CN106426164B - A kind of multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms - Google Patents

A kind of multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms Download PDF

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CN106426164B
CN106426164B CN201610858570.3A CN201610858570A CN106426164B CN 106426164 B CN106426164 B CN 106426164B CN 201610858570 A CN201610858570 A CN 201610858570A CN 106426164 B CN106426164 B CN 106426164B
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mechanical arm
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CN106426164A (en
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张智军
林裕峻
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South China University of Technology SCUT
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1643—Programme controls characterised by the control loop redundant control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1669—Programme controls characterised by programming, planning systems for manipulators characterised by special application, e.g. multi-arm co-operation, assembly, grasping
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1682—Dual arm manipulator; Coordination of several manipulators

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Numerical Control (AREA)

Abstract

The invention discloses a kind of multi objective coordinated movement of various economic factors planing methods of redundancy double mechanical arms, comprising steps of 1) be based on target problem, inverse kinematics parsing is carried out to double mechanical arms respectively on velocity layer using quadratic form prioritization scheme by host computer, the performance indicator of design is two norm of minimum speed, repeating motion and these three indexs of minimum speed Infinite Norm by index made of weighted array, constrained in the respective kinematical equation of double mechanical arms, joint angular limit and joint angle speed limit；2) the respective quadratic form prioritization scheme of double mechanical arms in step 1) is converted to the quadratic programming problem of standard；3) the respective quadratic programming problem of double mechanical arms in step 2) is unified into a quadratic programming problem；4) the primal-dual neural network solver based on linear variational inequality problem by quadratic programming problem simplification unified in step 3) solves；5) solving result of step 4) is passed to the movement of the next machine controller driving double mechanical arms.

