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Patent US8116601 - Fiber optic shape sensing - Google PatentsSearch Images Maps Play YouTube News Gmail Drive More »Sign in<nobr>Advanced Patent Search</nobr>PatentsA shape sensing system to determine the position and orientation of one link with respect to another link in a kinematic chain. An optical fiber is coupled to two or more links in a kinematic chain. A shape sensing segment is defined to start at a proximal link and to end at a distal link, crossing one...http://www.google.com/patents/US8116601?utm_source=gb-gplus-sharePatent US8116601 - Fiber optic shape sensingAdvanced Patent SearchPublication numberUS8116601 B2Publication typeGrantApplication numberUS 12/764,307Publication dateFeb 14, 2012Filing dateApr 21, 2010Priority dateJun 30, 2008Also published asUS7720322, US8358883, US20090324161, US20100202727, US20120132009Publication number12764307, 764307, US 8116601 B2, US 8116601B2, US-B2-8116601, US8116601 B2, US8116601B2InventorsGiuseppe Maria PriscoOriginal AssigneeIntuitive Surgical Operations, Inc.Export CitationBiBTeX, EndNote, RefManPatent Citations (45), Non-Patent Citations (4), Referenced by (3), Classifications (11) External Links: USPTO, USPTO Assignment, EspacenetFiber optic shape sensingUS 8116601 B2Abstract A shape sensing system to determine the position and orientation of one link with respect to another link in a kinematic chain. An optical fiber is coupled to two or more links in a kinematic chain. A shape sensing segment is defined to start at a proximal link and to end at a distal link, crossing one or more joints. A reference frame is defined at the start of the shape sensing segment. As the joints move, an interrogator senses strain in the shape sensing segment. The sensed strain is used to output a Cartesian position and orientation of the end of the shape sensing segment with respect to the reference frame defined at the start of the shape sensing segment. The pose of the kinematic chain is determined from the Cartesian positions and orientations of one or more shape sensing segments defined for the kinematic chain and from an a priori model and constraints of the kinematic chain.
I claim: 1. A shape sensing method, comprising:
interrogating the optical fiber for data associated with strain in the optical fiber;
outputting first bend information associated with the first segment, wherein the first bend information comprises a Cartesian position at an end location of the first segment with respect to the first reference frame and a Cartesian orientation of the end location with respect to the first reference frame;
defining a lengthwise second segment in the optical fiber;
defining a second three-dimensional reference frame at a start location of the second segment; and
outputting second bend information associated with the second segment, wherein the second bend information comprises a Cartesian position of an end location of the second segment with respect to the second reference frame and a Cartesian orientation of the end location with respect to the second reference frame.
wherein the first reference frame comprises an x-axis, a y-axis, and a z-axis; and
wherein the position of the end location is output as Δx, Δy, Δz.
wherein the first reference frame is a Cartesian frame; and
wherein the first reference frame comprises a first axis that is normal to the fiber at the start location and a second axis that is tangent to the fiber at the start location.
wherein the orientation of the end location is output as a tangent vector comprising direction cosines tx, ty, and tz.
7. The method of claim 1, further comprising determining a Cartesian orientation of the end location of the second segment with respect to the first reference frame using a product of rotation vectors associated with the Cartesian orientation of the end location of the first segment relative to the first reference frame and the Cartesian orientation of the end location of the second segment relative to the second reference frame.
8. The method of claim 1, wherein the first and second segments overlap along the length of the optical fiber.
9. The method of claim 1, wherein the first and second segments are separated from one another along the length of the optical fiber.
10. The method of claim 1, wherein the first and second segments are adjacent to each other along the length of the optical fiber.
the optical fiber extends through a kinematic chain including a first link, a second link, and a third link, a first joint between the first and second links, and a second joint between the second and third links;
the start location of the first segment is at the first link, and the end location of the first segment is at the second link; and
the start location of the second segment is at the second link, and the end location of the second segment is at the third link.
CROSS REFERENCE TO RELATED APPLICATIONS This application is a continuation of U.S. patent application Ser. No. 12/164,829 (filed Jun. 30, 2008; now U.S. Pat. No. 7,720,322), which is incorporated herein by reference.
