CN103720514B - For the parameter optimization method of the surgical robot of operative space - Google Patents

Abstract

The invention discloses a kind of parameter optimization method of the surgical robot for operative space, first suppose the coordinate transformation relation between the basis coordinates system of surgical robot and ending coordinates system: ⁿt ₀= ¹t ₀* ²t ₁* ³t ₂* ⁴t ₃* ⁵t ₄* ⁶t ₅... ⁱ⁺¹t _i... ⁿt _n-1; Then, object function is passed through the parameter of surgical robot is optimized, and gets the parameter of its minima as the surgical robot after optimization.Directly synchronously can obtain corresponding to high-precision joint parameter, for the working environment of surgical robot, in work space, farthest can improve the precision of robot more targetedly.

Description

For the parameter optimization method of the surgical robot of operative space

Technical field

The present invention relates to a kind of parameter optimization technique of surgical robot, particularly relate to a kind of parameter optimization method of the surgical robot for operative space.

Background technology

Along with the fast development of science and technology, robot is widely used in every field, also its precision is had higher requirement simultaneously, especially be applied to clinical surgical robot surgical robot and focus on precision especially, this is also the inevitable requirement that the life security of patient proposes surgical robot.

In recent years, occurred the modern calibration techniques such as shaft centerline measurement method, neutral net, but these methods more or less exist certain drawback, such as precision improves significantly, the learning efficiency is low, be easy to be absorbed in local optimum etc.

In prior art, shaft centerline measurement method is by optical camera, takes the method that shaft centerline measurement is demarcated, based on the process of method of least square to data, obtain the kinematics model of robot reality, and calculate the actual joint parameter of this robot by space geometry.

Primary calibration process is as follows:

By each joint motions of PC control surgical robot to joint zero-bit.

For the linear joint of robot, when other joint is all in joint zero-bit and remains unchanged, control this joint to move by certain step-length, when often moving to a position, measure by binocular camera and record the position coordinates of robot needle point point, then data measured is carried out to the matching of space line, just can try to achieve joints axes.

For the cradle head of surgical robot, when other joint is all in joint zero-bit and remains unchanged, control this joint to rotate by certain step-length, when often moving to a position, measure by binocular camera and record the position coordinates of robot needle point point, then data measured is carried out to the matching in space sphere peace face, just can to try to achieve by the centre of sphere and perpendicular to the joints axes of plane and central coordinate of circle.

As shown in Figure 1, the joints axes obtained by a series of matching and central coordinate of circle, just can set up the actual DH model of robot, and then calculated the actual structure parameters of trying to achieve celebral operating robot by space geometry.

At least there is following shortcoming in above-mentioned prior art:

To data measured carry out space line, sphere, plane matching there is error; The space geometry amount of calculation of DH model is large, and may ignore the parameter that there is micro-error.

Summary of the invention

The object of this invention is to provide a kind of parameter optimization method that can improve the surgical robot for operative space of robot precision.

The object of the invention is to be achieved through the following technical solutions:

The parameter optimization method of the surgical robot for operative space of the present invention, first suppose the coordinate transformation relation between the basis coordinates system of surgical robot and ending coordinates system: ⁿt ₀= ¹t ₀* ²t ₁* ³t ₂* ⁴t ₃* ⁵t ₄* ⁶t ₅... ⁱ⁺¹t _i... ⁿt _n-1, n is non-zero positive integer;

Then, be optimized by the parameter of following object function to surgical robot:

$F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|,$ In formula:

---X is joint parameter x _iset;

---Δ t _ifor joint is relative to variable quantity during zero-bit;

---Δ T ₀during for measuring registration point, joint is relative to the variable quantity of zero-bit;

---a _ifor the actual value put under the photographic head coordinate system that directly records;

---f (X+ Δ t _i) be the theoretical coordinate in lower i-th joint of robot coordinate system;

---g (X+ Δ T ₀) be tied to the transition matrix of robot coordinate system for photographic head coordinate;

---|| be Euclidean distance.

As seen from the above technical solution provided by the invention, the parameter optimization method of the surgical robot for operative space that the embodiment of the present invention provides, owing to passing through object function the parameter of surgical robot is optimized, and get the parameter of its minima as the surgical robot after optimization, can directly synchronously obtain corresponding to high-precision joint parameter, for the working environment of surgical robot, in work space, farthest can improve the precision of robot more targetedly.

Accompanying drawing explanation

In Fig. 1 prior art, matching obtains the DH model schematic of robot;

Fig. 2 is the DH model schematic that in the embodiment of the present invention, robot is corresponding.

Detailed description of the invention

To be described in further detail the embodiment of the present invention below.

