Research Article Collision Sensing Using Force/Torque Sensor

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1 Joural of Sesors Volume 2016, Article ID , 10 pages Research Article Collisio Sesig Usig /Torque Sesor Yu-Qua Leg, 1,2 Zheg-Cag Che, 1,2 Xu He, 1 Yag Zhag, 1 ad Wei Zhag 1 1 Departmet of Space Automatio Techologies & Systems, State Key Laboratory of Robotics, Sheyag Istitute of Automatio, Sheyag , Chia 2 Uiversity of Chiese Academy of Sciece, Beijig, Chia Correspodece should be addressed to Yu-Qua Leg; legyuqua@sia.c Received 15 Jue 2015; Accepted 27 August 2015 Academic Editor: Dog-ig Wag Copyright 2016 Yu-Qua Leg et al. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Collisio sesig icludig collisio positio, collisio directio, ad force size could make robots smoothly iteract with eviromet, so that the robots ca strogly adapt to the outside world. Ski sesor imitates priciples of huma ski usig special material ad physical structure to obtai collisio iformatio, but this method has some disadvatages, such as complex desig, low samplig rate, ad poor geerality. I this paper, a ew method usig force/torque sesor to calculate collisio positio, collisio directio, ad force size is proposed. Detailed algorithm is elaborated based o physical priciple ad uified modelig method for basic geometric surface. Gravity compesatio ad dyamic compesatio are also itroduced for workig maipulators/robots i gravity ad dyamic eviromet. I additio, cosiderig algorithm solvability ad uiqueess, four costraits are proposed, which are force costrait, geometric costrait, ormal vector costrait, ad curret mutatio costrait. I order to solve coflict solutio of algorithm i redudat costraits, compatibility solutio aalysis is proposed. Fially, a simulatio experimet shows that the proposed method ca achieve collisio iformatio efficietly ad accurately. 1. Itroductio I recet years, more ad more sesors are istalled o robots to realize sesig ad iteractig with eviromet. These sesors help robots achieve a large amout of iformatio about the eviromet, which cotributes robots to make correct decisio ad plaig. For example, visio sesor assists robots i obtaiig appearace iformatio of eviromet, which is used to realize target trackig ad object capture, ad so forth. Collisio sesig is also a importat eviromet sesig method, through which robots sese collisio poit ad collisio directio to avoid collisio agai, ad makes complimet cotrol come true [1, 2]. I the eviromet cotaiig huma ad robots, collisio sesig is extremely sigificat to avoid serious collisio. I additio, i [3], collisio sesig is also used for compliace assembly. Sice that collisio sesig has so may applicatios, realizatio of whole robotic body sesig is gradually carried out [4, 5]. Ski force sesor like huma ski system, which is pasted othewholesurfaceofrobots,couldseseforceactiopoit, force directio ad size [2, 5]. I the research filed, MIT has developed a special compoud material called QTC (Quatum Tuelig Composite), which is pressed by metal ad ometal [2, 6]. This sesor measures force iformatio by resistace chage whe it is pressed. Similar researches also iclude orgaic thi film composed of petacee molecular (U-Tokyo, Japa) ad E-ski (Philips Compay), ad so forth [1]. The ski force sesor looks like a ideal solutio for robotforcesesig,buttherearemaydisadvatagesthat make it hard to be used i real world, such as beig easy to damage durig collisio, expesive price, complex desig ad high eviromet requiremets, low samplig rate, ad poor geerality [4, 7]. Moreover, sesitivity of ski sesor system could ot achieve iformatio of collisio directio ad could be iflueced by may factors, such as temperature ad humidity [1]. Ski force sesor is the direct method to measure force iformatio; o the other way, it also could be checked out through idirect techiques [8, 9]. I [10] Maso ad Salisbury have proposed the theory of calculatig force iformatio usig force/torque sesor ad i [11] Bicchi et al. have developed experimets to verify it. Zhou ad Ha use the theory to realize ski force sese o the oe

