CN109807892A - A kind of Automobile Welding robot motion planning model - Google Patents
A kind of Automobile Welding robot motion planning model Download PDFInfo
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- CN109807892A CN109807892A CN201910123404.2A CN201910123404A CN109807892A CN 109807892 A CN109807892 A CN 109807892A CN 201910123404 A CN201910123404 A CN 201910123404A CN 109807892 A CN109807892 A CN 109807892A
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Abstract
The present invention relates to a kind of Automobile Welding robot motion planning model, the Automobile Welding robot is defined as the tree-like Automobile Welding robot that some rigid bodies are assembled by joint, i.e. main body is node, and joint is as side；The parameter vector in the joint is the control variable of the motion planning model, permissible function meets equation of motion EoM, a motion planning model is formed using it as constraint, the method for solving of the motion planning model is welding robot node space Non-smooth surface conversion method.Motion planning model problem is attributed to a nonsmooth optimization by the present invention, and the nonsmooth optimization can be solved using parallel computing.The present invention establishes motion planning mathematical model according to actual requirement, and the model optimizes the performance of Automobile Welding robot under conditions of guaranteeing Automobile Welding robot stabilization.
Description
Technical field
The invention belongs to technical field of automatic control, and in particular to a kind of Automobile Welding robot motion planning model.
Background technique
Robot technology is to be converted to the intellectual technology of physical action, any robot after numerical data is handled
The research and development core of system is all motion profile, and calculating robot's motion profile achievees the purpose that desired or completes desired task
Scientific scheme be exactly robot motion planning model.Because be used to carry out motion calculation model and environment diversification and not
Certainty, motion planning model will be realized by closed-loop control.In Automobile Welding robot, because task is to be determined in advance
, this requires under the constraint of movenent performance or Automobile Welding joint of robot range, speed, collision avoidance limitation under
Reach maximized movement velocity and robust performance.Therefore, motion planning model can be attributed to the solution of an optimization problem.So
And even a simple mechanical arm, it is also quite time-consuming for optimizing whole path.Current research is welding of automotive
Welding robot has taken away classical Large-scale Manufacturing and production line, and welding of automotive welding robot of today, which enters, more answers
With field, the service including small-scale flexibly production and other and mankind's communal space.From in this way from the point of view of welding of automotive weld
Welding robot movement does not need to be driven by traditional industrial requirement and the requirement to energy and performance, some welding of automotive welding
Robot has extra structure that can make more possible movements to complete given task or be completed at the same time multitask, as
It is a kind of direct as a result, speed issue must be taken into consideration in the algorithm established in terms of welding of automotive welding robot control, with satisfaction
Requirement of real-time.If not can be carried out rapid solving, machine task efficiency will seriously affect.
Summary of the invention
For overcome the deficiencies in the prior art, a kind of Automobile Welding robot motion planning model is proposed, movement is formed
After plan model problem, it is attributed to a nonsmooth optimization, the nonsmooth optimization can utilize parallel meter
Calculation method is solved.The present invention solves Automobile Welding robot motion optimization problem with optimization method, is built according to actual requirement
Vertical mathematical model, optimizes the performance of Automobile Welding robot under conditions of guaranteeing welding of automotive welding robot stability.
