CN102126219A - Fault-tolerant type motion planning method of redundancy mechanical arm - Google Patents

Fault-tolerant type motion planning method of redundancy mechanical arm Download PDF

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CN102126219A
CN102126219A CN 201010553189 CN201010553189A CN102126219A CN 102126219 A CN102126219 A CN 102126219A CN 201010553189 CN201010553189 CN 201010553189 CN 201010553189 A CN201010553189 A CN 201010553189A CN 102126219 A CN102126219 A CN 102126219A
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joint
mechanical arm
error
redundancy
fault
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CN102126219B (en
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张雨浓
李克讷
张智军
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Sun Yat Sen University
National Sun Yat Sen University
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Abstract

The invention provides a fault-tolerant type motion planning method of a redundancy mechanical arm, which comprises the following steps of: (1) determining a deadlocked joint caused by occurrence of a fault, and establishing a fault-tolerant type redundancy analysis scheme based on a secondary plan, wherein minimum performance indexes of the analysis scheme design are a speed vector, repeated motion or kinetic energy, a speed-restricted Jacobi matrix equation, joint velocity limit and joint angle limit, and the joint velocity limit changes as a joint angle changes; (2) solving the fault-tolerant type redundancy analysis scheme based on the secondary plan in the step (1) by using a numerical method; and (3) transmitting the solution of the step (2) to a lower computer controller to drive the mechanical arm to complete a given terminal task. The method is characterized in that: the automatic fault-tolerant processing can be performed and the given terminal task can be completed just by knowing the serial number and the locked angle of the deadlocked joint caused by occurrence of the fault.

Description

A kind of redundancy mechanical arm error-tolerance type motion planning method
Technical field
The present invention relates to redundant manipulator motion planning and control field, be specifically related to a kind of error-tolerance type motion planning method of redundancy mechanical arm.
Background technology
Redundancy mechanical arm is the terminal active mechanical device of a kind of free degree greater than the required least degree of freedom of task space, its motion task comprises welding, paint, assembling, excavation and drawing etc., is widely used in the national economy activities in production such as equipment manufacturing, product processing, machinery operation.The inverse kinematics problem of redundancy mechanical arm is meant the terminal pose of known mechanical arm, determines the joint angle problem of mechanical arm.When a certain joint of redundancy mechanical arm hinders (being equivalent to reduce the free degree of mechanical arm) when locked for some reason, with regard to general programme, the terminal task of just can't finish appointment of this mechanical arm according to the parsing scheme of being scheduled to; And the error-tolerance type redundancy is resolved scheme, exactly fault-tolerant processing (numbering, record locking angle and add is carried out in the joint that goes wrong
Figure 2010105531899100002DEST_PATH_IMAGE001
The type quadratic programming), make mechanical arm can finish given end track task.
Summary of the invention
Technical problem to be solved by this invention provides little, the error-tolerance type motion planning method when being used for redundancy mechanical arm generation knuckle failure of a kind of amount of calculation.
For solving the problems of the technologies described above, the present invention is achieved by the following technical programs:
1, a kind of redundancy mechanical arm error-tolerance type motion planning method comprises the steps:
1) determines to break down and locked joint occurs, promptly, by artificially or automatically detecting, the joint of sending out instruction any and not moving, foundation is resolved scheme based on the error-tolerance type redundancy of quadratic programming, the minimum performance index of described parsing conceptual design is velocity vector, repeating motion or kinetic energy, is tied in Jacobian matrix equation, the joint velocity limit and the joint angle limit of speed, and this joint velocity limit changes with joint angles;
2) the error-tolerance type redundancy parsing scheme utilization numerical method based on quadratic programming of step 1) is found the solution;
3) with step 2) solving result pass to the slave computer controller, the driving device arm is finished given terminal task.
2, redundancy mechanical arm error-tolerance type motion planning method, its parameter
Figure 439892DEST_PATH_IMAGE001
The status fault matrix (being used in scheme resolving persistent fault joint) of expression joint of mechanical arm locked joint numbering occurs according to breaking down, and adjusts the status fault matrix In respective element be 1(and
Figure 74453DEST_PATH_IMAGE001
In the surplus element in this Xingqi be 0).
