CN108714894A - A kind of dynamic method for solving dual redundant mechanical arm and colliding with each other - Google Patents
A kind of dynamic method for solving dual redundant mechanical arm and colliding with each other Download PDFInfo
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- CN108714894A CN108714894A CN201810412681.0A CN201810412681A CN108714894A CN 108714894 A CN108714894 A CN 108714894A CN 201810412681 A CN201810412681 A CN 201810412681A CN 108714894 A CN108714894 A CN 108714894A
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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
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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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Abstract
The invention discloses a kind of dynamic methods that solution dual redundant mechanical arm collides with each other, and include the following steps：S1, actual physical system is formalized, minimum speed two Norm Model of the system based on quadratic programming problem is established based on the mechanical arm of the left side；S2 expands the quadratic programming problem in step S1 according to the constraint for avoiding colliding between dual redundant mechanical arm, considers the inequality constraints avoided collision mutually；S3, according to dual redundant joint of mechanical arm angle and joint angle speed limit, the constraint of joint angles and angular speed is taken into account into quadratic programming problem；S4, the left side mechanical arm quadratic programming scheme in step S3 is applied on the mechanical arm of the right, and two sub- quadratic programming problems of dual redundant mechanical arm is integrated under a quadratic programming frame；S5, it is solved using linear variational inequality problem-primal-dual neural network, obtained solution is that the result of end task is completed in the case of dual redundant mechanical arm is hidden mutually.
Description
Technical field
The present invention relates to the kinematics technical fields of dual redundant mechanical arm, and in particular to a kind of solution dual redundant mechanical arm is mutual
The dynamic method to collide.
Background technology
In recent years, mechanical arm is widely used in many fields, as Medical Instruments and industry manufacture.It attracts such as
It is that can carry weight that as many as this, which pays close attention to the main reason for robotic manipulator, does the thing of repetition, and can dangerous and
It works in rugged environment.It is required to meet the complicated of required task, mechanical arm needs more flexible configuration and optional excellent
Change.Therefore, compared with non redundant manipulator, the need of more complicated task have been catered to equipped with the redundant mechanical arm of more freedom
It asks.With the increase of degree of freedom, mechanical arm can preferably complete basic task, preferably complete optional optimization task, simultaneously
Some additional but necessary targets can also be met, such as joint limitation avoids and unusual avoidance.
In addition, dual redundant mechanical arm becomes more and more popular, because dual redundant mechanical arm can complete single redundancy machinery
The collaborative task that arm cannot be completed.Therefore, in automation order radio frequency, the elderly and the disabled is helped to wear the clothes etc. various
In, they can be widely used.
However, in the field of operation dual redundant mechanical arm, some challenging problems are always existed：
1) redundancy parses problem.Inverse Kinematics Problem is one of key problem of Mechanical transmission test.Due to kinematics
Equation it is non-linear, Inverse Kinematics Problem solve it is often relatively difficult.In addition, the quantity due to degree of freedom is more than working space
Quantity, so the case where there are numerous solutions.Conventional method is the algorithm using pseudoinverse.However, there is apparent lack in pseudoinverse technique
The inverse matrix of point, i.e. calculating matrix requires a great deal of time.In addition, pseudoinverse technique cannot consider inequality constraints.Recently, base
It is widely studied in the scheme of optimization, in order to which optimization criteria is designed as optimal objective and equation/inequality constraints condition.
2) execution of dual redundant degree mechanical arm collaborative task.It is cooperateed with it is generally desirable to dual redundant mechanical arm and completes end effector
Task.It should consider how to control dual redundant degree mechanical arm simultaneously.Previous studies show that the method based on optimization is feasible
's.
3) mutual collision algorithm is avoided in real time.It is very important when dual redundant mechanical arm is when executing end effector task
The problem of be mutual collision problem.Once mutually collision occurs, dual redundant mechanical arm will be forced to deviate desired track and cause
Mission failure.What is more, may seriously damage dual redundant degree mechanical arm.To avoid this serious situation from occurring, mutually
The scheme avoided collision is necessary.
