On using an Array of Fiber Bragg Grating Sensors for Closed-Loop Control of Flexible Minimally Invasive Surgical Instruments

Transcription

1 213 IEEE/RSJ Intenational Confeence on Intelligent Robots and Systems (IROS) Novembe 3-7, 213. Tokyo, Japan On using an Aay of Fibe Bagg Gating Sensos fo Closed-Loop Contol of Flexible Minimally Invasive Sugical Instuments Roy J. Roesthuis, Sande Janssen and Sathak Misa Abstact Flexible minimally invasive sugical instuments can be used to taget difficult-to-each locations within the human body. Accuately steeing these instuments equies infomation about the thee-dimensional shape of the instument. In the cuent study, we use an aay of Fibe Bagg Gating (FBG) sensos to econstuct the shape of a flexible instument. FBG sensos have seveal advantages ove existing imaging modalities, which makes them well-suited fo use in a clinical envionment. An expeimental testbed is pesented in this study, which includes a tendon-diven manipulato. A nitinol FBG-wie is fabicated, on which an aay of twelve FBG sensos ae integated, and distibuted ove fou diffeent sets. This wie is positioned in the backbone of the manipulato. Axial stains ae measued using the FBG sensos, fom which the cuvatue of the manipulato is calculated. The thee-dimensional manipulato shape is econstucted fom the cuvatue, which is used to stee the manipulato tip. We ae able to stee the manipulato along vaious tajectoies (twodimensional and thee-dimensional), and also eject distubance loa. We obseve a minimum mean tacking eo of.67 mm fo the cicula tajectoy in closed-loop contol. This study demonstates the potential of steeing flexible minimally invasive sugical instuments using an aay of FBG sensos. I. INTRODUCTION Recent studies have shown geat inteest in steeing a vaiety of flexible, minimally invasive sugical (MIS) instuments. These instuments vay fom small diamete (φ 1 mm) needles with bevel tips (e.g., fo beast biopsies) to flexible cathetes (e.g., fo beating heat sugey) [1] [12]. These instuments often have a flexible stuctue, which causes them to bend when they ae subjected to inteaction foces. Hence, this allows them to be steeed aound obstacles, and enables tageting difficult-to-each locations in the human body. In ode to stee such instuments to a desied location, infomation is equied about the shape of the instument. Pevious eseach used steeo-vision camea systems to acquie infomation about the location of the instument [2]. Howeve, camea-based systems cannot be used in vivo. Electomagnetic sensos have also been used to locate the tip of the instument [1]. Such sensos can be used in vivo, but they ae sensitive to distotion induced by metallic objects and electical noise. Hence, this limits the use of electomagnetic localization in a clinical envionment. Pevious studies used medical imaging techniques, such as ultasound images, The authos ae affiliated with MIRA Institute fo Biomedical Technology and Technical Medicine, Univesity of Twente, The Nethelan. This eseach is suppoted by the Dutch Technology Foundation STW (H-Haptics Poject #12159), which is pat of the Nethelan Oganization fo Scientific Reseach (NWO) and patly funded by the Ministy of Economic Affais, Agicultue and Innovation. (A) neutal axis (B) dl dθ δ b γ a δ b b γ b FBG-sets Fig. 1. A section of a flexible instument (which could be a needle, cathete o colonoscope) is shown. An aay of co-located FBG sensos (i.e., FBGsets) ae placed along the instument shaft. (A) A set of thee co-located FBG sensos ae used to measue axial stain, which is used to calculate the cuvatue. (B) Instument shape is econstucted fom the cuvatue (κ = 1/). (C) A coss-section of the instument: The position of each fibe is given by the distance fom the cente of the instument ( a, b and c) and the angle with espect to the othe fibes (γ a, γ b and γ c). The distance fom the fibes to the neutal axis is indicated by δ a, δ b and δ c. x-ay computed tomogaphy (CT) scans and magnetic esonance imaging (MRI), in ode to aquie instument shape. Howeve, these metho have seveal dawbacks: Ultasound has low tissue contast. MRI