CN106914897A - Inverse Solution For Manipulator Kinematics method based on RBF neural - Google Patents
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Abstract
Field is solved the invention belongs to Manipulator Kinematics, a kind of Inverse Solution For Manipulator Kinematics method based on RBF neural is disclosed, including：Obtain robot movement sample pair；Sample input and the desired output of RBF neural are set, and the sample input of RBF neural is the pose of arm end effector, and the desired output of RBF neural is manipulator joint angle；Sample input and desired output according to RBF neural, the network parameter of RBF neural is determined using Orthogonal Least Squares method, is met the network parameter of the RBF neural of error requirements；The attained pose of arm end effector is obtained, attained pose is input to the input layer of the RBF neural for meeting error requirements, the output layer output manipulator joint angle of the RBF neural of error requirements is met, so as to complete Inverse Solution For Manipulator Kinematics；Manipulator trajectory planning and precision of real time control can be improved.
Description
Technical field
Field, more particularly to a kind of manipulator fortune based on RBF neural are solved the invention belongs to Manipulator Kinematics
It is dynamic to learn inverse solution method.
Background technology
Inverse Solution For Manipulator Kinematics are the bases of manipulator trajectory planning and control, occupy in robot control and weigh very much
The status wanted.The precision of Inverse Solution For Manipulator Kinematics directly influences the raising of manipulator control precision, due to robot movement
The complexity that inverse solution exists in itself is learned, algebraic approach and iterative method general at present all has computationally intensive, receipts to a certain extent
The shortcomings of holding back limited speed, and solving precision is low, real-time control poor performance.
The research that nerual network technique develops into the inverse solution of manipulator brings conveniently, RBF (Radial Basis
Function, RBF) neutral net is a kind of partial approximation network, learns with good None-linear approximation ability and faster
Speed.
K-means clustering algorithms are normally used for solving RBF network architecture parameters center vector, sound stage width and weights, but should
Algorithm is easily influenceed by initial parameter selection and is converged on local minimum, and from hidden layer output to network output
Linear relationship in, inverse dematrix seeks weight wijWhen due to inverse dematrix nonsingularity and it is difficult to ensure that the uniqueness of weights.
This will influence the final training result of network.
The content of the invention
For the shortcoming of above-mentioned prior art, it is an object of the invention to provide a kind of machinery based on RBF neural
The inverse solution method of hands movement, it is possible to increase manipulator trajectory planning and precision of real time control.
To reach above-mentioned purpose, the present invention is adopted the following technical scheme that and is achieved.
A kind of Inverse Solution For Manipulator Kinematics method based on RBF neural, methods described comprises the following steps：
Step 1, obtains robot movement sample pair, and the robot movement sample is to the position by arm end effector
Appearance and manipulator joint angle are constituted；
Step 2, sets sample input and the desired output of the RBF neural, and the sample of the RBF neural is defeated
It is the pose of the arm end effector to enter, and the desired output of the RBF neural is the manipulator joint angle；
Step 3, sample input and desired output according to the RBF neural are true using Orthogonal Least Squares method
The network parameter of the fixed RBF neural, is met the network parameter of the RBF neural of error requirements, the RBF god
Through the center vector of the network parameter comprising Gaussian bases and sound stage width vector of network, and network output weights；
Step 4, obtains the attained pose of arm end effector, the attained pose is input to and described meets error
It is required that RBF neural input layer, the RBF neural for meeting error requirements output layer output manipulator joint
Angle, so as to complete Inverse Solution For Manipulator Kinematics.
It is inverse that technical solution of the present invention carries out manipulator RBF neural by way of Orthogonal Least Square is combined
Kinematics solution, according to the non-linear partial approximation ability and Fast Learning ability and Orthogonal Least Square of RBF neural
Determine the characteristic of RBF neural network structure parameter so that the learning process can quickly converge on desired value and realize letter
It is single, and actual calculating output valve is small with the error of desired output；Robot inverse kinematics are carried out using the algorithm to solve and can obtain
Obtain precision higher and can largely reduce intensive problem when solving inverse matrix, be manipulator trajectory planning and reality
When control accuracy raising lay a good foundation.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
The accompanying drawing to be used needed for having technology description is briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is a kind of stream of Inverse Solution For Manipulator Kinematics method based on RBF neural provided in an embodiment of the present invention
Journey schematic diagram one；
Fig. 2 is the schematic network structure of RBF neural provided in an embodiment of the present invention；
Fig. 3 is a kind of stream of Inverse Solution For Manipulator Kinematics method based on RBF neural provided in an embodiment of the present invention
Journey schematic diagram two；
Fig. 4 is expectation provided in an embodiment of the present invention and reality output curve comparison schematic diagram.