In order to overcome robot and mechanical arm to need the scheme for proposing to avoid collision with the potential problems of barrier collision.
Invention content
The purpose of the present invention is to solve drawbacks described above in the prior art, and it is mutual to provide a kind of solution dual redundant mechanical arm
The dynamic method to collide, this is avoided mutual collision scheme, with meet obtain comprising joint limit avoid, avoid collision with it is complete
At the requirement of the optimal solution of end effector task.
The purpose of the present invention can be reached by adopting the following technical scheme that：
It is a kind of to solve the kinematic method mutually hidden between dual redundant mechanical arm, include the following steps：
S1, actual physical system is formalized, the system is established based on the mechanical arm of the left side and is asked based on quadratic programming
Two Norm Model of minimum speed of topic is realized and carries out speed while keeping mechanical arm precisely to complete end tracing path task
The optimization of level is handled；
With in application, first the system is established based on the mechanical arm of the right by left side mechanical arm or first and be based on secondary rule
Two Norm Model of minimum speed for the problem of drawing, does not constitute the limitation to technical solution of the present invention.
S2, basis avoid the constraint collided between dual redundant degree mechanical arm, are carried out to the quadratic programming problem in step S1
Expand, considers the inequality constraints for avoiding colliding with each other；
S3, basis avoid the constraint at dual redundant joint of mechanical arm angle and joint angular speed, by angle on the basis of step S2
Quadratic programming problem is added in the constraint of degree and angular speed；
S4, the quadratic programming problem of the left side mechanical arm in step S3 is similarly applicable on the mechanical arm of the right；
S5, will the dual redundant degree mechanical arm in step S4 quadratic programming problem it is unified under a quadratic programming frame；
S6, based on the standard quadratic programming problem in step S5 after reunification, utilize linear variational inequality problem-original antithesis nerve
Network is solved, and obtained solution is that can realize the result that dual redundant mechanical arm is hidden mutually.
Further, by actual physics system form in the step S1, being established based on the mechanical arm of the left side should
Minimum speed two Norm Model of the system based on quadratic programming problem, model are as follows：
In real number field, definitionFor left side joint of mechanical arm angular velocity matries,For it is refined can
Than matrix,For mechanical arm tail end target trajectory.In addition to this, | | | | indicate two norm of Euclid.
Motion planning method described in through the invention can be found and meet the optimal of quadratic programming problem (1)-(2)
SolutionMeanwhile n indicates that the degree of freedom of mechanical arm, m indicate the working space dimension residing for mechanical arm.In the application
In, the degree of freedom of used machinery is 8, and working space dimension is 3, therefore, n=8, m=3.
Further, the constraints avoided collision between dual redundant mechanical arm in the step S2 is specific as follows：
The shortest distance and critical point between double mechanical arms are calculated firstly the need of the knowledge with space geometry, at this
On the basis of a, face related with the shortest distance can be converted into about the constraints avoided collision between dual redundant mechanical arm
The constraints of boundary's point.Assuming that the shortest distance between dual redundant mechanical arm is d, the critical point on left arm is P, facing on right arm
Boundary's point is E.In this way, following constraint can be obtained tentatively：
Wherein,For the vector from critical point P to point E on direction,For the Jacobian matrix of critical point P,For left side joint of mechanical arm angular velocity matries, in addition,
SymbolThe product being defined as between every a line of matrix.
