CN1559355A - Plane location method for whole knee-joint replacement by robot - Google Patents

Abstract

A plane locating method for the whoel knee joint displacing operation performed by robot includes such steps as constituting the locating probe with 4 infrared LEDs and locating pane, creating its coordinate system, finding out the relation between the coordinate systems of probe and camera, aligning the locating plane of probe with any plane, sliding several times, finding out the equation of said locating planein the coordinate of camera, scaling probe, finding out the equation of locating plane in the coordinate system of probe, and using the scaled probe to locate the plane on object.

Description

Plain location method in the robot total knee arthroplasty

Technical field

The present invention relates to the plain location method in a kind of robot total knee arthroplasty, be used to not have the robot total knee replacement operation of CT.Belonging to advanced makes and automatization's (medical science) field.

Background technology

In China, all there is every year thousands of serious arthritic need carry out the total knee replacement operation.Total knee replacement is the implant surgery of typical Orthopeadic Surgery artificial prosthesis.Key operation is to five directed cuttings of patient's femur and vertical perforate of tibia.The precision of the riding position of prosthese, cutting and perforate all is directly connected to the quality of finishing of operation in the art.Position, the direction of cutting tool also directly determining the precision that operation is finished in the operation in addition.In all of these factors taken together, object plane plays crucial effects, and the location of object plane is determining the coordinate position of object and the mutual transformational relation of different coordinates.Grasp is rule of thumb controlled by the doctor entirely in orientation when operation tool cuts in the total knee replacement, and special-purpose locating template can only provide accuracy guarantee to a certain extent, and anthropic factor is still very big, is main error sources.The advantage of robotic surgical is and can selects the prosthese model according to femoral size, can carry out conceptual design before the art according to the prosthese shape again, and robot carries out key operation in the operation, and operation precision height, post-operative recovery are smooth.

The final purpose of total knee arthroplasty is to go out five planes that are used for fixing prosthese at the distal femur sawing, must determine direction and the position of operation tool with respect to femur in order to reach this purpose.Therefore, the location is the core of conceptual design in operation process.With U.S. Robodoc operating robot is the special one-time positioning operation of location technology needs of representative, on femur, implant sign titanium nail, reuse CT machine scanning femur, reconstruct the femur threedimensional model, virtual coordinate system by coupling threedimensional model place is realized femur location (Musits B. with the robot coordinate system, et al.Image-Driven Robot Assists Surgeons With Total HipReplacements.Industrial ROBOT.1993.Volume 20, Issue 5:12-14).The disadvantage of this class localization method is: need to carry out once implanting the positioning operation of titanium nail more, make the many suffers of patient; CT scan increases the operation expense greatly, and the three-dimensional reconstruction step needs a large amount of computer running times; In case the femur position changes, need the higher matching algorithm again of operation complexity.In position fixing process, what traditional method existed in a large number is the location of point, promptly directly certain point on instrument or the femur is put and fetched the three-dimensional coordinate that obtains this point by probe, but in actual environment, what exist in a large number is the plane of object, with conventional probe the measuring method of putting is obtained the plane and will produce very big error.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, a kind of new plain location method that is used for the robot total knee arthroplasty is proposed, method simple and flexible, realization can effectively solve the orientation problem of robot total knee arthroplasty midplane easily, improve location efficiency.

In the technical scheme of the present invention: at first, utilize, set up probe coordinate system and obtain the relation of probe coordinate system and camera coordinate system according to the position of index point in video camera by four infrarede emitting diode index points and the position probe that plane of orientation makes up.The second, the planar process targeting scheme is proposed, with probe plane of orientation any one plane of aliging, along planar slide for several times, determine the equation of the probe plane of orientation in the camera coordinate system.The 3rd, probe is demarcated, try to achieve the equation of probe plane of orientation under probe coordinate system.The 4th, good probe positions the localized object plane of want to utilize demarcation.

Method of the present invention specifically comprises following step:

1. formation level position probe and obtain the relation of probe coordinate system and camera coordinate system.

In order to carry out plane positioning, the present invention sets by four LED marker point A, B, C, D and plane of orientation E ₁E ₂E ₃E ₄The plane positioning probe of forming.The vector of choosing two index point formations on the position probe is formed Y-axis by the planar process vector perpendicular to 3 again as X-axis, and the right-hand rule by rectangular coordinate system constitutes the Z axle at last.After constituting probe coordinate system, according to four positions of index point in camera coordinate system obtain probe coordinate system and camera coordinate system between rotation and translation relation.