3, in the redundancy mechanical arm error-tolerance type motion planning method, design its performance indications and be: minimize
Figure 2010105531899100002DEST_PATH_IMAGE002
, be tied in
Figure 2010105531899100002DEST_PATH_IMAGE003
,
Figure 2010105531899100002DEST_PATH_IMAGE004
, ,
Figure 2010105531899100002DEST_PATH_IMAGE006
, wherein
Figure 2010105531899100002DEST_PATH_IMAGE007
Expression joint velocity vector, With
Figure 2010105531899100002DEST_PATH_IMAGE009
Be the matrix and the vector of suitable dimension, subscript
Figure 2010105531899100002DEST_PATH_IMAGE010
The transposition of representing matrix and vector,
Figure 2010105531899100002DEST_PATH_IMAGE011
The Jacobian matrix of expression mechanical arm,
Figure 2010105531899100002DEST_PATH_IMAGE012
Expression joint angle vector, Expression mechanical arm end effector velocity vector,
Figure 282711DEST_PATH_IMAGE005
,
Figure 97084DEST_PATH_IMAGE006
Represent joint angle limit range and joint velocity limit range respectively,
Figure 2010105531899100002DEST_PATH_IMAGE014
Expression joint angle bound,
Figure 2010105531899100002DEST_PATH_IMAGE015
Expression joint velocity bound.
4, above-mentioned error-tolerance type motion planning method is converted into a standard quadratic programming; That is, minimize
Figure 2010105531899100002DEST_PATH_IMAGE016
, be tied in , , wherein
Figure 2010105531899100002DEST_PATH_IMAGE019
,
Figure 2010105531899100002DEST_PATH_IMAGE020
,
Figure 2010105531899100002DEST_PATH_IMAGE021
,
Figure 2010105531899100002DEST_PATH_IMAGE022
,
Figure 2010105531899100002DEST_PATH_IMAGE023
, positive constant
Figure 2010105531899100002DEST_PATH_IMAGE024
Be used for regulating and guaranteeing the enough big feasible zone of joint velocity.
5, described standard quadratic programming is equivalent to a linear projection equation
Figure 2010105531899100002DEST_PATH_IMAGE025
, wherein Be the space
Figure 2010105531899100002DEST_PATH_IMAGE027
To set
Figure 2010105531899100002DEST_PATH_IMAGE028
The piecewise linearity projection operator,
Figure 2010105531899100002DEST_PATH_IMAGE029
Be the dimension of cartesian space,
Figure 2010105531899100002DEST_PATH_IMAGE030
Be the dimension of joint space,
Figure 2010105531899100002DEST_PATH_IMAGE031
Represent former dual variable,
Figure 2010105531899100002DEST_PATH_IMAGE032
Represent former dual variable limit inferior,
Figure 2010105531899100002DEST_PATH_IMAGE033
Represent former dual variable limes superiors, former dual variable
Figure 480398DEST_PATH_IMAGE031
And bound is defined as follows:
Figure 2010105531899100002DEST_PATH_IMAGE034
，
Figure 2010105531899100002DEST_PATH_IMAGE035
，
Figure 2010105531899100002DEST_PATH_IMAGE036
；
Wherein
Figure 2010105531899100002DEST_PATH_IMAGE037
Be corresponding to equality constraint The antithesis decision vector,
Figure 2010105531899100002DEST_PATH_IMAGE038
Be that element all is 1 respective dimension number vector; Be enough big constant, be used for substituting on the numerical value infinitely great
Figure 2010105531899100002DEST_PATH_IMAGE040
, and augmented matrix Be defined as follows:
Figure 2010105531899100002DEST_PATH_IMAGE042
；
Then, the linear projection equation is found the solution with numerical method, designs its error of calculation to be
Figure 2010105531899100002DEST_PATH_IMAGE043
: when error is zero, its correspondence
Figure 762311DEST_PATH_IMAGE031
Value is separating of piecewise linearity equation just, before it
Figure 2010105531899100002DEST_PATH_IMAGE044
Individual element is formed separating of quadratic programming
Figure 2010105531899100002DEST_PATH_IMAGE045
, given initial value , obtain by following iteration
Figure 368872DEST_PATH_IMAGE031
Make error
Figure 2010105531899100002DEST_PATH_IMAGE047
Reach default precision: , wherein
Figure 2010105531899100002DEST_PATH_IMAGE049
, With
Figure 2010105531899100002DEST_PATH_IMAGE051
Be defined as respectively
Figure 2010105531899100002DEST_PATH_IMAGE052
,
Figure 2010105531899100002DEST_PATH_IMAGE053
,, obtain piecewise linearity projection equation by the continuous iteration of algorithm
Figure 2010105531899100002DEST_PATH_IMAGE054
Separate, thereby obtain the optimal solution of redundancy mechanical arm error-tolerance type motion planning.
