CN106214320A - A kind of constrained motion control method of intraocular surgery robot - Google Patents

Abstract

The invention discloses the constrained motion control method of a kind of intraocular surgery robot, the method is applicable to the motor control to the surgical machine robot end device that eyeball internal space restraint and sclera sleeve pose retrain, including the centrostaltic rate-determining steps of virtual long, this rate-determining steps is: it is motionless that the end of control end device is in certain point, and control described end device walk around this point a certain straight line rotate, after incremental motion, axially falling on a taper seat of described end device.Constrained motion control method of the present invention can be according to the input (rocking bar, human-computer interaction interface etc.) of doctor, motion to robot end's device is controlled, end device is made to realize specifying attitude and arriving appointment position in eyeball, solve the apparatus work control problem that eyeball constraint is lower, go a step further to clinic is advanced in years so that robot assisted carries out intraocular surgery.

Description

A kind of constrained motion control method of intraocular surgery robot

Technical field

The present invention relates to medical instruments field, particularly relate to the constrained motion control method of a kind of intraocular surgery robot.

Background technology

Intraocular surgery belongs to the microsurgery of a kind of complexity.In current application practice, intraocular surgery such as retina Operation is carried out under surgery microscope, by the surgical operating instrument of thin rod shape (diameter is between 0.5-1.0mm) through 2 It is inserted into ophthalmic to 3 scleral incisions to be operated.Its high performance accuracy requires and limited working place, gives Doctor brings challenge greatly, and therefore, robot assisted completes ophthalmologic operation and is increasingly becoming the focus of scholars's research.

At present, intraocular surgery auxiliary machinery man-based development depends on dexterous robot mechanism and the design of end device, constraint Motor control and adaptive stabilizing control etc., control relatively difficult to achieve with constrained motion the most especially.In this type of operation, operating theater instruments is led to Cross scleral spur hand-hole to enter after intraccular part, in order to realize robot operation technique within the eye, thrust a constraint with In the case of ophthalmic space constraint, needed feeding/exit, rotate, the action such as rolling.

This problem is a typical constraint manipulation problem, there is presently no a kind of motion control for eyeball internal constraint Method processed, realizes the sequence of operations that robot assisted carries out performing the operation.

Summary of the invention

Present invention aim at providing the constrained motion control method of intraocular surgery robot.This method propose a kind of full The motion control method of the surgical machine robot end device of foot eyeball internal space restraint and the constraint of sclera sleeve pose.

In order to achieve the above object, the present invention provides following technical scheme:

A kind of constrained motion control method of intraocular surgery robot, the method be applicable to eyeball internal space restraint and The motor control of the surgical machine robot end device of sclera sleeve pose constraint, including the centrostaltic rate-determining steps of virtual long,

This rate-determining steps is: controlling the end of end device, to be in certain point motionless, and controls described end device and walk around this point A certain straight line rotate, after incremental motion, axially falling on a taper seat of described end device.

Optionally, the centrostaltic rate-determining steps of described virtual long meets following Linear Control equation

In above-mentioned equation:

R, for retraining bus and the described straight line formed plane spin moment in basis coordinates system of robot of described taper seat Battle array；

α=2 π i/n, i=0,1 ... n-1, for each summit of controlling polygon and the line at center and the folder of zero direction Angle, wherein zero direction is the line on polygonal arbitrary summit and center；

N, for the number of vertices of controlling polygon；

Increment of rotation for described end device is moved；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₁, for positive integer, it is used for defining the size of target area.

Optionally, the method includes a rate-determining steps retraining virtual fixing primitive,

This rate-determining steps is: the axial a certain position of the end or described end device that control described end device is gradually approached Target location in space；

This rate-determining steps meets following Linear Control equation

In above-mentioned equation:

N × m, for controlling polyhedral summit, was the top on the horizontal cross-section at polyhedron center and vertical section respectively Point number；

α_1i=2 π i/n, β_1j=2 π j/m, for controlling line and the folder of zero direction on each summit polyhedral and center Angle, wherein zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Translation incremental motion for described end device；

Shifting deviation for described end device current location Yu desired locations；

The next position and the deviation of desired locations for described end device；

ε₁, for positive integer, it is used for defining the size of target area.