Specific embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation is described, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.It is based on
Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under the premise of creative work is not made
Embodiment, belongs to the scope of protection of the invention.
A kind of Inverse Solution For Manipulator Kinematics method based on RBF neural, as shown in figure 1, methods described is including as follows
Step：
Step 1, obtains robot movement sample pair, and the robot movement sample is to the position by arm end effector
Appearance and manipulator joint angle are constituted.
Step 2, sets sample input and the desired output of the RBF neural, and the sample of the RBF neural is defeated
It is the pose of the arm end effector to enter, and the desired output of the RBF neural is the manipulator joint angle.
The schematic network structure of the RBF neural shown in reference picture 2, the input layer of the RBF neural with it is defeated
Go out layer comprising N number of neuron, the hidden layer neuron number of the RBF neural is M, wherein, N, M are more than zero
Positive integer；
The input layer receives input sample x=[x1, x2... xi..., xN]T, the input sample is manipulator end
Hold the pose of actuator；The hidden layer output matrix is H=[h1, h2..., hj... hM]T, and：
Wherein, hjThe output of j-th neuron of hidden layer is represented,It is Gaussian bases, Cj=[c1, c2... cM]TTable
Show the center vector of j-th neuron of hidden layer, bjIt is the sound stage width vector of hidden layer j-th neuron, and RBF neural
Sound stage width vector B=[b1, b2..., bj... bM]T, the sound stage width vector is set to constant vector, | | | | it is European norm, xiFor
The input sample of i-th neuron of RBF neural input layer；
The reality output sample for remembering the RBF neural is Y=[y1, y2... yN]T, the output sample is the machine
Tool swivel of hand angle, and the output valve y of i-th neuron of RBF neural output layer is：
Wherein, wijIt is the weights between j-th neuron of i-th neuron of output layer and hidden layer.
Step 3, sample input and desired output according to the RBF neural are true using Orthogonal Least Squares method
The network parameter of the fixed RBF neural, is met the network parameter of the RBF neural of error requirements, the RBF god
Through the center vector of the network parameter comprising Gaussian bases and sound stage width vector of network, and network output weights.
The schematic flow sheet of the Inverse Solution For Manipulator Kinematics method of reference picture 3, institute is determined using Orthogonal Least Squares method
The network parameter of RBF neural is stated, the network parameter of the RBF neural of error requirements is met, specifically included：
It is that M, the i.e. Hidden nodes of RBF neural are M that (3a) chooses hidden layer output neuron number in advance；And M
Initial value be 1；The maximum allowable Hidden nodes of the RBF neural are the maximum number of column of input sample；
(3b) selected input sample x=[x1, x2... xi..., xN]TSubset Cj=[c1, c2... cM]TSweared as center
Amount, the sound stage width vector B=[b of RBF neural1, b2..., bj... bM]TIn each element using fixed value 0.6；
(3c) calculates the hidden layer output arrow of the RBF neural according to selected center vector and input sample
Amount hj(1≤j≤M) exports the Orthogonal Least Squares solution g of weights with networkj(1≤j≤M)；
(3d) is by hidden layer output vector hj(1≤j≤M) is converted to orthogonal vector u by vectre setj(1
≤j≤M)；Calculate contribution energy value of each orthogonal vector to desired outputCorresponding to selection maximum contribution energy value
Orthogonal vector uj(j=1,2 ... M) as Gaussian bases final center vector cj(1≤j≤M)；Wherein, desired output d
=[d1, d2..., di..., dN]；
(3e) obtains upper triangular matrix A, by gj=AwijNetwork output weight w is carried out using generalized inverseijSolution, A is one
The upper triangular matrix of individual M × M, and diagonal element is 1,1≤i≤N, 1≤j≤M；
(3f) is obtained by the final center vector and sub-step (3e) of the Gaussian bases obtained in sub-step (3d)
Network exports weights, determines the final output vector h of each hidden nodej(1≤j≤M)；
(3g) calculates the real output value of the RBF neural1≤i≤N, 1≤j≤M；
(3h) calculates RBF according to the real output value of the RBF neural and the desired output of the RBF neural
The training error of neutral net
(3i) sets the error threshold of the RBF neural, if the training error is more than the error threshold, will
The Hidden nodes M of the RBF neural adds 1, and is repeated in performing sub-step (3b) to (3h)；
If the training error reaches the maximum allowable hidden section of RBF neural less than the value of the error threshold or M
Points, then record the network parameter of the RBF neural for finally being obtained.