In order to advanced optimize the performance of mechanical arm, reduce the mechanical arm influence that velocity jump is brought in avoidance and into
Enter the speed loss before safe distance, in the present invention, converts the mutation of speed to the process temporarily become.Therefore, one is defined
A βL, and enable βLShown in being defined as follows：
Wherein, function S () is defined as follows：
Wherein, d1And d2Be perfectly safe distance and comparatively safe distance are indicated respectively.When between dual redundant mechanical arm most
Short distance be less than be perfectly safe apart from when be then believed that between mechanical arm and collided, when most short between dual redundant mechanical arm
Distance be less than it is comparatively safe apart from when be then believed that and must be taken measures at this time to prevent colliding.Therefore need mechanical arm into
Scheduled running orbit is kept before entering comparatively safe distance, and is prohibited from entering and is perfectly safe apart from and collides, is determined
The β of justiceLIt then can be achieved as above to imagine function.At this point, the constraint to collide with each other between avoiding mechanical arm can be converted into it is following
Stationary process：
Also, it enablesQuadratic programming problem can be updated to following form：
Further, the step S3 processes are as follows：
The constraint of joint of mechanical arm angle and joint angular speed need to all solve on joint angle velocity layer.According to dual redundant machine
The parameter of tool arm itself can be obtained with lower inequality：
Due to needing to solve quadratic programming problem on velocity layer, so needing to convert the constraint of joint angles to joint
The constraint of angular speed layer then proposes that conversion regime below replaces the formula of the preceding part in (10)：
Wherein, α is parameter related with mechanical arm itself is connect.Meanwhile it then enabling
WithThen, the constraint of joint of mechanical arm angle and joint angular speed be converted into
Under form：
Further, according to above-mentioned quadratic programming problem formula (7)-(9) and the pact of joint angles and angular speed
Beam (12) can obtain the complete standard quadratic programming problem of left arm, the similar standard quadratic programming problem for obtaining right arm, specifically
It is as follows：A following right arm quadratic programming problem can be gone out with analogy according to formula (7)-(9) and (12)：
Wherein, it definesFor left side joint of mechanical arm angular velocity matries,For Jacobean matrix
Battle array,For right mechanical arm end target trajectory, | | | | indicate two norm of Euclid；JNRFor in right mechanical arm
The Jacobian matrix of critical point, βR,Definition and left arm on be defined as follows：
Further, the step S5, the quadratic programming problem of the dual redundant degree mechanical arm in step S4 uniformly arrived
It is specific as follows under one quadratic programming frame：
It is integrated into a unified quadratic programming problem according to two sub- quadratic programming problems of left and right arms, is convenient for neural network
Solver solves.According to matrix knowledge, the quadratic programming problem after integration is as follows：
Subject to Gz=R (14-1)
Dz≤B (15-1)
z-≤z≤z+ (16-1)
Each matrix is defined as follows in formula：
So far, it the quadratic programming problem of standard and is completely proposed.Therefore, this problem is solved to be equivalent to while solving
The trajectory track of dual redundant mechanical arm, hides mutually and joint angles and the problem of the angular speed constraint of joint.
Further, the step S6 processes are as follows：
Standard quadratic programming problem is solved by the primal-dual neural network based on linear variational inequality problem, quadratic programming
Problem is converted into linear variational inequality problem, and may further be converted to following piecewise linearity projection equation：
PΩ(Y- (MY+q))-Y=0 (27)
Wherein, PΩ() is a piecewise linearity projection function and is defined as follows：
MeanwhileIt is former antithesis decision vector, YiRepresent the i-th of matrix Y
Row, Yi -And Yi +The lower limit and the upper limit of the i-th row of Y are indicated respectively.It is the joint angles of dual redundant mechanical arm,WithThe respectively right half part of formula (14-1) and (15-1) inequality.In addition to this, matrix M and to
Shown in amount q is defined as follows：
Finally, above-mentioned piecewise linearity projection equation is solved by following primal-dual neural network：
Wherein, λ is a parameter for regulating networks rate of convergence.
The result of gained is that dual redundant mechanical arm is hiding collision and joint angles and joint angle speed limit mutually
On the basis of complete end task optimal solution.
The present invention has the following advantages and effects with respect to the prior art：
The present invention is based on QUADRATIC PROGRAMMING METHOD FOR, be different from traditional pseudoinverse technique, the solution dual redundant mechanical arm of proposition it
Between the kinematic method mutually hidden realize control dual redundant mechanical arm on the basis of, realize and seek the optimal of speed level
Solution, meanwhile, can make to realize between dual redundant mechanical arm by constraints it is mutual hide, in addition to this it is possible to have
Avoid to effect the constraint of joint angles and joint angular speed.The problem of solving motion planning using quadratic programming problem can keep away
Exempt to calculate complicated operand that pseudo inverse matrix etc. is brought, while the constraint of multigroup equation and inequality can be added, fully profit
With the degree of freedom of redundancy, the more perfect function of mechanical arm is realized.Meanwhile dual redundant mechanical arm is successfully completing times hidden mutually
Under business, the error of end orbit has reached a very small range, has further ensured that the accuracy of method, validity in this way
And utilizability.