2. planar process is obtained the equation of camera coordinate system middle probe plane of orientation

Plane of orientation E with probe ₁E ₂E ₃E ₄Any one plane of aliging, then with probe along the plane translation with rotate twice.The D coordinates value of four index points in camera coordinate system in the time of can obtaining each position, the coordinate figure when comprising initial position, coordinate figure after the plane motion once and the coordinate figure after the secondary motion.Because the trajectory plane that four index points seesaw is certain parallel with the plane of orientation of probe, so can try to achieve the normal vector of probe plane of orientation by the trajectory plane that index point seesaws, for fear of interference of noise, the present invention gets the normal vector of the normal vector average of these four trajectory planes as the probe plane of orientation simultaneously.

Determine the planar normal vector of probe, still can't determine the equation of probe plane of orientation.Because above normal vector is all satisfied on any one and the parallel plane plane of probe, know a point on the probe plane for these needs, just can finally determine this plane.The present invention is by the transformation relation before and after the index point motion, thereby the coordinate of obtaining a point on the probe plane of orientation is determined the equation of probe plane of orientation in camera coordinate system.

3. probe is demarcated

The probe plane of orientation equation that step 2 obtains is the plane equation under the camera coordinate system, according to the transformation relation of the probe coordinate system that obtains in the step 1 with camera coordinate system, can obtain the plane of orientation equation under probe coordinate system, so probe plane of orientation E ₁E ₂E ₃E ₄With four index point A, B, C, the relativeness of D is just decided.

4. utilize the good probe of demarcation that the plane of object is positioned.

Good probe plane of orientation E will be demarcated ₁E ₂E ₃E ₄The plane of the alignment positioning object of wanting can obtain the three-dimensional coordinate of following four index points of camera coordinate system, and the while is according to the plane of orientation E that obtains in the step 3 ₁E ₂E ₃E ₄With index point A, B, C, the relativeness of D can directly obtain the equation (probe no longer need move) of object plane under camera coordinate system, thereby finishes the location to object plane.

Method of the present invention is simple, flexibly, realize that easily the present invention only need once demarcate the back to probe just can directly be used for plane positioning, has improved localized efficient.The planar process targeting scheme that the present invention proposes has effectively solved the problem that exists in the traditional method, replaces the indirect plane positioning of multiple spot by using direct plane positioning, the error that has existed when having reduced the location greatly.Utilized principle of computer vision to position owing to the inventive method simultaneously, the various errors of also effectively having avoided the probe manufacturing process to bring.

Description of drawings

Fig. 1 used probe during for plane positioning of the present invention.

Fig. 2 is a sketch map for probe coordinate.

Fig. 3 is the transformation relation sketch map of camera coordinate system and probe coordinate system.

Fig. 4 is the planar process plane of orientation sketch map that the present invention utilized.

The specific embodiment

In order to understand technical scheme of the present invention better, be described in further detail below in conjunction with drawings and Examples.

Fig. 1 is that the present invention is the plane of orientation designed probe, and A, B, C, D are the index point that four infrarede emitting diodes are formed, E ₁E ₂E ₃E ₄Be the plane of orientation on the probe, A, B, C are on the same straight line as far as possible, and BD is vertical with the straight line that ABC forms as far as possible.Definition Be X-axis, because B, C, 3 coplanes of D, then definition

Be Y-axis, then X * Y is the Z axle, and B is initial point (as Fig. 2).

Fig. 3 is the concern sketch map of probe coordinate system with camera coordinate system.If the coordinate of A point in video camera is (X _A ^c, Y _A ^c, Z _A ^c), wherein subscript c represents camera coordinate system, subscript A represents the A point.Can establish the coordinate of B point in video camera equally is (X _B ^c, Y _B ^c, Z _B ^c), be (X with the coordinate of C point in video camera _C ^c, Y _C ^c, Z _C ^c), the coordinate of D point in video camera is (X _D ^c, Y _D ^c, Z _D ^c).

