CN108015765B - A kind of expansion disaggregation counter propagation neural network solution of robot motion planning - Google Patents
A kind of expansion disaggregation counter propagation neural network solution of robot motion planning Download PDFInfo
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Abstract
The invention discloses a kind of expansion disaggregation counter propagation neural network solutions of robot motion planning, comprising steps of obtaining robot current state by sensor, and carry out inverse kinematics parsing to robot trajectory on velocity layer using quadratic form prioritization scheme；Convert the quadratic form prioritization scheme of two norm index of minimum speed to the quadratic programming problem of a standard；Convert quadratic programming problem to the solution of Karush-Kuhn-Tucker optimal condition；The counter propagation neural network solver for expanding disaggregation using one is solved；Obtained result will be solved and pass to robot controller, driving robot body carries out track following.The present invention can be compatible with convex set constraint and non-convex set constraint by one Nonlinear Equality Constrained of design, eliminate preliminary examination error problem appeared in robot control, overcome the error accumulation problem in robot control process.
Description
Technical field
The present invention relates to robot motion planning and control technology field, in particular to a kind of robot motion planning is opened up
Open up disaggregation counter propagation neural network solution.
Background technique
In recent years, robot arm was applied in every field, such as medical rehabilitation, aviation, home services
Industry etc..More and more researchers also devote in the researchs such as control robot arm, the tracking of various complicated tracks.
Redundancy robots refer to that a kind of possessed freedom degree is greater than the robot for completing required by task least degree of freedom.
This makes redundancy robots possess greater flexibility and fault-tolerance.When the original task of completion end effector, additional
Freedom degree can be designed to optimize some secondary subtasks.
How in real time, the problem of inverse movement solution is a challenge in redundancy robots motion planning is accurately obtained.
This is because the nonlinear characteristic of the Forward kinematics mapping equation of redundancy robots, causes to be difficult to obtain in most cases
Analytic solutions.The common linearisation skill of one kind is to solve Inverse Kinematics Problem in movement level.Due to the redundancy of robot,
Inverse Kinematics Problem is a underdetermined problem on velocity layer.This means that the inverse of Jacobian matrix may be to be not present.It passes
The method of the pseudoinverse of system provides two Norm Solution of minimum, but it can not solve the problems, such as inequality, also can not be flexible
Ground setting optimizes index.In addition, the method for traditional pseudoinverse does not account for the constraint under system or such environmental effects.In recent years
Come, it is a kind of to be suggested based on the method for quadratic programming because of its superior flexibility.But it is existing based on quadratic programming
Equality constraint in method is all the Forward kinematics equation for being directly substituted into robot, and such equality constraint can not overcome initially
Error and error accumulation problem.In addition, most of in these methods only consider that robot works in convex set space,
The application extension of method by tradition based on quadratic programming is to non-convex set space and overcomes the problems, such as that above-mentioned two are necessary
's.
In the frame based on QUADRATIC PROGRAMMING METHOD FOR, one real-time Quadratic Programming Solution device of exploitation is important a step
Suddenly, there are mainly two types of solvers here: neural network and numerical method.Because the intrinsic characteristic of neural network parallel computing, makes
Obtaining neural network has advantage faster more accurate than numerical method.In recent years, many recurrent neural networks are applied to machine
In people's redundancy Solve problems, but the robot motion planning that these neural network methods are constrained primarily directed to convex set is asked
Topic.
In order to expand robot inverse kinematics disaggregation, needs to propose a kind of method, can be asked in convex and non-convex disaggregation
Solve the Inverse Kinematics Problem of robot.
Summary of the invention
The shortcomings that it is a primary object of the present invention to overcome the prior art and insufficient, provides a kind of robot motion planning
Expand disaggregation counter propagation neural network solution, can be compatible with it is convex merge with non-convex constraint set can overcome initial error and error
Accumulation problem.
The purpose of the present invention is realized by the following technical solution:
A kind of expansion disaggregation counter propagation neural network solution of robot motion planning, comprising the following steps:
S1, it is based on given problem, robot current state is obtained by sensor, and using quadratic form prioritization scheme in speed
It spends on layer and inverse kinematics parsing is carried out to robot trajectory, the performance indicator of design is two norm of minimum speed, constrained in machine
The joint angles limit and joint angle speed limit in each joint of device people and one it is relevant to robot motion non-linear etc.