2 2 Joural of Sesors x i y i p T x c c z i y c C T c z c Joit i z 2 T 2 x 2 f y 2 x B Figure 1: Collisio aalysis. z 1 z B o B T B freedom figer [12 14]. I this paper, theories of maipulator with multiple degrees of freedom are applied ad method of compatibility solutio aalysis to solve cotradictio of solutios is proposed. The rest of this paper is orgaized as follows. Sectio 2 describes detectio priciple, whe poit collisio happes, uified equatio for collisio sesig cosiderig gravity ad maipulator dyamics, ad uified modelig method for basic geometric surface. I the gravity eviromet, force aalysis is proposed i Sectio 3. I Sectio 4, force aalysis isshowwhemaipulatorisiaworkigcoditio.solvability aalysis is provided i Sectio 5, which icludes force costrait, geometric costrait, ormal vector costrait, curret mutatio costrait, ad compatibility solutio aalysis. I Sectio 6, the simulatio experimet ad results are show to prove effectiveess of the algorithm. Fially, the cocludigremarksfollowisectio7. 2. Detectio Priciple I this sectio, physical priciple about poit collisio o maipulator is itroduced. O the oe had, the whole process of force effect eeds meets force aalysis priciple, ad o the other had, the result of calculatio should suit physical laws, such as poit c which is o the maipulator surfaceadtheagleofforcedirectioadormalvectoris less tha π/ Aalysis. Assume that o gravity ad maipulator are static; force aalysis is show i Figure 1. I order to apperceive whole system, force/torque sesor is assembled o the base ad close to the first joit. The force/torque sesor could measure force i three directios ad torque rotated of three coordiate axes. I Figure 1, poit C meas collisio poit, which is assumed o ith joit. The ceter of force/torque sesor is T 1 y 1 y B x 1 m expressed as B,which is set as origi of B coordiate system. Every joit of maipulator is built coordiate system as T i accordig to DH parameter method. T i represets coordiate system of ith joit, ad p, f,adτ,respectively,meacollisio force, measured force, ad measured torque. c represets ormal vector of poit c. T c could be achieved by traslatig coordiate system T i adorotatio.thecoordiateof poit C i T B is obtaied by coordiate trasformatio, as show i the followig: i 1 c B T = 1 B T 2 1 T i i 1 T c i cθ i sθ i cα i sθ i sα i a i cθ i [ [[[[ i T = sθ i cθ i cα i cθ i sα i a i sθ i 0 sα i cα i d, i ] [ ] x ic [ c [[[[ i T = y ic z. ic ] [ ] T, (1) Whe collisio occurs, the outside force is p = (f cx,f cy,f cz ) T, ad data of force/torque sesor are f = (f x,f y,f z ) T ad τ =(τ x,τ y,τ z ) T. Accordig to force aalysis, data of outside force i T B should be equal to measured data i ideal coditio, as show i the followig: f = f cb, τ = τ cb, (2) f cb = (f cbx,f cby,f cbz ) T = (T (p Tc B T) 3,1 )T, (4) τ cb = (τ cbx,τ cby,τ cbz ) T = c B p = (T (c i c B T) 3,1 ) p. (5) I (4), (3) p = (f cx,f cy,f cz,1) T (6) ad T( ) 3,1 meas extractio of elemets of the first three rows ad the first colum. I (5), c i =(x ci,y ci,z ci,1) T. (7) Cosiderig factor of gravity ad maipulator dyamics i real world, geeral equatio could be show as follows: f = f cb + f GB + f db τ = τ cb + τ GB + τ db. I (8), f cb ad τ cb, respectively, express force ad torque caused by collisio mappig i basic coordiate system B; (8)

3 Joural of Sesors 3 z γ α z x x β β y y α=β=γ α 0 β γ Figure 2: Uified modelig method for basic geometric surface. f GB ad τ GB, respectively, mea force ad torque caused by gravity mappig i basic coordiate system B, whichwill be aalyzed i Sectio 3; f db ad τ db, respectively, express force ad torque caused by maipulator dyamics mappig i basic coordiate system B,whichwillbeshowiSectio4. I (8), f GB, τ GB, f db,adτ db couldbecalculatedbasedo states of maipulator ad joit physical properties, such as joit agle, joit velocity, joit acceleratio, ad joit quality. Collisio iformatio is just coteted i f cb ad τ cb,thatis, the parameters of f cx, f cy, f cz, x ci, y ci,adz ci Physical Costrait. Normal geometrical surface cotais ellipsoid, sphere, cylidrical surface, ad plae. They are able to costruct all simple surfaces icludig outlie of maipulators. Mathematical descriptio mode of all maipulator surface is achieved through coordiate trasformatio. Fromtheroleofgeometricalchage,thecoreoffourtypes of surface is ellipsoid, which is able to chage to other three types by chagig parameters, as show i Figure 2. Assume three axis legths of ellipsoid are 2α, 2β, ad 2γ, settig ceter as origi of coordiate system. Whe α= β=γ, sphere will be formed; whe γ +, cylidrical surface is achieved; ad whe α +, β 0,ad γ, plae surface is displayed. I summary, it just eeds to build ellipsoid mode to describe all surface, as show i the followig: S (c) = c T A T Ac =1, (9) 1 α 0 0 A = 0 1 β 0. (10) [ ] [ γ] Normal vector of poit C is set as c ad could be calculated with equatio as follows: c = S (c) S (c) = 2A2 c 2A2 c z x z x y y = A2 c, (11) A2 c x i y i T i G i 1 z i... D i G i r i 1 G 2 r i Joit i z 2 r 2 T 2 x 2... f y 2 Figure 3: Gravity aalysis. r 1 x B z 1 G 1 z B o B c =(x,y,z)meas coordiate values ad represets gradiet. 