FIG. 1 is a diagrammatic view of an optical fiber core portion 100. The surrounding cladding and fiber are omitted for clarity. Two fiber Bragg gratings (FBG's) 102 a,102 b are shown formed in fiber core portion 100, which are illustrative of many such FBG's typically formed along the full length of a core. The many vertical lines shown in each FBG 102 represent the changes in refractive index that characterize an FBG. As shown in FIG. 1, the FBG's 102 a,102 b are separated by a tether segment 104, which is completely transmissive.
As is known, each of the FBG's 102 may be interrogated for strain information. In a fiber that contains two or more cores, with FBG's in each core positioned at the same location along the fiber, the fiber's bend direction and amount of axial twist may be determined from the strains in each core's FBG's. From the strain information from each core at each FBG location, and from the known tether segment length (e.g., 5 mm, 1 cm), the position of the location with the next set of FBG's can be estimated. In this way, the fiber shape associated with the interrogated FBG's may be determined. U.S. Pat. App. Publ. No. 2006/0013523 A1 (filed 13 Jul. 2005), which is incorporated herein by reference, discloses a fiber optic position shape sensing device and method. In one instance, strain information is used to determine the bend angle between two links, as described in U.S. Pat. App. Publ. No. 2007/0156019 A1 (filed 20 Jul. 2006), which is incorporated herein by reference. Such bend information may be used in forward kinematic calculations to determine the position of the distal end of a kinematic chain (a set of links coupled by one or more movable mechanical constraints). One non-limiting example of such a kinematic chain is a minimally invasive surgical instrument with one or more revolute joints.
Known techniques to interrogate the FBG's by processing the light reflected back when an optical light source is coupled with the fiber are described in, for instance, Andreas Othonos & Kyriacos Kalli, Fundamentals and Applications in Telecommunications and Sensing Ch. 7, 301-388 (Arthech House 1999), which is incorporated herein by reference. Such interrogation techniques include on the use of edge filters, tunable filters, interferometers, tunable lasers, and CCD spectrometers. Each technique provides different spatial resolution in the measurement of strain along a fiber core, different speeds of interrogation, i.e., update of the measurement, and different levels of immunity to disturbances to the strain measurements such as those produced by variation of temperature, light polarization, source light variations, and losses of light along the fiber. Among the interferometric techniques that are based on detection of the phase of the reflected light are Optical Time Domain Reflectometry and Optical Frequency Domain Reflectometry (OFDR), as described in U.S. Pat. No. 5,798,521 (filed 27 Feb. 1997) and in U.S. Pat. App. Publ. No. 2007/0065077 A1 (filed 26 Sep. 2006), which are incorporated herein by reference.
There are, however, disadvantages to current optical fiber shape sensing methods. To begin with, such methods are based on the average strain measured in each FBG, and so the FBG size limits the measurement resolution. In addition, the shape (or state) of the fiber is reconstructed as a vector of equally spaced three-dimensional (3D) points in world coordinates. The result is a large data set that gets larger as measurement resolution is increased. Also, the resolution of the 3D points is limited by the spacing between FBG's. Further, in these methods there is an assumption that the length of fiber between measured FBG's has a constant bend radius, and this assumption can reduce the accuracy of the sensed shape as compared with the fiber's actual shape. Another disadvantage is that the computation of the fiber tangent vector at a particular fiber location (i.e., the direction the fiber is pointing at that location) requires differentiation of the 3D points. This differentiation delivers even lower measurement resolution. Yet another disadvantage is that the 3D point data set is not in a form that is required for the type of processing needed when the fiber is embedded into a kinematic chain, and therefore the kinematic chain's pose has to be inferred from the sensed fiber position. This limitation is especially true if the fiber is embedded in a kinematic chain but is allowed to slide with reference to one or more links. In such configurations, the fiber may not follow a path that exactly corresponds to a bend in one or more of the kinematic chain's joints, and friction between the fiber's surface and a surrounding conduit through one or more links may influence the fiber's shape.
FIG. 9A is an illustrative schematic of parallel motion mechanism in a displaced pose, and
FIGS. 9B and 9C are elevation views of an illustrative embodiment showing the parallel motion mechanism in line with a shaft of the surgical instrument (FIG. 9B) and displaced in position (FIG. 9C).