has a low efesh ate and hence, is not well-suited fo eal-time applications. CT exposes the patient to high doses of adiation and hence, is also not ecommended fo continuous use. Fibe Bagg Gating (FBG) sensos can be an altenative to acquie thee-dimensional (3D) instument shape in vivo. FBG sensos have seveal popeties which makes them wellsuited fo biomedical applications, e.g., biocompatibility, non-toxic, chemical inetness and electomagnetical inetness [13]. Also, cuent technologies enable data acquisition at ates up to 2 khz with FBG sensos. Hence, this makes them applicable fo eal-time applications. FBG sensos can be used to measue mechanical stain [14]. Due to the small size of FBG sensos (φ 25 µm), they can be integated along the shaft of a flexible MIS instument (Fig. 1). Integating an aay of FBG sensos along the instument shaft enables measuing the stain caused by the bending of the instument. This stain can be used to detemine the cuvatue along the shaft of the instument at the location of the FBG sensos. This cuvatue is then used to econstuct the 3D instument shape. Pevious studies have used FBG sensos to econstuct the shape of a colonoscope and flexible sugical needles [15] [19]. These studies have shown that instument shape can be econstucted with high accuacy using FBG sensos. In the cuent study, we demonstate using an aay of FBG (C) δ a ' a c δ c c a γ c /13/$ IEEE 2545

2 sensos to stee a flexible instument. Recently, Abayazid et al. demonstated flexible needle steeing using an aay of FBG sensos [19]. Howeve, the tip deflections in that study wee small (i.e., 5 mm) compaed to ou study. The goal of ou study is to show that FBG sensos have the potential to be used to contol a lage vaiety of flexible MIS instuments. In ode to demonstate this, we have constucted a tendondiven manipulato. This manipulato is actuated by a total of fou tendons, allowing it to bend in all diections. A flexible nitinol wie with an aay of twelve FGB sensos has been fabicated, and is placed in the hollow backbone of the manipulato. This allows to econstuct the shape of the manipulato as it deflects. The econstucted position of the manipulato tip is then used as feedback in a closedloop contol system. The fowad and invese kinematics of the manipulato ae deived, and ae used in a closed-loop contol system to stee the tip of the manipulato to a desied position. The pefomance of the system is demonstated in vaious tajectoy tacking expeiments. We also evaluate the ability of the system to eject load distubances. The pape is oganized as follows: Section II descibes the metho fo econstucting the 3D shape of a flexible instument using an aay of FBG sensos. In Section III, the kinematics of the obotic manipulato is pesented. The expeimental setup is pesented in Section IV, and the expeimental esults ae discussed in Section V. Finally, we conclude the pape in Section VI, and diections fo futue wok ae given. II. THREE-DIMENSIONAL SHAPE SENSING USING FIBER BRAGG GRATING SENSORS This section descibes the metho to econstuct the 3D shape of a flexible instument using an aay of FBG sensos. Fist, we descibe the method to calculate stain fom an FBG senso. This is followed by the computation of cuvatue and its diection fom a set of FBG sensos. Finally, we descibe 3D econstuction of instument shape. A. Stain Measuement An FBG has the popety to eflect light of a specific wavelength, called the Bagg wavelength (λ B ), which is given by [14] λ B = 2n e Λ, (1) whee n e is the effective efactive index of the gating in the fibe coe and Λ is the gating peiod. The effective efactive index and the gating peiod ae affected by changes in mechanical stain and tempeatue and hence, this esults in a change in the Bagg wavelength. This enables an FBG to be used as a senso fo measuing mechanical stain o tempeatue. Assuming constant tempeatue, the shift in Bagg wavelength due to mechanical stain (ε x ) is given by [2] λ B = λ B (1 p e ) ε x. (2) The axial stain of an instument (ε x ) can be measued using FBG sensos. This is done by placing an optical fibe with FBG sensos paallel to the