Formula；
S2, one is converted by the quadratic form prioritization scheme of the two norm index of robot minimum speed designed in step S1
The quadratic programming problem of standard；
S3, Karush-Kuhn-Tucker optimal condition is converted by the quadratic programming problem of robot in step S2
It solves；
S4, the counter propagation neural network solver of disaggregation is expanded using one to the Karush-Kuhn-Tucker of step S3 most
Optimal conditions solve；
S5, the result solved in step S4 is passed to robot controller, driving robot body carries out track
Tracking.
Preferably, step S1 specifically: based on given problem, robot current state is obtained by sensor,
And inverse kinematics parsing is carried out to robot trajectory on velocity layer using quadratic form prioritization scheme, the performance indicator of design is most
Small two norm of speedIt is constrained composed by the joint angles limit and joint angle speed limit in each joint of robot
Joint angle rate capability domain Ω and a nonlinear equation relevant to robot kinematics
WhereinFor two norm index of robot minimum speed,Indicate each joint angles pair of redundancy robots
Angular speed column vector in joint composed by the derivative of time, subscript T representing matrix transposition；Equality constraintIt is one based on Robot kinematics equations and considers convex to set with non-convex set constraint
The nonlinear equation that meter comes out；Wherein J is the Jacobian matrix of redundancy robots；ε is the adjustment of error convergence rate
Parameter；rdIt is respectively expected path velocity vector in three dimensions, the position of expected path in three dimensions with r
Vector and the position vector of robot actual path in three dimensions；PΩ() be Ω collection close from n tie up real number space to
One mapping function in the space Ω, the function are defined as PΩ(x)=y=argminy∈Ω| | y-x | |, constraint set therein
Ω can effectively be compatible with convex and non-convex set constraint；With PΩΩ in () indicates redundancy robots joint angle speed
The feas ible space set of degree, the spatial aggregation are convex space set or non-convex spatial aggregation；
The quadratic form prioritization scheme of the two norm index of the minimum designed can be expressed as:
Further, the design of the Nonlinear Equality Constrained can promote error e=rd- r is from arbitrary initial error e0At any time
Between converge to 0, this means that the track following of robot can eliminate the disturbance and error being subjected in control process.
Preferably, step S2 specifically: for the quadratic form prioritization scheme in solution procedure S1, be first standardized as one
The quadratic programming problem of a standard:
min.xTWx/2+cTX,
S.t.Ax=q,
x-≤x≤x+；
Quadratic programming problem after standardization and the two norm index quadratic form prioritization scheme of minimum designed originally
With one-to-one relationship:
C=0 ∈ Rn, A=J ∈ Rm×n,W=In×n∈Rn ×n, Ω=[x-,x+]∈Rn, wherein x-And x+Respectively the broad sense lower boundary of set omega and broad sense coboundary.
Preferably, step S3 specifically: after being converted into the quadratic programming problem of standard, be translated into a Karush-
The solution of Kuhn-Tucker optimization problem:
In that case, Lagrange function is
L (x, λ)=xTx/2+λT(Ax-q),
λ ∈ R thereinnFor Lagrange multiplier vector, the local derviation of the function are as follows:
It is optimized according to Karush-Kuhn-Tucker, is separately zero with the partial derivative of Lagrange function and considers independent variable
The domain of x, it is known that the standard quadratic programming problem of robot and the solution of following equation group are of equal value:
Ax=q；
In the case where Ω is convex set, according to definition PΩ(x)=y=argminy∈Ω| | y-x | | it is found that PΩ(x)
I calculating elements is defined as:
In the case where Ω is non-convex set, specific function expression then needs basis to be defined as deforming accordingly.
Preferably, step S4 specifically: one counter propagation neural network solver of design seeks it, substitutes into former optimal
Pa-rameter symbols in change scheme, designed expansion disaggregation it is as follows to couple Neural Networks Solution device:
0 < ζ < < 1 is the adjusting parameter for expanding the rate of convergence of counter propagation neural network of disaggregation.