Optionally, the method includes that direction retrains the rate-determining steps of virtual fixing primitive,

This rate-determining steps is: control described end device axially gradually approaches desired orientation；

This rate-determining steps meets following Linear Control equation

In above-mentioned equation:

N × m, for controlling polyhedral summit, was the top on the horizontal cross-section at polyhedron center and vertical section respectively Point number；

α_2i=2 π i/n, β_2j=2 π j/m, for controlling line and the folder of zero direction on each summit polyhedral and center Angle, wherein zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₂, for positive integer, it is used for defining the size of target area.

Optionally, the method includes that line retrains the rate-determining steps of virtual fixing primitive,

This rate-determining steps is: control the described end device a certain bar linear motion along three dimensions；

This rate-determining steps meets following Linear Control equation

In above-mentioned equation:

R₃, for the vertical plane spin matrix in basis coordinates system of robot of constraint straight line；

N, for the number of vertices of controlling polygon；

α_3i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction Line for polygonal arbitrary summit Yu center；

Translation incremental motion for described end device；

Current location and the shifting deviation of desired locations for described end device；

The next position and the deviation of desired locations for described end device；

ε₃, for positive integer, it is used for defining the size of target area.

Optionally, the method includes the rate-determining steps of the virtual fixing primitive of rotation condition,

This rate-determining steps is: control described end device straight line vertical rotary axially in three dimensions；

This rate-determining steps meets following Linear Control equation

In above-mentioned equation:

R₄, for the vertical plane of the rotation centerline spin matrix in basis coordinates system of robot；

N, for the number of vertices of controlling polygon；

α_4i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction Line for polygonal arbitrary summit Yu center；

Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₄, for positive integer, it is used for defining the size of target area.

The beneficial effects of the present invention is:

Constrained motion control method of the present invention can be right according to the input (rocking bar, human-computer interaction interface etc.) of doctor The motion of robot end's device is controlled, and makes end device realize specifying attitude and arriving appointment position in eyeball, solves The apparatus work control problem that eyeball constraint is lower, goes a step further so that robot assisted carries out intraocular surgery to clinic is advanced in years.

Accompanying drawing explanation

Fig. 1 is implementation method and the constraint simulation result schematic diagram of the Dot VF primitive rate-determining steps of the present invention；

Fig. 2 is implementation method and the constraint simulation result schematic diagram of the Direction VF primitive rate-determining steps of the present invention；

Fig. 3 is the implementation method schematic diagram of the Line VF primitive rate-determining steps of the present invention；

Fig. 4 is the simulation result schematic diagram of the Line VF primitive rate-determining steps of simple three-link mechanism and the present invention；

Fig. 5 is implementation method and the constraint simulation result schematic diagram of the Spin VF primitive rate-determining steps of the present invention；

Fig. 6 is implementation method and the constraint simulation result schematic diagram of the VRCM constrained motion rate-determining steps of the present invention.

Detailed description of the invention

The present invention is described in detail below in conjunction with the accompanying drawings, and this explanation controls according to constrained motion of the present invention The description of preferred embodiment, does not represent the only form that the present invention may be constructed or uses.

The constrained motion control method of the intraocular surgery robot that the application provides, mainly includes 5 steps, can use 5 Any one in individual step or multiple combination.Specifically include (sequence is in no particular order): 1, retrain the control of virtual fixing primitive Step processed (Dot VF), this step is: control the axial a certain position of the end of described end device or described end device gradually Target location in approximate spatial；2, direction retrains the rate-determining steps (Drection VF) of virtual fixing primitive, and this step is: Control described end device axially gradually approaches desired orientation；3, line retrains the rate-determining steps (Line VF) of virtual fixing primitive, This step is: control the described end device a certain bar linear motion along three dimensions；4, rotation condition virtual fixing primitive Rate-determining steps (Spin VF), this step is: control described end device straight line vertical rotary axially in three dimensions； 5, the centrostaltic rate-determining steps of virtual long (VRCM), this step is: it is motionless that the end of control end device is in certain point, and Control described end device and walk around a certain straight line rotation of this point, after incremental motion, axially falling at a circle of described end device On the conical surface.