Compared with prior art, the present invention has following advantage:
, break down when locked when a certain joint of redundancy mechanical arm in the past, and needed the redesign scheme usually or utilize to optimize algorithm and constantly regulate parameter to adapt to the last free degree, process is comparatively loaded down with trivial details.The present invention only need know joint numbering and the locking angle that breaks down locked, just can carry out automatic fault tolerant handles, finish given terminal task, thereby avoided redesigning the additional workload that is brought and optimized the complicated processes that parameter was constantly soundd out/adjusted to algorithm.
Description of drawings
Fig. 1 is a flow chart of the present invention;
Fig. 2 is the concrete mechanical arm three-dimensional model diagram of the present invention of implementing;
Fig. 3 is for realizing redundancy mechanical arm error-tolerance type motion planning schematic diagram of the present invention.
The specific embodiment
The present invention is described further below in conjunction with accompanying drawing.
Redundancy mechanical arm error-tolerance type motion planning method shown in Figure 1 is mainly by definite fault joint, set up based on the error-tolerance type redundancy of quadratic programming resolve scheme 1, utilization numerical method to the quadratic programming scheme find the solution 2, slave computer controller 3 and mechanical arm 4 form.
Fig. 2 has showed and has realized that mechanical arm of the present invention is the mechanical arm of a plane six degree of freedom.This mechanical arm is made up of six connecting rods, is connected by joint 5, joint 6, joint 7, joint 8, joint 9 and joint 10.11 tracks of being finished for the mechanical arm end.In the present invention, this joint of mechanical arm 5-10 initial angle is set to Radian, its joint angles limes superiors is set to
Figure DEST_PATH_IMAGE056
Radian, its joint angles limit inferior is set to
Figure DEST_PATH_IMAGE057
Radian, the length of connecting rod of this plane six degree of freedom redundancy mechanical arm
Figure DEST_PATH_IMAGE058
Rice.
Fig. 3 is for realizing the fault-tolerant movement locus schematic diagram of redundancy mechanical arm of the present invention.In this concrete example, the task of mechanical arm is equilateral triangle of picture, and joint of mechanical arm 9 is locked because of breaking down, and its angle value in whole task implementation remains
Figure DEST_PATH_IMAGE059
Radian.Adopt redundancy mechanical arm error-tolerance type motion planning method, that is: according to the numbering configuration of fault joint
Figure DEST_PATH_IMAGE060
, and utilization quadratic programming numerical method is found the solution.Send the result who calculates to the mechanical arm controller, thereby the control mechanical arm is finished the end orbit task, as shown in Figure 3.
Be the present invention below about redundancy mechanical arm error-tolerance type motion planning method:
Figure 2010105531899A00800041
Wherein,
Figure 65378DEST_PATH_IMAGE002
Be the exercise performance index of desire optimization, Expression joint velocity vector,
Figure 736848DEST_PATH_IMAGE008
With
Figure 11971DEST_PATH_IMAGE009
Be the matrix and the vector of suitable dimension, subscript
Figure 593126DEST_PATH_IMAGE010
The transposition of representing matrix and vector, equality constraint
Figure 928292DEST_PATH_IMAGE003
The terminal movement locus of corresponding mechanical arm,
Figure 657214DEST_PATH_IMAGE011
The Jacobian matrix of expression mechanical arm,
Figure 670781DEST_PATH_IMAGE001
The status fault matrix (being used for) of expression joint of mechanical arm in scheme resolving persistent fault joint, Expression joint angle vector,
Figure 940406DEST_PATH_IMAGE013
Corresponding mechanical arm end effector velocity vector,
Figure 891044DEST_PATH_IMAGE005
,
Figure 711233DEST_PATH_IMAGE006
Represent joint angle limit range and joint velocity limit range respectively,
Figure 63717DEST_PATH_IMAGE014
Expression joint angle bound, Expression joint velocity bound.It is worthy of note that the joint velocity limit herein is along with joint angle changes.