Further, this description's terminology is not intended to limit the invention. For example, spatially relative terms�such as �beneath�, �below�, �lower�, �above�, �upper�, �proximal�, �distal�, and the like�may be used to describe one element's or feature's relationship to another element or feature as illustrated in the figures. These spatially relative terms are intended to encompass different positions and orientations of the device in use or operation in addition to the position and orientation shown in the figures. For example, if the device in the figures is turned over, elements described as �below� or �beneath� other elements or features would then be �above� or �over� the other elements or features. Thus, the exemplary term �below� can encompass both positions and orientations of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. Likewise, descriptions of movement along and around various axes includes various special device positions and orientations. In addition, the singular forms �a�, �an�, and �the� are intended to include the plural forms as well, unless the context indicates otherwise. And, the terms �comprises�, �comprising�, �includes�, and the like specify the presence of stated features, steps, operations, elements, and/or components but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and/or groups. Components described as coupled may be electrically or mechanically directly coupled, or they may be indirectly coupled via one or more intermediate components. All examples and illustrative references are non-limiting and should not be used to limit the claims to specific implementations and embodiments described herein and their equivalents. The headings are solely for formatting and should not be used to limit the subject matter in any way, because text under one heading may cross reference or apply to text under one or more headings.
FIG. 5 is a diagrammatic view that illustrates reference frames at segment starts in an optical fiber used for shape sensing. FIG. 5 depicts an optical fiber 500 that is, in one embodiment, configured with three cores as illustrated in FIG. 4A (four cores as illustrated above, or other core configurations, may be used). In this illustrative example, each core is configured as shown in FIG. 3A, although various FBG configurations may be used, as described above. Two shape sensing segments are defined in fiber 500. The first segment 502 a is defined from curvilinear reference location L1 (segment start) to curvilinear reference location L1+s1 (segment end). The second segment 502 b is defined from curvilinear reference location L2 (segment start) to curvilinear reference location L2+s2 (segment end). In accordance with an aspect of the invention, a first Cartesian reference frame 504 a is defined at segment start L1. Reference frame 504 a's z-axis is tangent to the centerline of fiber 500 at segment start L1, and reference frame 504 a's x-axis runs through one of the cores as illustratively shown and described in FIG. 4A. Similarly, a second Cartesian reference frame 504 b is defined at segment start L2, with reference frame 504 b's z-axis tangent to the centerline of fiber 500 at segment start L2, and reference frame 504 b's x-axis running through the same core as reference frame 504 a's x-axis.
In accordance with aspects of the invention, the position and orientation of each shape sensing segment end is determined with respect to the reference frame defined at the corresponding segment start. FIGS. 6A and 6B are diagrammatic views that illustrate determining segment end position and orientation. In FIG. 6A, an illustrative shape sensing segment 600 of a fiber is shown. Segment 600 begins at segment start L1 and ends at segment end L1+s1. A Cartesian segment start reference frame is defined at segment start L1 as described above. The position of the segment end is identified by the distance change along each of the reference frame's axes; i.e., the position of the segment end with respect to the segment start reference frame is Δx, Δy, Δz as shown in FIG. 6A. The orientation of the segment end is identified by tangent unit vector {right arrow over (t)} as depicted, whose three scalar components are the three direction cosines tx, ty, tz with respect to the Cartesian reference frame. In FIG. 6A, segment 600 is shown with a simple, planar bend. But position and orientation may be determined for fiber segments having multiple bends within the three dimensions of the reference frame.
A. Computation Example for Three Cores The following is an illustration of computations carried out by an electronic data processing unit. Skilled individuals will understand that many hardware, firmware, and software options exist for constructing an electronic data processing unit, and that implementation of necessary computations will be routine in light of this description.
where Δd is the distance increment per index n. The Δd value is set by the resolution of the OFDR-based interrogator. For instance the local strain ε(s) as a function of distance along each fiber core is obtained by making use of an �Optical Backscatter Reflectometer�, a commercially available product from Luna Innovations Incorporated, Roanoke, Va., for each core. Such a device is able to output the phase derivative of the reflected light as a function of the distance along the fiber core, as shown in Optical Backscatter Reflectometer User Guide Chaps 5-6, 33-60 (Luna Technologies, Inc. 2004) (Document version 1.0 for OBR control software version 0.42 Beta), which is incorporated herein by reference. Such Phase Derivative information is proportional to the desired local strain ε(s) in (1).
