CN110303501A - It is a kind of to hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar - Google Patents

It is a kind of to hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar Download PDF

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Publication number
CN110303501A
CN110303501A CN201910676577.7A CN201910676577A CN110303501A CN 110303501 A CN110303501 A CN 110303501A CN 201910676577 A CN201910676577 A CN 201910676577A CN 110303501 A CN110303501 A CN 110303501A
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mechanical arm
uproar
acceleration layer
indicate
avoidance
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CN110303501B (en
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郭东生
蔡建煌
冯庆山
刘庆平
李泽昕
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Huaqiao University
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Huaqiao University
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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
    • B25J9/1656—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
    • B25J9/1666—Avoiding collision or forbidden zones

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

Abstract

The present invention provides one kind can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, and by introducing the feedback of end of arm speed error and location error, designing has the acceleration layer Jacobian matrix equation for holding characteristic of making an uproar；Foundation can hold the acceleration layer avoidance programme made an uproar, and the programme is constrained in Jacobian matrix equation, avoidance inequality, the joint angles limit, the joint velocity limit and the joint velocity limit；It converts above-mentioned programme to the quadratic form optimization problem an of standard, and it is solved using numerical algorithm solver；Solving result of the next machine controller according to algorithm, the end planning tasks that driving mechanical arm makes it complete to give.The acceleration layer avoidance programme designed the present invention is based on error feedback and inequality criterion, enabling to mechanical arm at the same time has still achievable given end planning tasks in the case where noise jamming and extraneous barrier.