If i, it is X that j, k are respectively probe coordinate _p, Y _p, Z _pUnit vector on the direction.Cause $\stackrel{\→}{\mathrm{BC}}=\stackrel{\→}{C}-\stackrel{\→}{B},$ The X of probe coordinate system then _pThe unit vector of axle is $i=\stackrel{\→}{\mathrm{BC}}/\left|\stackrel{\→}{\mathrm{BC}}\right|,$ So can determine the X of probe coordinate system by i _pThe direction of axle.Cause $\stackrel{\→}{\mathrm{BD}}=\stackrel{\→}{D}-\stackrel{\→}{B},$ So can determine probe coordinate is Z _pThe direction of axle $k=i\×\frac{\stackrel{\→}{\mathrm{BD}}}{\left|\stackrel{\→}{\mathrm{BD}}\right|}.$ Determining probe coordinate at last is Y _pDirection j=i * k.In probe coordinate system, choose the B point as coordinate origin.Can obtain the rotation transformation matrix of camera coordinate system and probe coordinate system $\stackrel{\→}{R}=[i,j,k],$ Translation matrix is $\stackrel{\→}{T}=\stackrel{\→}{B}.$ Then camera coordinate system and probe coordinate are that the transformation relation of mid point is:

${\stackrel{\→}{P}}_c=\stackrel{\→}{R}{\stackrel{\→}{P}}_p+\stackrel{\→}{T}---\left(1\right)$

The planar process targeting scheme that Fig. 4 proposes for the present invention is with the plane of orientation E of probe ₁E ₂E ₃E ₄Any one plane of aliging, then with probe along the plane translation or rotate twice.The D coordinates value of four index points in camera coordinate system might as well be established in the time of can obtaining each position ${\stackrel{\→}{A}}_1=(X_{A1},Y_{A1},Z_{A1}),$ ${\stackrel{\→}{B}}_1=(X_{B1},Y_{B1},Z_{B1}),$ ${\stackrel{\→}{C}}_1=(X_{C1},Y_{C1},Z_{C1}),$ ${\stackrel{\→}{D}}_1=(X_{D1},Y_{D1},Z_{D1})$ Coordinate when initial position, in like manner

Be the coordinate figure after the plane motion once, The coordinate figure of four index points in camera coordinate system for for the third time the time.Because the trajectory plane that four index points seesaw is certain parallel with the plane of orientation of probe, so can try to achieve the planar normal vector of probe by the trajectory plane that index point seesaws.

As Fig. 4,

The vector that seesaws for index point, then ${\stackrel{\→}{n}}_1={\stackrel{\→}{A}}_1{\stackrel{\→}{A}}_2\×{\stackrel{\→}{A}}_1{\stackrel{\→}{A}}_3$ Be the normal vector of plane of orientation.In like manner ${\stackrel{\→}{n}}_2={\stackrel{\→}{B}}_1{\stackrel{\→}{B}}_2\×{\stackrel{\→}{B}}_1{\stackrel{\→}{B}}_3,$ ${\stackrel{\→}{n}}_3={\stackrel{\→}{C}}_1{\stackrel{\→}{C}}_2\×{\stackrel{\→}{C}}_1{\stackrel{\→}{C}}_3,$ ${\stackrel{\→}{n}}_4={\stackrel{\→}{D}}_1{\stackrel{\→}{D}}_2\×{\stackrel{\→}{D}}_1{\stackrel{\→}{D}}_3$ Also for being the normal vector of plane of orientation.N in theory ₁, n ₂, n ₃, n ₄Equate, but in the reality because various interference of noise, n ₁, n ₂, n ₃, n ₄And unequal, therefore get n ₁, n ₂, n ₃, n ₄Average as the planar normal vector of probe.Promptly $\stackrel{\→}{n}=(n_x,n_y,n_z)=({\stackrel{\→}{n}}_1+{\stackrel{\→}{n}}_2+{\stackrel{\→}{n}}_3+{\stackrel{\→}{n}}_4)/4.$

Below determined the normal vector of probe plane of orientation, but still can't determine planar equation, because above normal vector is all satisfied on any one and the parallel plane plane of probe, know a point on the probe plane for these needs, just can finally determine this plane.Therefore analyze the transformation relation of motion front and back for the first time, the rotation translation relation of establishing motion for the first time is Then necessarily satisfy:

${\stackrel{\→}{P}}_2={\stackrel{\→}{R}}_p({\stackrel{\→}{P}}_1-\stackrel{\→}{M})+{\stackrel{\→}{T}}_p+\stackrel{\→}{M}---\left(2\right)$

Here

Be the position of the point before moving,

Be the position of point after the motion, For on the probe plane of orientation a bit.