Description of the drawings
Fig. 1 is a kind of flow solving the kinematic method mutually hidden between dual redundant mechanical arm disclosed by the invention
Figure；
Fig. 2 is the path and state signal using dual redundant mechanical arm before and after the method for the present invention during cooperative cooperating
Figure；
Wherein, Fig. 2 (a) is path schematic diagram when task 1 does not apply the method for the present invention；
Wherein, path schematic diagram when Fig. 2 (b) is the application the method for the present invention of task 1；
Wherein, Fig. 2 (c) is path schematic diagram when task 2 does not apply the method for the present invention；
Wherein, path schematic diagram when Fig. 2 (d) is the application the method for the present invention of task 2；
Fig. 3 is using the shortest distance schematic diagram between each period dual redundant mechanical arm before and after the method for the present invention；
Wherein, Fig. 3 (a) is the shortest distance schematic diagram before the application the method for the present invention of task 1；
Wherein, Fig. 3 (b) is the shortest distance schematic diagram after the application the method for the present invention of task 1；
Wherein, Fig. 3 (c) is the shortest distance schematic diagram before the application the method for the present invention of task 2；
Wherein, Fig. 3 (d) is the shortest distance schematic diagram before the application the method for the present invention of task 2；
Fig. 4 is the primal-dual neural network based on linear variational inequality problem after providing the quadratic programming problem of standard
Flow chart when solver solves.
Specific implementation mode
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
The every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
Embodiment
Fig. 1 show present example based on standard quadratic programming problem solve dual redundant mechanical arm between mutually hide
The flow chart of problem；The kinematic method mutually hidden between solution dual redundant mechanical arm based on standard quadratic programming problem,
Include the following steps：
S1, actual physical system is formalized, the system is established based on the mechanical arm of the left side and is asked based on quadratic programming
Two Norm Model of minimum speed of topic is realized and carries out speed while keeping mechanical arm precisely to complete end tracing path task
The optimization of level is handled；
S2, basis avoid the constraint collided between dual redundant degree mechanical arm, are carried out to the quadratic programming problem in step S1
Expand, considers the inequality constraints for avoiding colliding with each other；
S3, basis avoid the constraint at dual redundant joint of mechanical arm angle and joint angular speed, by angle on the basis of step S2
Quadratic programming problem is added in the constraint of degree and angular speed；
S4, the quadratic programming problem of the left side mechanical arm in step S3 is similarly applicable on the mechanical arm of the right；
S5, will the dual redundant degree mechanical arm in step S4 quadratic programming problem it is unified under a quadratic programming frame；
S6, based on the standard quadratic programming problem in step S5 after reunification, utilize linear variational inequality problem-original antithesis nerve
Network is solved, and obtained solution is that can realize the result that dual redundant mechanical arm is hidden mutually.
Fig. 2 show path of the dual redundant mechanical arm before and after application teachings herein, can be seen by the comparison of picture
Go out, the circle of intersection no matter is drawn in completion or ' the returning ' of Chinese character, this method suffer from relatively good effect, it can be on the whole
Find out the state that dual redundant mechanical arm is hidden mutually during cooperative cooperating.If as shown in Fig. 2 (a), Fig. 2 (c), double
During redundant mechanical arm cooperative cooperating, if the collision problem between not accounting for mechanical arm, it is easy to cause the mistake of task
It loses, even the damage of mechanical arm.After present context, as shown in Fig. 2 (b), Fig. 2 (d), dual redundant mechanical arm is complete
Task that is whole, being safely completed entire setting.