Exemplary, the maximum allowable Hidden nodes MAX for setting the RBF neural is the maximum column of input sample
Number.
Further, according to selected center vector and input sample, the hidden layer for calculating the RBF neural is defeated
Go out vector hj(1≤j≤M) exports the Orthogonal Least Squares solution g of weights with networkj(1≤j≤M)；Specifically include：
Orthogonal Least Square make use of linear regression model (LRM), be expressed from the next：
Wherein, diRepresent the desired output of the RBF neural, wijRefer to that hidden layer exports power to the network of output layer
Value；E (i) is referred to as the error matrix of network desired output and reality output；M is hidden layer unit number, and N is input layer and output layer
Neuron number, 1≤M≤N；
Above formula is expressed as matrix form：D=Hw+e；
Wherein：D=(d1, d2... dN)T, e=(e1, e2... eN)T；
Each row of hidden layer output matrix H constitute one group of base vector, to ensure the linear independence between each base vector,
By its Orthogonal Decomposition：H=UA, wherein：A is a upper triangular matrix of M*M, and diagonal element is that 1, U is the matrix of N*M, and its is each
Row uj(j=1,2 ... M) are orthogonal；And meet UTU=Q, Q are that diagonal element is QjDiagonal matrix,
With Gram-Schmidt methods by hjCarry out following orthogonalization and obtain its corresponding orthogonal vectors uj：In kth step, make
The row that kth has been arranged with the individual orthogonalizations of preceding k-1 are orthogonal, to k=2,3 ..., M, and step in repetition, i.e.,：
u1=h1
Can be obtained from above：D=UAw+e=Ug+e；The Orthogonal Least Squares solution for solving above formula is：
And gj=Awij, then can calculate hidden layer and export weights to the network between output layer.
Step 4, obtains the attained pose of arm end effector, the attained pose is input to and described meets error
It is required that RBF neural input layer, the RBF neural for meeting error requirements output layer output manipulator joint
Angle, so as to complete Inverse Solution For Manipulator Kinematics.
Simulation result and analysis
The embodiment of the present invention is on the basis of manipulator forward kinematics equation is set up by Matlab to forward kinematics equation
Acquisition sample is programmed, after 400 groups of training samples are obtained, using the newrb functions of Neural Network Toolbox in Matlab
The establishment and training of RBF neural are carried out, and is programmed in Matlab, Gaussian bases are determined using least-squares algorithm
Center and width, and consider optimal compliance criterion when solution is inverted, finally with newrb function creations neutral net and instructed
Practice.According to repeatedly training, target error is set and takes 0.01.15 groups of samples to be tested two have been brought into after network training is stable
The trained RBF networks to stabilization, obtain result of calculation as shown in table 1, the contrast of the simulation datas of joint angle θ 1 and desired output
As shown in Fig. 4 (a), the simulation datas of joint angle θ 2 are with desired output to such as Fig. 4 (b) Suo Shi.
The neural computing result of table 1
The error very little between reality output and desired output is can be seen that from table 1 and Fig. 4, and reality output curve connects
It is continuous smooth, illustrate that Orthogonal Least Square carries out Inverse Kinematics Solution and has precision higher and can for RBF neural
To avoid carrying out substantial amounts of matrix computations.
