CN108427282A - A kind of solution of Inverse Kinematics method based on learning from instruction - Google Patents
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Abstract
The invention belongs to robot kinematics to solve field, and specifically disclose a kind of solution of Inverse Kinematics method based on learning from instruction, include the following steps：The joint angles of N groups robot and the Cartesian position and Eulerian angles of end effector are acquired, data set f is obtained；Data set f is optimized and obtains data set f1；To data set f1Iteratively solve out the gauss hybrid models parameter of Gauss model number 2~50；The corresponding bayesian information criterion value of each gauss hybrid models is calculated, bayesian information criterion curve is drawn, Gauss number k is determined according to curve；Solve the parameter for the gauss hybrid models that Gauss model number is k；Using model parameter to data set f1Cartesian position and Eulerian angles carry out Gauss return processing solve inverse kinematics joint angle angle value；Compare joint angle angle value and data set f1In joint angle angle value, correct Gauss model number obtain desired solving precision.The advantages that present invention has calculating speed fast, strong applicability, real-time control effect is good.
Description
Technical field
The invention belongs to robot kinematics to solve field, more particularly, to a kind of robot based on learning from instruction
Inverse kinematics method.
Background technology
Solution of Inverse Kinematics is the basis of robot real-time control.It is directly related to robot off-line programming,
Trajectory planning, the work such as motion control, for the robot such as nR humanoid robots of arbitrary configuration, PR humanoid robots and flexible machine
Device people is only detached from traditional robot kinematics expression formula, using the form of data-driven inverse kinematics, could realize pair
The cartesian space of arbitrary robot modeling establishes mapping relations with joint space, has great importance for real-time control.
Patent CN201410121131.5 discloses a kind of general method for solving of the inverse kinematics of multi-freedom robot, fortune
The popular motion equation that nR robots are established with Generality Space theory is realized by the projection weighted value of each joint vector of determination
The semi analytic of inverse kinematics solves, while taking into account space avoidance, can improve calculating speed and calculation accuracy, but be only limitted to nR
Humanoid robot and the analytical form for still relying on inverse kinematics can not spread over other configuration robots, real-time control effect
It can not further be promoted.
Invention content
For the disadvantages described above or Improvement requirement of the prior art, the present invention provides a kind of robots based on learning from instruction
Thus inverse kinematics method solves to depend on analytical expression by using the machine learning algorithm of gauss hybrid models
The slow problem of solution of Inverse Kinematics calculating speed, have calculating speed fast, strong applicability, real-time control effect is good etc.
Advantage can be applied in the control of all kinds of humanoid robots.
To achieve the above object, the present invention proposes a kind of solution of Inverse Kinematics method based on learning from instruction,
This method comprises the following steps：
(a) the Cartesian position P and Eulerian angles of the joint angles θ and end effector of robot of acquisition N groups robot
R obtains data set f={ θ (i), P (i), R (i), i=1,2 ..., N }；
(b) processing is optimized to data set f, obtains the data set f with inverse kinematics mapping1={ θ (j), P (j), R
(j), j=1,2 ..., n (n ＜ N) }；
(c) to data set f1It is iterated solution, solves the Gaussian Mixture mould that Gauss model number m is 2~50 respectively
The parameter of type；
(d) the bayesian information criterion value corresponding to the gauss hybrid models that Gauss model number m is 2~50 is calculated separately
BIC, and bayesian information criterion curve is drawn, determine that bayesian information criterion curve declines according to bayesian information criterion curve
The corresponding Gauss number k in the most slow place of speed；
(e) again to data set f1It is iterated solution, to solve Gauss model number as the ginseng of the gauss hybrid models of k
Number (π, μ, Σ)；
(f) utilize the parameter (π, μ, Σ) of gauss hybrid models to data set f1In Cartesian position P (j) and Eulerian angles
R (j) carries out Gauss recurrence processing, to solve inverse kinematics joint angle angle value θ*(j)；
(g) comparison inverse kinematics joint angle angle value θ*(j) with data set f1In joint angle angle value θ (j), judge whether full
Sufficient inverse kinematics required precision, if it is not, it is k+1 and return to step (e) then to correct Gauss model number, if so, θ*(j)
As required inverse kinematics joint angle angle value；The inverse kinematics of robot are completed by this method.