Description

A kind of multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms
Technical field
The invention belongs to the motion planning methods of redundancy mechanical arm and more mechanical arms, are based on joint more particularly to one kind The control of angular speed layer, multi-index optimization make the multi objective coordinated movement of various economic factors of the redundancy double mechanical arms of two mechanical arm co-ordinations Planing method.
Background technique
Redundancy mechanical arm is that a kind of freedom degree is greater than the active mechanical device in end for completing required by task least degree of freedom. Redundancy mechanical arm can also complete some secondary tasks while completing end main task, such as avoiding barrier, hide Avoiding joint limits hide singular point and the other objective functions of optimization etc..It can complete includes welding, paint, assembling, excavate and The tasks such as drawing, are widely used in the national economy production activities such as equipment manufacturing, product processing, machinery operation.Traditional is superfluous The method that remaining analytic method and industrial machinery arm control method are mainly based upon pseudoinverse.And in recent years, calculation amount is small, real-time Property the strong redundancy analytic method based on quadratic form optimization be suggested and apply.However, current quadratic form optimization method is only Only consider single index optimization or Two indices optimization, it can not meet demand under specific circumstances.
Meanwhile working relative to single mechanical arm, double mechanical arms or multi-arms coordination work can not only improve work Efficiency can also complete some impossible tasks of single mechanical arm, such as carry an object, assembly element and cooking are cooked Deng.Therefore dual robot coordination control is widely studied always.
Summary of the invention
The technical problem to be solved in the present invention is to provide a kind of redundancy double-mechanicals that three kinds of indexs are considered by weighting Arm multi objective coordinated movement of various economic factors planing method.
In order to achieve the above-mentioned object of the invention, the technical solution adopted is as follows:
A kind of multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms, includes the following steps:
1) be based on target problem, by host computer using quadratic form prioritization scheme on velocity layer respectively to double mechanical arms into The parsing of row inverse kinematics, the optimality criterion of design are two norm of minimum speed, repeating motion and minimum speed Infinite Norm, These three index persons are formed by two weighted factor weighted arrays, constrained in the respective kinematical equation of double mechanical arms, pass Save angular limit and joint angle speed limit；
2) the respective quadratic form prioritization scheme of double mechanical arms in step 1) is converted to the quadratic programming problem of standard；
3) by the respective joint angle of double mechanical arms in step 2), Jacobian matrix, end orbit, joint angular limit and joint The angular speed limit is combined, and generates the joint angle, combination Jacobian matrix, combination end orbit, combination joint angle pole of combination Limit and combination joint angle speed limit, so that two quadratic programming problems are unified into a quadratic programming problem；
4) the former antithesis nerve based on linear variational inequality problem that quadratic programming problem unified in step 3) is simplified Solution To The Network device is solved；
5) solving result of step 4) is passed to the movement of the next machine controller driving double mechanical arms.
The present invention carries out weight distribution to three indexs by two weighted factors, can be by adjusting the big of weighted factor Property combinations small and then that formation is different, to meet different task demand.The coordinated movement of various economic factors planning of two mechanical arms simultaneously Working efficiency not only can be improved, some impossible tasks of single mechanical arm can also be completed.
Detailed description of the invention
Fig. 1 is flow diagram of the invention；
Fig. 2 is double mechanical arms model schematic of the invention.
As shown in the figure are as follows: 1- left mechanical arm；2- right mechanical arm；The first joint 3-；4- second joint；5 third joints；6- Four joints；The 5th joint 7-；The 6th joint 8-.
Specific embodiment
Following further describes the present invention with reference to the drawings.
Redundancy double mechanical arms multi objective coordinated movement of various economic factors planing method shown in FIG. 1 is mainly by target problem, left mechanical arm Multi objective quadratic form prioritization scheme and the multi objective quadratic form prioritization scheme of right mechanical arm, left mechanical arm quadratic programming problem With the quadratic programming problem of right mechanical arm, unified quadratic programming problem, simplification based on linear variational inequality problem original antithesis mind Through Solution To The Network device, the next machine controller and bis- (left and right) mechanical arms composition.
It is primarily based on target problem, using quadratic form prioritization scheme, first by the respective inverse kinematics of left and right mechanical arm It is designed as minimizing on velocity layerWithWhereinIt is constrained in It is constrained in The performance indicator to be optimizedWithFor by adding Weight factor αL/RAnd βL/RTo minimum speed norm indexRepeating motion index(its Middle cL/R=λL/R(θL/R-θL/R(0)), λL/R> 0 is the positive design parameter for controlling joint displacements amplitude) and minimum speed it is infinite Norm indexThese three indexs, which are weighted, to be composed, and mathematic(al) representation is as follows:
Then, respective quadratic programming problem is converted by the above-mentioned respective quadratic form prioritization scheme of left and right mechanical arm, Unified quadratic programming problem is converted by the respective quadratic programming problem of left and right mechanical arm again.Then using simplified based on line Property variational inequality primal-dual neural network solver solve, and solving result is passed into the bis- (left sides of the next machine controller driving It is right) the mechanical arm coordinated movement of various economic factors.
Double mechanical arms model shown in Fig. 2 is mainly made of left mechanical arm 1 and right mechanical arm 2, and each mechanical arm has 6 Joint, i.e. the first joint 3, second joint 4, third joint 5, the 4th joint 6, the 5th joint 7 and the 6th joint 8, two machinery Arm can while and execute a certain task in phase.
It is primarily based on target problem, the inverse kinematics of left mechanical arm multi objective quadratic form prioritization scheme are on velocity layer It may be designed as:
Wherein,The left mechanical arm movement performance indicator to be optimized is represented, mathematic(al) representation isWherein, CL =λL(θL-θL(0)), λL> 0 is the positive design parameter for controlling joint displacements amplitude, αL、βL(1- αL-βL) it is respectively minimum The weighting parameters of speed norm index, repeating motion index and minimum speed Infinite Norm index；Equality constraint Indicate the kinematical equation of left mechanical arm, JLIndicate the Jacobian matrix of left mechanical arm,Indicate left mechanical arm joint velocity, Indicate the velocity vector of left mechanical arm end effector；Inequality constraintsWithRespectively Indicate the joint angles limit and joint angle speed limit of left mechanical arm.
The inverse kinematics of right mechanical arm multi objective quadratic form prioritization scheme may be designed as on velocity layer:
Wherein,The right mechanical arm movement performance indicator to be optimized is represented, mathematic(al) representation isWherein, cR=λR(θR-θR(0)), λR> 0 is the positive design parameter for controlling joint displacements amplitude, αR、βR(1- αR-βR) it is respectively most The weighting parameters of small speed norm index, repeating motion index and minimum speed Infinite Norm index；Equality constraintIndicate the kinematical equation of right mechanical arm, JRIndicate the Jacobian matrix of right mechanical arm,Indicate right mechanical arm Joint velocity,Indicate the velocity vector of right mechanical arm end effector；Inequality constraintsRespectively indicate the joint angles limit and the joint angular speed pole of right mechanical arm Limit.
Then, respective standard quadratic programming is converted by the multi objective quadratic form prioritization scheme of above-mentioned left and right mechanical arm to ask Topic.The quadratic programming problem of left mechanical arm can be written as following form:
s.t.ALxL=bL, (10)
CLxL≤dL, (11)
It enablesThen decision variable xLIt can be defined asAnd coefficient matrix or vector are
I is unit matrix, Element is all 1 corresponding dimension vector), dL=0；Inequality constraints (3) expression formula being transformed on velocity layer isWherein coefficient μL> 0 is to use It adjusts the feasible zone of joint angular speed, enablesWithAvailable new both-end constrains (12), whereinIt is sufficiently large constant, for numerically substituting infinity+∞).
The quadratic programming problem of right mechanical arm can similarly be written as following form:
s.t.ARxR=bR, (14)
CRxR≤dR, (15)
It enablesThen decision variable xRIt can be defined asAnd coefficient matrix or vector are
I is unit matrix, Element is all 1 corresponding dimension vector), dR=0；Inequality constraints (3) expression formula being transformed on velocity layer isWherein coefficient μR> 0 be for The feasible zone of joint angular speed is adjusted, is enabled Available new both-end constrains (12), whereinIt is sufficiently large constant, uses In numerically substitution infinity+∞).
Then, a unified quadratic programming problem is converted by the above-mentioned respective quadratic programming problem of left and right mechanical arm. Unified quadratic programming problem can be written as follow form:
min.zTKz/2+wTZ, (17)
S.t.Gz=h, (18)
Dz≤e, (19)
z-≤z≤z+； (20)
Wherein decision variableCoefficient matrix or vector
After obtaining above-mentioned unified quadratic programming problem (17)-(20) formula, method for solving of the invention is using simplification Primal-dual neural network algorithm based on linear variational inequality problem is come this quadratic programming problem of Real-time solution.
Firstly, converting a linear projection equation P for unified quadratic programming problemΩ[y- (My+q)]-y=0 is asked It solves, wherein PΩ[] is space R2(3n+m+1)To set Piecewise linearity Projection operator, PΩ(y) i-th of computing unit is defined as:
M is the cartesian space dimension of single mechanical arm, and n is the joint space dimension of single mechanical arm, y ∈ R2(3n+m+1) Indicate former dual variable, y-Indicate former dual variable limit inferior, y+Indicate former dual variable limes superiors, former dual variable y and thereon Lower limit is defined as follows:
u∈R2mCorrespond to the antithesis decision vector of equality constraint Gz=h, v ∈ R4nCorrespond to inequality constraints Dz≤ The antithesis decision vector of e, and extended matrix M, q are defined respectively as:
Then, above-mentioned linear variation etc. is solved based on the primal-dual neural network of linear variational inequality problem with simplified Formula problem and quadratic programming problem:
Finally the above-mentioned angular speed being calculated is sent to left and right mechanical arm respective the next machine controller to control Left and right mechanical arm moves in phase simultaneously, realizes method of the invention.
The above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be to the present invention Embodiment restriction.For those of ordinary skill in the art, it can also make on the basis of the above description Other various forms of variations or variation.There is no necessity and possibility to exhaust all the enbodiments.It is all of the invention Made any modifications, equivalent replacements, and improvements etc., should be included in the protection of the claims in the present invention within spirit and principle Within the scope of.