For realizing the control of constrained motion under specific task coordinate system, by operating theater instruments actual end state representation it is Joint variable and the function of joint motions increment, it would be desirable to end state is expressed as the letter of user inputted variable and joint variable Number, then object function is virtual condition and expectation state the difference between the two.In joint motions increment and the pact of actual end state In the range of bundle, solving so that the joint motions increment of object function minimum can realize the control of constrained motion, governing equation is:

For virtual condition (terminal position of operating theater instruments or direction),For the expectation state.Virtual condition It it is joint variableWith joint incremental motionFunction.Expectation stateIt it is User Defined inputAnd joint VariableFunction.It is the object function relevant to virtual condition and expectation state the difference between the two.AndRepresent constraints, strict regulations solution vectorZone of reasonableness.

1, the rate-determining steps (Dot VF) of virtual fixing primitive is retrained

The governing equation of Dot VF is as follows: the end physical location of robot end's deviceHave only to translation Motion can be close to desired locationsWithRepresent that current location is poor, thenOnly exist translational componentDo not exist Rotational componentThereforeThe purpose of Dot VF is through incremental motionAfter, end device The next positionAs close possible to target locationI.e. make next alternate position spikeAgreeing to the greatest extent can be little, describes with equation It is:Wherein ε₁For the least positive integer, define the size in impact point region, now impact point region It is ε for radius₁Ball, this is nonlinear Control condition.If representing with Linear Constraints, can be by constraint equation Regard asThrough impact pointAll directions on projection be respectively less than ε₁If, with impact pointCentered by, with ε₁ For the polyhedron on one n × m summit of radius definition, then Linear Control equation is:

Wherein:

N × m, for controlling polyhedral summit, was the top on the horizontal cross-section at polyhedron center and vertical section respectively Point number；

α_1i=2 π i/n, β_1j=2 π j/m, for controlling line and the folder of zero direction on each summit polyhedral and center Angle, wherein zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Translation incremental motion for described end device；

Shifting deviation for described end device current location Yu desired locations；

The next position and the deviation of desired locations for described end device；

ε₁, for positive integer, such as the least positive integer, it is used for defining the size of target area.

In a particular embodiment:

As shown in Fig. 1 .a, in linear approximation, a series of hyperplane is used to surround a polyhedron, for approximate geometry Constraint.Constraint equation | | δ | |₂≤ ε defines a spherical tolerance region, can generate a polyhedron, make this spherical For inscribed sphere.Novel Algorithm, the end initial position point of amendment end device is utilized to lay respectively at eight in Matlab software Individual different position, it is desirable to position is defined as coordinate origin, first uses nonlinear governing equationImitate Very, result is as shown in Fig. 1 .b, it can be seen that nonlinear restriction simulation result precision is the highest, the disturbance of any deviation desired locations All having converged at zero, image is amplified to the limit just can find out position deviation, and site error is less than 1 × 10^-4Mm is full Foot motion control accuracy requirement.Make Dot VF Linear Control equation

In n=m=12, the simulation result tried to achieve is as shown in Fig. 1 .c.Zero is deviateed equally with initial position Being reference point at 0.5mm, it can be seen that linear restriction simulation result precision is relatively low, motion algorithm is passed through in the disturbance of deviation desired locations Having converged near zero, site error is less than 2 × 10^-1Mm, and initial position is the nearest away from desired locations, then and precision is more Height, substantially meets motion control accuracy requirement.Therefore, the occasion that efficiency requirements is the highest precision is higher, can be selected for non-linear Constraint；Otherwise employing linear restriction.

2, direction retrains the rate-determining steps (Drection VF) of virtual fixing primitive

The governing equation of Drection VF is as follows: robot end's device directionHaving only to rotary motion can be close to expectation DirectionWithRepresent that current direction is poor, thenOnly exist rotational componentThere is not translational componentTherefore current direction is poor ForThe purpose of Drection VF is through incremental motionAfter, under end device axis One directionAs close possible to desired orientationI.e. make next direction poorThe least, describe with equation It is:ε₂For the least positive integer, defining the range size of desired orientation, this is nonlinear Control Condition.If representing with Linear Constraints, Linear Constraints can be described asPassing throughWithIntersection pointEach Projection on direction is respectively less than ε₂If, with intersection pointCentered by, with ε₂The polyhedron on a n × m summit is defined, then for radius Linear Control equation is:

Wherein:

N × m, for controlling polyhedral summit, was the top on the horizontal cross-section at polyhedron center and vertical section respectively Point number；

α_2i=2 π i/n, β_2j=2 π j/m, for controlling line and the folder of zero direction on each summit polyhedral and center Angle, wherein zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₂, for positive integer, such as the least positive integer, it is used for defining the size of target area.