R _ _ x , n = [ 1 0 0 0 cos   θ - sin   θ 0 sin   θ cos   θ ]   R _ _ y , n = [ cos   θ 0 sin   θ 0 1 0 - sin   θ 0 cos   θ ]   R _ _ n = R _ _ x , n  R _ _ y , n ( 4  a ) For small angle approximation, the above expression simplifies to:
R _ _ n = [ 1 0 θ x , n 0 1 θ y , n - θ x , n - θ y , n 1 ] ( 5  a ) where, because a first order small angle approximation is used, Rn is a valid rotation matrix only if θx<<1 and θy<<1.
C _ _ p = C _ _ 0  R _ _ 0  R _ _ 1  R _ _ 2   ⋯   R _ _ p = C _ _ 0  ∏ n = 0 p   R _ _ n ( 8 ) The initial value of this coordinate system matrix,
C 0 _ _ = [ c 11 c 12 c 13 c 21 c 22 c 23 c 31 c 32 c 33 ] 0 ( 9 ) describes the initial orientation of the fiber in the exterior coordinate system. If the fiber is initially aligned along the z-axis, the matrix will be,
C 0 _ _ = [ 1 0 0 0 1 0 0 0 1 ] 0 ( 11 ) B. Computation Example for Four Cores For the case of four cores, as illustrated in FIG. 4B for instance, a similar derivation is possible, and it can be shown that in such a case also the fiber rotation around its axis can be measured. With four cores,
R _ _ x , n = [ 1 0 0 0 cos   θ - sin   θ 0 sin   θ cos   θ ]   R _ _ y , n = [ cos   θ 0 sin   θ 0 1 0 - sin   θ 0 cos   θ ]   R _ _ z , n = [ cos   θ - sin   θ 0 sin   θ cos   θ 0 0 0 1 ]   R _ _ n = R _ _ x , n  R _ _ y , n  R _ _ z , n ( 4  b ) For small angle approximation, the above expression simplifies to:
C _ _ p = C _ _ 0  R _ _ 0  R _ _ 1  R _ _ 2   �   R _ _ p = C _ _ 0  ∏ n = 0 p  R _ _ n ( 8 ) The initial value of this coordinate system matrix,
C 0 _ _ = [ 1 0 0 0 1 0 0 0 1 ] 0 ( 11 ) C. Computation Example for Three and Four Cores The mathematical treatment that proceeds from now on is identical for both the three and four core fiber cases in the above examples.
t -> = C _ _ � [ 0 0 1 ] ( 12 ) Accordingly, the tangent vector at any particular point is the product of all of the previous rotation vectors,
t -> p = C _ _ 0  ∏ n = 0 p  R _ _ n � [ 0 0 1 ] ( 13 ) The position at any point along the fiber is the sum of all of the previous tangent vectors, multiplied by the length of fiber that they represent,
[ x y z ] q = Δ   d  ∑ p = 0 q  t -> p ( 14 ) Substituting in the expression for the tangent vector gives,
[ x y z ] q = Δ   d  ∑ p = 0 q  [ { C _ _ 0  ∏ n = 0 p  R _ _ n } � [ 0 0 1 ] ] ( 15 ) For generality, an arbitrary offset vector can be added to place the calculated coordinates into any arbitrary coordinate system.
[ x y z ] q = Δ   d  ∑ p = 0 q  [ { C _ _ 0  ∏ n = 0 p  R _ _ n } � z ^ ] + v -> 0   where , ( 16 ) v -> 0 = [ x 0 y 0 z 0 ]   and , ( 17 ) z ^ = [ 0 0 1 ] ( 18 ) For the computation of the position and orientation of the frame of reference at the end of a segment with respect to the frame of reference at the start of the segment, C 0 is the identity matrix, and ν 0 is a vector of zeros, which represents the frame of reference at the start of the segment. Alternatively, the computation can be carried in another base or world frame located, for instance, at the base of the kinematic chain. In this case C 0 is the 3�3 matrix specifying the orientation of the frame of reference at the start of the segment with respect to the above-mentioned base frame, and ν 0 is the 3�1 vector specifying the position of the origin of the frame of reference at the start segment with respect to the above-mentioned base frame.