Claims (5)

1. a kind of multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms, which comprises the steps of:
1) it is based on target problem, it is inverse to double mechanical arms progress respectively on velocity layer using quadratic form prioritization scheme by host computer Kinematics parsing, the optimality criterion of design be two norm of minimum speed, repeating motion and minimum speed Infinite Norm this three A index, by two weighted factor weighted arrays form new index, it is constrained in the respective kinematical equation of double mechanical arms, Joint angular limit and joint angle speed limit；
2) the respective quadratic form prioritization scheme of double mechanical arms in step 1) is converted to the quadratic programming problem of standard；
3) by the respective joint angle of double mechanical arms in step 2), Jacobian matrix, end orbit, joint angular limit and joint angle speed Degree the limit be combined, generate combination joint angle, combination Jacobian matrix, combination end orbit, combination joint angular limit and Joint angle speed limit is combined, so that two quadratic programming problems are unified into a quadratic programming problem；
4) by the primal-dual neural network based on linear variational inequality problem of quadratic programming problem simplification unified in step 3) Solver is solved；
5) solving result of step 4) is passed to the movement of the next machine controller driving double mechanical arms.
2. the multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms according to claim 1, which is characterized in that institute The respective quadratic form optimizing redundancy degree parsing scheme of double mechanical arms in step 1) is stated by the inverse kinematics of mechanical arm in speed It is designed on layer are as follows:
Left mechanical arm: it minimizesIt is constrained in WhereinRepresent the left mechanical arm performance index function to be optimized, θLWithRespectively indicate the joint angle of left mechanical arm Degree and joint angular speed, equality constraintIndicate the kinematical equation of left mechanical arm, JLIndicate left mechanical arm end fortune Dynamic rail mark rLAbout joint angles θLJacobian matrix,Indicate the velocity vector of mechanical arm tail end,The joint angles limit, the joint angle speed limit of left mechanical arm are respectively indicated,WithThe bound of left mechanical arm joint angles is respectively indicated,WithRespectively indicate left mechanical arm joint angular speed Bound；
Right mechanical arm: it minimizesIt is constrained in WhereinIndicate the excellent of right mechanical arm Change target function, kinematical equation, joint angular limit and joint angle speed limit, JRIndicate right mechanical arm end movement track rR About joint angles θRJacobian matrix,Indicate the velocity vector of right mechanical arm end,WithRespectively indicate right machinery The bound of shoulder joint angle,WithRespectively indicate the bound of right mechanical arm joint angular speed；
The performance indicator to be optimizedWithThe optimization for parsing scheme for double mechanical arms redundancy is sentenced According to passing through weighted factorL/RAnd βL/RTo minimum speed norm indexRepeating motion indexWith minimum speed Infinite Norm indexThese three indexs, which are weighted, to be composed, Wherein cL/R=λL/R(θL/R-θL/R(0)), λL/R> 0 is the positive design parameter for controlling joint displacements amplitude, θL/R(0) it indicates The initial value of joint of mechanical arm angle, mathematic(al) representation are as follows:
。
3. the multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms according to claim 2, which is characterized in that institute It states the respective quadratic form optimization of double mechanical arms in step 2) and is converted into standard quadratic programming problem specifically:
The quadratic programming problem of left mechanical arm is as follows:
s.t.ALxL=bL,
CLxL≤dL,
WhereinIndicate the decision variable of left mechanical arm,Indicate the joint of left mechanical arm The Infinite Norm of angle vector,Indicate the quadratic coefficients square of left mechanical arm Battle array, I are unit matrix,Indicate the linear coefficient vector of left mechanical arm, ΛL=2 λL, AL =[JL0] the linear coefficient matrix of the equality constraint of left mechanical arm is indicated,Indicate the normal of the equality constraint of left mechanical arm Vector,The linear coefficient matrix of the inequality constraints matrix of expression left mechanical arm, 1v=[1 ... 1]T Element is all 1 corresponding dimension vector, dL=0 indicates the constant vector of the inequality constraints of left mechanical arm,WithIndicate left machine The bound of the decision variable of tool arm；
The quadratic programming problem of right mechanical arm is as follows:
s.t.ARxR=bR,
CRxR≤dR,
WhereinIndicate the decision variable of right mechanical arm,Indicate the joint of right mechanical arm The Infinite Norm of angle vector,Indicate the quadratic coefficients of right mechanical arm Matrix, I are unit matrix,Indicate the linear coefficient vector of right mechanical arm, ΛR=2 λR, AR=[JR0] the linear coefficient matrix of the equality constraint of right mechanical arm is indicated,Indicate the equation of right mechanical arm about The constant vector of beam,The linear coefficient matrix of the inequality constraints matrix of expression right mechanical arm, 1v= [1 ... 1]TElement is all 1 corresponding dimension vector, dR=0 indicates the constant vector of the inequality constraints of right mechanical arm,With Indicate the bound of the decision variable of right mechanical arm.
4. the multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms according to claim 3, which is characterized in that institute It states and two quadratic programming problems are unified into a quadratic programming problem in step 3) specifically include:
It is as follows that double mechanical arms quadratic programming problem is unified for a quadratic programming problem:
min.zTKz/2+wTZ,
S.t.Gz=h,
Dz≤e,
z-≤z≤z+,
Wherein Indicate unified decision variable,Indicate the quadratic coefficients matrix of unified quadratic programming problem,Indicate unified secondary rule The linear coefficient vector for the problem of drawing,Indicate the linear coefficient matrix of unified equality constraint, Indicate the constant vector of unified equality constraint,Indicate the linear coefficient matrix of unified inequality constraints, e =0 indicates the constant vector of unified inequality constraints,Indicate the unified decision variable upper limit,Table Show unified decision variable lower limit.
5. the multi objective coordinated movement of various economic factors planing method of redundancy double mechanical arms according to claim 4, which is characterized in that institute State the primal-dual neural network based on linear variational inequality problem of quadratic programming problem simplification of the step 4) by standard after reunification Solver solve and is specifically included:
41) a linear projection equation P is converted by unified quadratic programming problemΩThe solution of [y- (My+q)]-y=0, wherein PΩ[] is space R2(3n+m+1)To set Piecewise linearity project calculate Son, PΩ(y) i-th of computing unit is defined as:
Wherein m is the cartesian space dimension of single mechanical arm, and n is the joint space dimension of single mechanical arm, y ∈ R2(3n+m+1) Indicate former dual variable, y-Indicate former dual variable limit inferior, y+Indicate former dual variable limes superiors, former dual variable y and thereon Lower limit is defined as follows:
u∈R2mCorrespond to equality constraint GzThe antithesis decision vector of=h, v ∈ R4nCorrespond to pair of inequality constraints Dz≤e Even decision vector, and extended matrix M, q are defined respectively as:
42) linear variational inequality problem problem and two are solved based on the primal-dual neural network of linear variational inequality problem with simplified Secondary planning problem:
。
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