longitudinal axis of the k k z s= (s) θ(s) n(s) s=l (k(s),z(s)) t(s) Fig. 2. A plana cuve ( (s) ) is paametized by the ac length (s). The slope of the cuve with espect to the z-axis is denoted by θ(s). The Fenet-Seet vectos ae also shown: The tangent vecto (t(s)) and nomal vecto (n(s)). instument (Fig. 1). Assuming pue bending, the following elationship exists between the axial stain in the fibe and the distance (δ) of the fibe to the neutal bending plane of the instument [21]: dl ε x = = δ = κδ, (3) dl whee κ and ae the cuvatue and adius of cuvatue of the instument, espectively (Fig. 1). Substituting (3) into (2) gives an expession which elates the shift in Bagg wavelength to cuvatue λ B = λ B (1 p e ) κδ. (4) In the next subsection, we descibe the calculation of cuvatue (κ) and its diection (ϕ) using the stain measuements fom a set of multiple co-located FBG sensos. B. Cuvatue Calculation The cuvatue and its diection can be detemined using stain measuements fom a set of multiple FBG sensos at the same location along the instument shaft (Fig. 1). In theoy, two stain mausuements ae sufficient to detemine the cuvatue. In pactice, tempaatue changes and axial foces also contibute to the axial stain by an offset (ε ). Hence, thee stain measuements ae used to compensate fo this offset. The elationship between the axial stain due to bending and the distance fom the neutal bending plane is given by (3). Thus, the following set of equations ae deived fo the stains at the location of thee fibes (denoted by a, b and c) at a coss-section of the needle (Fig. 1): ε a = κδ a + ε = κ a sin(ϕ) + ε, ε b = κδ b + ε = κ b sin(ϕ + γ a ) + ε, ε c = κδ c + ε = κ c sin(ϕ + γ a + γ b ) + ε, whee ϕ is the angle between a and the neutal axis (Fig. 1), and indicates the diection of the cuvatue. The position ( a, b and c ) and oientation (γ a, γ b and γ c ) of the FBG sensos ae assumed to be known and constant (i.e., the neutal plane is always assumed to be at the cente of the needle). By solving the set of equations (5), the unknowns ae detemined (i.e., κ, ϕ and ε ). Since the cuvatue can only be detemined at the locations of the FBG sensos, z (5) 2546

3 intepolation nee to be pefomed to evaluate the cuvatue along the entie instument shaft. In the next subsection, we explain the econstuction of 3D instument shape using the cuvatue and its diection. C. Thee-Dimensional Shape Reconstuction Fo this study, we conside the instument to bend in a single plane, and theefoe it can be seen as a plana cuve. Fist, Fenet-Seet fames ae used to econstuct the instument shape. Next, the diection of cuvatue (ϕ) is used to calculate the position of the plana cuve in 3D space. Let (s) be a plana cuve (Fig. 2) paametized by the ac length (s) [ ] z(s) (s) =. (6) k(s) The cuvatue of this plana cuve is given by κ(s) = dθ(s), (7) whee θ(s) is the angle between the tangent at a point along the cuve and the positive diection of the z-axis (i.e., slope of the cuve). Using Fenet-Seet fames, the tangent vecto of this cuve is defined as t(s) = d(s) = [ dz(s) ] T dk(s) = [ cos(θ(s)) sin(θ(s)) ] T. (8) Since the cuvatue is known fom the FBG senso measuements, the slope of the cuve ( θ(s) ) is calculated by integating the cuvatue (7) θ(s) = s κ(s) + θ, (9) whee θ is the intial slope (i.e., s = ). The cuve ((s)) can then be calculated by integating the tangent vecto in (8) [ ] s z(s) (s) = = t(s) k(s) [ ] s = cos(θ(s)) + z (1) s sin(θ(s)) + k, whee z and k ae the initial deflections. The diection of the cuvatue (ϕ) and deflection k(s) ae used to calculate the x-position and y-position of the cuve x(s) = k(s) cos(ϕ), y(s) = k(s) sin(ϕ). (11) Thus, the 3D ( position of a point along the shaft of the instument (s) = [ x(s), y(s), z(s) ] ) T can be calculated using the cuvatue and its diection. III. KINEMATICS OF THE MANIPULATOR This section descibes the kinematics (fowad and invese) of the manipulato that will be used fo closed-loop expeiments with the FBG sensos (Fig. 3). The manipulato consists of a flexible backbone (of length l b ) on which a seies of equally spaced tendon guides ae mounted. Fou z y