As it is further preferred that optimizing processing to data set f in step (b) and being specially：Data set is deleted first
In be unsatisfactory for the data point of condition, the data point for meeting performance requirement is then filtered out from remaining data point.
As it is further preferred that optimizing processing to data set f in step (b) and being preferably：Data set f is deleted first
Middle robot is in unusual data point and inverse kinematics redundancy solution, is then filtered out from remaining data point and meets performance
It is required that data point.
As it is further preferred that the performance requirement is preferably dexterity demands or operability requirement.
As it is further preferred that the dexterity demands are specially to make dexterity evaluation index kF(J (θ (i))) is more than
Dexterity preset value, the dexterity evaluation index kF(J (θ (i))) is calculated using following formula：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and s is the line number of Jacobian matrix J (θ (i)), θ (i)
For the joint angle angle value of i-th of data point in data set, tr () is the oeprator for seeking trace of a matrix.
As it is further preferred that the operability requires to be specially to keep operational evaluation index w default more than operability
Value, the operability evaluation index w are calculated using following formula：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and det () is the value for seeking matrix determinant.
As it is further preferred that preferably being changed to data collection using the maximum algorithm of expectation in step (c) and step (e)
In generation, solves.
As it is further preferred that bayesian information criterion value BIC is calculated using following formula：
Wherein, L is data set f1Gauss hybrid models likelihood probability value logarithmic form, m be gauss hybrid models in
The number of Gauss model, D are data set f1Data dimension, n be data set f1Data point number.
As it is further preferred that data set f1Gauss hybrid models likelihood probability value logarithmic form L using as follows
Formula calculates：
Wherein, n is data set f1The number of middle data point, m are the number of Gauss model in gauss hybrid models, and N is height
This distribution calculating formula, j are data set f1In j-th of data point, i be gauss hybrid models in i-th of Gauss model, ξj=[θ
(j),P(j),R(j)]T, θ (j) is data set f1In j-th of joint angles, P (j) be data set f1In j-th of Cartesian position,
R (j) is data set f1In j-th of Euler angle, πi,μi,ΣiFor the corresponding Gauss of i-th of Gauss model in gauss hybrid models
Parameter.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, mainly have below
Technological merit：
1. the present invention establishes robot cartesian space and joint space by using the modeling method of gauss hybrid models
Single mapping, by calculate bayesian information criterion (BIC) value, determine the Gauss number of Gauss model, can completely disengage
Traditional inverse kinematics parses expression formula, improves the calculating speed that inverse movement solves.
2. the present invention is built by carrying out offline inverse kinematics mapping for the teaching exercise data collection of arbitrary robot modeling
The mode that mould is combined with online inverse kinematics carries out solution of Inverse Kinematics, can be evaluated and be referred to according to robot performance
Mark, screens teaching exercise data collection appropriate.
3. the present invention is by using the processed offline combined with gauss hybrid models based on movement teaching and online inverse movement
The mode solved is learned, off-line process can be established robot cartesian space and close according to robot performance's evaluation index
The single mapping in space, online inverse kinematics process are saved, the gauss hybrid models parameter obtained according to processed offline is realized
The high real-time of robot joint angles is calculated online, whole process has not only taken into account robot performance, but also independent of
The analytical expression of Robotic inverse kinematics, and the high real-time that Robotic inverse kinematics may be implemented calculates, and can effectively expire
Requirement of the foot to robot system real-time control.