The parameter optimization method of the surgical robot for operative space of the present invention, its preferably detailed description of the invention be:

First the coordinate transformation relation between the basis coordinates system of surgical robot and ending coordinates system is supposed: ⁿt ₀= ¹t ₀* ²t ₁* ³t ₂* ⁴t ₃* ⁵t ₄* ⁶t ₅... ⁱ⁺¹t _i... ⁿt _n-1, n is non-zero positive integer;

Then, be optimized by the parameter of following object function to surgical robot:

$F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|,$ In formula:

---X is joint parameter x _iset;

---Δ t _ifor joint is relative to variable quantity during zero-bit;

---Δ T ₀during for measuring registration point, joint is relative to the variable quantity of zero-bit;

---a _ifor the actual value put under the photographic head coordinate system that directly records;

---f (X+ Δ t _i) be the theoretical coordinate in lower i-th joint of robot coordinate system;

---g (X+ Δ T ₀) be tied to the transition matrix of robot coordinate system for photographic head coordinate;

---|| be Euclidean distance.

The parameter of minima as the surgical robot after optimization of described object function can be got by following formula:

$\left\{\begin{array}{c}\min F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|\\ |x_i-x_i^{*}|\≤{\mathrm{\δ}}_i\end{array}\right.,$ In formula:

---x _ibe i-th joint parameter;

---δ _iit is the range of error of i-th joint parameter;

--- it is the theoretical value of i-th joint parameter.

Compared to the parameter identification of traditional robot, for saving time, saving trouble and there is effective consideration, the definitiveness of its work space in addition, only need to ensure that robot has higher positioning precision at operative space and just can.Therefore the present invention is directed to the method that operative space attempts parameter optimization compensation, obtain and allow robot application in clinical positioning precision, and obtain corresponding joint parameter.

The parameter optimization method of the surgical robot for operative space of the present invention, without the need to there are the computational methods of error by process of fitting treatment etc., but adopts most optimally method, the reduction error of maximum likelihood; After Optimization Compensation, directly synchronously obtain corresponding to high-precision joint parameter, without the need to separately asking joint parameter with wasting time and energy; For the working environment of surgical robot, in work space, farthest improve the precision of robot more targetedly.

Specific embodiment:

As shown in Figure 2, according to the architectural characteristic of surgical robot, set up corresponding DH model.Wherein footmark sequence number 0 represents the basis coordinates system of robot, and footmark sequence number 6 is the ending coordinates system of end effector of robot, and other sequence numbers are followed successively by the joint of robot.

According to the DH model set up, the theoretical joint parameter by robot carries out forward kinematics solution to it.Set up the transformation relation between adjacent Two coordinate system ⁱ⁺¹t _i(also T can be write _i), as the coordinate transformation relation between basis coordinates system and 1 joint coordinate system ¹t ₀, other the like.Then the coordinate transformation relation between basis coordinates system and ending coordinates system is set up: ⁶t ₀= ¹t ₀* ²t ₁* ³t ₂* ⁴t ₃* ⁵t ₄* ⁶t ₅.

Data measure: for surgical robot, due to the both qualitative of its work space and centrality, we are also pointed accordingly to the acquisition of experimental data, its puncture needle is mainly made to move in the operative space determined, as much as possible with different attitude orientation in different positions, now record the true spatial location of needle point point with optical camera, record each joint variable of robot simultaneously, and calculate the theoretical space position of needle point point by joint variable.Detailed process is as follows:

(1) the defining of work space: the work space square chest (graph paper of dot matrix is posted on surface) measuring needle point point and need to use firmly being positioned over robot.

(2) the measuring of registration point: mobile robot artificially, makes its needle point point move on square chest not conllinear, 4 not coplanar four registration point at 3.Whenever needle point point arrives one of them registration point, by the spatial value of this point of photographic head record, and the joint variable of recorder people.The transformational relation between two different spaces coordinate systems can be set up by the registration point coordinate under the robot coordinate system calculated and the registration point coordinate system under photographic head coordinate system.

(3) the measuring of Optimum Points: mobile robot artificially, makes puncture needle arrive at coordinate points on square chest, the same position with photographic head recording needle cusp, and the joint variable of recorder people with different attitudes.By unified for the coordinate figure under two coordinate systems under same coordinate system, value of calculation is as theoretical value, and photographic head side value is as actual value.

Note ensureing that the relative position of photographic head, square chest and robot immobilizes in above-mentioned operating process.

Parameter optimization: main thought is the difference by reducing between needle point point theoretical coordinate and true coordinate the trace adjustment of joint parameter, improves the positioning precision of robot.In the measuring of needle point point, recorded the true coordinate of needle point point by photographic head, calculated the theoretical coordinate of needle point point by joint variable and kinematics model, under two coordinate figures are transformed into same coordinate system, carry out data analysis:

Set up object function:

---a _ifor the actual value put under the photographic head coordinate system that directly records;

---M is the transition matrix that photographic head coordinate is tied to robot coordinate system;

--- the true coordinate under robot coordinate system is transformed into for this point.

If the joint parameter of robot is accurately, namely theoretical parameter is identical with actual parameter, can set up following equation:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|b_i-b_i^{*}|=0$

---b _ifor the theoretical coordinate of this point under robot coordinate system;

---|| be Euclidean distance.