In one embodiment:

As shown in Fig. 2 .a, definition desired orientation falls in OXY plane, will problem reduction be two dimensional surface.At Matlab Utilizing Novel Algorithm in software, amendment end device the most axially lays respectively at six different positions, it is desirable to direction is with the The straight line in one 45 ° of directions of quadrant defines, and utilizes nonlinear governing equationEmulate, obtain result such as figure Shown in 2.b.With 45 ° of straight lines of first quartile as reference direction, nonlinear restriction simulation result precision is the highest as seen from Figure 37, The disturbance of any deviation desired orientation has all been converged at reference direction by motion algorithm.Image amplification just can be seen that direction Deviation, angular error is about 0.0057 °, the well beyond required precision of direction controlling.Make Drection VF linear restriction bar PartIn N=m=12, the simulation result tried to achieve is as shown in Fig. 2 .c.As reference direction at 45 ° of straight lines, it can be seen that linear restriction emulates Result precision is relatively low, and the disturbance of deviation desired orientation has converged near reference direction by motion algorithm, and angular error is less than 3 °, and inceptive direction deviation desired orientation is the least, then and precision is the highest, substantially meets direction controlling required precision.Therefore, in essence Spend higher and that efficiency requirements is the highest occasion, can be selected for nonlinear restriction；Otherwise employing linear restriction.

3, line retrains the rate-determining steps (Line VF) of virtual fixing primitive

The governing equation of Line VF is as follows: the initial position of known instrument endEquation with straight line LWhereinBeing a bit on straight line, the direction of straight line is by unit vectorRepresent, can calculate on straight line L away fromNearest point (i.e. intersection point) And hang down away from, hang down away from being current location deviation, be designated asIntersection pointCoordinate can pass through vertical line It is 0 that dot product straight line L amasss and intersection point the two condition simultaneous on the linel is tried to achieve, it may be assumed that

Solve further, obtain:

The purpose of Line VF is through incremental motionAfter, the next position of endOn the linel hang down away from The least, hang down away from the new position of endWith a upper intersection pointLine in any plane being perpendicular to straight line L Projected length is expressed, i.e. with vectorIn any plane being perpendicular to straight line L Projective representation hang down away from, then governing equation is represented by:ε₃For the least positive integer, define with reference to straight line L The size of neighbouring range of disturbance, this is nonlinear governing equation.If representing with Linear Constraints, first appoint one difference of definition InVectorBe perpendicular to any plane Π of straight line L, calculate subsequently and can open into plane Π and be perpendicular toTwo units VectorWith Obtain spin matrixThus, in plane Π Arbitrary unit vector is expressed as in basis coordinates system of robot: R₃·[cosα₃ sinα₃ 0]^T.The description of Linear Constraints For:Through pointPlane Π in projection on arbitrary lineBoth less than ε₃.If withPoint is the center of circle, ε₃For radius Define a n limit shape, then Linear Control equation is:

Wherein:

R₃, for the vertical plane spin matrix in basis coordinates system of robot of constraint straight line；

N, for the number of vertices of controlling polygon；

α_3i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction Line for polygonal arbitrary summit Yu center；

Translation incremental motion for described end device；

Current location and the shifting deviation of desired locations for described end device；

The next position and the deviation of desired locations for described end device；

ε₃, for positive integer, such as the least positive integer, it is used for defining the size of target area.