Compared with the prior art, the invention has the following advantages and beneficial effects:
The present invention can be compatible with convex set constraint and non-convex set constraint, be disappeared by one Nonlinear Equality Constrained of design
Except preliminary examination error problem appeared in robot control, the error accumulation problem in robot control process is overcome.
Detailed description of the invention
Fig. 1 is the flow diagram of embodiment method；
Fig. 2 is the redundancy robots model schematic of embodiment.
As shown in the figure are as follows: 1- redundancy robots；First rotary joint of 2-；Second rotary joint of 3-；The rotation of 4 thirds
Turn joint；The 4th rotary joint of 5-；The 5th rotary joint of 6-；The 6th rotary joint of 7-.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Embodiment 1
A kind of counter propagation neural network solution for expanding disaggregation robot motion planning, includes the following steps:
S1, it is based on given problem, robot current state is obtained by sensor, and using quadratic form prioritization scheme in speed
It spends on layer and inverse kinematics parsing is carried out to robot trajectory, the performance indicator of design is two norm of minimum speed, constrained in machine
The joint angles limit and joint angle speed limit in each joint of device people and one it is relevant to robot motion non-linear etc.
Formula；
S2, one is converted by the quadratic form prioritization scheme of the two norm index of robot minimum speed designed in step S1
The quadratic programming problem of standard；
S3, Karush-Kuhn-Tucker optimal condition is converted by the quadratic programming problem of robot in step S2
It solves；
S4, the counter propagation neural network solver of disaggregation is expanded using one to the Karush-Kuhn-Tucker of step S3 most
Optimal conditions solve；
S5, the result solved in step S4 is passed to robot controller, driving robot body carries out track
Tracking.
It is specific:
Based on given problem, robot current state is obtained by sensor, and uses quadratic form prioritization scheme
Inverse kinematics parsing is carried out to robot trajectory on velocity layer, the performance indicator of design is two norm of minimum speedBy about
Beam joint angle rate capability domain Ω composed by the joint angles limit and joint angle speed limit in each joint of robot with
An and nonlinear equation relevant to robot kinematicsWhereinFor machine
Two norm index of people's minimum speed,Indicate joint angle composed by derivative of each joint angles of redundancy robots to the time
Speed column vector, subscript T representing matrix transposition；Equality constraintIt is one based on robot
Kinematical equation simultaneously considers the convex nonlinear equation designed with non-convex set constraint；Wherein J is redundancy machine
The Jacobian matrix of people；ε is the adjusting parameter of error convergence rate；rdWith r be respectively expected path in three dimensions
The position vector of velocity vector, expected path in three dimensions and the position of robot actual path in three dimensions to
Amount；PΩ() is to close a mapping function from n dimension real number space to the space Ω in Ω collection, which is defined as PΩ(x)
=y=argminy∈Ω| | y-x | |, constraint set omega therein can effectively be compatible with convex and non-convex set constraint.In addition, this is non-
The design of linear equality constraints can promote error e=rd- r is from arbitrary initial error e00 is converged at any time, this means that machine
The track following of device people can eliminate the disturbance and error being subjected in control process；With PΩΩ in () indicates superfluous
The feas ible space set of remaining joint of robot angular speed, the spatial aggregation are convex space set or non-convex spatial aggregation.
The quadratic form prioritization scheme of the two norm index of the minimum designed can be expressed as:
In order to solve above-mentioned quadratic form prioritization scheme, it is first standardized as the quadratic programming problem of a standard:
min.xTWx/2+cTX,
S.t.Ax=q,
x-≤x≤x+；
Quadratic programming problem after standardization and the two norm index quadratic form prioritization scheme of minimum designed originally
With one-to-one relationship:
C=0 ∈ Rn, A=J ∈ Rm×n,W=In×n∈Rn ×n, Ω=[x-,x+]∈Rn, wherein x-And x+Respectively the broad sense lower boundary of set omega and broad sense coboundary, while being also machine
The broad sense lower boundary of person joint's angular speed constraint and broad sense coboundary.
After being converted into the quadratic programming problem of standard, it is translated into a Karush-Kuhn-Tucker optimization problem
Solution:
In that case, Lagrange function is
L (x, λ)=xTx/2+λT(Ax-q),
λ ∈ R thereinnFor Lagrange multiplier vector, the local derviation of the function are as follows:
It is optimized according to Karush-Kuhn-Tucker, is separately zero with the partial derivative of Lagrange function and considers independent variable
The domain of x, it is known that the standard quadratic programming problem of robot and the solution of following equation group are of equal value:
Ax=q.