The above, specific embodiment only of the invention, but protection scope of the present invention is not limited thereto, and it is any
Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all contain
Cover within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (3)
1. a kind of Inverse Solution For Manipulator Kinematics method based on RBF neural, it is characterised in that methods described includes following step
Suddenly：
Step 1, obtains robot movement sample pair, the robot movement sample to the pose by arm end effector and
Manipulator joint angle is constituted；
Step 2, sets sample input and the desired output of the RBF neural, and the sample input of the RBF neural is
The pose of the arm end effector, the desired output of the RBF neural is the manipulator joint angle；
Step 3, sample input and desired output according to the RBF neural, institute is determined using Orthogonal Least Squares method
The network parameter of RBF neural is stated, the network parameter of the RBF neural of error requirements, the RBF nerve nets is met
Center vector of the network parameter of network comprising Gaussian bases and sound stage width vector, and network output weights；
Step 4, obtains the attained pose of arm end effector, the attained pose is input to and described meets error requirements
RBF neural input layer, the output layer output manipulator joint angle of the RBF neural for meeting error requirements
Degree, so as to complete Inverse Solution For Manipulator Kinematics.
2. a kind of Inverse Solution For Manipulator Kinematics method based on RBF neural according to claim 1, its feature exists
In, the RBF neural includes input layer, hidden layer and output layer, in step 2,
The input layer of the RBF neural includes N number of neuron, the hidden layer god of the RBF neural with output layer
It is M through first number, wherein, N, M are the positive integer more than zero；
The input layer receives input sample X=[x1,x2,…xi,…,xN]T, the input sample holds for the arm end
The pose of row device；The hidden layer output matrix is H=[h1,h2,…,hj,…hM]T, and：
Wherein, hjThe output of j-th neuron of hidden layer is represented,It is Gaussian bases, Cj=[c1,c2,…cM]TRepresent hidden
Center vector containing j-th neuron of layer, bjBe j-th neuron of hidden layer sound stage width vector, and RBF neural sound stage width
Vectorial B=[b1,b2,…,bj,…bM]T, the sound stage width vector is set to constant vector, | | | | it is European norm, xiIt is RBF
The input sample of i-th neuron of neural network input layer；
The reality output sample for remembering the RBF neural is Y=[y1,y2,…yN]T, the output sample is the manipulator
Joint angles, and i-th neuron of RBF neural output layer output valve yiFor：
Wherein, wijIt is the weights between j-th neuron of i-th neuron of output layer and hidden layer.
3. a kind of Inverse Solution For Manipulator Kinematics method based on RBF neural according to claim 2, its feature exists
In, in step 3, the network parameter of the RBF neural is determined using Orthogonal Least Squares method, it is met error requirements
RBF neural network parameter, specifically include：
It is that M, the i.e. Hidden nodes of RBF neural are M that (3a) chooses hidden layer output neuron number in advance；And M's is first
Be worth is 1；The maximum allowable Hidden nodes of the RBF neural are the maximum number of column of input sample；
(3b) selected input sample X=[x1,x2,…xi,…,xN]TSubset Cj=[c1,c2,…cM]TAs center vector, RBF
The sound stage width vector B=[b of neutral net1,b2,…,bj,…bM]TIn each element using fixed value 0.6；
(3c) calculates the hidden layer output vector h of the RBF neural according to selected center vector and input samplej(1
≤ j≤M) with network export weights Orthogonal Least Squares solution gj(1≤j≤M)；
(3d) is by hidden layer output vector hj(1≤j≤M) is converted to orthogonal vector u by vectre setj(1≤j≤
M)；Calculate contribution energy value of each orthogonal vector to desired outputCorresponding to selection maximum contribution energy value just
Hand over vector uj(j=1,2 ... M) as Gaussian bases final center vector cj(1≤j≤M)；Wherein, desired output d=
[d1,d2,...,di,...,dN]；
(3e) obtains upper triangular matrix A, by gj=AwijNetwork output weight w is carried out using generalized inverseijSolution, A be a M
The upper triangular matrix of × M, and diagonal element is 1,1≤i≤N, 1≤j≤M；
The network that (3f) is obtained by the final center vector and sub-step (3e) of the Gaussian bases obtained in sub-step (3d)
Output weights, determine the final output vector h of each hidden nodej(1≤j≤M)；
(3g) calculates the real output value of the RBF neural1≤i≤N, 1≤j≤M；
(3h) calculates RBF nerves according to the real output value of the RBF neural and the desired output of the RBF neural
The training error of network
(3i) sets the error threshold of the RBF neural, if the training error is more than the error threshold, will be described
The Hidden nodes M of RBF neural adds 1, and is repeated in performing sub-step (3b) to (3h)；
If the training error reaches the maximum allowable Hidden nodes of RBF neural less than the value of the error threshold or M,
Then record the network parameter of the RBF neural for finally being obtained.