Description of the drawings
Fig. 1 is the solution of Inverse Kinematics method based on learning from instruction of preferred embodiment structure according to the invention
Flow chart；
Fig. 2 is that robot motion's teaching of preferred embodiment structure according to the invention obtains robot motion's data procedures
Used in equipment drawing；
Fig. 3 be the collected raw data set of robot motion's teaching of preferred embodiment according to the invention structure from
The process of line processing；
Fig. 4 is the BIC curve graphs of preferred embodiment according to the invention；
Fig. 5 is the deviation schematic diagram between the theoretical joint angle angle value in robot joint angles value and data set；
Fig. 6 is that the flow of the Gauss recurrence online Real-time solution of inverse kinematics of preferred embodiment structure according to the invention is shown
It is intended to.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
It does not constitute a conflict with each other and can be combined with each other.
As shown in Figure 1, a kind of solution of Inverse Kinematics method based on learning from instruction provided in an embodiment of the present invention,
This method comprises the following steps：
(a) teaching robot is made to move, the joint angles θ of acquisition N groups robot and the flute of end effector of robot
N group joint angles θ, Cartesian position P and Eulerian angles R are combined and are generated cube by karr position P and Eulerian angles R, structure
Data set f=θ (i), P (i), R (i), i=1,2 ..., N }；
(b) processing is optimized to data set f, obtains the data set f with the mapping of one-to-one inverse kinematics1=θ (j),
P (j), R (j), j=1,2 ..., n (n ＜ N) }；Specifically in the following way into the optimization processing of line data set f：It deletes first
It is unsatisfactory for the data point of condition in data set f, the data point for meeting performance requirement is then filtered out from remaining data point, it will
These data points structure obtains data set f1。
Preferably, robot in data set f is deleted first and is in unusual data point, while deleting the inverse fortune in data set
It is dynamic to learn redundancy solution, the data point for meeting performance requirement is then filtered out from remaining data point.In the deletion data set
Inverse kinematics redundancy solution refers to the case where corresponding to same group of Cartesian position P and Eulerian angles R to multigroup joint angles and screens, and presses
Unified criterion retains one of which, and deletes other group of joint angles, and filter criteria can be defined according to actual needs, such as
Retain the joint angles etc. near robot zero-bit.
Further, performance requirement is preferably that dexterity demands or operability require, naturally it is also possible to be wanted for other performances
It asks, wherein dexterity demands are specially to make dexterity evaluation index kF(J (θ (i))) is more than dexterity preset value, i.e., will calculate
Dexterity evaluation index kF(J (θ (i))) satisfaction is filtered out more than the corresponding data point of dexterity preset value condition, and is calculated
Dexterity evaluation index kF(J (θ (i))) is unsatisfactory for being deleted more than the corresponding data point of dexterity preset value condition, should
Dexterity preset value can be defined according to actual needs, dexterity evaluation index kF(J (θ (i))) is calculated using following formula：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and s is the line number of Jacobian matrix J (θ (i)), θ (i)
For the joint angle angle value of i-th of data point in data set f, tr () is the oeprator for seeking trace of a matrix.
And operability requires to be specially that operational evaluation index w is made to be more than operational preset value, i.e., by the operability of calculating
The corresponding data point that evaluation index w satisfactions are more than operational preset value condition filters out, and the operational evaluation index w calculated is not
The data point met more than operational preset value condition is deleted, which can be limited according to actual needs
Fixed, operational evaluation index w is calculated using following formula：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and θ (i) is the joint of i-th of data point in data set f
Angle value, det () are the value for seeking matrix determinant.
(c) to data set f1It is iterated solution, solves the Gaussian Mixture mould that Gauss model number m is 2~50 respectively
The parameter of type (GMM) solves the corresponding parameter of gauss hybrid models that Gauss model number m is 2, Gauss model respectively
The corresponding parameter of gauss hybrid models that number m is 3, and so on, until solving the Gaussian Mixture that Gauss model number m is 50
The corresponding parameter of model；Each Gauss model in gauss hybrid models is required to be iterated solution, to solve respectively
Go out the corresponding Gaussian Profile of each Gauss model the prior probability coefficient of Gaussian Profile (also referred to as), mean value and covariance these three
Parameter, the corresponding three parameters composition parameter sets of each Gauss model are the parameter of gauss hybrid models, and for iteration
Number can be selected according to actual needs.