3. Gravity Compesatio I the above sectio, gravity elemet is sampled as f GB ad τ GB. I this sectio, gravity ifluece o sesor will be aalyzed, which relates to joit legth, joit agle gravity ceter of joit, ad quality. All joits cause force ad torque o sesor, so each of them eeds to be calculated. aalysis is show i Figure 3 i gravity. I Figure 3, D i =(x di,y di,z di ) T is gravity ceter positio i T i coordiate; the r i meas coordiate of gravity ceter of ith joit ad is expressed as G 0 r i = (T ( i B TD i) 3,1 ) T, (12) D i =(x di,y di,z di,1) T. (13) Assumig variety of sesors is f GB R 3, τ GB R 3,the (14) ad (15) are achieved: f GB = G 0 + G 1 + G 2 + +G i + +G = r 0 T 1 i=0 τ GB = r 0 G 0 + r 1 G 1 + +r i G i + +r = G = Ĝ 0 r 0 + Ĝ 1 r 1 + +Ĝ i r i + +Ĝ r i=0 Ĝ i r i. y 1 y B x 1 m G i, (14) (15) I (14), G i = (0, 0, G i ) T (i )ad is the total umber of joits.

4 4 Joural of Sesors... f db z B τ db Due to the fact that T i is a motioal coordiate, Coriolis force emerges i the whole system, which is expressed as f kdi =2m i k Ti ω Ti. (20) xi T i y i ω i α i z i D i ω Ti Joit i a i o x B B y 1 y B I (20), ω Ti ad k Ti, respectively, mea velocity vector ad agular velocity vector of T i coordiate relative to basic coordiate. Based o the priciple of equivalece, the above forces ad torque of i joit are trasfered to B, whichcouldbe expressed as v Ti z 1 T 1 x 1 f fbdi =(T(f T D di B T) 3,1 )T,... T 2 y 2 z 2 x 2 Figure 4: Dyamic force aalysis. f kbdi =(T(f T kdi B T) 3,1 )T, i τ fbdi = f fbdi D Bi = f fbdi (T ( i B TD i) 3,1 ) T, τ kbdi = f kbdi T i = f kbdi (T ( i B T) 3,1 )T, τ αbdi = τ αdi. (21) I (15), i order to easily calculate with matrix, vector G i is trasformed ito matrix Ĝ i : 0 0 G i Ĝ i = [ ], (i ). (16) [ G i 0 0 ] 4. Dyamic Compesatio I Sectio 3, maipulator dyamic is sampled as f db ad τ db. I this sectio, dyamic factor is aalyzed. Whe maipulator works, it also causes reactio force to sesor, so calculatio is also eeded. Dyamic force is very complex, which relates to joit legth, joit agle, joit agular velocity, joit agular acceleratio, ad so o. I Figure 4, dyamic force is aalyzed. I Figure 4, assume α i is joit agular acceleratio ad D i =(x di,y di,z di ) T is gravity ceter positio i T i coordiate. The, acceleratio of gravity ceter is expressed as a i = α i D i. (17) I T i coordiate, i order to keep movig as i Figure 4, theforceadtorquearecalculatedasshowithefollowig: f di =m i a i =m i a i D i =m i â i D i, τ αdi = I i α i. (18) I (18), m i ad I i, respectively, express quality ad iertia of ith joit, ad â i = [ 0 a iz a iy [ a iz 0 a ix ]. (19) [ a iy a ix 0 ] I the above equatio, f fbdi ad f kbdi,respectively,mea acceleratio force ad Coriolis force i the basic coordiate; τ fbdi ad τ kbdi express torque of force trasformatio; torque could trasfer with o other chages, so τ αbdi = τ αdi. Maipulator cotais may joits, so all effect of force of joits o the basic coordiate is show as f db = τ db = i=1 i=1 f Bdi = τ Bdi = i=1 i=1 5. Solvability Aalysis (f fbdi + f kbdi ), (τ fbdi + τ kbdi + τ αbdi ). (22) At preset, problem will be aalyzed uder the followig limits i this subsectio: (a) Material of maipulator is rigid, which meas o deformatio produce. (b) Collisio is caused by maipulator ad poit of object. (c) All sesor is ideal. (d) Gravity is igored i this subsectio, because it has to be calculated i Sectio 5.3. (e) Maipulator dyamic is discussed i Sectio 5.4, so assume maipulator is static ad motio of outside object causes collisio. I order to esure solvability ad uiqueess, four costraits are provided ad compatibility priciple is proposed Costrait. From Sectio 2, combie (8) ad (9); seve equatios are achieved with six variables. Moreover, f GB, τ GB, f db,adτ db arezeroudertheaboveassumptio.