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108890630A (en) * | 2018-08-21 | 2018-11-27 | 广东工业大学 | A kind of robot teaching system and method |
| CN110039537A (en) * | 2019-03-15 | 2019-07-23 | 北京精密机电控制设备研究所 | A kind of automatic measure on line multi joint motion planing method neural network based |
| CN110238840A (en) * | 2019-04-24 | 2019-09-17 | 中山大学 | A kind of autonomous grasping means of the mechanical arm of view-based access control model |
| CN111673739A (en) * | 2020-05-15 | 2020-09-18 | 成都飞机工业（集团）有限责任公司 | Robot pose reachability judgment method based on RBF neural network |
| CN111993416A (en) * | 2020-07-30 | 2020-11-27 | 浙江大华技术股份有限公司 | Method, equipment, system and device for controlling movement of mechanical arm |
| CN112294599A (en) * | 2020-10-30 | 2021-02-02 | 中国科学院自动化研究所 | Training track generation model construction method, system and device based on human body parameters |
| CN112733423A (en) * | 2020-12-03 | 2021-04-30 | 重庆邮智机器人研究院有限公司 | Industrial robot inverse kinematics solving method based on PSO-RBFNN |
| CN113627584A (en) * | 2020-05-08 | 2021-11-09 | 南京大学 | Neural network-based inverse kinematics solving method for mechanical arm, electronic equipment and storage medium |
| CN114523478A (en) * | 2022-04-24 | 2022-05-24 | 季华实验室 | Method for obtaining compensation model of mechanical arm structure parameters and compensation method |
| WO2022205844A1 (en) * | 2021-03-29 | 2022-10-06 | 深圳市优必选科技股份有限公司 | Robot forward kinematics solution method and apparatus, readable storage medium, and robot |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108890630A (en) * | 2018-08-21 | 2018-11-27 | 广东工业大学 | A kind of robot teaching system and method |
| CN110039537A (en) * | 2019-03-15 | 2019-07-23 | 北京精密机电控制设备研究所 | A kind of automatic measure on line multi joint motion planing method neural network based |
| CN110238840A (en) * | 2019-04-24 | 2019-09-17 | 中山大学 | A kind of autonomous grasping means of the mechanical arm of view-based access control model |
| CN113627584A (en) * | 2020-05-08 | 2021-11-09 | 南京大学 | Neural network-based inverse kinematics solving method for mechanical arm, electronic equipment and storage medium |
| CN113627584B (en) * | 2020-05-08 | 2024-04-12 | 南京大学 | Mechanical arm inverse kinematics solving method based on neural network, electronic equipment and storage medium |
| CN111673739A (en) * | 2020-05-15 | 2020-09-18 | 成都飞机工业（集团）有限责任公司 | Robot pose reachability judgment method based on RBF neural network |
| CN111993416A (en) * | 2020-07-30 | 2020-11-27 | 浙江大华技术股份有限公司 | Method, equipment, system and device for controlling movement of mechanical arm |
| CN112294599A (en) * | 2020-10-30 | 2021-02-02 | 中国科学院自动化研究所 | Training track generation model construction method, system and device based on human body parameters |
| CN112733423A (en) * | 2020-12-03 | 2021-04-30 | 重庆邮智机器人研究院有限公司 | Industrial robot inverse kinematics solving method based on PSO-RBFNN |
| WO2022205844A1 (en) * | 2021-03-29 | 2022-10-06 | 深圳市优必选科技股份有限公司 | Robot forward kinematics solution method and apparatus, readable storage medium, and robot |
| CN114523478A (en) * | 2022-04-24 | 2022-05-24 | 季华实验室 | Method for obtaining compensation model of mechanical arm structure parameters and compensation method |
| CN114523478B (en) * | 2022-04-24 | 2022-06-28 | 季华实验室 | Method for obtaining compensation model of mechanical arm structure parameters and compensation method |
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