Preferably, using the maximum algorithm of expectation to data collection f1Iteratively solve Gaussian Mixture moulds of the Gauss number m from 2 to 50
Shape parameter uses the maximum algorithm of expectation to calculate gauss hybrid models parameter as the prior art, and this will not be repeated here, only makees briefly
It is bright.
Such as be briefly described so that Gauss model number m is 3 gauss hybrid models as an example, it needs to Gaussian Mixture
Each Gauss model in model is iterated solution to solve corresponding parameter respectively, i.e., iterative solution kth t is a respectively
These three parameters of the prior probability, mean value and the covariance of Gaussian Profile of (kt 1,2,3) Gauss model, by u+1 iteration
Three parameters afterwards are respectively adopted following formula and calculate：
Wherein,For the prior probability of the Gaussian Profile of the u+1 times iteration of t Gauss model of kth,For kth t
The mean value of the Gaussian Profile of the u+1 times iteration of a Gauss model,For the height of the u+1 times iteration of t Gauss model of kth
The covariance of this distribution：Kt is the serial number of Gauss model；N is data set f1Data point number；For ξjPosterior probability, ξj
For data set f1In j-th of data point, ξj=[θ (j), P (j), R (j)]T；U is iterations；
Specifically：
Wherein,For the prior probability of the Gaussian Profile of the u times iteration of t Gauss model of kth；Table
Show ξjObey distributionProbability；ξjFor data set f1In j-th of data point, ξj=[θ (j), P (j), R (j)]T；
For the mean value of the Gaussian Profile of the u times iteration of t Gauss model of kth；For the height of the u times iteration of t Gauss model of kth
The covariance of this distribution；For the prior probability of the Gaussian Profile of the u times iteration of i-th of Gauss model；Table
Show ξjObey distributionProbability；For the mean value of the Gaussian Profile of the u times iteration of i-th of Gauss model；For
The covariance of the Gaussian Profile of the u times iteration of i-th of Gauss model；M is the number of Gauss model in gauss hybrid models.
(d) parameter calculated according to step (c) calculates separately Gauss model number m as 2~50 gauss hybrid models institute
Corresponding bayesian information criterion value BIC, and bayesian information criterion (BIC) curve is drawn, according under BIC Curve selection curves
The corresponding Gauss number k in the most slow place of reduction of speed degree；
Specifically, the most slow place of decrease speed corresponds to a line segment, which corresponds to two Gauss model numerical value, with front
Point is used as k, i.e., using small that as k, for example, as shown in figure 4, the most slow place of decrease speed it is corresponding be by Gauss number
For 44 and Gauss number be 45 line segment, then be k with that small Gauss number, i.e. k be 44.If there is decrease speed one at two
It causes, and has two sections of line segment slopes consistent, and decrease speed is most gentle then with the point of front for k for the most slow place of decrease speed,
So this two sections of line segments correspond to four Gauss model numbers, then with that Gauss model minimum in four Gauss model numbers
Number is k
Further, bayesian information criterion value BIC is calculated using following formula：
Wherein, L is data set f1Gauss hybrid models likelihood probability value logarithmic form, m be gauss hybrid models in
The number of Gauss model, D are data set f1Data dimension, n be data set f1Data point number.
Further, data set f1Gauss hybrid models likelihood probability value logarithmic form L using following formula calculate：
ξj=[θ (j), P (j), R (j)]T
Wherein, n is data set f1The number of middle data point, m are the number of Gauss model in gauss hybrid models, and N is height
This distribution calculating formula, j are data set f1In j-th of data point, i be gauss hybrid models in i-th of Gauss model, ξjFor data
Collect f1In j-th of data point, θ (j) be data set f1In j-th of joint angles, P (j) be data set f1In j-th Descartes position
It sets, R (j) is data set f1In j-th of Euler angle, πi,μi,ΣiIt is corresponding for i-th of Gauss model in gauss hybrid models
Gaussian parameter, i.e. πi,μi,ΣiThe prior probability of i-th of Gauss model respectively in gauss hybrid models, in gauss hybrid models
The mean value of i-th of Gauss model, the covariance of i-th of Gauss model in gauss hybrid models.