5 Joural of Sesors 5 I order to easily calculate with matrix, vector p is trasformed ito matrix p: Calculate rak(m) p = [ 0 f cz f cy [ f cz 0 f cx ]. (23) [ f cy f cx 0 ] The, part of (8) could be chaged to Whether rak(m) =6? Yes Get six groups of solutios No c τ cb = p (T (c i B T) 3,1 ). (24) Combiig (1), (8), ad (24), the followig equatio is achieved: Remove sigular solutios Average of solutio Calculatio [ f τ ]=M [ (T (p T c B T) 3,1 )T ], (25) c [ (T (c i B T) 3,1 ) ] M = f cz f. (26) cy [ f cz 0 f cx ] [ f cy f cx 0 ] M is relatio matrix ad it is sigular matrix i ideal coditio, that is, rak(m) = 5. A series of solutios about (24) are obtaied. There are may states that make rak(m) = 6, such as oise of sesor, precisio of sesor, ad deformatio. This problem will be solved i Sectio Geometric Costrait. act o the surface of maipulator, so mathematical directio of whole outlie is ecessary to costrait solutio, that is, S (c) =0. (27) S( ) meas mathematical directio of maipulator surface Normal Vector Costrait. Because that force ca oly apply to maipulator from outside, the agle of force directio ad ormal vector is less tha π/2. Based o this costrait, equatio could be show as p T <0. (28) 5.4. Curret Mutatio Costrait. Strage geometries of maipulator surface ad multiple degrees of freedom of maipulator may cause differet force actio with the same data of force/torque sesor. I this coditio, uiqueess solutio could ot be calculated, so curret mutatio costrait is draw i. Assumig collisio poit is o the ith joit, the the curret of this joit will chage suddely. I additio, the curret of kth (k i < 0) joit also produces mutatio, but Select poit o outlie close to average solutio Calculate force size i every axis Figure 5: Process of compatibility. Fiish the curret of kth (k i>0) joit will ot chage suddely. I this law, collisio poit will be judged o the ith joit. O the oe had, this costrait avoids multiple solutios,adotheotherhad,itcouldesuretherageof collisiopoitadacceleratethespeedofcalculatio Compatibility Solutio Aalysis. I Sectio 5.1, if rak(m) = 5, the uiqueess solutio will be achieved combiig with (9) which meas compatibility is the best. But may elemets cause rak(m) = 6,such as oise of sesor, precisio of sesor, ad deformatio. There is o solutio through combiig (8) ad (9), so compatibility solutio aalysis is proposed to esure a approximate solutio. I Figure 5, process of method is show. From Figure 5, whe rak(m) =6,fiveequatioswillbe chose from matrix equatio (25) ad combiig with (9); the oe group of solutio is obtaied. Other five groups of solutios will be also achieved by the same way. Every solutio icludes the iformatio about positio ad force size i three coordiate axes. Six ormal vectors about solutio positio are achieved through (25). The sigular solutios should be removed by deviatio of positios ad ormal vectors. At this momet, average values of the rest of solutios are calculated, ad choose the closest poit i outlie of maipulator as approximate solutio. At last, force size i three coordiate axes will be achieved by (25). This method avoids o solutio coditio ad achieves a approximate solutio. 6. Simulatio Experimet Oe maipulator with three degrees of freedom is established, as show i Figure 6. I order to simplify aalysis,

