Iterative Learning Control and Applications in Rehabilitation

Transcription

1 Ierave Learnng Conrol and Applcaons n Rehablaon Yng Tan The Deparmen of Elecrcal and Elecronc Engneerng School of Engneerng The Unversy of Melbourne

2 Oulne 1. A bref nroducon of he Unversy of Melbourne 2. A bref nroducon of my research neress. 3. Ierave learnng conrol (ILC) 4. Applcaons n rehablaons: rehablaon roboc sysems and human moor sysems 5. Mul-loop ILC movaed from applcaons

3 The Unversy of Melbourne 1. The Unversy of Melbourne was esablshed n I s one of op unverses n Ausrala. 3. I has 6500 full and par-me saff and a suden body of more han ncludng more han nernaonal sudens from over 120 counres.

4 The School of Engneerng 1. The School of Engneerng was founded n I has 6 deparmens: 3. I has 2700 sudens n coursework programs (nearly 700 a he Masers level) and more han 500 sudens n research ranng eachng and research saff.

5 The EEE Deparmen Rankng he 15 h around he world (Elecrcal engneerng rankng 2011) 5 IEEE Fellows (7 alogeher 2 lef) 3 Fellow of Ausralan Academy of Scence 3 Fellow of Ausralan Academy of echnologcal Scence and Engneerng 4 man research groups: Sgnals and Sysems; Communcaon; Phooncs; Bo-engneerng.

6 My research neress On-lne opmzaon usng exremum seekng. Formaon conrol (leader follower consensus). Sampled-daa of dsrbued parameer sysems. Sably analyss of nonlnear me-varyng sysems. Conrol of maglev ran sysems. Inellgen sysems and conrol (Ierave Learnng Conrol).

7 Exremum Seekng Conrol A movang example: a dal urbne. flowng waer blades spnnng energy (power)

8 Exremum Seekng Conrol A movang example: a dal urbne. P C p 0. 5 AV 3 P : C p : A : V 3 : : he power generaed (n was); he urbne coeffcen of performance ; he densy of he waer (seawaer s 1025 kg/m³) ; he sweep area of he urbne (n m²) ; he velocy of he flow cubed

9 Exremum Seekng Conrol A movang example: a dal urbne. Assume ha he urbne can roae wh such ha A f unknown. P C I s desred o fnd * such ha P s maxmzed. Exremum seekng can fnd p by usng he measuremens of P and a specal mechansm f V *

10 Exremum Seekng Conrol A dagram of ESC The sysem Q( ) s unknown. y y * * s.. max R Q * Q y Q y exracs he graden Conrol objecve: * fndng such ha + ˆ s lm y * y asn probng

11 Exremum Seekng Conrol Some resuls obaned: Varous global ESC algorhms The performance analyss of ESC n erms of he choce of he dher sgnals Applcaons n bo-reacors A unfed ESC desgn framework ESC wh npu sauraon

12 Ierave Learnng Conrol Wha s an erave learnng conrol? I s a mehod of rackng conrol for sysems ha work n a repeve mode. The movaon of ILC: s o ge a beer ransen response. A sandard conrol loop Fnd a conroller (feedback) such ha: Reference - Error + Conroller Dynamc sysem Oupu The conroller can ensure sably and zero seady-sae error.

13 Ierave Learnng Conrol The key dea s o use he repeon of he sysem o mprove he ransen response. Ths s jus lke human-learnng. We learn hrough he experence. The conrol npu uses (error nformaon) obaned las ral o predc and correc.

14 Applcaons of ILC Roboc sysems; Bach processes; Hgh precson CNC machnng; Hard dsc drve; Mllng and laser cung Traffc flow conrol; Rehablaon Ierave Learnng Conrol

15 Ierave Learnng Conrol A smple case: a nonlnear me-varyng dscree-me plan x y k 1 f k x k u k k hk x k u k k 0 1 N Conrol objecve: for a desred rajecory sequence of npu e k u k such ha lm 0 k 0 1 N e k y k y k d y d k fnd a

16 Ierave Learnng Conrol A possble learnng mechansm (1) Tral (-1) Tral () Tral (+1) Error k-1 k k+1 k-1 k k+1 k-1 k k+1 Inpu u e k-1 k k+1 k-1 k k+1 k-1 k k+1 1k u k ge k e1 k e1 k n n N k yd k y k u1k u k qe k k 0 1 N The smples one:

17 Ierave Learnng Conrol A possble learnng mechansm (2): non-causal one. Tral (-1) Tral () Tral (+1) Error k-1 k k+1 k-1 k k+1 k-1 k k+1 Inpu u k-1 k k+1 k-1 k k+1 k u k ge k 1 e k y k y k 1 ; d k-1 k k+1 I s possble o desgn ILC algorhm o ensure ha he rackng error converges (along he eraon doman) wh a very lmed knowledge of he plan (learn he plan by repeons).

18 Ierave Learnng Conrol rackng error Common feaures: The same conrol ask. The same duraon lm k k 0 1 e k N N s eraon 2nd eraon 3rd eraon 4 h eraon 5 h eraon 6 h eraon 7 h eraon me (s)

19 Ierave Learnng Conrol There s a hybrd naure n ILC: connuous n fne-me doman (mos real plans are connuous-me) and dscree n eraon doman. There are no many effecve ways o analyze he properes of ILC. Tools are relave smple. There are hree major ools: conracon mappng based ILC (CM-ILC) 2D ILC and composon energy funcon based ILC (CEF-ILC).

