CN1559354A - Edge positioning method for whole knee-joint displacement by robot - Google Patents

Abstract

An edge locating method for the whole knee joint displacing operation performed by robot includes such steps as creating the probe locating system by use of edge locating probe with 4 marker dots and straight locating slots, finding out the relation between the corrdinate systems of said probe and camera, using cylinder method to find out the position of locating slot in the coordinate system of camera, scaling probe, finding out the equation of locating slot in the coordinate system of probe, and using the scaled probe to locate the edge of object.

Description

Edge localization method in the robot total knee arthroplasty

Technical field

The present invention relates to the edge localization 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 edge plays crucial effects, and the location of object edge 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 linear edge of object, with conventional probe the measuring method of putting is obtained straight line and will produce very big error.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, edge localization method in a kind of robot total knee arthroplasty is proposed, method simple and flexible, realization can effectively solve the accurate orientation problem at robot total knee arthroplasty cathetus edge easily, improve location efficiency.

In the technical scheme of the present invention: at first, the edge position probe that utilization is made up by four infrarede emitting diode index points and straight line locating slot is set up probe coordinate system, and obtains the relation of probe coordinate system and camera coordinate system according to the position of index point in video camera.The second, cylinder method targeting scheme is proposed, with the linear edge of the locating slot alignment arbitrary objects of probe,, obtain the position of locating slot in camera coordinate system around the locating slot rotated several times.The 3rd, probe is demarcated, try to achieve the equation of probe locating slot in probe coordinate system.The 4th, utilize the good probe of demarcation that the linear edge of want positioning object is positioned.

Method of the present invention specifically comprises following step:

1. make up the edge position probe and obtain the relation of probe coordinate system and camera coordinate system.

In order to carry out linear edge location, the present invention set by four LED marker points (A, B, C, D) and straight line locating slot E ₁E ₂Form the linear edge position probe.The vector of choosing two index points formations 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, obtain rotation and translation relation between probe coordinate system and the camera coordinate system according to four positions of index point in camera coordinate system.

2. the cylinder method is obtained the linear equation of camera coordinate system middle probe locating slot

Locating slot E with probe ₁E ₂The linear edge of alignment arbitrary objects is that axle rotates several times then with the locating slot with probe, makes four index point A, and B, C, D are respectively with locating slot E ₁E ₂For the axle rotation, on rotating shaft, obtain four center of circle Os corresponding with index point _A, O _B, O _C, O _DSince A, B, C, 4 of D all are around E ₁E ₂Rotation is so these four centers of circle should be at rotating shaft (straight line E in theory ₁E ₂) on, but in practice owing to various interference of noise, these four centers of circle are point-blank not strict, with linear equation match carried out in these four centers of circle for this reason, and the fitting a straight line of gained is E ₁E ₂Thereby obtain the linear equation of probe locating slot under camera coordinate system.

3. probe is demarcated

According to the linear equation of probe locating slot under camera coordinate system that step 2 obtains, utilize the probe coordinate that obtains in the step 1 to be and the transformation relation of camera coordinate system, can obtain the linear equation under probe coordinate system, so E ₁E ₂With four index point A, B, C, the relativeness of D is just decided.

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

Good probe locating slot E will be demarcated ₁E ₂The linear edge 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 E in the step 3 ₁E ₂With A, B, C, the relativeness of D can directly obtain the equation (probe no longer need rotate) of object edge under camera coordinate system, finally finishes the location to the object linear edge.

Method of the present invention is simple, flexible, realization is easy, and the present invention only need once demarcate the back to probe and just can directly be used for having improved localized efficient in the straight line location.The cylinder method straight line targeting scheme that the present invention proposes has effectively solved the problem that exists in the traditional method, replaces the indirect straight line of multiple spot location, the error that has existed when having reduced the location greatly by using direct straight line location.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 location, edge 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 carries out linear edge location sketch map for the present invention utilizes the cylinder method.

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 location linear edge designed probe, and A, B, C, D are the index point that four infrarede emitting diodes are formed, E ₁E ₂Be a straight line locating slot, 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:

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

Fig. 4 carries out the localized sketch map of linear edge for the cylinder method that the present invention proposes.Locating slot E with probe ₁E ₂The align linear edge (Fig. 1) of any one object is that axle rotates several times then with the locating slot with probe, because A, and B, C, 4 of D are respectively with E ₁E ₂For the axle rotation, be example with the B point, rotate n corresponding different point and be respectively B ₁, B ₂..., B _n, from B ₁, B ₂..., B _nTo E ₁E ₂Make vertical line and intersect at O respectively _B1, O _B2..., O _Bn, O in theory _B1, O _B2..., O _BnJust intersect at E ₁E ₂On 1 O _B, but in practice owing to various interference of noise, O _B1, O _B2..., O _BnAnd non-intersect, with a sphere this n point carried out match for this reason, then n point should be distributed on the same great circle of this sphere, and the sphere of gained error minimum is O _B1, O _B2..., O _BnThe sphere at place, the centre of sphere of this ball is just thought O _B

If the equation of this ball in camera coordinate system is (X-X ₀) ²+ (Y-Y ₀) ²+ (Z-Z ₀) ²=R ², R is the radius of ball.B ₁, B ₂..., B _nCoordinate be respectively (X _B1, Y _B1, Z _B1), (X _B2, Y _B2, Z _B2) ..., (X _Bn, Y _Bn, Z _Bn).Can obtain:

f ₁＝(X _B1-X ₀) ²+(Y _B1-Y ₀) ²+(Z _B1-Z ₀) ²-R ²

f ₂＝(X _B2-X ₀) ²+(Y _B2-Y ₀) ²+(Z _B2-Z ₀) ²-R ²



f _n＝(X _Bn-X ₀) ²+(Y _Bn-Y ₀) ²+(Z _Bn-Z ₀) ²-R ²

Defining following error function is:

$e=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{f}_i^2$

Make the error function minimum, promptly $\min e=\min \underset{i=1}{\overset{n}{\mathrm{\Σ}}}{f}_i^2$

Because above-mentioned equation is a nonlinear equation, the present invention finds the solution with the Levenberg-Marquart algorithm.(the X that draws ₀, Y ₀, Z ₀) be O _BThree-dimensional coordinate in camera coordinate system.In like manner can obtain A, C, the coordinate O of 3 center of rotation of D _A, O _C, O _DSince A, B, C, 4 of D all are around E ₁E ₂Rotation is so these four points should constitute straight line E in theory ₁E ₂, but in practice owing to various interference of noise, these four points are point-blank not strict, with linear equation these four points carried out match for this reason, and the fitting a straight line of gained is E ₁E ₂

If E ₁E ₂Linear equation is:

If the coordinate of four points is respectively: (X _A, Y _A, Z _A), (X _B, Y _B, Z _B), (X _C, Y _C, Z _C), (X _D, Y _D, Z _D) then can obtain:

f ₁₁＝A ₁X _A+B ₁Y _A+C ₁Z _A-D ₁，f ₁₂＝A ₂X _A+B ₂Y _A+C ₂Z _A-D ₂

f ₂₁＝A ₁X _B+B ₁Y _B+C ₁Z _B-D ₁，f ₂₂＝A ₂X _B+B ₂Y _B+C ₂Z _B-D ₂

f ₃₁＝A ₁X _C+B ₁Y _C+C ₁Z _C-D ₁，f ₃₂＝A ₂X _C+B ₂Y _C+C ₂Z _C-D ₂

f ₄₁＝A ₁X _D+B ₁Y _B+C ₁Z _D-D ₁，f ₄₂＝A ₂X _D+B ₂Y _D+C ₂Z _D-D ₂

Defining following error function is:

$e=\underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="f\; ij"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{ij}}^{}$

Make the error function minimum, promptly $\min e=\min \underset{i=1}{\overset{4}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{2}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="f\; ij"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">f</figure-callout>}}_{\mathrm{ij}}^{}$

Then can obtain the equation of edge line.

The linear equation that cause obtains is the representation in the camera coordinate system,

(1) is expressed as matrix form: $\left[\begin{array}{c}{X}_c\\ Y_c\\ Z_c\end{array}\right]=\stackrel{\&RightArrow;}{R}\left[\begin{array}{c}{X}_p\\ Y_p\\ Z_p\end{array}\right]+\stackrel{\&RightArrow;}{T}---\left(3\right)$

(2) are expressed as matrix form:

The representation of linear equation in probe coordinate system will can be got in (3) substitution (4).

(5) are further merged into:

Order: $P_1=(A_1,B_1,C_1)\stackrel{\&RightArrow;}{R},Q_1=(A_1,B_1,C_1)\stackrel{\&RightArrow;}{T}+D_1,$

${\mathrm{<figure-callout\; id="2"\; label="P"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">P</figure-callout>}}_2=(A_2,{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">B</figure-callout>}}_2,C_2)\stackrel{\&RightArrow;}{R},{\mathrm{<figure-callout\; id="2"\; label="Q"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">Q</figure-callout>}}_2=(A_2,{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="A20041001686400093.png"\; state="\{\{state\}\}">B</figure-callout>}}_2,C_2)\stackrel{\&RightArrow;}{T}+D_2---\left(7\right)$

So finally can obtain the linear equation under probe coordinate system:

P in the equation (7) ₁, P ₂, Q ₁, Q ₂After once demarcating, be known.

The locating slot E of probe will have been demarcated ₁E ₂The linear edge of the alignment positioning object of wanting can obtain the three-dimensional coordinate of following four index points of camera coordinate system, and then can obtain the rotation translation relation R that at this moment camera coordinate system and probe coordinate are, T is according to known P ₁, P ₂, Q ₁, Q ₂Utilize equation (7) can obtain equation (4) simultaneously.Also just obtained last needed linear equation, thereby finished location the object linear edge.

Claims (1)

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

1) make up edge 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 straight line locating slot (E ₁E ₂) composition linear edge position probe, the vector of choosing two index points formations 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, obtain rotation and translation relation between probe coordinate system and the camera coordinate system according to four positions of index point in camera coordinate system;

2) the cylinder method is obtained the linear equation of camera coordinate system middle probe locating slot: with the straight line locating slot (E of probe ₁E ₂) linear edge of alignment arbitrary objects, be that axle rotates several times then with probe with the locating slot, (C is D) respectively with locating slot (E for A, B to make four index points ₁E ₂) be the axle rotation, on rotating shaft, obtain four the center of circle (Os corresponding with index point _A, O _B, O _C, O _D), with linear equation match is carried out in these four centers of circle, obtain fitting a straight line, thereby obtain the linear equation of probe locating slot under camera coordinate system;

3) probe is demarcated: the linear equation of probe locating slot under 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 linear equation under probe coordinate system, determine probe locating slot (E thus ₁E ₂) and four index points (A, B, C, relativenesses D);

4) utilize the good probe of demarcation that the linear edge of object is positioned: will demarcate good probe locating slot (E ₁E ₂) linear edge 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 probe locating slot (E in the step 3 ₁E ₂) with four index points (A, B, C, relativeness D) directly obtains the equation of object edge under camera coordinate system, finally finishes the location to the object linear edge.

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