tendon guide l c /n tendon x flexible backbone l /n i d i ' zb y b /2n x b y t /n t 3 x t z t t 2 d tb d 4 Fig. 3. The manipulato consists of a flexible backbone on which tendon guides ae mounted. Actuating a total of fou tendons (t 1,..., t 4 ) causes the manipulato to deflect with a constant adius of cuvatue () and outof-plane bending angle (ϕ). In this figue, the manipulato ben in the xzplane (i.e., ϕ = ). Top view of a section of the continuum manipulato in a bent configuation. The manipulato is divided into n segments, whee each segment is defined between two subsequent tendon guides. tendons ae outed though these guides at 9 angles fom one anothe. The tendons ae all connected to the tendon guide at the tip. The manipulato deflects in a single-bend shape when the tendons ae actuated (i.e., pulled). A. Fowad Kinematics We detemine the fowad kinematics of the manipulato to deive the elationship between the tendon lengths (l 1,..., l 4 ) and the position of the manipulato tip (x t, y t, z t ). The fowad kinematics of such a continuum-style manipulato has been descibed by Jones and Walke fo a thee-tendon diven manipulato [22]. Futhe, Webste and Jones pesented a simplified deivation of these kinematics [6] both fo the case of thee actuatos and fou actuatos. Thei appoach assumes that the manipulato ben with a constant adius of cuvatue (). We use the same appoach to deive the kinematics of ou fou-tendon diven manipulato (Fig. 3a). The position of the manipulato tip is detemined by the adius of cuvatue (), and the out-of-plane bending angle (ϕ). Note that this angle is equal to the diection of the cuvatue (Section II-B), in case the fist tendon (t 1 ) is aligned with i tip t 4 ' t

4 fibe a. The length of a hypothetical cente cable (Fig. 3b) is given by l c = 2n sin ( β/2n ), (12) whee n indicates the numbe of segments and β is equal to l b /. Futhe, the lengths of the individual tendons (l i, fo i = ) ae given by l i = 2n i sin ( β/2n ), (13) The adius of cuvatue ( i ) at fo each tendon is elated to the distance of the tendon to the neutal axis (d i ) by i = d i, (14) whee d i is elated to the out-of-plane bending angle by d i = d tb cos ( ϕ + (i 1)π/2 ), (15) whee d tb is the distance fom the tendon to the backbone (Fig. 3a). Substituting (15) into (13), and combining with (12) gives l c = l i + 2nd tb cos ( ϕ + (i 1)π/2 ) sin ( β/2n ). (16) Combining (16) fo all fou tendons, esults in the following: l c = l 1 + l 2 + l 3 + l 4. (17) 4 As was shown by Webste and Jones, the out-of-plane bending angle is detemined by [6] ( ) ϕ = tan 1 l4 l 2. (18) l 3 l 1 Applying tigonmetic elation to a section of the manipulato (Fig. 3b), the following elationship can be deived fo the adius of cuvatue: l c /n = i l i /n = ( d i) l c/n l i /n = d l c i. (19) l c l i Substituting (15) fo d i (fo i = 1), and (17) fo l c into (19) gives the adius of cuvatue as a function of the tendon lengths. Afte simplifying, the esult is given as: d tb (l 1 + l 2 + l 3 + l 4 ) (l 1 l 3 ) =. (2) (l 2 3l 1 + l 3 + l 4 ) (l 2 l 4 ) 2 + (l 1 l 3 ) 2 The position of the tip of the manipulato is now completely descibed by the out-of-plane bending angle (18), and adius of cuvatue (2). In the next subsection, the invese kinematics ae deived which ae equied fo contolling the manipulato. B. Invese Kinematics In ode to stee the tip towa a desied position (p d = [ ] ) T x d y d z d, the invese kinematics of the manipulato nee to be deived. These povide the inputs of the system (i.e., tendon lengths) as a function of the tip position. Given the desied position of the manipulato tip, the out-of-plane bending angle is calculated by ( ) ϕ = tan 1 yd (21) x d base l b Fig. 4. Top view of the manipulato (with length l b ) as it ben with a constant adius of cuvatue (). The angle β is elated to the adius of cuvatue by: β = l b /. The deflection of the tip with espect to the base is given by k. The equied adius of cuvatue is then given by (Fig. 4) whee k and m ae and k m tip = k + m, (22) k = (x d2 + y d2 ), (23) m = cos (β) = cos ( ) lb. (24) Substituting (23) and (24) into (22) povides us with