But in fact the actual parameter of robot can not be the same with theoretical parameter, so

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|b_i-b_i^{*}|>0$

That is:

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|b_i-{\mathrm{Ma}}_i|>0$

Again due to

b _i=f(t _i)=f(t ₀+Δt _i)

M=g(t ₀+ΔT ₀)

---t ₀for joint parameter during robot zero-bit;

---Δ t _ifor joint is relative to variable quantity during zero-bit;

---Δ T ₀during for measuring registration point, joint is relative to the variable quantity of zero-bit.

So have

$\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(t_0+{\mathrm{\Δt}}_i)-g(t_0+{\mathrm{\ΔT}}_0)a_i|>0$

At this, by the t in above formula ₀be considered as variable, and replace, by the Δ t measured with X _i, Δ T ₀, a _ibe considered as given value, be defined as follows function:

$F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|$

Reduce as much as possible based on the difference made between true coordinate car following-theory coordinate, to improve the target of robot precision.The minima of above formula F (X) is sought in the range of error that joint of robot parameter allows.

Determine the object function of parameter optimization:

$\left\{\begin{array}{c}\min F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|\\ |x_i-x_i^{*}|\≤{\mathrm{\δ}}_i\end{array}\right.$

---X is joint parameter x _iset;

---x _ibe i-th joint parameter;

--- it is the theoretical value of i-th joint parameter;

---δ _iit is the range of error of i-th joint parameter.

The object function set up by this thinking can reflect the comprehensive locating effect of mechanism, and mechanism kinematic mathematic(al) parameter when object function obtains minima can make the repetitive positioning accuracy of mechanism in whole work space best.So far, kinematics model parametric solution problem is just converted into the multivariate Constrained and Unconstrained Optimization asked and meet prescribed limit, and for the non-linear Constrained and Unconstrained Optimization of this Multivariable Constrained, the OptimizationToolbox instrument in available Matlab solves.

Using the theoretical value of joint of robot parameter as variable initial value, determine the range of error that each joint parameter is possible just can be optimized calculating according to mechanism's practical situation, the minimum error values that result of calculation meeting simultaneous display is final and corresponding optimal joint parameter.

The beneficial effect that technical solution of the present invention is brought:

1, the method reduces the workload of previous methods, and optimization aim directly corresponds to the positioning precision of robot, has more specific aim.

2, it is relatively more rational for optimizing parameters obtained, and just on the basis of theoretical parameter, done small adjustment, this point meets the manufacture of robot and the situation of rigging error, and makes theoretical value approaching to reality value more, thus reduces position error.By being optimized surgical robot kinematics model parameter, reducing the gap between kinematics model and mechanism, the positioning precision of surgical robot can be significantly improved.This has realistic meaning very much to the robot being applied to clinical treatment.

In concrete enforcement, the use of photographic head can be omitted.Measure actual value without photographic head, when measuring registration point, value of calculation, as the position of registration point, can set up space coordinate conversion relation between this coordinate figure and basis coordinates system (0,0,0); When Optimum Points measures, only select a fixing point in space, value of calculation is as theoretical value, and the meansigma methods of value of calculation, as actual value, so also can reach similar object.

Choosing about majorized function, problem of calibrating is converted into multivariable optimization problem by the present invention, and in concrete enforcement, choosing of majorized function is unique, and some other majorized function can reach identical effect equally.

The above; be only the present invention's preferably detailed description of the invention, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; the change that can expect easily or replacement, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.

Claims (1)

1. for a parameter optimization method for the surgical robot of operative space, it is characterized in that, first suppose the coordinate transformation relation between the basis coordinates system of surgical robot and ending coordinates system: ⁿt _n= ¹t ₀* ²t ₁* ³t ₂* ⁴t ₃* ⁵t ₄* ⁶t ₅... ⁱ⁺¹t _i... ⁿt _n-1, n is non-zero positive integer;

Then, be optimized by the parameter of following object function to surgical robot:

$F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|$ , in formula:

---X is joint parameter x _iset;

---Δ t _ifor joint is relative to variable quantity during zero-bit;

---Δ T ₀during for measuring registration point, joint is relative to the variable quantity of zero-bit;

---a _ifor the actual value put under the photographic head coordinate system that directly records;

---f (X+ Δ t _i) be the theoretical coordinate in lower i-th joint of robot coordinate system;

---g (X+ Δ T ₀) be tied to the transition matrix of robot coordinate system for photographic head coordinate;

---|| be Euclidean distance;

The parameter of minima as the surgical robot after optimization of described object function is got by following formula:

$\left\{\begin{array}{c}\min F\left(X\right)=\frac{1}{n}\underset{i=1}{\overset{n}{\Σ}}|f(X+{\mathrm{\Δt}}_i)-g(X+{\mathrm{\ΔT}}_0)a_i|\\ |x_i-x_i^{*}|\≤{\mathrm{\δ}}_i\end{array}\right.,$ In formula:

---x _ibe i-th joint parameter;

---δ _iit is the range of error of i-th joint parameter;

--- it is the theoretical value of i-th joint parameter.