The proximal end of fiber 812 is affixed in an illustrative connector 814, to be attached to a fiber strain interrogator unit. Connector 814 is further illustrative of embodiments in which each core of fiber 812 is coupled to an individual single core fiber, and each individual fiber is coupled to the interrogator unit. See e.g., U.S. Pat. App. Publ. No. 2006/0013523 A1 referenced above.
FIG. 9 is a schematic view of another illustrative minimally invasive surgical instrument 900. Surgical instrument 900 includes several components (e.g., shaft, cables, wrist mechanism, end effector) similar to those of surgical instrument 800. Surgical instrument 900 also includes a parallel motion mechanism 902 between shaft 904 and link 906, in addition to a flexible wrist mechanism 908 between link 906 and distal end link 910. Parallel motion mechanism 902 functions to change link 906's position (e.g., heave, sway) without changing link 906's orientation with respect to shaft 904. FIG. 9A is an illustrative schematic of parallel motion mechanism 902 in a displaced pose, and FIGS. 9B and 9C are elevation views of an illustrative embodiment showing the parallel motion mechanism in line with shaft 904 (FIG. 9B) and displaced in position (FIG. 9C). Details of parallel motion mechanism 902 are described in U.S. Pat. Appl. Pub. No. 2008/0065102 A1 (filed 13 Jun. 2007), which is incorporated herein by reference.
Referring to FIG. 9, multi-core fiber 912 is routed through the instrument 900 components in a manner similar to that described for instrument 800. In one aspect, a single shape sensing segment is defined between segment start L1S and segment end L1EA. This single shape sensing segment includes parallel mechanism 902, link 906, wrist mechanism 908, and at least a portion of distal link 910. Alternatively, a first shape sensing segment is defined between segment start L1S and segment end L1EB, and a second shape sensing segment is defined between segment start L2S and segment end L2E. The first shape sensing segment is used to determine changes in position and orientation that result from moving parallel motion mechanism 902. The second shape sensing segment is used to determine changes in position and orientation that result from moving wrist mechanism 908. As shown in FIG. 9, in one aspect segment end L1ES and segment start L2S are not coincident. In this aspect the spatial relationship between segment end L1EB and segment start L2S is known because they are both in an unchanging relationship within rigid link 906. In some aspects, however, a segment end and a segment start may be coincident or may overlap, as described above.
FIG. 10 is a diagrammatic view of a kinematic chain 1000 that includes two links 1002 a,1002 b interconnected by a revolute joint 1004. A shape sensing optical fiber 1006 in accordance with aspects of the invention is shown in phantom line passing through link 1002 a, joint 1004, and link 1002 b. As shown in FIG. 10, a portion 1008 of fiber 1006 moves freely within joint 1004. Shape sensing as described herein is used to determine position and orientation of segment end LE defined within link 1002 b with reference to segment start LS defined within link 1002 a. This embodiment is illustrative of shape sensing as described herein applied to various kinematic chain configurations. It can be seen that a similar configuration can be used for a prismatic joint between two links, as long as a sufficient loop of fiber is available to accommodate the prismatic joint's movement. And, aspects of the invention are not limited to kinematic chains that have long, rigid links coupled by single-axis revolute joints.
For snake-like mechanisms, the number of controlled. DOF's is usually much smaller than the number of actual mechanical links, and thus the mechanism's actual DOF's are redundant. In some cases the redundancy problem is solved by using a central spring element that forces the links to assume the minimum energy configuration compatible with the controlled DOF's (at least absent external forces along the snake body and statically). For example, a pair of controlled DOF's under this configuration can set the final orientation change over a set of contiguous links in the pitch and yaw directions. Therefore, for flexible devices (both snake-like and continuously bending), a shape sensing segment is defined for each length of the device that is controlled by one or more DOF's. For example, if a 10 cm length of the device is controllable in pitch, and an immediately adjacent 10 cm length of the device is controllable in yaw (or pitch, or some other orientation or position), then each controllable length of the device will have a corresponding shape sensing segment defined. If a 10 cm length is controllable in both pitch and yaw, then the length will still have a single corresponding shape sensing defined. If controllable lengths of a device overlap (e.g., a length controllable in yaw begins at a mid-point of a length controllable in pitch), then each overlapping controllable length will have a corresponding shape sensing segment defined.