Consider that above-mentioned optimization problem is to find the solution on velocity layer, therefore need joint angles constraint (4), the joint velocity constraint (5) of mechanical arm are merged, thereby can obtain based on speed
Figure DEST_PATH_IMAGE063
The both-end inequality constraints:
img?id="idf0010"?file="2010105531899A00800049.GIF"?wi="139"?he="6"?top="138"?left="25"?img-content="drawing"?img-format="GIF"?orientation="portrait"?inline="no"/>
Wherein,
Figure DEST_PATH_IMAGE065
With
Figure DEST_PATH_IMAGE066
In
Figure 381882DEST_PATH_IMAGE067
Individual element is defined as respectively: , Positive constant
Figure 326202DEST_PATH_IMAGE024
(as being taken as 4) is used for regulating the feasible zone of joint velocity.With
Figure 251432DEST_PATH_IMAGE045
The joint velocity of expression mechanical arm , mechanical arm quadratic form prioritization scheme (1)-(5) of band physical constraint just can be described as following standard quadratic programming scheme:
Figure 2010105531899A008000413
Wherein
Figure 137480DEST_PATH_IMAGE019
,
Figure 319063DEST_PATH_IMAGE020
,
Figure DEST_PATH_IMAGE068
In this specific embodiment, can choose
Figure 508736DEST_PATH_IMAGE008
Be unit matrix,
Figure DEST_PATH_IMAGE069
Above-mentioned standard quadratic programming can be converted into a linear projection equation
Figure 346242DEST_PATH_IMAGE025
Find the solution, wherein
Figure 912352DEST_PATH_IMAGE026
Be the space
Figure 214020DEST_PATH_IMAGE027
To set
Figure 512278DEST_PATH_IMAGE028
The piecewise linearity projection operator,
Figure 899397DEST_PATH_IMAGE029
Be the dimension of cartesian space,
Figure 269198DEST_PATH_IMAGE030
Be the dimension of joint space,
Figure 159794DEST_PATH_IMAGE031
Represent former dual variable,
Figure 885743DEST_PATH_IMAGE032
Represent former dual variable limit inferior, Represent former dual variable limes superiors, former dual variable
Figure 668071DEST_PATH_IMAGE031
And bound is defined as follows:
Figure 678752DEST_PATH_IMAGE034
，
Figure 584391DEST_PATH_IMAGE035
，
Figure 680523DEST_PATH_IMAGE036
；
Wherein
Figure 392127DEST_PATH_IMAGE037
Be corresponding to equality constraint
Figure 257315DEST_PATH_IMAGE017
The antithesis decision vector,
Figure 333856DEST_PATH_IMAGE038
Be that element all is 1 respective dimension number vector;
Figure 917284DEST_PATH_IMAGE039
Be enough big constant, be used for substituting on the numerical value infinitely great , and augmented matrix Be defined as follows:
Figure 399715DEST_PATH_IMAGE042
。
Then, the linear projection equation is found the solution with numerical method.Designing its error of calculation is
Figure 470439DEST_PATH_IMAGE043
: when error is zero, its correspondence
Figure 523845DEST_PATH_IMAGE031
Value is separating of piecewise linearity equation just, before it
Figure 363625DEST_PATH_IMAGE044
Individual element is formed separating of quadratic programming
Figure 781968DEST_PATH_IMAGE045
Given initial value
Figure 74410DEST_PATH_IMAGE046
, obtain by following iteration
Figure 931507DEST_PATH_IMAGE031
Make error
Figure 625794DEST_PATH_IMAGE047
Reach default precision:
Figure 215038DEST_PATH_IMAGE048
, wherein
Figure 260354DEST_PATH_IMAGE049
, With Be defined as respectively
Figure 230081DEST_PATH_IMAGE052
,
Figure 497115DEST_PATH_IMAGE053
,, just can obtain piecewise linearity projection equation by the continuous iteration of algorithm (general) for several times to hundreds of times
Figure 696015DEST_PATH_IMAGE054
Separate, thereby obtain the optimal solution of redundancy mechanical arm error-tolerance type motion planning.

Claims (6)

1. a redundancy mechanical arm error-tolerance type motion planning method is characterized in that comprising the steps:
1) determines to break down and locked joint occurs, foundation is resolved scheme based on the error-tolerance type redundancy of quadratic programming, the minimum performance index of described parsing conceptual design is velocity vector, repeating motion or kinetic energy, be tied in Jacobian matrix equation, the joint velocity limit and the joint angle limit of speed, this joint velocity limit changes with joint angles;
2) the error-tolerance type redundancy parsing scheme utilization numerical method based on quadratic programming of step 1) is found the solution;
3) with step 2) solving result pass to the slave computer controller, the driving device arm is finished given terminal task.