(e) again to data set f1It is iterated solution, to solve Gauss model number as the gauss hybrid models parameter of k
π, μ, Σ, preferably by the maximum algorithm of expectation to data collection f1Iteratively solve the parameter for the Gauss model (GMM) that Gauss number is k
π, μ, Σ, the π, μ, tri- parameters of Σ are set, respectively include 1-k corresponding parameters, i.e. π is with k Gauss model
Gauss hybrid models in first Gauss model prior probability to the set of k-th of Gauss model prior probability, μ is mixed for Gauss
For the mean value of first Gauss model to the set of the mean value of k-th of Gauss model, Σ is the in gauss hybrid models in molding type
The covariance of one Gauss model to the covariance of k-th of Gauss model set.
Wherein, the mean value μ of each Gauss modeliIt indicates, i=1,2 ..., k；μiFor 12 × 1 matrix, indicated
For For μi6 × 1 matrixes being located above are defined as the mean value of i-th of Gauss model of input signal,For
μiUnderlying 6 × 1 matrix is defined as the mean value of i-th of Gauss model of output signal, i.e., by matrix μiIt is divided into up and down
Two pieces；The covariance Σ of each Gauss modeliIt indicates, i=1,2 ..., k；ΣiFor 12 × 12 matrix, it is denoted as For ΣiCorresponding 6 × 6 matrix in the upper left corner, is defined as the association of i-th of Gauss model of input signal
Variance,For ΣiCorresponding 6 × 6 matrix in the upper right corner, is defined as the covariance of i-th of Gauss model of input-output signal,For ΣiCorresponding 6 × 6 matrix in the lower left corner, is defined as the transposition of the covariance of i-th of Gauss model of input-output signal
Matrix,For ΣiCorresponding 6 × 6 matrix in the lower right corner, is defined as the covariance of i-th of Gauss model of output signal, i.e., by square
Battle array ΣiIt is divided into four pieces up and down.
(f) utilize the parameter π, μ, Σ of gauss hybrid models to data set f1In Cartesian position P (j) and Eulerian angles R
(j) Gauss recurrence processing (GMR) is carried out, solves and obtains inverse kinematics joint angle angle value θ*(j)；
Specifically, inverse kinematics joint angle angle value θ*(j) it is calculated and is obtained using following formula：
Wherein, k is the number of Gauss model in gauss hybrid models, and i is the serial number of Gauss model；
For the mean value of i-th of Gauss model of output signal,For input signal
I-th of Gauss model mean value,For the transposed matrix of the covariance of i-th of Gauss model of input-output signal,
For the covariance of i-th of Gauss model of input signal,
πiIt is high for i-th
The prior probability of this model, N are Gaussian Profile calculating formula, πsFor the prior probability of s-th of Gauss model,For input signal
The mean value of s-th of Gauss model,For the covariance of s-th of Gauss model of input signal；
(g) by inverse kinematics joint angle angle value θ*(j) with data set f1In corresponding joint angle angle value θ (j) be compared,
Judge whether to meet inverse kinematics required precision, if it is not, it is k+1 simultaneously return to step (e) then to correct Gauss model number, with
Continue to solve Gauss model number as parameter π, μ, the Σ of the gauss hybrid models of k+1, i.e., Gauss model number k is updated to k+
1 (making the k=k+1 in step (e)), to solve Gauss model number as the parameter of the gauss hybrid models of k+1；If so, θ*
(j) it is required inverse kinematics joint angle angle value；The inverse kinematics of robot, robot controller are completed by this method
According to each joint motions of the inverse kinematics joint angle angle value control machine device people acquired.
Specifically, inverse kinematics precision can be defined according to actual needs, for example, solving precision is defined as
0.002rad (radian), then make | θ*(j)-θ (j) |≤0.002rad is to meet solving precision requirement.