In one embodiment:

As it is shown on figure 3, as a example by simple three-link mechanism, this algorithm is emulated.Plane 3R serial mechanism is transported Dynamic model of learning is as shown in Fig. 4 .a, and this serial manipulator chooses mechanism end point P as output, it is known that three length of connecting rods are respectively l₁、 l₂And l₃It is respectively θ with the relative angle in a upper joint₁、θ₂And θ₃, just it is counterclockwise, it is assumed that θ₁=10 ° of holdings are constant, just Initial value θ₂=10 °, θ₃=20 °.Desired motion is: the linkage distal point P red dotted line L along space all the time moves (just Under beginning state, some P does not falls on this straight line).Known joint variable θ=[θ₁ θ₂ θ₃]^T(θ₁=10 ° are constant), solve output P= [x y z]^TIt is forward kinematics solution, then has:

Differential is also write as matrix form:

Therefore, Jacobian matrix is

Object function is defined as:Wherein Δ x_dFor user-defined desired motion increment,For Each joint variable increment.In Matlab software, utilize Novel Algorithm, use Linear Control equationEmulate, Result is as shown in Fig. 4 .b.Can be seen that the effectiveness of this algorithm: red point is linkage original end point, after incremental motion, Distal point has all been fallen on predefined straight line.

4, the rate-determining steps (Spin VF) of the virtual fixing primitive of rotation condition

The governing equation of Spin VF is as follows: known end device axis inceptive directionWith the equation of center of rotation straight line L and DirectionPlane Π being perpendicular to straight line L, and end device axis inceptive direction can be calculatedProjection unit in plane Π Vector Computing formula as follows:End device direction can be obtainedWith projection unit vectorDirection difference beThis direction difference is rotating deviation.The purpose of Spin VF is for through increasing Amount motionAfterwards, the next axis direction of end deviceFall as far as possible in plane Π, i.e. make next axis Direction between direction and its projection unit vector is poorThe least, definitionFor vectorFall in plane Π Projection, obtaining governing equation is:ε in formula₄For the least positive integer, define with reference to disturbance near straight line L The size of scope, this is nonlinear governing equation.If representing with Linear Constraints, definition one is first appointed to be different fromArrow AmountBe perpendicular to any plane Π of straight line L, calculate subsequently and can open into plane Π and be perpendicular toTwo unit vectorsWith Obtain spin matrixThus, the arbitrary unit in plane Π Vector is expressed as in basis coordinates system of robot: R₄·[cosα₄ sinα₄ 0]^T.Being described as of Linear Constraints: Through pointPlane Π in projection on arbitrary lineBoth less than ε₄.If withPoint is the center of circle, ε₄One is defined for radius N limit shape, can obtain Linear Control equation equation is:

Wherein:

R₄, for the vertical plane of the rotation centerline spin matrix in basis coordinates system of robot；

N, for the number of vertices of controlling polygon；

α_4i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction Line for polygonal arbitrary summit Yu center；Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₄, for positive integer, such as the least positive integer, it is used for defining the size of target area.

In one embodiment:

As shown in Fig. 5 .a, algorithm steps is as follows:

1), the direction of the straight line L in known spatial is vector along the z-axis direction

2), current inceptive direction(similar close to vector a), in OXZ plane；

3), byWithCan release

4), byWithCan calculate

5), desired step-length be defined as often making a move into aroundRotate 2 ° counterclockwise, it may be assumed that

6), object function is:

7), subsequently according to Linear Control equation

CalculateReturn to step 2, loop iteration, ultimately produce Fig. 5 .b.As can be seen from Figure, this motion algorithm can keep operating theater instruments pose all the time vertically InPlane on, demonstrate the effectiveness of algorithm.

5, the centrostaltic rate-determining steps of virtual long (VRCM)

VRCM the end of end device can be kept to be in certain some invariant position by combination Dot VF and Spin VF protects Hold the axial of end device to realize around certain line vertical rotary, it is achieved method is as follows: known fixed pointNote is perpendicular to axis side ToAnd the plane of Planar Mechanisms element of cone is Π₁, element of cone withPlace plane is Π₂, plane Π₁With plane Π₂Mutually Vertically, then circular cone centrageIt is also at plane Π₂On.Note:ThenIt is positioned at plane Π₁On, it is perpendicular toHang down Straight in plane Π₂.Note:ThenIt is positioned at plane Π₂On, both it was perpendicular toIt is perpendicular to againPlane Π₂In robot Spin matrix in basis coordinates system is:Due to rotation axisCan be by plane Π₂On arbitrary unit vector representation, Obtain rotation axisSubsequently, calculateFall in plane Π₁Upper projectionThis The purpose of one constrained motion primitive is after incremental motion, and the next position of end device axis needs at element of cone On, therefore errors table is shown as:According to the description of Spin VF, linearly control Equation processed can be written as:

Wherein:

R, for retraining bus and the described straight line formed plane spin moment in basis coordinates system of robot of described taper seat Battle array；

α=2 π i/n, i=0,1 ... n-1, for each summit of controlling polygon and the line at center and the folder of zero direction Angle, wherein zero direction is the line on polygonal arbitrary summit and center；

N, for the number of vertices of controlling polygon；

Increment of rotation for described end device is moved；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₁, for positive integer, such as the least positive integer, it is used for defining the size of target area.

In one embodiment:

As shown in Fig. 6 .a, specific algorithm step is as follows:

1) definitionThe most successively according to formula CalculateIncrease according to Spin VF definition expectation Amount motionThe most each step is all around calculating gained axleRotate 2 ° counterclockwise；

2) by Linear Control equation Middle n=6, can calculate A and b, moves through multiple incremental, obtains VRCM analogous diagram as shown in Fig. 6 .b, as seen from the figure, end The movement locus of device meets VRCM moving condition, demonstrates the effectiveness of algorithm.In robot realizes operative process, can With keep the distal point of end device all the time with thrust and overlap on the premise of, utilize VRCM to adjust the ophthalmic initial appearance of end device State, in order to end device imports in sleeve pipe smoothly.

To sum up, the technical scheme that the application provides, order by generating a series of incremental motion for intraocular surgery robot Order, guided robot end device realizes specifying attitude and arriving the control method specifying position inside eyeball.

Claims (6)

1. the constrained motion control method of an intraocular surgery robot, it is characterised in that the method is applicable to eyeball inside The motor control of the surgical machine robot end device of space constraint and the constraint of sclera sleeve pose, centrostaltic including virtual long Rate-determining steps,

This rate-determining steps is: controlling the end of end device, to be in certain point motionless, and controls described end device and walk around certain of this point One straight line rotates, after incremental motion, and axially falling on a taper seat of described end device.

The constrained motion control method of intraocular surgery robot the most according to claim 1, it is characterised in that described virtual The rate-determining steps of remote centre of motion meets following Linear Control equation

$\left[\begin{array}{cccc}0& 0& 0& {\[R\·{\left[\begin{array}{ccc}cos\mathrm{\α}& sin\mathrm{\α}& 0\end{array}\right]}^T\]}^T\end{array}\right]\·({\stackrel{\→}{\mathrm{\δ}}}_r+\mathrm{\Δ}{\stackrel{\→}{x}}_r)\≤\mathrm{\ϵ},$

In above-mentioned equation:

R, for bus and the described straight line formed plane spin matrix in basis coordinates system of robot of the described restrained circle conical surface；

α=2 π i/n, i=0,1 ... n-1, for each summit of controlling polygon and the line at center and the angle of zero direction, its Middle zero direction is the line on polygonal arbitrary summit and center；

N, for the number of vertices of controlling polygon；

Increment of rotation for described end device is moved；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₁, for positive integer, it is used for defining the size of target area.

The constrained motion control method of intraocular surgery robot the most according to claim 1 and 2, it is characterised in that the party Method includes a rate-determining steps retraining virtual fixing primitive,

This rate-determining steps is: control the end of described end device or the axial a certain position gradually approximate spatial of described end device In target location；

This rate-determining steps meets following Linear Control equation

$\left[\begin{array}{cccccc}{\mathrm{cos\α}}_{1i}{\mathrm{cos\β}}_{1j}& {\mathrm{cos\α}}_{1i}{\mathrm{sin\β}}_{1j}& {\mathrm{sin\α}}_{1i}& 0& 0& 0\end{array}\right]\·\left({\stackrel{\→}{\mathrm{\δ}}}_p+\mathrm{\Δ}{\stackrel{\→}{x}}_p\right)\≤{\mathrm{\ϵ}}_1,i=0,1,...,n-1;j=0,1,...,m-1$

In above-mentioned equation:

N × m, for controlling polyhedral summit, was the summit on the horizontal cross-section at polyhedron center and vertical section respectively Number；

α_1i=2 π i/n, β_1j=2 π j/m, for controlling line and the angle of zero direction on each summit polyhedral and center, wherein Zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Translation incremental motion for described end device；

Shifting deviation for described end device current location Yu desired locations；

The next position and the deviation of desired locations for described end device；

ε₁, for positive integer, it is used for defining the size of target area.