For four index points, get by (2):

${\stackrel{\→}{A}}_2={\stackrel{\→}{R}}_p({\stackrel{\→}{A}}_1-\stackrel{\→}{M})+{\stackrel{\→}{T}}_p+\stackrel{\→}{M}$

${\stackrel{\→}{B}}_2={\stackrel{\→}{R}}_p({\stackrel{\→}{B}}_1-\stackrel{\→}{M})+{\stackrel{\→}{T}}_p+\stackrel{\→}{M}$

${\stackrel{\→}{C}}_2={\stackrel{\→}{R}}_p({\stackrel{\→}{C}}_1-\stackrel{\→}{M})+{\stackrel{\→}{T}}_p+\stackrel{\→}{M}$

${\stackrel{\→}{D}}_2={\stackrel{\→}{R}}_p({\stackrel{\→}{D}}_1-\stackrel{\→}{M})+{\stackrel{\→}{T}}_p+\stackrel{\→}{M}---\left(3\right)$

By (3) can in the hope of $\stackrel{\→}{M}=(X_M,Y_M,Z_M).$

By Can obtain the plane equation asked:

n _x(X-X _M)+n _y(Y-Y _M)+n _z(Z-Z _M)＝0 (4)

Being write as vector form is: $\stackrel{\→}{n}(X_c-\stackrel{\→}{M})=0$ X wherein _c=(X, Y, Z)

The plane equation of equation (4) is the plane equation in camera coordinate system, is that transformation relation (1) can obtain according to camera coordinate system and probe coordinate

$\stackrel{\→}{n}(\stackrel{\→}{R}{X}_p+\stackrel{\→}{T}-\stackrel{\→}{M})=0---\left(5\right)$

Can obtain the probe plane of orientation equation in the probe coordinate system: $\stackrel{\→}{n}(\stackrel{\→}{R}{X}_p+\stackrel{\→}{N})=0---\left(6\right)$

Wherein: $\stackrel{\→}{N}=\stackrel{\→}{T}-\stackrel{\→}{M}---\left(7\right)$

With demarcating the plane of the good probe plane of orientation alignment positioning object of wanting, the three-dimensional coordinate of following four index points of camera coordinate system can be obtained, and then the rotation translation relation R that camera coordinate system and probe coordinate at this moment are can be obtained, T is according to known Utilize equation (7) can obtain equation (4) simultaneously.Also just obtained last needed plane equation, thereby finished location object plane.

Claims (1)

1, the plain location method in a kind of robot total knee arthroplasty is characterized in that comprising following concrete steps:

1) formation level position probe and obtain the relation of probe coordinate system and camera coordinate system: set by four LED marker points (A, B, C, D) and plane of orientation (E ₁E ₂E ₃E ₄) the plane positioning probe formed, the vector of choosing two index point formations on the position probe is as X-axis, form Y-axis by planar process vector again perpendicular to 3, right-hand rule by rectangular coordinate system constitutes the Z axle at last, after constituting probe coordinate system, according to four positions of index point in camera coordinate system obtain probe coordinate system and camera coordinate system between rotation and translation relation;

2) planar process is obtained the equation of camera coordinate system middle probe plane of orientation: with the plane of orientation (E of probe ₁E ₂E ₃E ₄) any one plane of aliging, then with probe along the plane translation with rotate twice, the D coordinates value of four index points in camera coordinate system when obtaining each position, index point is seesawed the average of trajectory plane normal vector as the normal vector of probe plane of orientation, and by the transformation relation before and after the index point motion, thereby the coordinate of obtaining a point on the probe plane of orientation is determined the equation of probe plane of orientation in camera coordinate system;

3) probe is demarcated: the probe plane of orientation equation under the camera coordinate system that obtains according to step 2, utilize the transformation relation of the probe coordinate system that obtains in the step 1 and camera coordinate system, obtain the probe plane of orientation equation under probe coordinate system, determine probe plane of orientation (E thus ₁E ₂E ₃E ₄) and four index points (A, B, C, relativenesses D);

4) utilize the good probe of demarcation that the plane of object is positioned: will demarcate good probe plane of orientation (E ₁E ₂E ₃E ₄) plane of the alignment positioning object of wanting, obtaining the three-dimensional coordinate of following four index points of camera coordinate system, the while is according to the plane of orientation (E that obtains in the step 3 ₁E ₂E ₃E ₄) and index point (A, B, C, relativeness D) directly obtains the equation of object plane under camera coordinate system, thereby finishes the location to object plane.

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