The technical solution of the present invention is as follows: a kind of Automobile Welding robot motion planning model, the Automobile Welding robot
Be defined as a kind of tree-like Automobile Welding robot that rigid bodies are assembled by joint, i.e. main body is node, joint as side,
Main body is equipped with Bit andits control variable q (t), and the motion planning model includes the Bit andits control variable q (t), and q (t) is abbreviated as
Q, permissible function q need to meet the following equation of motion EoM with physical significance:
Wherein, subscript r represents Automobile Welding robot, and subscript j represents joint, MrIndicate the used of Automobile Welding robot
Property, BrIndicate the gravity and speed bring impact factor of Automobile Welding robot, MjIndicate the inertia in joint, BjIndicate joint
Gravity and speed bring impact factor, τ is the torque vector in joint, and f is being applied to Automobile Welding robot pthkIt is a
The power f of pointkThe vector for the composition that is superimposed, JrIndicate Automobile Welding robot to all the points pkJacobian matrixThe matrix for the composition that is superimposed, JjIndicate joint to all the points pkJacobian matrixBe superimposed composition
Matrix,WithRespectively indicate JrAnd JjTransposed matrix, the top half of equation of motion EoM is Automobile Welding machine
People indicates Euler-newton rule expression that Automobile Welding robot acceleration and angular speed changes as single rigid body, is outer
The function of portion's power, the lower half portion of equation of motion EoM represent inertia and the external force to joint moment；When being configured to q (t),
xi(q (t)) indicates position vector of the Automobile Welding robot in world coordinate system, Oi(q (t)) indicates that Automobile Welding robot exists
The direction vector of world coordinate system, Automobile Welding robot pass through x in i-th of main body of world coordinate systemi(q (t)) and Oi(q
(t)) it provides, one is O in coordinate of the point under world coordinate system that rectangular coordinate system coordinate is pi(q(t))p+xi(q(t))；
Automobile Welding robot world coordinate system space velocity by vectorIt indicates, acceleration isAutomobile
Welding robot is ω in the angular speed of world coordinate systemi(q (t)), acceleration areP point is in world coordinate system
Speed beThe change rate of its acceleration and angular speed is
All x are indicated with G (t)i(q (t)) and OiThe set of (q (t)), K (t) indicate their first derivative and the set of second dervative；
The motion planning model can be attributed to following form:
Here h and ciIt is real-valued function, m is the number of constraint,It is disjoint time interval, h here
And ciWhole q (t), f (t), τ (t), G (t), K (t) need not be relied on；Cost function h is to minimize jerk or system capacity, constraint
ciInclude the inherent limitations constraint of Automobile Welding robot, joint position constraint, joint velocity constraint, joint moment constraint, automobile
Welding robot position constraint and global restriction, the Automobile Welding robot location constraint may be expressed as: to sit at i-th of right angle
Being designated as the point of the p coordinate in the world is pdes, i.e. Oi(q(t))p+xi(q (t))=pdes, it is desirable that the main body i of Automobile Welding robot
The distance between main body j of Automobile Welding robotGreater than one secure threshold avoids collision；The overall situation
Constraint includes the centroid position and systemic velocity of Automobile Welding robot, and global restriction can guarantee the stabilization of Automobile Welding robot
Property；
The motion planning model needs are solved in an infinite dimensional space, this is unsolvable, the movement
The method for solving of plan model is a kind of welding robot node space Non-smooth surface conversion method；
The step of welding robot node space Non-smooth surface conversion method are as follows:
Problem is limited in the constraint space of a finite dimension by the first step by objective function and constraint function parameter；
By the lower half portion of equation of motion EoM, solve:
It follows that f1It can be by f2Substitution,It indicatesThrough the transformed matrix of space,It indicatesThrough the transformed matrix of space,Indicate Mr(q) through the transformed matrix of space,It is corresponding point of vector of f.
The motion planning model can be changed into motion planning model after amendment as a result:
Indicate new constraint condition,
Second step, using L interpolation q and f2Parametrization:
Wherein, ηiIt (t) is interpolating function, ηiIt is ηi(t) interpolation condition at interpolation point t, t have L+1, interpolation condition
ηiThere are L+1, L is positive integer, pi,jFor interpolating function coefficient, i=1,2,3 ..., m, j=0,1,2,3 ..., L, q (t)=(q1
(t),q2(t),q3(t),...,qi(t),...)T, T expression transposed matrix,f2(t)=(f21(t),f22
(t),f23(t),...,f2i(t),...)T,
Quick in order to calculate, L takes 3 here, utilizes interpolation condition ηi, q (t) and f are found out respectively2Each component interpolation
Function coefficients pi,j, (q (t), the f of discretization are indicated with vector p (t)2(t)) vector, this vector is by pi,jIt is constituted,
Constraint conditionCan equivalently by
Expression,Indicate byObtained new constraint function is guided,
It enablesThen, following third step has been obtained；
Third step, by the parametrization of second step, motion planning model after the amendment:
Become:
P is indicated by pi,jThe vector of composition,Indicate new constraint condition, this is one based on non smooth optimization
Automobile Welding robot motion planning model.