6 6 Joural of Sesors Table 1: Parameters of maipulator. Name Quality (Kg) Positio of gravity ceter i local coordiate (mm) Lik (0,0,60) Lik (0, 0, ) Lik (86.256,0,0) Lik ( , 0, 0) l 4 Lik 3 z 2 l 3 Lik 2 x 2 l 2 l 1 Lik 1 Lik 0 o 2 y 2 /torque sesor f o 3 y 3 z 3 p r c x 0 x 3 c z 1 o 1 Figure 6: Maipulator structure. o 4 y 1 z 4 y 4 x 1 x 4 i Top of Lik 3: x 2 4 +y2 4 +z2 4 =r2 R, (32) x 4 >0. Accordig to coordiate trasformatio matrix as show cos θ 1 si θ [ 1 [[[[ 0 T= si θ 1 cos θ l, 1 ] [ ] cos θ 2 0 si θ 2 0 [ 2 [[[[ 1 T= si θ 2 0 cos θ l, 2 ] [ ] (33) cos θ 3 si θ 3 0 l 3 cos θ 3 [ 3 [[[[ 2 T= si θ 3 cos θ 3 0 l 3 si θ , ] [ ] the outlie of maipulator is composed of cylidrical surface ad semisphere, ad the size is set to r R. I additio, the material of every joit is uiform ad set as 1060 alloys (ρ = 2700 kg/m 3 ) ad geometry of every joit is cetral symmetry; the gravity ceter of joit lies o cetral axis. Whe collisio occurs, data of force/torque sesor chage with time. I egieerig applicatio, some sigal processig methodswillbeadoptedtoachieveeffectivedata.ithis paper, our attetio is focused o the method of collisio sesig, so i order to simplify aalysis, assume that maipulator is static. Parameters of liks are listed i Table 1. I Figure 6, l 1 = 120 mm, l 2 = 150 mm, l 3 = 200 mm, l 4 = 200 mm, ad r R = 40mm. Due to the fact that joit coected surface is complex, assume collisio poit is oly o lik rod. Surface of each joit is described i coordiate of itself as follows: Lik 1: x 2 1 +y2 1 =r2 R, (29) 0<z 1 l 2 r R. Lik 2: Lik 3: y 2 2 +z2 2 =r2 R, r R x 2 l 3 r R. y 2 3 +z2 3 =r2 R, r R x 3 l 4 r R. (30) (31) l 4 [ 4 [[[[ 3 T= , ] [ ] equatios of liks outlie i basic coordiate will be obtaied asshowithefollowig: Lik 1: (x 1 cos θ 1 y 1 si θ 1 ) 2 +(x 1 si θ 1 y 1 cos θ 1 ) 2 =r 2 R, l 1 <z 1 l 1 +l 2 r R. Lik 2: Lik 3: (x 2 A+y 2 B) 2 +(l 1 +l 2 ) 2 =r 2 R, (l 1 )C<x 2 C y 2 B (l 1 +l 2 r R )C. (x 3 (cθ 3 A+sθ 3 C) y 3 (cθ 3 C sθ 3 A) + l 3 sθ 3 C +l 3 cθ 3 A) 2 +(l 1 +l 2 +z 3 ) 2 =r 2 R, r R (cθ 3 C sθ 3 A) l 3 sθ 3 A+l 3 cθ 3 C x 3 (cθ 3 C sθ 3 A) y 3 (cθ 3 A+sθ 3 C) l 3 sθ 3 A+l 3 cθ 3 C (l 4 r R )(cθ 3 C sθ 3 A) l 3 sθ 3 A+l 3 cθ 3 C. (34) (35) (36)

7 Joural of Sesors 7 Table 2: Differet poit experimet. Number size (N) directio (N) positio (mm) Detected force (N) Detected torque (N m) Calculated positio (mm) Calculated force (mm) size error (%) directio error ( ) Positio error (%) TopofLik3: (l 4 C sθ 3 D+x 4 (cθ 3 C sθ 3 A) y 4 (cθ 3 A+sθ 3 C) Cosiderig gravity compesatio, the maipulator is aalyzed as show i Figure 7, a 1 = mm ad a 2 = mm, l 3 sθ 3 A+l 3 cθ 3 C) 2 +(l 4 (cθ 3 A) + sθ 3 C r 1 =[a 1 cos θ 1 cos θ 2,a 1 si θ 1 cos θ 2,l 1 +l 2 +x 3 (cθ 3 A+sθ 3 C) y 3 (cθ 3 C sθ 3 D) + l 3 sθ 3 C (37) +a 1 si θ 2 ] T, r 2 =[a 1 cos θ 1 cos θ 2 (39) +l 3 cθ 3 D) 2 +(l 1 +l 2 +z 4 ) 2 =r 2 R, +a 2 cos θ 1 cos θ 3,a 1 si θ 1 cos θ 2 x 4 (cθ 3 C sθ 3 D) > 0, +a 2 si θ 1 cos θ 3,l 1 +l 2 +a 1 si θ 2 +a 2 si θ 3 ] T. A=cθ 1 sθ 2 +sθ 1 cθ 2, B=cθ 1 cθ 2 +sθ 2 sθ 1, C=cθ 1 cθ 2 sθ 2 sθ 1, D=cθ 1 sθ 2 sθ 1 cθ 2. (38) Mode of maipulator is built i ADAMS, ad two groups ofdataaretestedtoverifyouralgorithm. Assume θ 1 =π/6, θ 2 = π/6,adθ 3 = π/4,ad100n force applies o the surface. Te poits are tested, throughout the etire surface. I aother experimet, assume θ 1 =π/6, θ 2 = π/6,ad θ 3 = π/4,butforcesizeischagedatthesamepositioc = ( ). I Tables 2 ad 3, force size, force directio, ad force positio are kow ad set as iput coditios; detected