It is double after Fig. 3 is shown by solving the problems, such as the method mutually hidden between dual redundant degree mechanical arm using the application
The shortest distance between redundancy mechanical arm is as shown in Figure 3.Before application present context, between dual redundant mechanical arm
The shortest distance as shown in Fig. 3 (a), Fig. 3 (c), entered in t=4.1s and t=64.3s respectively collision safety absolutely
Distance, this also means that dual redundant mechanical arm is collided and affects the completion of task at this moment, in addition to this,
As can be seen from the figure dual redundant mechanical arm application this patent content after, respectively t=3.12s and t=59.89s when
Time is changed with for the path of application process, and it is exactly to be avoided mutually so that being realized between dual redundant mechanical arm that these, which change,
Major embodiment.Meanwhile the mode for being achieved such function is as follows：
By taking the left side as an example：Firstly the need of the knowledge with space geometry calculate the shortest distance between double mechanical arms and
Critical point, on this basis, about the constraints avoided collision between dual redundant mechanical arm can be converted into it is most short
The constraints of the critical point of distance dependent.Assuming that the shortest distance between dual redundant mechanical arm is d, the critical point on left arm is
P, the critical point on right arm are E.In this way, following constraint can be obtained tentatively：
WhereinFor the vector from critical point P to point E on direction,For the Jacobian matrix of critical point P,It is the angular speed of left side mechanical arm then as defined in 2.This
Outside, symbolThe product being defined as between every a line of matrix.In order to advanced optimize the performance of mechanical arm, reduces mechanical arm and exist
Velocity jump is brought when avoidance influence and enter speed loss before safe distance, in this patent, by the prominent of speed
Change is converted into the process temporarily become.Therefore, β defined in the present embodimentL, and enable βLShown in being defined as follows：
Function S () therein is defined as follows：
Wherein, d1And d2Be perfectly safe distance and comparatively safe distance are indicated respectively.When between dual redundant mechanical arm most
Short distance be less than be perfectly safe apart from when be then believed that between mechanical arm and collided, when most short between dual redundant mechanical arm
Distance be less than it is comparatively safe apart from when be then believed that and must be taken measures at this time to prevent colliding.Therefore we need mechanical arm
Scheduled running orbit is kept before entering comparatively safe distance, and is prohibited from entering and is perfectly safe apart from and collides,
Defined βLIt then can be achieved as above to imagine function.At this point, the constraint to collide with each other between avoiding mechanical arm can be converted into
Stationary process below：
Also, it enablesQuadratic programming problem can be updated to following form：
In this manner it is possible to obtain the constraint of left side mechanical arm avoided collision and represented with standard quadratic programming problem
Come.
The step S3 processes are as follows：
The constraint of joint of mechanical arm angle and joint angular speed need to all solve on joint angle velocity layer.According to dual redundant machine
The parameter of tool arm itself can be obtained with lower inequality：
Due to needing to solve quadratic programming problem on velocity layer, so needing to convert the constraint of joint angles to joint
The constraint of angular speed layer then proposes that conversion regime below replaces the formula of the preceding part in (10)：
Wherein, α is parameter related with mechanical arm itself is connect.Meanwhile it then enabling
WithThen, the constraint of joint of mechanical arm angle and joint angular speed be converted into
Under form：
According to the duality of dual redundant degree mechanical arm, it can be deduced that the standard quadratic programming problem of the right mechanical arm：
Wherein, it definesFor left side joint of mechanical arm angular velocity matries,For Jacobean matrix
Battle array,For right mechanical arm end target trajectory, | | | | indicate two norm of Euclid；JNRFor in right mechanical arm
The Jacobian matrix of critical point, βR,Definition and left arm on be defined as follows：
In this way, the left side and the right of dual redundant mechanical arm are all showed in the form of standard quadratic programming problem, it is next
The work of step is then the quadratic programming unified the quadratic programming problem of left arm and right arm according to the knowledge of matrix to a standard
Above problem, as follows：
Subject to Gz=R (14-1)
Dz≤B (15-1)
z-≤z≤z+ (16-1)
Each matrix is defined as follows in formula：
So far, it the quadratic programming problem of standard and is completely proposed.Therefore, this problem is solved to be equivalent to while solving
The trajectory track of dual redundant mechanical arm, hides mutually and joint angles and the problem of the angular speed constraint of joint.