Beneficial effect of the present invention
1, the present invention proposes that a kind of welding robot node space Non-smooth surface conversion method, the method are converted into problem
Nonsmooth optimization can thus be solved using parallel computing, can greatly improve processing speed.
2, the present invention solves Automobile Welding robot motion optimization problem with optimization method, establishes mathematics according to actual requirement
Model optimizes the performance of Automobile Welding robot under conditions of guaranteeing Automobile Welding robot stabilization.
Specific embodiment
Motion planning model of the present invention, the Automobile Welding robot are defined as some rigid bodies by joint group
Tree-like Automobile Welding robot made of dress, i.e. main body are node, and joint is as side；The motion planning model includes displacement control
Variable q (t) processed is called configuration, and the parameter vector in the joint is the control variable of the motion planning model, by q (t) letter
It is denoted as q, permissible function q needs to meet the following equation of motion EoM with physical significance:
=wherein subscript r represent Automobile Welding robot, subscript j represents joint, MrIndicate the used of Automobile Welding robot
Property, BrIndicate the gravity and speed bring impact factor of Automobile Welding robot, MjIndicate the inertia in joint, BjIndicate joint
Gravity and speed bring impact factor, τ is the torque vector in joint, and f is being applied to Automobile Welding robot pthkIt is a
The power f of pointkThe vector for the composition that is superimposed, JrIndicate Automobile Welding robot to all the points pkJacobian matrixThe matrix for the composition that is superimposed, JjIndicate joint to all the points pkJacobian matrixBe superimposed structure
At matrix,WithRespectively indicate JrAnd JjTransposition, the top half of equation of motion EoM is Automobile Welding robot
As single rigid body, Euler-newton rule expression that Automobile Welding robot acceleration and angular speed changes is indicated, be external
The function of power, the lower half portion of equation of motion EoM represent inertia and the external force to joint moment；When being configured to q (t), xi
(q (t)) indicates position vector of the Automobile Welding robot in world coordinate system, Oi(q (t)) indicates that Automobile Welding robot is alive
The direction vector of boundary's coordinate system, Automobile Welding robot pass through x in i-th of main body of world coordinate systemi(q (t)) and Oi(q(t))
It provides, one is O in coordinate of the point under world coordinate system that rectangular coordinate system coordinate is pi(q(t))p+xi(q(t))；Automobile
Welding robot world coordinate system space velocity by vectorIt indicates, acceleration isAutomobile Welding
Robot is ω in the angular speed of world coordinate systemi(q (t)), acceleration areSpeed of the p point in world coordinate system
It isThe change rate of its acceleration and angular speed isWith G (t)
Indicate all xi(q (t)) and OiThe set of (q (t)), K (t) indicate their first derivative and the set of second dervative；The fortune
Dynamic plan model can be attributed to following form:
Here h and ciIt is real-valued function, m is the number of constraint,It is disjoint time interval, h here
And ciWhole q (t), f (t), τ (t), G (t), K (t) need not be relied on；Cost function h is to minimize jerk or system capacity, constraint
ciIt is constrained comprising the inherent limitations of Automobile Welding robot, joint position constraint, joint velocity constraint, joint moment constraint, automobile
Welding robot position constraint and global restriction, the Automobile Welding robot location constraint may be expressed as: to sit at i-th of right angle
Being designated as the point of the p coordinate in the world is pdes, i.e. Oi(q(t))p+xi(q (t))=pdes, it is desirable that the main body i of Automobile Welding robot
The distance between main body j of Automobile Welding robotGreater than one secure threshold avoids collision；The overall situation
Constraint includes the centroid position and systemic velocity of Automobile Welding robot, and global restriction can guarantee the stabilization of Automobile Welding robot
Property；
The method for solving of the motion planning model is welding robot node space Non-smooth surface conversion method；
The motion planning model needs are solved in an infinite dimensional space, this is unsolvable, the welding
The step of robot node space Non-smooth surface conversion method are as follows:
Problem is limited in the constraint space of a finite dimension by the first step by objective function and constraint function parameter；
By the lower half portion of equation of motion EoM, solve:
It follows that f1It can be by f2Substitution,It indicatesThrough the transformed matrix of space,It indicatesThrough the transformed matrix of space,Indicate Mr(q) through the transformed matrix of space,It is corresponding point of vector of f.