Description

It is a kind of to hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar
Technical field
The present invention relates to the motion planning of redundancy mechanical arm and control fields, and the redundancy made an uproar can be held by particularly relating to one kind Mechanical arm acceleration layer avoidance planing method.
Background technique
As a kind of mechanical device that end is active, redundancy mechanical arm is widely used to assembling, welding and spray painting etc. In industrial automation production activity.A research hotspot is Obstacle avoidance in the motion planning of redundancy mechanical arm and control: Can this is related to mechanical arm successfully complete given end planning tasks in complex industrial environment.There are many avoidances at present Programme is suggested and mechanical arm is enabled effectively to hide extraneous barrier.However, most scheme is all in speed Obstacle avoidance is realized on layer, and scheme only few in number is that Obstacle avoidance is realized on acceleration layer.Importantly, These avoidance programmes are designed and study in the case where not considering noise.Obviously, once suffering from noise Interference, then scheme will fail, mechanical arm, which is effectively realized, hides and successfully completes given end rule to barrier The task of drawing is not known where to begin yet.
Summary of the invention
It is a primary object of the present invention to overcome drawbacks described above in the prior art, propose that one kind can hold the redundancy machine made an uproar Tool arm acceleration layer avoidance planing method.
The present invention adopts the following technical scheme:
It is a kind of to hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, it is characterised in that:
By introducing the feedback of end of arm speed error and location error, designing has the acceleration layer for holding characteristic of making an uproar Jacobian matrix equation；
Foundation can hold the acceleration layer avoidance programme made an uproar, and it is constrained that this can hold the acceleration layer avoidance programme made an uproar In Jacobian matrix equation, avoidance inequality, the joint angles limit, the joint velocity limit and the joint velocity limit；
It converts acceleration layer avoidance programme to the quadratic form optimization problem an of standard, and is asked by numerical algorithm Solution device solves it；
The next machine controller drives mechanical arm that it is made to complete given end planning tasks according to solving result.
It is preferably, described that there is the acceleration layer Jacobian matrix equation for holding characteristic of making an uproar are as follows:
Wherein design parameter λ > 0, μ > 0, and the two meets λ2> μ；Indicate joint of mechanical arm acceleration,Expression machine Tool shoulder joint speed, J indicate the Jacobian matrix of mechanical arm,Indicate the time-derivative of J；The speed of ε (t) expression mechanical arm tail end It spends error and is defined asT indicates the time,Indicate rdTime-derivative, rdIndicate mechanical arm tail end expectation rule The motion profile drawn；E (t) indicates the location error of mechanical arm tail end and is defined as e (t)=φ (θ)-rd, θ expression mechanical arm pass Angle is saved, φ () indicates a nonlinear mapping function；In addition,It indicatesTime-derivative, σ indicate integration variable.
It is preferably, described to hold the acceleration layer avoidance programme made an uproar are as follows:
It minimizes
It is constrained inθ-≤θ≤θ+,
Wherein subscriptTThe transposition of representing matrix or vector, vector d are defined as
Equality constraintCorresponding to mechanical arm end End is in the motion planning track of acceleration layer；Inequality constraintsHide mechanical arm realization to extraneous barrier, Coefficient matrices A and B are defined asWith (xC,yC,zC) indicate mechanical arm criterion point space coordinate, (xO,yO,zO) indicate the space coordinate of extraneous obstacle object point, JCTable Show the Jacobian matrix of mechanical arm criterion point,Indicate JCTime-derivative, computational operatorIndicate vector each element and matrix The multiplication of corresponding row vector；θ±、WithRespectively indicate the joint angles limit, the joint velocity limit and the joint velocity limit.
Preferably, acceleration layer avoidance programme is converted to the quadratic form optimization problem an of standard, performance refers to It is designated as xTx/2+pTX, constraint condition Cx=d, Ax≤b, x-≤x≤x+, whereinP=0, C=J,x± Indicate the bound of x.
Preferably, it carries out solving quadratic form optimization problem using numerical algorithm solver, specifically: quadratic form optimization is asked Topic is converted into a piecewise linearity projection equation, to solve projection equation and optimization problem using corresponding numerical algorithm.
By the above-mentioned description of this invention it is found that compared with prior art, the invention has the following beneficial effects:
The present invention can be overcomed the shortcomings of existing methods effectively, provide one kind and redundancy mechanical arm is enabled to have at the same time There is the acceleration layer motion planning side of still achievable given end planning tasks in the case where noise jamming and extraneous barrier Method carries out effective motion planning in complex industrial environment to mechanical arm and is of great significance and is worth.
Detailed description of the invention
Fig. 1 is flow chart of the invention.
Below in conjunction with the drawings and specific embodiments, the invention will be further described.
Specific embodiment
Below by way of specific embodiment, the invention will be further described.
One kind shown in FIG. 1, which can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, mainly has appearance by design The acceleration layer Jacobian matrix equation 1 for characteristic of making an uproar, foundation can hold the acceleration layer avoidance programme 2 made an uproar, switch to standard Quadratic form optimization problem 3, numerical algorithm solver 4, the next machine controller 5, redundancy mechanical arm 6 this six partial content groups At.
First according to the requirement of mechanical arm acceleration layer motion planning, by introducing end of arm speed error and position The feedback of error, designing has the acceleration layer Jacobian matrix equation for holding characteristic of making an uproar；Then in conjunction with achievable Obstacle avoidance Inequality criterion and required optimization performance indicator, foundation can hold the acceleration layer avoidance programme made an uproar, and by its It is converted into the quadratic form optimization problem an of standard, is asked to solve quadratic form optimization using numerical algorithm solver Topic；Finally by solving result be used to drive mechanical arm each joint so that mechanical arm there are noise and barrier Still achievable given end planning tasks.
According to the requirement of mechanical arm acceleration layer motion planning, by introducing end of arm speed error and location error Feedback, have hold make an uproar characteristic acceleration layer Jacobian matrix equation design are as follows:
Wherein design parameter λ > 0, μ > 0, and the two meets λ2> μ；Indicate joint of mechanical arm acceleration,Expression machine Tool shoulder joint speed, J indicate the Jacobian matrix of mechanical arm,Indicate the time-derivative of J；The speed of ε (t) expression mechanical arm tail end It spends error and is defined asT indicates the time,Indicate rdTime-derivative, rdIndicate mechanical arm tail end expectation rule The motion profile drawn；E (t) indicates the location error of mechanical arm tail end and is defined as e (t)=φ (θ)-rd, θ expression mechanical arm pass Angle is saved, φ () indicates a nonlinear mapping function；In addition,It indicatesTime-derivative, σ indicate integration variable.
Based on above-mentioned equation (1), in conjunction with the inequality criterion of achievable Obstacle avoidance and the performance of required optimization Index can be established and following hold the acceleration layer avoidance programme made an uproar:
It minimizes
Constraint condition:
θ-≤θ≤θ+ (5)
Wherein subscriptTThe transposition of representing matrix or vector, vector d are defined as
Equality constraintCorresponding to mechanical arm end End is in the motion planning track of acceleration layer；Inequality constraintsMechanical arm realization can be made to hide extraneous barrier It keeps away, coefficient matrices A and B are defined asWith(xC,yC,zC) indicate mechanical arm criterion point space coordinate, (xO,yO,zO) Indicate the space coordinate of extraneous obstacle object point, JCIndicate the Jacobian matrix of mechanical arm criterion point,Indicate JCTime-derivative, Computational operatorIndicate the multiplication of vector each element row vector corresponding to matrix；θ±、WithRespectively indicate joint angles pole Limit, the joint velocity limit and the joint velocity limit.
Hold acceleration layer avoidance programme (2)-(7) made an uproar for above-mentioned, the secondary of following standard can be converted into Type optimization problem:
Minimize xTx/2+pTx (8)
Constraint condition: Cx=d (9)
Ax≤b (10)
x-≤x≤x+ (11)
Wherein,P=0, C=J,x±Indicate the bound of x.
Also, solving above-mentioned quadratic form optimization problem (8)-(11) can be equivalent to solve following piecewise linearity projection side Journey:
PΩ(u- (Mu+q))-u=0 (12)
Wherein, PΩ() indicates piecewise linearity projection operator.Decision vector u in piecewise linearity projection equation (12) is Matrix number M and vector q are defined respectively as:
Wherein, I indicates unit matrix, and dual variable w and v correspond respectively to equality constraint (9) and inequality constraints (10). In order to solve piecewise linearity projection equation (12) and quadratic form optimization problem (8)-(11), following numerical algorithm can be used:
δ(uk)=uk-PΩ(uk-(Muk+q))
Wherein, | | | |2Two norms of expression vector, subscript k expression the number of iterations and k=0,1,2 ....It is one given Initial value u0, by the continuous iterative calculation of the numerical algorithm, the Theory Solution of piecewise linearity projection equation (12) can be obtained, from And obtain quadratic form optimization problem (8)-(11) optimal solution namely previously described acceleration layer avoidance programme (2)- (7) optimal solution.
Using above-mentioned numerical algorithm solver be calculated acceleration layer avoidance programme (2)-(7) optimal solution it Afterwards, then by corresponding solving result the next machine controller is passed to drive the movement in each joint of mechanical arm, so that machine Tool arm still achievable given end planning tasks there are noise and barrier.
The above is only a specific embodiment of the present invention, but the design concept of the present invention is not limited to this, all to utilize this Design makes a non-material change to the present invention, and should all belong to behavior that violates the scope of protection of the present invention.