Finally, the solution of required joint angles can be obtained by the above-mentioned standard quadratic programming problem of Neural Networks Solution
Certainly scheme can obtain the result in Fig. 3.
Fig. 4 is the primal-dual neural network based on linear variational inequality problem after providing the quadratic programming problem of standard
Flow chart when solver solves, and its solution procedure is told as follows：
Standard quadratic programming problem can be solved by the primal-dual neural network based on linear variational inequality problem.Quadratic programming
Problem can be converted into linear variational inequality problem, and may further be converted to following piecewise linearity projection equation：
PΩ(Y- (MY+q))-Y=0 (27)
Wherein, PΩ() is a piecewise linearity projection function and is defined as follows：
MeanwhileIt is former antithesis decision vector, YiRepresent the i-th of matrix Y
Row, Yi -And Yi +The lower limit and the upper limit of the i-th row of Y are indicated respectively.It is the joint angles of dual redundant mechanical arm,WithThe respectively right half part of formula (14-1) and (15-1) inequality.In addition to this, matrix M and to
Shown in amount q is defined as follows：
Finally, above-mentioned piecewise linearity projection equation can be solved by following primal-dual neural network：
Wherein, λ is a parameter for regulating networks rate of convergence.
The result of gained is that dual redundant mechanical arm is hiding collision and joint angles and joint angle speed limit mutually
On the basis of complete end task optimal solution.
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, it is other it is any without departing from the spirit and principles of the present invention made by changes, modifications, substitutions, combinations, simplifications,
Equivalent substitute mode is should be, is included within the scope of the present invention.
Claims (7)
1. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other, which is characterized in that the dynamic method packet
Include following steps：
S1, actual physical system is formalized, the system is established based on the mechanical arm of the left side based on quadratic programming problem
Two Norm Model of minimum speed is realized and carries out speed level while keeping mechanical arm precisely to complete end tracing path task
Optimization processing；
S2, basis avoid the constraint collided between dual redundant degree mechanical arm, expand the quadratic programming problem in step S1,
Consider the inequality constraints for avoiding colliding with each other；
S3, according to avoiding the constraint at dual redundant joint of mechanical arm angle and joint angular speed, on the basis of step S2 by angle with
And quadratic programming problem is added in the constraint of angular speed；
S4, the quadratic programming problem of the left side mechanical arm in step S3 is applied on the mechanical arm of the right；
S5, will the dual redundant degree mechanical arm in step S4 quadratic programming problem it is unified under a quadratic programming frame；
S6, based on the standard quadratic programming problem in step S5 after reunification, utilize linear variational inequality problem-primal-dual neural network
It is solved, obtained solution is that can realize the result that dual redundant mechanical arm is hidden mutually.
2. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 1, which is characterized in that
By actual physics system form in the step S1, the system is established based on the mechanical arm of the left side and is asked based on quadratic programming
Two Norm Model of minimum speed of topic, model are as follows：
In real number field, definitionFor left side joint of mechanical arm angular velocity matries,For Jacobean matrix
Battle array,For mechanical arm tail end target trajectory, | | | | indicate two norm of Euclid；
Searching meets the optimal solution of quadratic programming problem (1)-(2)Meanwhile n indicates the degree of freedom of mechanical arm, m
Indicate the working space dimension residing for mechanical arm.
3. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 2, which is characterized in that
The constraints avoided collision between dual redundant mechanical arm in the step S2 is specific as follows：
The shortest distance and critical point between double mechanical arms are calculated with the knowledge of space geometry first, it then will be about double
The constraints avoided collision between redundant mechanical arm is converted into the constraints of critical point related with the shortest distance, it is assumed that double
The shortest distance between redundant mechanical arm is d, and the critical point on left arm is P, and the critical point on right arm is E, in this way, tentatively obtaining
It constrains below：
Wherein,For the vector from critical point P to point E on direction,For the Jacobian matrix of critical point P,For left side joint of mechanical arm angular velocity matries, in addition,
SymbolThe product being defined as between every a line of matrix；
It converts the mutation of speed to the process temporarily become, defines a βL, and enable βLShown in being defined as follows：
Wherein, function S () is defined as follows：
Wherein, d1And d2Be perfectly safe distance and comparatively safe distance are indicated respectively, when the most short distance between dual redundant mechanical arm
Then think to be collided between mechanical arm when from less than with a distance from being perfectly safe, when the shortest distance between dual redundant mechanical arm is small
In it is comparatively safe apart from when then think to take measures at this time to prevent colliding；
At this point, the constraint to collide with each other between avoiding mechanical arm, being converted into stationary process below：
Also, it enablesQuadratic programming problem is updated to following form：
4. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 3, which is characterized in that
The step S3 processes are as follows：
It will be solved on the constraints conversion of joint of mechanical arm angle and joint angular speed to joint angle velocity layer, according to dual redundant machinery
The parameter of arm itself, obtains with lower inequality：
It converts the constraint of joint angles to the constraint of joint angle velocity layer, then, proposes that conversion regime below replaces (10)
In preceding part formula：
Wherein, α is parameter related with mechanical arm itself is connect, meanwhile, then enable WithThen, the constraint of joint of mechanical arm angle and joint angular speed is converted into following
Form：
5. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 4, which is characterized in that
The step S4 processes are as follows：
Go out a following right arm quadratic programming problem according to formula (7)-(9) and (12) analogy：
Wherein, it definesFor left side joint of mechanical arm angular velocity matries,For Jacobian matrix,For right mechanical arm end target trajectory, | | | | indicate two norm of Euclid；JNRIt is critical in right mechanical arm
The Jacobian matrix of point, βR,Definition and left arm on be defined as follows：
6. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 5, which is characterized in that
The step S5 processes are as follows：
According to matrix knowledge, the quadratic programming problem after integration is as follows：
Subject to Gz=R (14-1)
Dz≤B (15-1)
z-≤z≤z+ (16-1)
Each matrix is defined as follows in formula：
7. a kind of dynamic method for solving dual redundant mechanical arm and colliding with each other according to claim 6, which is characterized in that
The step S6 processes are as follows：
Standard quadratic programming problem is solved by the primal-dual neural network based on linear variational inequality problem, quadratic programming problem
It is converted into linear variational inequality problem, and is further converted into following piecewise linearity projection equation：
PΩ(Y- (MY+q))-Y=0 (27)
Wherein, PΩ() is a piecewise linearity projection function and is defined as follows：
MeanwhileIt is former antithesis decision vector, YiRepresent the i-th row of matrix Y, Yi -
And Yi +The lower limit and the upper limit of the i-th row of Y are indicated respectively,It is the joint angles of dual redundant mechanical arm,
WithShown in the respectively right half part of formula (14) and (15) inequality, matrix M and vector q are defined as follows：
Finally, above-mentioned piecewise linearity projection equation is solved by following primal-dual neural network：
Wherein, λ is a parameter for regulating networks rate of convergence,
The result of gained is dual redundant mechanical arm in the base for hiding collision and joint angles and joint angle speed limit mutually
The optimal solution of end task is completed on plinth.
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN113547521A (en) * | 2021-07-29 | 2021-10-26 | 中国科学技术大学 | Method and system for autonomous grabbing and accurate moving of mobile robot guided by vision |
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| CN111037560A (en) * | 2019-12-25 | 2020-04-21 | 广东省智能制造研究所 | Cooperative robot compliance control method and system |
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| CN113618739A (en) * | 2021-08-24 | 2021-11-09 | 深圳市优必选科技股份有限公司 | Robot dynamic obstacle avoidance method and device and robot |
| CN113618739B (en) * | 2021-08-24 | 2022-07-29 | 深圳市优必选科技股份有限公司 | Robot dynamic obstacle avoidance method and device and robot |
| CN116061188A (en) * | 2023-03-07 | 2023-05-05 | 遨博(北京)智能科技股份有限公司 | Method and device for determining joint movement increment of robot |
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