihnegss,paonndsocroinngclaugsieonncsy.or recommendations expressed in state input-to-output mapping with a local (or global) Publisher Copyright: {\textcopyright} 2019",
year = "2019",
month = jan,
day = "1",
doi = "10.1016/j.ifacol.2019.01.060",
language = "English (US)",
volume = "51",
pages = "164--169",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "IFAC Secretariat",
number = "34",
}