Claims (5)

1. one kind can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, it is characterised in that:
By introducing the feedback of end of arm speed error and location error, designing has the acceleration layer for holding characteristic of making an uproar is refined can Compare matrix equality；
Foundation can hold the acceleration layer avoidance programme made an uproar, and it is constrained in refined that this can hold the acceleration layer avoidance programme made an uproar Than matrix equality, avoidance inequality, the joint angles limit, the joint velocity limit and the joint velocity limit；
It converts acceleration layer avoidance programme to the quadratic form optimization problem an of standard, and passes through numerical algorithm solver It is solved；
The next machine controller drives mechanical arm that it is made to complete given end planning tasks according to solving result.
2. one kind as described in claim 1 can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, feature exists In: it is described that there is the acceleration layer Jacobian matrix equation for holding characteristic of making an uproar are as follows:
Wherein design parameter λ > 0, μ > 0, and the two meets λ2> μ；Indicate joint of mechanical arm acceleration,Indicate mechanical arm Joint velocity, J indicate the Jacobian matrix of mechanical arm,Indicate the time-derivative of J；ε (t) indicates that the speed of mechanical arm tail end is missed Difference and be defined asT indicates the time,Indicate rdTime-derivative, rdIndicate mechanical arm tail end expectation programming Motion profile；E (t) indicates the location error of mechanical arm tail end and is defined as e (t)=φ (θ)-rd, θ expression joint of mechanical arm angle Degree, φ () indicate a nonlinear mapping function；In addition,It indicatesTime-derivative, σ indicate integration variable.
3. one kind as claimed in claim 2 can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, feature exists In: it is described to hold the acceleration layer avoidance programme made an uproar are as follows:
It minimizes
It is constrained inθ-≤θ≤θ+,
Wherein subscriptTThe transposition of representing matrix or vector, vector d are defined asEquality constraintAccelerating corresponding to mechanical arm tail end Spend the motion planning track of layer；Inequality constraintsHide mechanical arm realization to extraneous barrier, coefficient matrices A It is defined as with BWith(xC, yC,zC) indicate mechanical arm criterion point space coordinate, (xO,yO,zO) indicate the space coordinate of extraneous obstacle object point, JCExpression machine The Jacobian matrix of tool arm criterion point,Indicate JCTime-derivative, computational operatorIndicate that vector each element is corresponding to matrix The multiplication of row vector；θ±、WithRespectively indicate the joint angles limit, the joint velocity limit and the joint velocity limit.
4. one kind as claimed in claim 3 can hold the redundancy mechanical arm acceleration layer avoidance planing method made an uproar, feature exists In: convert acceleration layer avoidance programme to the quadratic form optimization problem an of standard, performance indicator xTx/2+pTX, Constraint condition is Cx=d, Ax≤b, x-≤x≤x+, whereinP=0, C=J,x±Indicate the bound of x.
5. one kind according to claim 1 or 2 or 3 or 4 can hold the redundancy mechanical arm acceleration layer avoidance planning side to make an uproar Method, which is characterized in that it carries out solving quadratic form optimization problem using numerical algorithm solver, specifically: quadratic form optimization is asked Topic is converted into a piecewise linearity projection equation, to solve projection equation and optimization problem using corresponding numerical algorithm.
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