FIG. 11 is a schematic view of a kinematic chain 1100 that is illustrative of kinematic chains made of one, two, or more flexible mechanical sections. As shown in FIG. 11, kinematic chain 1100 has a base section 1102, four flexible sections 1104 a-1104 d coupled in line distally of base section 1102, and an illustrative distal end effector 1106 (e.g., grasper, needle driver, shears, cautery tool, camera, and the like) coupled to the distal end of the most distal section 1104 d. In some cases, the end effector may be omitted, and kinematic chain 1100 may function as a guide that allows other mechanical devices to be routed through, over, or adjacent chain 1100. An actuator mechanism 1108 is coupled to the proximal end of base section 1102. Actuator mechanism 1108 includes components (e.g., servomotors, hand-operated wheels) coupled to cables (not shown) that are coupled to the various flexible sections 1104. Tension on the cables causes associated flexible sections 1104 to bend in one or more directions. U.S. Pats. Nos. 4,873,965 (filed 15 Jul. 1988) and 5,174,276 (filed 28 Jun. 1991), which are incorporated herein by reference, are illustrative of such mechanisms.
The Cartesian information produced by the shape sensor consists of the position and orientation of the end point of each of the defined segments with respect to each segment's initial frame of reference. The position is a 3D vector {right arrow over (p)}s, and the orientation is represented for instance by the tangent vector {right arrow over (t)}s. An additional roll angle rs can be used to specify the rotation of the fiber around its axis at the end of the segment. All three quantities are computed for each segment as described in equations 13 and 15 above.
Further, in this third sensed/actual DOF case, two special subcases can be solved by using just one sensing segment of fiber. The first subcase concerns a kinematic chain representing flexible kinematics of a device with a central spring. In this first subcase, the potential energy E({right arrow over (q)}) of the spring can be minimized as part of the overall minimization, and thus the whole vector {right arrow over (q)} can be uniquely determined under the restrictive hypothesis of no external forces acting on the mechanical structure. The second subcase concerns a kinematic chain whose links have constraints to their motions that are in addition to the ones from the joints. For example, there may be constraints due to mechanical construction, such as from cables running through the links with coupled motions, as in a snake-like wrist composed of four links and four joints but having only two degrees of freedom as a result of the kinematic coupling enforced by the actuation cables. In this second subcase, the additional constraints reduce the kinematic DOF's, and the case is reduced to the first or second sensed/actual DOE cases described above.
Min with respect to {right arrow over (q)} 1 ,{right arrow over (q)} 2 of {Abs(t s −t k)} (21)
B. Example 2 Referring to FIG. 10, a single-DOE rotational joint {right arrow over (q)}1 can be described by the kinematic model of the form:
Min with respect to {right arrow over (q)} 1 of {Abs(t s −t k)} (23)
Min with respect to {right arrow over (q)} 1 of {Abs└(t s −t k)−(t s −t k)�z j┘} (24)
Min with respect to {right arrow over (q)} 1 ,{right arrow over (q)} 2 of {Abs[(p s −p k)−(p s −p k)�z 1]} (26)
Alternatively, especially if the two mechanisms blend into one another over a short distance, the configuration of the entire distal end of the instrument can be sensed by using a single sensing segment. The kinematic chain describing the whole distal end has two DOF's in mechanism 902 and two more in mechanism 908, as described above. Consequently, the kinematic model is specified by four kinematic parameters {right arrow over (q)}1, {right arrow over (q)}2, {right arrow over (q)}3, {right arrow over (q)}4 in the form:
Min with respect to {right arrow over (q)} 1 ,{right arrow over (q)} 2 ,{right arrow over (q)} 3 ,{right arrow over (q)} 4 of {w p�Abs(p s −p k)+w t�Abs(t s −t k)} (28)
with wp and wt being scalar weights that represent the relative confidence in the position data with respect to the orientation data. Accordingly, the tricore shape sensing fiber provides four DOF's of measurement that enable finding the {right arrow over (q)}1, {right arrow over (q)}2, {right arrow over (q)}3 and {right arrow over (q)}4 values and minimizing the noise.