8 8 Joural of Sesors Table 3: Differet force experimet. Number size (N) directio (N) positio (mm) Detected force (N) Detected torque (N m) Calculated positio (mm) Calculated force (mm) size error (%) directio error ( ) Positio error (%) a 1 a 2 θ 3 positio ad calculated force could be obtaied by (8) ad coordiate trasformatio with a series of calculatios; force size error, force directio error, ad positio error are put forward to judge accuracy ad validity of the calculatio. Equatio of each error is show as follows: θ 2 G 3 size error: θ 1 r 1 G 2 r2 ΔS = f2 sx +f2 sy +f2 sz f2 cbx +f2 cby +f2 cbz. (40) fcbx 2 +f2 cby +f2 cbz G 1 G 0 o 0 z 0 Figure 7: Gravity compesatio aalysis. force ad detected torque express the data of force/torque sesor, which could be achieved by measuremet; calculated y 0 x 0 Δθ directio error: = arccos ( f sx f cbx +f sy f cby +f sz f cbz fsx 2 +f2 sy +f2 sz fcbx 2 +f2 cby +f2 cbz ). (41) Positio error: ΔP = x cb x sb + y cb y sb + z cb z sb. (42) xcb 2 +y2 cb +z2 cb

9 Joural of Sesors 9 Error (%) Error ( ) test collisio iformatio, it must esure whether the biggest errors meet accuracy requiremets at the farthest poit of maipulator. I Figure 9, force directio error ad positio error become smaller with bigger force, ad force size error is fluctuatig. Sesitivity of this method is almost certai at the same poit, so force directio error ad positio error become smaller with bigger force. About fluctuatig of force size error, (40) has give our explaatio that umerator ad deomiator ifluece force size error at the same time ad have the same tred. Error (%) Distace (mm) size error directio error Positio error Figure 8: Relatio betwee collisio positios ad errors size error directio error Positio error (N) Figure 9: Relatio betwee force ad errors. I these three equatios, f sx, f sy,adf sz mea force size of calculated force ad x sb, y sb,adz sb mea calculated positio mappig to three axes i basic coordiatio; f cbx, f cby,adf cbz mea force size of force ad x cb, y cb,ad z cb mea calculated positio mappig to three axes i basic coordiatio. From Tables 2 ad 3, collisio detectio is effective ad the relative error is extremely small i simulatio eviromet. I order to ituitively express data relatio, Figures 8 ad 9 are draw to show them. I Figure 8, relatio betwee differet collisio positios ad each error is established. I Figure 9, relatio betwee differet force sizes ad each error is established. I Figure 8, force size error, force directio error, ad positio error all become larger with farther distace. Differet collisio poit produces differet error ad each error will be larger with farther distace. If we use this method to Error ( ) 7. Summary Both aimal s arm ad perso s arm are wrapped by skis, which help them protect their biological orgaizatio ad apperceive evirometal iformatio, such as temperature chage ad object collisio. Researchers except maipulators alsohavethesamefuctiowithbiologicalarm,butthe method is expesive ad easily damaged by distributig sesors o the whole maipulator s outlie, so oe idirect method to detect collisio poit ad directio by usig force/torque sesor is put forward. Compared to ski force sesor, the force/torque sesor is easy to be istalled ad maitaied. I our method, costrait equatios ad compatibility solutio aalysis is used to esure existece