θ with respect to time is

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1 From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. A MINIMAL JERK PROSTHESIS CONTROL SYSTEM Primary Auhor: Sewar Scoland Hill Oher Auhors: T. D Binnie, D. J. Gow* Napier Universiy, Edinburgh, 10 Colinon Road, Edinburgh, Scoland *Rehabiliaion Engineering Services, Lohian Primary Care Trus Absrac: Efficien proshesis conrol is dependan on he user s abiliy o conrol he desired movemens of he proshesis. Observed manifesaions of jerk on a complee arm proshesis can lead o difficuly in performing conrolled movemens, especially under load on graviy assised downward movemens. The applicaion of so called sof sar and sof sop rouines for conrolling he velociy profile of he proshesis join hrough is roaional movemen can go some way o reducing his effec. I is proposed ha an adapive velociy conrol sysem can be applied o he same proshesis under he same es condiions and reduce he discernible jerk considerably. This adapive sysem moniors he change is angular velociy hus conrolling he second and hird derivaives of posiion. The implicaion of acively conrolled angular velociy lends iself o minimize jerk, combined wih reduced power consumpion, and an increase in pars life and reliabiliy. This conrol is applicable o all exernally powered prosheic limbs, regardless of user inerface. Inroducion o Jerk θ wih respec o ime is velociy ( & θ ), and he second is eleraion ( & θ ). The hird derivaive is he rae of change of eleraion ( & θ & ), known echnically as jerk (jol in English). Jerk is a vecor bu may also be used loosely as a scalar quaniy because here is no a separae erm for he magniude of jerk, equivalen o speed as he magniude of velociy. The uni of jerk is meres per second cubed (m/s 3 ), alhough here is no universally agreemen on a symbol for jerk. I is well known ha he firs derivaive of posiion ( ) In he field of prosheics, he conrol of jerk can be seen in anoher dimension. Tha is, hrough conrolling he rae of change of eleraion i is possible o smooh he profile of he arm as i moves rough he specrum of is revoluion. Smoohed Velociy Profile Moor Conrol A sysem wih a feedback conroller will drive he sysem o a sae described by he inpu value. This desired value can be in erm of posiion or of velociy. The combinaion of a moion conroller and a drive acuaor is referred o as an axis. A sysem which has more han one of hese axes can be referred o as a complex moion conrol sysem. An example of such a sysem would be ha of a complee prosheic arm, where he shoulder, elbow, wris and hand are all axes. Where posiion is he desired oupu of he conrol sysem, a movemen from poin A o poin B dicaes ha Disribued under a Creaive Commons Aribuion-Noncommercial-No Derivaive Works 3.0 Unied Saes License by UNB and he Insiue of Biomedical Engineering, hrough a parnership wih Duke Universiy and he Open Prosheics Projec.

2 From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. a Poin A he velociy should be 0, and a poin B he velociy should be 0. Beween poin A and Poin B here should be a velociy. Figure 1. Change in Posion (θ) wih respec o ime (). A condiion of moving beween poin A and Poin B (Figure 1) will be ha he velociy and he change in velociy be conrolled. In his insance a velociy profile graph would produce a rapezoidal profile (Figure ). The op level of he rapezoid is he imum velociy. The oal area under he profile is he disance moved, and he slopes are he imum eleraion/deceleraion allowed. Figure. Trapezoidal Velociy (ω) wih respec o ime () Jerk (m/s 3 ), described as he rae of change in eleraion wih respec o ime, can be seen o manifes iself in he rapezoidal profile where changes in eleraion can be seen as sharp corners. To minimise he effecs of jerk on he proshesis, a mehod ha generaes a smoohed profile is presened. Where: ω = imum velociy = imum eleraion = eleraion ime dec = deceleraion ime = ime a imum velociy oal = he oal ime in moion I can be seen ha, he iniial eleraion from sandsill can be generaed using: ω ( ) = A. (1) Where A is defined as: A = () Where is defined as: Disribued under a Creaive Commons Aribuion-Noncommercial-No Derivaive Works 3.0 Unied Saes License by UNB and he Insiue of Biomedical Engineering, hrough a parnership wih Duke Universiy and he Open Prosheics Projec.