Min with respect to {right arrow over (q)}1, {right arrow over (q)}2, {right arrow over (q)}3, {right arrow over (q)}4 of
{ w p � Abs  [ ( p s - p k ) Abs  ( p s - p k ) - t s ] + w t � Abs  ( t s - t k ) } ( 29 ) In such a case, the fiber provides four DOF's of measurement which uniquely define the {right arrow over (q)}1, {right arrow over (q)}2, {right arrow over (q)}3, and {right arrow over (q)}4 values.
{ w p � Abs  [ ( p s - p k ) Abs  ( p s - p k ) - z 0 ] + w t � Abs  ( t s - t k ) } ( 30 ) where z0 is the z-axis vector of the frame of reference attached to the fiber segment start. In this approach, the fiber also provides four DOF's of measurement which uniquely define the {right arrow over (q)}1, {right arrow over (q)}2, {right arrow over (q)}3, and {right arrow over (q)}4 values.
Min with respect to {right arrow over (q)} 1 ,{right arrow over (q)} 2 of {Abs(t s −t k)} (32)
FIG. 12 also shows fiber shape measurement processor 1208 coupled to communicate (e.g., wired, wireless, optical coupling) with instrument position measurement processor 1211. As described above, fiber shape measurement processor 1208 receives strain information from each of the three OBR 1204 units and outputs bend information as Δx, Δy, Δz, and {right arrow over (t)} for each of the segments 1206 in a signal 1210 to Instrument Position Measurement Processor 1211. In one illustrative aspect, the bend information for each shape sensing segment is output as seven 16-bit words. The first six of the words each contain the fixed point representation of one of the Δx, Δy, Δz, tx, ty, and t z values. A seventh word includes data counter, fiber identification number, shape sensing segment identification number, and fault bits. Thus the position and orientation information for each shape sensing segment is output to instrument position measurement processor 1211 in a format that is easily subject to further processing. Instrument position measurement processor 1211 also receives the instrument kinematic model fkin and the description of the geometrical constraints between the fiber and the kinematic chain of the instrument as described in Examples 1-4. Instrument position measurement processor 1211 thus performs the numerical optimization that leads to the estimate of the joint variables {right arrow over (q)} for the surgical instrument as described above in Examples 1-4 and equations 19-32. The surgical telerobotic motion controller 1212 then uses the joint position measurements to control the pose of the kinematic chain whose shape is being sensed by fiber 1202 (e.g., by receiving inputs from a hand-operated controller and outputting servomotor command signals that correspond to the received inputs). The operation of motion controller 1212 is for example as described in, e.g., U.S. Pat. Nos. 6,493,608 (filed 7 Apr. 1999) and 6,424,885 (filed 13 Aug. 1999), and in U.S. Pat. Appl. No. 2007/0151389 (filed 20 Dec. 2006), all of which are incorporated herein by reference, with the joint encoder input substituted with the joint position measurements from controller 1212.
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"Robot Technology: Teleoperation and Robotics Evolution and Development�vol. 3A", English translation Prentice-Hall, Inc., Inglewood Cliffs, NJ, USA 1986, vol. 3A, 332 pages.Referenced byCiting PatentFiling datePublication dateApplicantTitleUS8746076 *Aug 22, 2012Jun 10, 2014The United States Of America As Represented By The Administrator Of The National Aeronautics And Space AdministrationShape sensing using a multi-core optical fiber having an arbitrary initial shape in the presence of extrinsic forcesUS20110319910 *Jun 24, 2010Dec 29, 2011Hansen Medical, Inc.Methods and devices for controlling a shapeable instrumentUS20140053654 *Aug 22, 2012Feb 27, 2014U.S.A As Represented By The Administrator Of The National Aeronautics And Space AdministrationShape Sensing Using a Multi-Core Optical Fiber Having an Arbitrary Initial Shape in the Presence of Extrinsic Forces* Cited by examinerClassifications U.S. Classification385/12International ClassificationG02B6/00Cooperative ClassificationA61B2019/461, G02B6/02042, A61B2019/223, G01L1/246, A61B2019/5261, A61B19/2203European ClassificationG01L1/24B4, G02B6/02C, A61B19/22BRotateOriginal ImageGoogle Home - Sitemap - USPTO Bulk Downloads - Privacy Policy - Terms of Service - About Google Patents - Send FeedbackData provided by IFI CLAIMS Patent Services©2012 Google