20 Ierave Learnng Conrol CM-ILC: focus on npu-oupu mappng gnorng he dynamcs of plan. x y f x u h x u 0T f x uand h x u x u wh respec o h u are GLC unformly n x u x 0 T 0 1 2

21 Ierave Learnng Conrol By desgn a sequence of npu sgnal u N such ha e e e max e 0 T e 0 When s suffcenly large he dynamcs of he sysem s gnored and he oupu mappng wll domnae.

22 Ierave Learnng Conrol 2D-ILC: manly workng for dscree-me plans. N k k u k x k h k y k u k x k f k x Mos resuls are focused on lnear-me-nvaran sysems. No many nonlnear resuls are avalable.

23 Ierave Learnng Conrol E CEF-ILC: usng he concep of compose energy funcon: ncludng energy along me and energy along eraon as well. I can work well for boh connuous-me plans and dscree-me plans. E x u 0 0 T x u E x u e T e lm 0

24 Ierave Learnng Conrol However a sysemac developmen of CEF-ILC s sll no avalable. Compared wh Lyapunov mehods wdely used n nonlnear conrol sysems (n me doman only) here are no many resuls n consrucng CEF for ILC. I s non-rval o exend some well-known resuls such as small-gan heorem n nonlnear conrol sysems o CEF-ILC.

25 Applcaons on Rehab ILC conrol s now used n rehablaon area especally n he area of rehab afer sroke. Rehablaon of sensory and cognve funcon ypcally nvolves mehods for reranng neural pahways or ranng new neural pahways o regan or mprove neuro-cognve funconng ha has been dmnshed by dsease or rauma

26 Applcaons on Rehab Sroke s Ausrala s second sngle greaes kller afer coronary hear dsease and a leadng cause of dsably. The number of sroke survvors n Ausrala s over Tha s one sroke every 10 mnues. Abou 88 per cen of sroke survvors lve a home and mos have a dsably. Srokes cos Ausrala an esmaed $2.14 bllon a year. Of hose who survve sroke wh severe paralyss only 5% regan upper lmb funcon

27 Applcaons on Rehab We are dong wo dfferen ypes of work for rehab: One s o buld a rehab-roboc sysem o help paen o recover; The oher s ry o undersand how human moor sysem (HMS) works for healh people by consrucng a compuaon model of human moor sysems. These wo ypes of work are all closely relaed o erave learnng conrol as he key concep of rehab s learnng/pracsng promoes recovery

28 Rehablaon Roboc Sysems I am now workng wh Chrs Freeman from New Souhampon Unversy mprove he rehablaon roboc sysems

29 Applcaons on Rehab

30 Rehablaon Roboc Sysems The mul-loop ILC algorhms are needed n hs projec. Learnng a personalzed rajecory for each paen Three loops are ner-conneced. The me-scale may be dfferen. Learnng he muscle model (or dynamcs) of each paen Desgn ILC for a gven ask

31 Compuaon Model of HMS Wha s HMS? HMS descrbes he capably of an ndvdual o calbrae he characerscs of hs body so as To produce he desred moon. To adjus o he dynamcs of he envronmen.

32 Compuaon Model of HMS Why a compuaon model of HMS s needed I can provde beer undersandng of ndvdual human learnng. Ths wll lead o beer dagnoss of ndvdual paens sufferng from abnormal behavour such as afer-sroke paens. Buldng such compuaon model needs well-desgned expermens and expermens daa

33 Compuaon Model of HMS We have buld a compuaon model for HMS when performng a reachng ask n me-varyng envronmen.

34 Compuaon Model of HMS

35 Resul of expermens Compuaon Model of HMS

36 Compuaon Model of HMS Compuaon model from ILC (ILC updaes he model from oupu). Smulaon resuls from compuaon model are:

37 Compuaon Model of HMS Smulaon resuls from compuaon model of HMS mach well o expermenal resuls. Ths shows he compuaon model obaned capures he learnng ably of human bengs. HMS has a herarchcal srucure of hree nerconneced processes: (1) moor plannng (2) moor conrol and (3) moor execuon. Therefore mul-loop ILC desgn s also needed.

38 Mul-loop ILC Mul-loop ILC conceps are movaed from varous applcaons. The work of mul-loop ILC has jus sared only some prelmnary resuls are obaned. Here we consder only wo ner-conneced sysems. x 1 y ) ( ) ( : u x h z u x f x z u x y z x f x ) ( :

39 Mul-loop ILC Each subsysem here exss an ILC loop o make work x y z x f x : wsely - pon 0 updang law lm. ) ( e s e z g z T C y d

40 Mul-loop ILC Each subsysem here exss an ILC loop o make work z z δ s u g u T C z d d unformly 0 updang law lm. ) ( u x h z u x f x :

41 Mul-loop ILC The queson s how o ensure he overall sysem can work when hese wo loops are conneced. Loop 1 wll provde he desred rajecory for Loop 2. We use me-scale separaon echnque: Loop 1 was unl Loop 2 converges. Tha s: Loop 1 updaes every N eraons when Loop 2 already behaves well. Then he overall sysem can converge o a small neghborhood of desred rajecory.

42 Mul-loop ILC r N 1 ( s ) g1( s r N ( s ) e N ( s )) ILC Loop 1 1 r ( s) r N2 ( 1 s ) zn ( ) ( ) 21 s zn 2 s z ( ) N 2 s z ( N 2 2 s ) N2 1 z ( ) z ( ) 2 s 1 s 1 N 2 1 u1( s ) g2( s u( s ) ( s )) ILC Loop 2 N 2 2N2 Ierao n numbe r

43 Conclusons ILC s very useful n many engneerng applcaons Bu he ools are no rch enough o desgn proper ILC schemes for complcaed sysems or analyze he performance. We are ryng developng more approprae ools now. These ools should be smple enough for engneers o use bu s also flexble enough o cover varous engneerng applcaons. We need work wh mahemacans.