The motion planning model can be changed into motion planning model after amendment as a result:
Indicate new constraint condition,
Second step, using L interpolation q and f2Parametrization:
Wherein ηiIt is interpolation condition, pi,jFor interpolating function coefficient, i=1,2,3 ..., m, j=0,1,2 ..., L.
L is bigger, and operation time is longer, and the present invention takes L=3.
Q (t)=(q1(t),q2(t),q3(t),...,qi(t),...)T, T expression transposed matrix,
f2(t)=(f21(t),f22(t),f23(t),...,f2i(t),...)T,
Quick in order to calculate, L takes 3 here, utilizes interpolation condition ηi, q (t) and f are found out respectively2Each component interpolation
Function coefficients pi,j, (q (t), the f of discretization are indicated with vector p (t)2(t)) vector, this vector is by pi,jIt is constituted,
Constraint conditionCan equivalently by
Expression,Indicate byObtained new constraint function is guided,
It enablesThen, following third step has been obtained；
Third step, by the parametrization of second step, motion planning model after the amendment:
Become:
P is indicated by pi,jThe vector of composition,Indicate new constraint condition, this is one based on non smooth optimization
Automobile Welding robot motion planning model.
This is a non smooth optimization, solves the non smooth optimization and carries out parameter identification, will obtain automobile
Welding robot dynamical system obtains Automobile Welding robot controller, using Automobile Welding robot energy as performance indicator
Optimized model under, controller obtained by calculation stablizes the control system of Automobile Welding robot, and has reached institute
Need the relatively small consumption of energy.
Claims (5)
1. a kind of Automobile Welding robot motion planning model, the Automobile Welding robot is defined as some rigid bodies by closing
The tree-like Automobile Welding robot assembled is saved, i.e. main body is node, and joint is as side；A kind of Automobile Welding robot motion
Plan model, the Automobile Welding robot are defined as a kind of tree-like Automobile Welding machine that rigid bodies are assembled by joint
People, i.e. main body are node, and as side, main body is equipped with Bit andits control variable q (t) in joint, and the motion planning model includes described
Bit andits control variable q (t), q (t) are abbreviated as q, and permissible function q needs to meet the following equation of motion with physical significance
EoM:
Wherein, subscript r represents Automobile Welding robot, and subscript j represents joint, MrIndicate the inertia of Automobile Welding robot, BrTable
Show the gravity and speed bring impact factor of Automobile Welding robot, MjIndicate the inertia in joint, BjIndicate joint gravity and
Speed bring impact factor, τ are the torque vectors in joint, and f is that handle is applied to Automobile Welding robot pthkThe power f of a pointkIt is folded
It is added together the vector of composition, JrIndicate Automobile Welding robot to all the points pkJacobian matrixIt is superimposed upon one
Act the matrix constituted, JjIndicate joint to all the points pkJacobian matrixThe matrix for the composition that is superimposed, JT rWith
JT jRespectively indicate JrAnd JjTransposed matrix, the top half of equation of motion EoM be Automobile Welding robot as it is single just
Body indicates Euler-newton rule expression that Automobile Welding robot acceleration and angular speed changes, is the function of external force,
The lower half portion of equation of motion EoM represents inertia and the external force to joint moment；When being configured to q (t), xi(q (t)) is indicated
Position vector of the Automobile Welding robot in world coordinate system, Oi(q (t)) indicates Automobile Welding robot in world coordinate system
Direction vector, Automobile Welding robot pass through x in i-th of main body of world coordinate systemi(q (t)) and Oi(q (t)) is provided, and one
It is O in coordinate of the point under world coordinate system that rectangular coordinate system coordinate is pi(q(t))p+xi(q(t))；Automobile Welding robot
World coordinate system space velocity by vectorIt indicates, acceleration isAutomobile Welding robot is alive