3 From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. ω = (3) By subsiuion A = (4) ω ( ) This gives he equaion, A = (5) And herefore, ω ( ) =. (6) ω (s) Figure 3. Acceleraion from res owards ω wih respec o ime () This equaion provides a exponenial growh funcion from res, bu does no provide for smoohing oward he ω value. In order o perform he smoohing funcion owards ω, hen a second equaion mus be applied. So his firs equaion is applied o he firs half of he eleraion ( ). The condiional saemen is made ha if: (7) hen ω ( ) =. (8) For values greaer han he firs equaion can be used o find he second equaion. Disribued under a Creaive Commons Aribuion-Noncommercial-No Derivaive Works 3.0 Unied Saes License by UNB and he Insiue of Biomedical Engineering, hrough a parnership wih Duke Universiy and he Open Prosheics Projec.

4 From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. ( ) 4 ω ( ) = ω (9) ω This equaion now gives he following response. ω (s) ω Figure 4. Acceleraion from owards ω wih respec o ime. If = hen ω() would be equal o ω. Given ha ω is an indefinie period of ime conrolled by he user, hen he deceleraion will come immediaely afer he suspension of he users desired moion. ω ω (s) ω dec Figure 5. Deceleraion from ω owards Figure 6. Deceleraion from owards ω = 0. The deceleraion dec facor can be relaed o he eleraion facor. However a oally differen value for deceleraion can be used, hus he ime for could be differen in value o dec. This facor can be ailored o each user s requiremen, o minimise he amoun of perceived over-run. Given ha he human sysem is able o predic and adap o he fac ha here is a perceivable overrun, i is hoped ha he dec 0 0 Disribued under a Creaive Commons Aribuion-Noncommercial-No Derivaive Works 3.0 Unied Saes License by UNB and he Insiue of Biomedical Engineering, hrough a parnership wih Duke Universiy and he Open Prosheics Projec.

5 From MEC '05 Inergraing Prosheics and Medicine, Proceedings of he 005 MyoElecric Conrols/Powered Prosheics Symposium, held in Fredericon, New Brunswick, Canada, Augus 17-19, 005. human can ommodae for his consan facor. Each of he elemens can be implemened as a separae funcion. The iniial condiion of zero velociy o is assigned he seg1 designaion, similarly he elemen from o ω is designaed as funcion: seg. I can be seen ha hese funcions can only be used for a posiive or forward velociy. An addiional 4 segs allocaions are made o describe he negaive or reverse velociy. By combining hese segmens wih he appropriae logic and modelled in mahworks malab. The armaure resisance, roor ineria and roor inducance, and oher characerisics of he moor can be encompassed in he simulaion. Hardware Implemenaion The hardware akes he form of an embedded bus based communicaion sysem. The bus chosen was conroller area nework (CAN) bus [1,]. This communicaion sysem akes user inpu signals from he proshesis/user inerface, and disribues hese signals along he complee prosheic arm. The posiional ransducer chosen was an absolue encoder, giving 18 posiional saes, equaing o.851 /sep. Acceleraion is measured by monioring he rae of change of hese posiional saes. Given he modelling of he moor response o volage, i is possible o build a se of rules ha describe he eleraion of he moor wihou having o acively monior he sep changes of he posiional ransducer. CAN BUS Microconroller Drive Circui Moor 8 bi Posiional Daa Encoder Figure 7. Hardware implemenaion of Minimal Jerk Conrol Conclusions: I can be seen on a pracical level ha his velociy profiling approach can reduce he effecs of jerk. Moreover his represens a significan improvemen for conrolling he amoun of momenum arefac ha exhibis iself on he user. No only does his approach increase he pars-life of he proshesis, bu i also simplifies conrol of he proshesis by making movemens more reliable and conrolled. References: 1. Hill, S.S, Binnie, T.D, Gow, D J CONTROL STRATEGIES FOR THE EDINBURGH MODULAR ARM SYSTEM, EPSRC PREP Conference Proceedings (Posers), Universiy of Exeer, UK, pp 1-0, 14 h -16 h April 003,. Poulon, A.S, Hill, S, Binnie, T.D, Gow, DJ Nework Technologies for Inelligen Modular Prosheses, ISEK Conference, Boson, 18 h -1 s June 004. Disribued under a Creaive Commons Aribuion-Noncommercial-No Derivaive Works 3.0 Unied Saes License by UNB and he Insiue of Biomedical Engineering, hrough a parnership wih Duke Universiy and he Open Prosheics Projec.