In the case where Ω is convex set, according to definition PΩ(x)=y=argminy∈Ω| | y-x | | it is found that PΩ(x)
I calculating elements is defined as:
In the case where Ω is non-convex set, specific function expression is then needed according to being defined as deforming accordingly, herein
It can not carry out exhaustion.Wherein n is the dimension of the joint space of redundancy robots.
After converting a Karush-Kuhn-Tucker optimization problem for optimization scheme, an antithesis nerve is designed
Solution To The Network device seeks it, substitutes into the pa-rameter symbols in former optimization scheme, designed expansion disaggregation to couple
Neural Networks Solution device is as follows:
0 < ζ < < 1 is the adjusting parameter for expanding the rate of convergence of counter propagation neural network of disaggregation.
Finally machine will be sent to by the above-mentioned joint angles solved to the even Neural Networks Solution device for expanding disaggregation
Device people's controller, and then redundancy robots ontology is controlled, it realizes the track following function of end effector, realizes this
The method of embodiment.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (6)
1. a kind of expansion disaggregation counter propagation neural network solution of robot motion planning, which is characterized in that including following step
It is rapid:
S1, it is based on given problem, robot current state is obtained by sensor, and using quadratic form prioritization scheme in velocity layer
On inverse kinematics parsing is carried out to robot trajectory, the performance indicator of design is two norm of minimum speed, constrained in robot
The joint angles limit and joint angle speed limit in each joint and a nonlinear equation relevant to robot motion；
S2, a standard is converted by the quadratic form prioritization scheme of the two norm index of robot minimum speed designed in step S1
Quadratic programming problem；
S3, asking for Karush-Kuhn-Tucker optimal condition is converted by the quadratic programming problem of robot in step S2
Solution；
S4, the counter propagation neural network solver that disaggregation is expanded using one optimize the Karush-Kuhn-Tucker of step S3
Condition solves；
S5, the result solved in step S4 is passed to robot controller, driving robot body carries out track following；
Wherein, step S1 specifically: based on given problem, robot current state is obtained by sensor, and uses
Quadratic form prioritization scheme carries out inverse kinematics parsing to robot trajectory on velocity layer, and the performance indicator of design is minimum speed
Two normsThe constrained joint angle composed by the joint angles limit and joint angle speed limit in each joint of robot
Rate capability domain Ω and a nonlinear equation relevant to robot kinematics
WhereinFor two norm index of robot minimum speed,Indicate each joint angles of redundancy robots to the time
Derivative composed by joint angular speed column vector, subscript T representing matrix transposition；Equality constraintIt is one based on Robot kinematics equations and considers convex to set with non-convex set constraint
The nonlinear equation that meter comes out；Wherein J is the Jacobian matrix of redundancy robots；ε is the adjustment of error convergence rate
Parameter；rdIt is respectively expected path velocity vector in three dimensions, the position of expected path in three dimensions with r
Vector and the position vector of robot actual path in three dimensions；PΩ() be Ω collection close from n tie up real number space to
One mapping function in the space Ω, the function are defined as PΩ(x)=y=argminy∈Ω| | y-x | |, constraint set therein
Ω can effectively be compatible with convex and non-convex set constraint；With PΩΩ in () indicates redundancy robots joint angle speed
The feas ible space set of degree, the spatial aggregation are convex space set or non-convex spatial aggregation.
2. the method according to claim 1, which is characterized in that in S1, the two of the two norm index of the minimum designed
Secondary type prioritization scheme can be expressed as:
3. the method according to claim 1, wherein the design of the Nonlinear Equality Constrained can promote error e
=rd- r is from arbitrary initial error e00 is converged at any time.
4. the method according to claim 1, wherein step S2 specifically: in order to secondary in solution procedure S1
Type prioritization scheme is first standardized as the quadratic programming problem of a standard:
min.xTWx/2+cTX,
S.t.Ax=q,
x-≤x≤x+；
Quadratic programming problem after standardization has with the two norm index quadratic form prioritization scheme of minimum designed originally
One-to-one relationship:
C=0 ∈ Rn, A=J ∈ Rm×n, W=In×n∈Rn×n,
Ω=[x-, x+]∈Rn, wherein x-And x+Respectively the broad sense lower boundary of set omega and broad sense coboundary.