In practical application, the above-mentioned steps of the present invention can be written as to program, and with reality in the controller of embedded robot
Existing Robotic inverse kinematics Real-time solution.
The method of the present invention is described further with reference to specific example.
As shown in Fig. 2, the equipment that the present invention uses includes robot body 1, Kinect vision cameras 2, robot control
Device 3 and industrial computer 4 processed, robot body 1 are fixed on horizontal base station, for moving and making within the scope of desk-top space
Industry；Kinect vision cameras 2 are used for the Cartesian position and Euler angle of robot measurement end；Robot controller 3 is located at
Where robot in the lower section of horizontal base station, for driving each joint motor of robot to realize robot motion；Industry meter
Calculation machine 4 is for processed offline training data collection and writes Robotic inverse kinematics real-time online solver, passes through Ethernet
Realize the communication with robot controller 3.
In embodiments, target machine human body includes robot arm, robot driver, wherein：Robot
Motion arm has six degree of freedom articulated structure；The control program controlled device device that robot driver provides according to industrial computer
People rotates according to each joint motor of requirement driving robot of user.
Fig. 3 be preferred embodiment according to the invention structure the collected raw data set of robot motion's teaching from
Line processing procedure, to obtain the gauss hybrid models parameter (π, μ, Σ) of training data collection.
Fig. 4 is BIC curve graphs, to determine the number of Gauss model in gauss hybrid models.Fig. 5 is the Gauss of data set
The deviation returned between the theoretical joint angle angle value in the obtained robot joint angles value of processed offline and data set (only arranges
Lift third joint angles), to correct the number of Gauss in gauss hybrid models and improve inverse kinematics precision.Fig. 6 is
The Gauss of preferred embodiment structure according to the invention returns the flow diagram of the online Real-time solution of inverse kinematics, such as Fig. 6 institutes
Show, in actual implementation, acquire robot terminal position and Euler angle, is returned into gauss hybrid models, and then by Gauss
Return to obtain the joint angles result of robot.
The specific solution procedure of the specific embodiment is：Robot motion's teaching experiment is carried out first, collects experiment
Data set f in the process, off-line process according to Fig.3, carry out processed offline to data set f, obtain Gaussian Mixture mould
Shape parameter (π, μ, Σ) then carries out Gauss to Cartesian position and Eulerian angles according to gauss hybrid models parameter (π, μ, Σ) and returns
Processing (GMR) is returned to solve inverse kinematics joint angle angle value θ*, the joint control of last robot is according to inverse kinematics joint angle
Angle value θ*Control the movement of robot.
In the present invention the online of motion planning and robot control is carried out using the gauss hybrid models based on movement training data collection
The method of real-time inverse kinematics is established the offline gauss hybrid models based on movement teaching sampled data set and was clustered
Journey is realized according to the gauss hybrid models parameter obtained offline at the real-time inverse kinematics of online robot joint angles
Reason.
It is given by the invention it is possible to be realized with the method that online inverse kinematics are combined by off line data analysis
The real-time online inverse kinematics of end effector of robot position, solve Robotic inverse kinematics singular position evade with
The problems such as choosing solution of redundancy solution, while without calculating explicit Robotic inverse kinematics expression formula, improving the control of robot system
Real-time processed.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all within the spirits and principles of the present invention made by all any modification, equivalent and improvement etc., should all include
Within protection scope of the present invention.