The constrained motion control method of intraocular surgery robot the most according to claim 1 and 2, it is characterised in that the party Method includes that direction retrains the rate-determining steps of virtual fixing primitive,

This rate-determining steps is: control described end device axially gradually approaches desired orientation；

This rate-determining steps meets following Linear Control equation

$\left[\begin{array}{cccccc}0& 0& 0& {\mathrm{cos\α}}_{2i}{\mathrm{cos\β}}_{2j}& {\mathrm{cos\α}}_{2i}{\mathrm{sin\β}}_{2j}& {\mathrm{sin\α}}_{2i}\end{array}\right]\·({\stackrel{\→}{\mathrm{\δ}}}_r+\mathrm{\Δ}{\stackrel{\→}{x}}_r)\≤{\mathrm{\ϵ}}_2,i=0,1,...,n-1;j=0,1,...,m-1$

In above-mentioned equation:

N × m, for controlling polyhedral summit, was the summit on the horizontal cross-section at polyhedron center and vertical section respectively Number；

α_2i=2 π i/n, β_2j=2 π j/m, for controlling line and the angle of zero direction on each summit polyhedral and center, wherein Zero direction is the line on polygon arbitrary summit of crossing on the cross section at center and center；

Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₂, for positive integer, it is used for defining the size of target area.

The constrained motion control method of intraocular surgery robot the most according to claim 1 and 2, it is characterised in that the party Method includes that line retrains the rate-determining steps of virtual fixing primitive,

This rate-determining steps is: control the described end device a certain bar linear motion along three dimensions；

This rate-determining steps meets following Linear Control equation

$\left[\begin{array}{cccc}{\[R_3\·{\left[\begin{array}{ccc}{\mathrm{cos\α}}_{3i}& {\mathrm{sin\α}}_{3i}& 0\end{array}\right]}^T\]}^T& 0& 0& 0\end{array}\right]\·({\stackrel{\→}{\mathrm{\δ}}}_p+\mathrm{\Δ}{\stackrel{\→}{x}}_p)\≤{\mathrm{\ϵ}}_3,i=0,1,...n-1$

In above-mentioned equation:

R₃, for the vertical plane spin matrix in basis coordinates system of robot of constraint straight line；

N, for the number of vertices of controlling polygon；

α_3i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction is many Arbitrary summit of limit shape and the line at center；

Translation incremental motion for described end device；

Current location and the shifting deviation of desired locations for described end device；

The next position and the deviation of desired locations for described end device；

ε₃, for positive integer, it is used for defining the size of target area.

The constrained motion control method of intraocular surgery robot the most according to claim 1 and 2, it is characterised in that the party Method includes the rate-determining steps of the virtual fixing primitive of rotation condition,

This rate-determining steps is: control described end device straight line vertical rotary axially in three dimensions；

This rate-determining steps meets following Linear Control equation

$\left[\begin{array}{cccc}0& 0& 0& {\[R_4{\left[\begin{array}{ccc}{\mathrm{cos\α}}_{4i}& {\mathrm{sin\α}}_{4i}& 0\end{array}\right]}^T\]}^T\end{array}\right]\·({\stackrel{\→}{\mathrm{\δ}}}_r+\mathrm{\Δ}{\stackrel{\→}{x}}_r)\≤{\mathrm{\ϵ}}_4,i=0,1,...n-1$

In above-mentioned equation:

R₄, for the vertical plane of the rotation centerline spin matrix in basis coordinates system of robot；

N, for the number of vertices of controlling polygon；

α_4i=2 π i/n, for each summit of controlling polygon and the line at center and the angle of zero direction, wherein zero direction is many Arbitrary summit of limit shape and the line at center；

Increment rotary motion for described end device；

Current direction and the rotating deviation of desired orientation for described end device；

Next direction and the deviation of desired orientation for described end device；

ε₄, for positive integer, it is used for defining the size of target area.