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The Tender Heart (Pocket Puritan): Amazon.co.uk: Richard Sibbes: 9781848711051: Books
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The Tender Heart (Pocket Puritan) [Paperback]
Richard Sibbes (Author)
This item: The Tender Heart (Pocket Puritan) by Richard Sibbes Paperback �3.73
The Heart of Christ (Puritan Paperbacks) by Thomas Goodwin Paperback �5.59
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The Bruised Reed (Puritan Paperbacks) Richard Sibbes
The Heart of Christ (Puritan Paperbacks) › Thomas Goodwin
The Acceptable Sacrifice (Puritan Paperbacks) › John Bunyan
Precious Remedies Against Satan's Devices  › Thomas Brooks
0851517404,1848711468,0851518524,0851510027,1909611646,1619491591,1842277448,1906173419,1848710224,1844744957,1596382414,1844743853,1444702157,184474325X,1576830276,0851106528,0851515959,1844745694,1844744280,1908762063,1844745856
Publisher: The Banner of Truth Trust (May 2011)
ISBN-10: 1848711050
ISBN-13: 978-1848711051
Product Dimensions: 13.2 x 9.1 x 0.8 cm
Amazon Bestsellers Rank: 925,555 in Books (See Top 100 in Books)
1414135543
The Bruised Reed (Puritan Paperbacks) by Richard Sibbes Paperback
The Heart of Christ (Puritan Paperbacks) by Thomas Goodwin Paperback
Precious Remedies Against Satan's Devices (Puritan Paperbacks) by Thomas Brooks Paperback
Josiah's Reformation (Puritan Paperbacks) by Michael Reeves Paperback
Format:Paperback|Verified Purchase Written nearly 400 years ago, yet just as relevant today. A change of heart is what matters to God; always has.
By Sharon L. Banks
- Published on Amazon.com Format:Paperback|Verified Purchase Great book, great author, one of the very best Puritan writers. It will reach your heart. The Puritan writers are closer to the real truth than any I have ever read, except for J.L. Packer who also loves the Puritans.
- Published on Amazon.com Format:Kindle Edition|Verified Purchase Great reminder to pursue keeping your heart tender toward God. Good little book to use as a devotional or a study group.
God Delights In Such A Heart
- Published on Amazon.com Format:Paperback|Verified Purchase This pocket Puritan book is taken from 'The Banner Of Truth's' paperback Josiah's Reformation.Richard Sibbes in his preaching and writing was not aiming for mere outward reformation,it was directed to the heart(the inner man).In the intro.p.12 "No,hearts must be turned ,and evil desires eclipsed by stronger ones for Christ." The author understood that the strength and vigor of a godly life flows from one that has communed closely with the Lord Jesus and desires an ever closer walk with Him.Speaking of Mr.Sibbes(Michael Reeves writes in the intro.)"knowing God's love he became loving"-love and grace are similar in this way(the more we have experienced the grace of God,the more gracious we can be with our fellow man).The writer gives us one of the essential components of a tender heart-p.52"...a true,tender heart yields to the Word of God,and is fit to run on any errand."-Whatever service the Lord may have for you,a heart that is tender will equip you for that task.Pastor Sibbes gives wise and godly counsel on how to preserve a tender heart-p.28-29 "...by all means take heed of the least sin against conscience,for the least sin in this kind makes way to hardness of heart." A conscience that is seared and not sensitive to sin strikes at the heart of spiritual strength and vitality,it has a crippling effect upon one's spiritual life. Another preservative is to labor for a legal and evangelical faith-p.27 "It is the nature of faith to see things absent as present before us ... so faith setting the day of judgement before our eyes,will make us to tremble." When we read or hear of the Lord's judgements upon the ungodly and impenitent,often these things appear to be far off,like a distant dream but faith brings these realities nearer to us,so that the impression of them upon our hearts and minds are not easily dismissed(this can have a sanctifying effect upon our lives,a preservative against taking sin lightly.That is why we are exhorted in the word of God 'to set our hearts and minds upon the things above'.Richard Sibbes was very influential in the lives of some of the Puritans who would be part of the Westminster assembly and would produce perhaps the finest confession of faith that has been written.His written ministry is highly valued by many who earnestly seek to be godly and useful in Christ's Church.

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