Claims (9)
1. a kind of solution of Inverse Kinematics method based on learning from instruction, which is characterized in that this method comprises the following steps：
(a) the Cartesian position P and Eulerian angles R of the joint angles θ and end effector of robot of acquisition N groups robot, is obtained
Data set f={ θ (i), P (i), R (i), i=1,2 ..., N }；
(b) processing is optimized to data set f, obtains the data set f with inverse kinematics mapping1={ θ (j), P (j), R (j), j
=1,2 ..., n (n ＜ N) }；
(c) to data set f1It is iterated solution, solves the ginseng for the gauss hybrid models that Gauss model number m is 2~50 respectively
Number；
(d) the bayesian information criterion value BIC corresponding to the gauss hybrid models that Gauss model number m is 2~50 is calculated separately,
And bayesian information criterion curve is drawn, bayesian information criterion curve decrease speed is determined according to bayesian information criterion curve
The corresponding Gauss number k in most slow place；
(e) again to data set f1Be iterated solution, with solve Gauss model number for the gauss hybrid models of k parameter (π,
μ,Σ)；
(f) utilize the parameter (π, μ, Σ) of gauss hybrid models to data set f1In Cartesian position P (j) and Eulerian angles R (j)
Gauss recurrence processing is carried out, to solve inverse kinematics joint angle angle value θ*(j)；
(g) comparison inverse kinematics joint angle angle value θ*(j) with data set f1In joint angle angle value θ (j), judge whether to meet inverse
Kinematics solution required precision, if it is not, it is k+1 and return to step (e) then to correct Gauss model number, if so, θ*(j) it is
Required inverse kinematics joint angle angle value；The inverse kinematics of robot are completed by this method.
2. the solution of Inverse Kinematics method based on learning from instruction as described in claim 1, which is characterized in that step
(b) optimizing processing to data set f in is specially：The data point that condition is unsatisfactory in data set is deleted first, then from surplus
Under data point in filter out the data point for meeting performance requirement.
3. the solution of Inverse Kinematics method based on learning from instruction as claimed in claim 2, which is characterized in that step
(b) optimizing processing to data set f in is preferably：Delete first robot in data set f be in unusual data point and
Inverse kinematics redundancy solution, then filters out the data point for meeting performance requirement from remaining data point.
4. the solution of Inverse Kinematics method based on learning from instruction as claimed in claim 2 or claim 3, which is characterized in that institute
It is preferably that dexterity demands or operability require to state performance requirement.
5. the solution of Inverse Kinematics method based on learning from instruction as claimed in claim 4, which is characterized in that the spirit
Skilful property requires to be specially to make dexterity evaluation index kF(J (θ (i))) is more than dexterity preset value, the dexterity evaluation index kF
(J (θ (i))) is calculated using following formula：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and s is the line number of Jacobian matrix J (θ (i)), and θ (i) is number
According to the joint angle angle value for concentrating i-th of data point, tr () is the oeprator for seeking trace of a matrix.
6. the solution of Inverse Kinematics method based on learning from instruction as described in claim 4 or 5, which is characterized in that institute
It states operability and requires to be specially that operational evaluation index w is made to be more than operational preset value, the operability evaluation index w is using such as
Lower formula calculates：
Wherein, J (θ (i)) is robot kinematics' Jacobian matrix, and det () is the value for seeking matrix determinant.
7. the solution of Inverse Kinematics method based on learning from instruction as described in claim 1, which is characterized in that step
(c) and in step (e) solution is preferably iterated to data collection using the maximum algorithm of expectation.
8. the solution of Inverse Kinematics method based on learning from instruction as described in claim 1, which is characterized in that Bayes
Information criterion value BIC is calculated using following formula：
Wherein, L is data set f1Gauss hybrid models likelihood probability value logarithmic form, m be gauss hybrid models in Gaussian mode
The number of type, D are data set f1Data dimension, n be data set f1Data point number.
9. the solution of Inverse Kinematics method based on learning from instruction as claimed in claim 8, which is characterized in that data set
f1Gauss hybrid models likelihood probability value logarithmic form L using following formula calculate：
Wherein, n is data set f1The number of middle data point, m are the number of Gauss model in gauss hybrid models, and N is Gaussian Profile
Calculating formula, j are data set f1In j-th of data point, i be gauss hybrid models in i-th of Gauss model, ξj=[θ (j), P (j),
R(j)]T, θ (j) is data set f1In j-th of joint angles, P (j) be data set f1In j-th of Cartesian position, R (j) be number
According to collection f1In j-th of Euler angle, πi,μi,ΣiFor the corresponding Gaussian parameter of i-th of Gauss model in gauss hybrid models.
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