the following expession: = ( ) lb (x d2 + y d2 ) + cos. (25) We solve (25) numeically to detemine the adius of cuvatue (). Knowing the equied adius of cuvatue and substituting the out-of-plane bending angle fom (21) into (15), we can calculate the individual tendon lengths using (13). IV. EXPERIMENTAL TESTBED This section descibes the setup which is used as a testbed fo expeiments with the manipulato. We also pesent the contolle which is used to stee the manipulato tip. A. Setup A setup (Fig. 5) is fabicated to actuate the fou tendons and allows insetion of the manipulato, whose kinematics ae pesented in Section III. The manipulato is connected to a caiage which is mounted onto a linea stage. The caiage hol fou motos which enables independent actuation of the tendons. The linea stage allows tanslation of the manipulato along the insetion axis (z-axis). The backbone of the manipulato consists of a nitinol tube (φ oute 1.6 mm and φ inne 1.2 mm) with a length of 16 mm. The tendon guides ae cicula polyme disks (φ 2 mm), and these ae glued onto the backbone. The tendons ae made fom fishing wie (φ.4 mm), and ae outed though the tendon guides at a distance of 7.5 mm fom the cente of the backbone (d tb = 7.5 mm). A total of eight tendon guides ae glued onto the backbone, spaced 2 mm apat. This spacing is chosen such that the atio 2548

5 calibation jig input motos efeence points multitheaded C++-pogam Deminsys inteogato FBG eadout shape econstuction contol FBG sensos motos moto contolles steeing y Fibe a Fibe b Fibe c caiage x z insetion diection linea stage nitinol backbone 175 mm mm 3 mm 3 mm 18 mm manipulato Fig. 5. The expeimental setup consists of a linea stage which enables tanslation of the manipulato in the insetion diection (i.e., z-axis). A caiage is mounted on the linea stage, and hol the fou motos to actuate the fou tendons. The manipulato itself is also mounted onto this caiage. The top ight pictue shows the jig which is used to calibate the Fibe Bagg Gating (FBG) sensos. The nitinol wie (φ 1. mm) with the aay of twelve FBG sensos, distibuted ove fou sets (FBG 1,..., FBG 4 ). The inset shows the gooves at the tip of the wie in which the fibes ae integated. between tendon offset (d tb ) and spacing of cable suppots is nea the optimal atio of.4 [23]. A nitinol wie (φ 1. mm) with an integated aay of FBG sensos is used to sense the shape of the manipulato (Fig. 5b). This wie is inseted into the hollow backbone of the manipulato. Additional details about the fabication of this FBG wie ae pesented in Roesthuis et al. [18]. B. Contolle Implementation The system achitectue of the expeimental testbed is shown in Fig. 6. The tip of the manipulato is contolled along each axis using a Popotional-Integal-Deivative (PID-) contolle. The eo between the desied tip position and the econstucted tip position using FBG sensos is used as input fo the PID-contolle. The output of the PIDcontolle is a modified tip position. Using the invese kinematics of the manipulato (Section III-B), the coesponding tendon lengths ae detemined. The manipulato is contolled at a ate of 1 Hz. The stain infomation is ead fom the FBG sensos using a Deminsys Python Inteogato (Technobis Mechatonics, Uitgeest, The Nethelan). This inteogato communicates with a desktop compute using the UDP-potocol. A multitheaded C++-pogam is witten which ea the UDPpackets and calculates the appopiate contol outputs. This pogam also communicates with Elmo moto contolles (Elmo Motion Contol Ltd., Petach-Tikva, Isael) which dive the motos to the desied position. manipulato Fig. 6. The system achitectue of the expeimental testbed. The Fibe Bagg Gating (FBG) sensos poduce a change in Bagg wavelength as they ae subjected to stain. This change in wavelength is tansfeed though the Deminsys inteogato to the C++-pogam, and is then conveted to stains. The shape econstuction algoithm calculates tip position fom these stains. The output of the contol depen on the eo between the desied tip position povided by the input, and the econstucted tip position. The steeing algoithm calculates moto positions fom the