The angular speed of boundary's coordinate system is ωi(q (t)), acceleration areP point is in the speed of world coordinate systemThe change rate of its acceleration and angular speed isWith G (t) table
Show all xi(q (t)) and OiThe set of (q (t)), K (t) indicate their first derivative and the set of second dervative；The movement
Plan model can be attributed to following form:
Here h and ciIt is real-valued function, m is the number of constraint,It is disjoint time interval, h and c herei
Whole q (t), f (t), τ (t), G (t), K (t) need not be relied on；Cost function h is to minimize jerk or system capacity, constrains ciPacket
The inherent limitations constraint of robot containing Automobile Welding, joint position constraint, joint velocity constraint, joint moment constraint, Automobile Welding
Robot location's constraint and global restriction；
It is characterized in that:
The motion planning model needs are solved in an infinite dimensional space, this is unsolvable, the motion planning
Model can be converted into a kind of non-smooth blade motion planning mould using a kind of welding robot node space Non-smooth surface conversion method
Type.
2. Automobile Welding robot motion planning model according to claim 1, it is characterized in that: the welding robot section
The step of space of points Non-smooth surface conversion method are as follows:
Problem is limited in the constraint space of a finite dimension by the first step by objective function and constraint function parameter；
By the lower half portion of equation of motion EoM, solve:
It follows that f1It can be by f2Substitution,It indicatesThrough the transformed matrix of space,Table
ShowThrough the transformed matrix of space,Indicate Mr(q) through the transformed matrix of space,It is f corresponding
Divide vector.
The motion planning model can be changed into motion planning model after amendment as a result:
Indicate new constraint condition,
Second step, using L interpolation q and f2Parametrization:
Wherein, ηiIt (t) is interpolating function, ηiIt is ηi(t) interpolation condition at interpolation point t, t have L+1, interpolation condition ηiThere is L+
1, L is positive integer, pi,jFor interpolating function coefficient, i=1,2,3 ..., m, j=0,1,2,3 ..., L, q (t)=(q1(t),q2
(t),q3(t),...,qi(t),...)T, T expression transposed matrix,f2(t)=(f21(t),f22(t),
f23(t),...,f2i(t),...)T,
Quick in order to calculate, L takes 3 here, utilizes interpolation condition ηi, q (t) and f are found out respectively2Each component interpolating function
Coefficient pi,j, (q (t), the f of discretization are indicated with vector p (t)2(t)) vector, this vector is by pi,jIt is constituted, constraint conditionCan equivalently byExpression,It indicates
ByObtained new constraint function is guided,
It enablesThen, following third step has been obtained；
Third step, by the parametrization of second step, motion planning model after the amendment:
Become:
P is indicated by pi,jThe vector of composition,Indicate new constraint condition, this is the automobile based on non smooth optimization
Welding robot motion planning model.
3. Automobile Welding robot motion planning model according to claim 1, it is characterized in that: constraint ciIt is welded comprising automobile
Welding robot inherent limitations constraint, joint position constraint, joint velocity constraint, joint moment constraint, Automobile Welding robot position
Set constraint and global restriction.
4. welding robot node space Non-smooth surface conversion method according to claim 2, it is characterized in that: the automobile welds
Welding robot position constraint may be expressed as: i-th of rectangular co-ordinate be p point in the world coordinate be pdes, i.e. Oi(q(t))p+
xi(q (t))=pdes, it is desirable that the distance between main body i and the main body j of Automobile Welding robot of Automobile Welding robotGreater than one secure threshold avoids collision.
5. a kind of Automobile Welding robot motion planning model according to claim 1, it is characterized in that: the global restriction
Centroid position and systemic velocity comprising Automobile Welding robot, global restriction can guarantee the stability of Automobile Welding robot.
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