of solutio. Moreover, gravity compesatio ad dyamic compesatio are also described, which idicate this theory could be effective i gravity eviromet ad whe maipulators are exercisig. At last, the simulatio experimet is executed to verify our algorithm ad the result is perfect. But there exist a lot of egieerig problems, if this method is used i real system, which could be as follows: (1) how to extract more accurate force ad torque iformatio, basedothefactthatsigalofsesorisfluctuat;(2) how to describe maipulator s outlie accurately, because it has complex shape; (3) how to measure force ad torque i a istat whe maipulator collides; (4) how to realize realtime perceptio, o the coditio that this theory cotets a lot of calculatios. I order to promote the theory i egieerig applicatio some experimets will be doe o a real system, especially puttig focus o the above problems. Coflict of Iterests The authors declare that there is o coflict of iterests regardig the publicatio of this paper. Ackowledgmet This work is supported by Natioal Postdoctoral Foudatio of Chia uder Grat 2013M541258, State Key Laboratory of Robotics (2015-Z08). Refereces [1] J.Shi,H.Wu,adZ.Ma, Desigofaewrobotski, Robot, vol. 35, o. 1, pp , 2013.

10 10 Joural of Sesors [2]M.I.Tiwaa,A.Shashak,S.J.Redmod,adN.H.Lovell, Characterizatio of a capacitive tactile shear sesor for applicatio i robotic ad upper limb prostheses, Sesors ad Actuators A: Physical,vol.165,o.2,pp ,2011. [3] R. Hog, Compliat cotrol o six axis maipulator, Robot, vol. 22, o. 3, pp , [4]Y.Huag,W.Lu,X.Zhao,C.Lia,adY.Ge, Desigad experimet of flexible multi-fuctioal tactile sesors for robot ski, Robot,vol.33,o.3,pp ,2011. [5]T.Someya,Y.Kato,T.Sekitaietal., Coformable,flexible, large-area etworks of pressure ad thermal sesors with orgaic trasistor active matrixes, Proceedigs of the Natioal Academy of Scieces of the Uited States of America,vol.102,o. 35, pp , [6] L. Wag, T. Dig, ad P. Wag, Research o stress ad electrical resistace of ski-sesig silicoe rubber/carbo black aocomposite durig decompressive stress relaxatio, Smart Materials ad Structures,vol.18,o.6,ArticleID065002, [7] L. Zhag, W. He, ad Y. Jia, Research of bioic ski sesor for robot, Robot, vol. 21, o. 4, pp , [8] Y.Huag,X.Mig,adB.Xiag, Twotypesofflexibletactile sesor arrays of robot for three-dimesio force based o piezoresistive effects, i Proceedigs of the IEEE Iteratioal Coferece o Robotics ad Biomimetics,pp ,February [9] T. Tsujimura ad T. Yabuta, Object detectio by tactile sesig method employig F/T iformatio, i Proceedigs of the Iteratioal Coferece o Robotics ad Automatio, pp , Scottsdale, Ariz, USA, April [10] M. Maso ad J. Salisbury, Robot Hads ad the Mechaical of Maipulatio, MIT Press, [11] A. Bicchi, J. Salisbury, ad D. Brock, Cotact Sesig from Measuremet, MIT Press, [12] X. Zhou, Q. Shi, ad Z. Li, Cotact localizatio usig force/torque measuremets, i Proceedigs of the 13th IEEE Iteratioal Coferece o Robotics ad Automatio,vol.2,pp , IEEE, Mieapolis, Mi, USA, April [13] X. Zhou, Z. Li, ad Q. Zhag, Tactile sesatio based o wrist force sesor, Robot,vol.19, o.4,pp , [14] Z. Ha, T. Wag, Y. Zhag, ad J. Liu, Selectio of calculatio model for cotact sesig of robot had usig force/torque measuremet, Joural of Beijig Uiversity of Aeroautics ad Astroautics, vol. 30, o. 5, pp , 2004.

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