contolle output, and the manipulato is actuated accodingly. V. EXPERIMENTAL RESULTS This section descibes the esults of the vaious expeimental studies conducted with ou testbed. Fist, the FBG sensos ae calibated and the gains of the PID-contolle ae tuned. Next, expeiments ae pefomed to evaluate the tajectoy tacking pefomance of the system. Finally, the ability of the system to eject distubance loa ae also evaluated. A. Setup Calibation The positions and oientations of the FBG sensos along the shaft of the FBG wie ae assumed to be known. Howeve, thee ae uncetainties duing the fabication of the FBG sensos and theefoe, calibation of the FBG sensos ae equied. A calibation jig is made which consists of a numbe of efeence points which ae distibuted along a cicle (φ 6 mm), as shown in Fig. 5. The FBG sensos ae calibated by manually positioning the manipulato tip at the efeence points (x ef, y ef ), and then econstucting the tip position. The econstucted tip positions (x t, y t ) ae scaled both along the x-axis and y-axis such that the eo between the econstuction and the efeence point is minimized. Scaling factos of.89 and.87 along the x-axis and y-axis ae detemined to give minimum eos. The eos befoe and afte the calibation pocedue ae povided in Table I. The gains of the PID-contolle ae tuned by obseving the step-esponse of the system. The following gains esult in a TABLE I THE MEAN ERRORS AND STANDARD DEVIATION (IN BRACKETS) ARE PROVIDED BEFORE AND AFTER CALIBRATION OF THE FIBER BRAGG GRATING (FBG) SENSORS. THE MANIPULATOR TIP IS DIRECTED TOWARDS EACH REFERENCE POSITION (x REF, y REF) IN MM. EACH EXPERIMENT IS REPEATED THREE TIMES. Befoe calibation (mm) Afte calibation (mm) (x ef, y ef ) x y x y (3, ) 1.97 (.57).48 (.2) 1.6 (.52).42 (.17) (, 3).57 (.49) 4.24 (.35).52 (.44).54 (.31) (-3, ) 4.42 (.53).32 (.28) 1.15 (.48).29 (.25) (, -3) 1.21 (.28) 3.6 (.41) 1.9 (.26).51 (.37) Mean 2.4 (1.58) 2.3 (1.77).96 (.46).44 (.26) 2549

6 (c) z (mm) (e) (d) z (mm) Fig. 7. Tajectoy tacking with manipulato tip fo a cicle (2D), a squae (2D) and a helix (3D). esults (ed) ae compaed with closed-loop esults (blue). Cicle (4 mm adius), speed is 2 deg/s. Cicle (4 mm adius), speed is 3 deg/s. (c) Squae (8 mm edges), speed is 5 mm/s. (d) Squae (8 mm edges), speed is 2 mm/s. (e) Helix, (4 mm adius), speed is 2 deg/s. (f) Helix, (4 mm adius), speed is 3 deg/s. Please efe to the attached video that demonstates the esults of the tajectoy tacking expeiments using ou testbed. fast eponse with little oveshoot ( 1%): K p = 2.2, K i = 1. and K d =.2. These gains ae used in all of the following expeiments in this study. B. Tajectoy Tacking The tajectoy tacking pefomance of the system is evaluated by contolling the tip of the manipulato fo thee diffeent cases; tacking a cicle (two-dimensional (2D)), a squae (2D) and a helix (3D). The cicle has a adius of 4 mm and is evaluated at a slow speed (2 deg/s) and a high speed (3 deg/s). The squae has edges of 8 mm, and is also evaluated at a slow speed (5 mm/s) and a high speed (2 mm/s). The helix has a adius of 4 mm and a pitch of 1 mm, and is evaluated at a slow speed (2 deg/s) and a high speed (3 deg/s). The expeiments ae done both in open-loop and closed-loop contol. The efeence and (f) Deflection (mm) Time (s) Deflection (mm) Time (s) Fig. 8. The esponse of the system to a load distubance fo openloop contol and closed-loop contol. A weight is added to the tip of the manipulato at 5 s. 2 g. weight. 5 g. weight. Please efe to the attached video that demonstates the esults of the load distubance expeiments using ou testbed. expeimental tajectoies ae shown in Fig 7. The esulting tacking eos ae povided in Table II. The mean eos become significantly smalle fo closed-loop contol. Lage eos occu nea the cones of the squae due to change of diection when the speed is inceased. It can be seen that in all the expeiments the system suffes fom systematic eos which could be attibuted to the mechanical system. The holes though which the tendons ae outed ae not smooth, and this esults in a eatic behaviou of the manipulato tip in some pats of the