5. according to the method described in claim 2, it is characterized in that, step S3 specifically: the quadratic programming for being converted into standard is asked
After topic, it is translated into the solution of a Karush-Kuhn-Tucker optimization problem:
In that case, Lagrange function is
L (x, λ)=xTx/2+λT(Ax-q),
λ ∈ R thereinnFor Lagrange multiplier vector, the local derviation of the function are as follows:
It is optimized according to Karush-Kuhn-Tucker, is separately zero with the partial derivative of Lagrange function and considers independent variable x
Domain, it is known that the standard quadratic programming problem of robot and the solution of following equation group are of equal value:
Ax=q；
In the case where Ω is convex set, according to definition PΩ(x)=y=argminy∈Ω| | y-x | | it is found that PΩ(x) i-th of meter
Calculate element definition are as follows:
In the case where Ω is non-convex set, specific function expression then needs basis to be defined as deforming accordingly.
6. the method according to claim 1, wherein step S4 specifically: one counter propagation neural network of design is asked
Solution device seeks it, substitutes into the pa-rameter symbols in former optimization scheme, designed expansion disaggregation to couple nerve net
Network solver is as follows:
0 < ζ < < 1 is the adjusting parameter for expanding the rate of convergence of counter propagation neural network of disaggregation.
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| CN108015765B (en) * | 2017-11-22 | 2019-06-18 | 华南理工大学 | A kind of expansion disaggregation counter propagation neural network solution of robot motion planning |
| CN108381555B (en) * | 2018-05-30 | 2020-05-22 | 华南理工大学 | Design method of lower controller of redundancy mechanical arm of flying operation robot |
| CN108958238B (en) * | 2018-06-01 | 2021-05-07 | 哈尔滨理工大学 | Robot point-to-area path planning method based on covariant cost function |
| CN110000780B (en) * | 2019-03-31 | 2021-11-05 | 华南理工大学 | Runge-Kutta periodic rhythm neural network method capable of resisting periodic noise |
| CN111152224B (en) * | 2020-01-10 | 2022-05-10 | 温州大学 | Dual-optimization robot motion trajectory optimization method |
| CN111844005B (en) * | 2020-07-08 | 2022-06-28 | 哈尔滨工业大学 | 2R-P-2R-P-2R mechanical arm motion planning method applied to tunnel wet spraying |
| CN114571448A (en) * | 2021-12-30 | 2022-06-03 | 广州铁路职业技术学院（广州铁路机械学校） | Joint-limited pseudo-inverse repetitive motion planning method for redundant manipulator |
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| CN101804627A (en) * | 2010-04-02 | 2010-08-18 | 中山大学 | Redundant manipulator motion planning method |
| CN102126219A (en) * | 2010-11-22 | 2011-07-20 | 中山大学 | Fault-tolerant type motion planning method of redundancy mechanical arm |
| CN105538327A (en) * | 2016-03-03 | 2016-05-04 | 吉首大学 | Redundant manipulator repeated motion programming method based on abrupt acceleration |
| CN106426164A (en) * | 2016-09-27 | 2017-02-22 | 华南理工大学 | Redundancy dual-mechanical-arm multi-index coordinate exercise planning method |
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| CN108015765B (en) * | 2017-11-22 | 2019-06-18 | 华南理工大学 | A kind of expansion disaggregation counter propagation neural network solution of robot motion planning |
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| CN101804627A (en) * | 2010-04-02 | 2010-08-18 | 中山大学 | Redundant manipulator motion planning method |
| CN102126219A (en) * | 2010-11-22 | 2011-07-20 | 中山大学 | Fault-tolerant type motion planning method of redundancy mechanical arm |
| CN105538327A (en) * | 2016-03-03 | 2016-05-04 | 吉首大学 | Redundant manipulator repeated motion programming method based on abrupt acceleration |
| CN106426164A (en) * | 2016-09-27 | 2017-02-22 | 华南理工大学 | Redundancy dual-mechanical-arm multi-index coordinate exercise planning method |
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