tajectoy. The lage spikes ae the esult of systematic eos in the measuement of the tip position. The cause fo these measuement eos is cuently unknown and equies futhe investigation. C. Load Distubance Rejection The ability of the system to eject load distubances is evaluated fo two expeimental cases. The manipulato is commanded to a staight oientation (i.e., x d = y d = ). In the fist case a weight of 2 g. is placed at the manipulato tip, and in the second case of weight of 5 g. is used. The esulting esponse of the system is evaluated both fo openloop contol and closed-loop contol (Fig. 8). It can be seen that in both cases the system quickly ( 7s.) eacts to the load distubance, and is able to maintain the desied position without becoming unstable. VI. CONCLUSIONS AND FUTURE WORK In this study, we demonstated using an aay of FBG sensos fo the closed-loop contol of a flexible manipulato. An expeimental testbed is pesented, which consists of a flexible, fou tendon-diven manipulato. A total of twelve sensos, distibuted ove fou diffeent sets ae embedded on a flexible nitinol wie. This wie is intoduced into the hollow backbone of the manipulato. Stain measuements fom the FBG sensos ae used to econstuct 3D manipulato shape. The econstucted tip position is used as feedback in a PIDcontolle to stee the tip of the manipulato to a desied position. A. Conclusions The pefomance of the system is demonstated fo thee tajectoy-tacking cases, evaluated at a slow speed and a 255

7 TABLE II COMPARISON BETWEEN THE TRAJECTORY TRACKING ERRORS (IN MM) FOR OPEN-LOOP CONTROL AND CLOSED-LOOP CONTROL. THE MEAN ERROR AND THE STANDARD DEVIATION (IN BRACKETS) ARE GIVEN. Case Cicle (2 deg/s) 1.47 (1.82).67 (1.13) Cicle (3 deg/s) 8.79 (1.73) 2.96 (.83) Squae (5 mm/s) 11.7 (1.91) 1.17 (1.2) Squae (2 mm/s) 1.38 (1.52) 2.48 (1.92) Helix (2 deg/s) 14. (3.39).87 (1.88) Helix (3 deg/s) (3.15) 3.93 (1.5) high speed: cicle (2D), a squae (2D) and a helix (3D). The tajectoy tacking pefomance is shown to be geatly impoved when closed-loop contol is applied. The mean tajectoy tacking eos fo the open-loop at slow spee ae; 1.47 mm fo the cicle, 11.7 mm fo the squae and 14. mm fo the helix. contol shows significant pefomance incease. The mean tajectoy tacking eos ae:.67 mm fo the cicle, 1.17 mm fo the squae and.87 mm fo the helix. Finally, the ability of the system to eject distubance loa is demonstated fo two expeimental cases: 2 g. and 5 g. weights ae hung at the tip. The system is able to maintain the tip at the desied location despite the added load. The esults of this study show that FBG sensos can be integated on a flexible instument, and used fo closed-loop contol of the instument. B. Futue Wok In the cuent wok, we demonstated closed-loop contol using an aay of FBG sensos on a manipulato with a single bending segment. As pat of futue studies, we will investigate shape sensing (using FBG sensos) fo instuments with multiple bending segments. The cuent manipulato did not suffe fom non-linea effects such as backlash o hysteesis. Hence, we wee able to succesfully contol the manipulato using a simple (linea) PID-contolle. In pactice, sugical instuments often suffe fom non-linea effects. A PID-contolle will not suffice in those cases, and we will investigate using a non-linea contol method in ode to stee moe clinically elevant instuments. While we aim to continue to impove ou contolle achitectue, ou cuent study demonstates the feasibility and potential of econstucting the shape of flexible MIS instuments, and steeing them fo a vaiety of clinical applications. REFERENCES [1] N. Abolhassani, R. V. Patel, and M. Moallem, Needle insetion into soft tissue: A suvey, Medical Engineeing and Physics, vol. 29, no. 4, pp , 27. [2] D. B. Camaillo, C. R. Calson, and J. K. Salisbuy, Task-space contol of continuum manipulatos with coupled tendon dive, in The Intenational Symposium on Expeimental Robotics (ISER) (O. Khatib, V. Kuma, and G. J. Pappas, e.), vol. 54 of Spinge Tacts in Advanced Robotics, pp , Athens, Geece, Spinge, July 28. [3] D. Tivedi, C. D. Rahn, W. M. Kie, and I. D. Walke, Soft obotics: Biological inspiation, state of the at, and futue eseach, Jounal of Applied Bionics and Biomechanics, vol. 5, pp , Septembe 28. [4] J. Ding, K. Xu, R. Goldman, P. Allen, D. Fowle, and N. Simaan, Design, simulation and evaluation of kinematic altenatives fo insetable obotic effectos platfoms in single pot access sugey, in Poceedings of the IEEE Intenational Confeence on Robotics and Automation (ICRA), pp , Anchoage, USA, May 21. [5] P. Dupont, J. Lock, B. Itkowitz, and E. Butle, Design and contol of concentic-tube obots, IEEE Tansactions on Robotics, vol. 26, pp , Apil 21. [6] R. J. Webste and B. A. Jones, Design and kinematic modeling of constant cuvatue continuum obots: A eview, The Intenational Jounal of Robotics Reseach, vol. 29, no. 13, pp , 21. [7] B. Badou, P. Zanne, F. Nageotte, and M. De Mathelin, Contol of a multiple sections flexible endoscopic system, in Poceedings IEEE Intenational Confeence of Intelligent Robots and Systems (IROS), pp , Taipei, Taiwan, Octobe 21. [8] A. Bajo, R. E. Goldman, and N. Simaan, Configuation and joint feedback fo enhanced pefomance of multi-segment continuum obots, in Poceedings of the IEEE Intenational Confeence on Robotics and Automation (ICRA), pp , Shanghai, China, May 211. [9] S. B. Kesne and R. D. Howe, Position contol of motion compensation cadiac cathetes, IEEE Tansactions on Robotics, vol. 27, no. 6, pp , 211. [1] R. S. Penning, J. Jung, N. J. Feie, and M. R. Zinn, An evaluation of closed-loop contol options fo continuum manipulatos, in Poceedings of the IEEE Intenational Confeence on Robotics and Automation (ICRA), pp , St. Paul, Minnesota, USA, May 212. [11] A. Reite, A. Bajo, K. Iliopoulos, N. Simaan, and P. K. Allen, Leaning-based configuation estimation of a multi-segment continuum obot, in Poceedings of the IEEE/EMBS Intenational Confeence in Biomedical Robotics and Biomechatonics (BioRob), pp , Rome, Italy, June 212. [12] E. Butle, R. Hammond-Oakley, S. Chawaski, A. Gosline, P. Codd, T. Ano, J. Maen, P. Dupont, and J. Lock, Robotic neuoemdoscope with concentic tube augmentation, in Poceedings IEEE Intenational Confeence of Intelligent Robots and Systems (IROS), pp , Vilamoua, Potugal, Octobe 212. [13] V. Misha, N. Singh, U. Tiwai, and P. Kapu, Fibe gating sensos in medicine: Cuent and emeging applications, Sensos and Actuatos A: Physical, vol. 167, no. 2, pp , 211. [14] A. Othonos, K. Kalli, D. Pueau, and A. Mugnie, Optical Sciences, ch. Fibe Bagg Gatings, pp Spinge, 26. [15] X. Yi, J. Qian, L. Shen, Y. Zhang, and Z. Zhang, An innovative 3d colonoscope shape sensing senso based on fbg senso aay, in Poceedings of the IEEE Intenational Confeence on Infomation Acquisition (ICIA), pp , Jefu Island, Republic of Koea, July 27. [16] Y. L. Pak, S. Elayapeumal, B. Daniel, S. C. Ryu, M. Shin, J. Savall, R. Black, B. Moslehi, and M. Cutkosky, Real-time estimation of 3-d needle shape and deflection fo mi-guided inteventions, IEEE/ASME Tansactions on Mechatonics, vol. 15, no. 6, pp , 21. [17] K. Henken, D. van Gewen, J. Dankelman, and J. J. van den Dobbelsteen, Accuacy of needle position measuements using fibe bagg gatings, Minimally Invasive Theapy & Allied Technologies, vol. 21, no. 6, pp , 212. [18] R. J. Roesthuis, M. Kemp, J. J. van den Dobbelsteen, and S. Misa, Thee-dimensional needle shape econstuction using an aay of fibe bagg gating sensos, IEEE/ASME Tansactions on Mechatonics, 213. In Pess, doi: 1.119/TMECH [19] M. Abayazid, M. Kemp, and S. Misa, 3d flexible needle steeing in soft-tissue phantoms using fibe bagg gating sensos, in Poceedings of the IEEE Intenational Confeence on Robotics and Automation (ICRA), pp , Kalsuhe, Gemany, May 213. [2] O. Hill and G. Meltz, Fibe bagg gating technology fundamentals and oveview, Jounal of Lightwave Technology, vol. 15, pp , August [21] J. Gee and S. Timoshenko, Mechanics of Mateials. Stanley Thones, [22] B. Jones and I. Walke, Kinematics fo multisection continuum obots, IEEE Tansactions on Robotics, vol. 22, pp , Febuay 26. [23] C. Li and C. D. Rahn, Design of continuous backbone, cable-diven obots, Jounal of Mechanical Design, vol. 124, no. 2, pp ,