2. redundancy mechanical arm error-tolerance type motion planning method according to claim 1 is characterized in that: resolving conceptual design based on the error-tolerance type redundancy of quadratic programming in the described step 1) is: minimize
Figure DEST_PATH_IMAGE001
, be tied in
Figure DEST_PATH_IMAGE002
,
Figure DEST_PATH_IMAGE003
,
Figure DEST_PATH_IMAGE004
,
Figure DEST_PATH_IMAGE005
, wherein
Figure 457774DEST_PATH_IMAGE001
Be the exercise performance index of desire optimization,
Figure DEST_PATH_IMAGE006
Expression joint velocity vector, With
Figure DEST_PATH_IMAGE008
Be the matrix and the vector of suitable dimension, subscript
Figure DEST_PATH_IMAGE009
The transposition of representing matrix and vector, equality constraint The terminal movement locus of corresponding mechanical arm,
Figure DEST_PATH_IMAGE010
The Jacobian matrix of expression mechanical arm,
Figure DEST_PATH_IMAGE011
Expression joint angle vector,
Figure DEST_PATH_IMAGE012
Expression mechanical arm end effector velocity vector, ,
Figure 21107DEST_PATH_IMAGE005
Represent joint angle scope and joint velocity scope respectively,
Figure DEST_PATH_IMAGE013
Expression joint angle bound,
Figure DEST_PATH_IMAGE014
Expression joint velocity bound,
Figure DEST_PATH_IMAGE015
The status fault matrix of expression joint of mechanical arm is used for determining the fault joint in the parsing scheme.
3. redundancy mechanical arm error-tolerance type motion planning method according to claim 2 is characterized in that: described status fault matrix
Figure 482176DEST_PATH_IMAGE015
, locked joint numbering appears according to breaking down, adjust the status fault matrix
Figure 912020DEST_PATH_IMAGE015
In respective element be 1, and
Figure 888066DEST_PATH_IMAGE015
In the surplus element in this Xingqi be 0.
4. redundancy mechanical arm error-tolerance type motion planning method according to claim 2, it is characterized in that: in the error-tolerance type redundancy parsing scheme based on quadratic programming of described step 1), described error-tolerance type motion planning method is converted into a standard quadratic programming: minimize
Figure DEST_PATH_IMAGE016
, be tied in
Figure DEST_PATH_IMAGE017
,
Figure DEST_PATH_IMAGE018
, wherein
Figure DEST_PATH_IMAGE019
,
Figure DEST_PATH_IMAGE020
,
Figure DEST_PATH_IMAGE021
, ,
Figure DEST_PATH_IMAGE023
, positive constant
Figure DEST_PATH_IMAGE024
Be used for regulating and guaranteeing the enough big feasible zone of joint velocity.
5. redundancy mechanical arm error-tolerance type motion planning method according to claim 4 is characterized in that: described standard quadratic programming is equivalent to a linear projection equation
Figure DEST_PATH_IMAGE025
, wherein Be the space
Figure DEST_PATH_IMAGE027
To set
Figure DEST_PATH_IMAGE028
The piecewise linearity projection operator,
Figure DEST_PATH_IMAGE029
Be the dimension of cartesian space,
Figure DEST_PATH_IMAGE030
Be the dimension of joint space,
Figure DEST_PATH_IMAGE031
Represent former dual variable,
Figure DEST_PATH_IMAGE032
Represent former dual variable limit inferior,
Figure DEST_PATH_IMAGE033
Represent former dual variable limes superiors, former dual variable
Figure 989621DEST_PATH_IMAGE031
And bound is defined as follows:
Figure DEST_PATH_IMAGE034
，
Figure DEST_PATH_IMAGE035
， ；
Wherein
Figure DEST_PATH_IMAGE037
Be corresponding to equality constraint
Figure 570775DEST_PATH_IMAGE017
The antithesis decision vector,
Figure DEST_PATH_IMAGE038
Be that element all is 1 respective dimension number vector;
Figure DEST_PATH_IMAGE039
Be enough big constant, be used for substituting on the numerical value infinitely great
Figure DEST_PATH_IMAGE040
, and augmented matrix
Figure DEST_PATH_IMAGE041
Be defined as follows:
Figure DEST_PATH_IMAGE042
；
Then, the linear projection equation is found the solution with numerical method.
6. linear projection equation according to claim 5 is characterized in that: designing its error of calculation is
Figure DEST_PATH_IMAGE043
: when error is zero, its correspondence
Figure 781308DEST_PATH_IMAGE031
Value is separating of piecewise linearity equation just, before it Individual element is formed separating of quadratic programming , given initial value
Figure DEST_PATH_IMAGE046
, obtain by following iteration
Figure 450842DEST_PATH_IMAGE031
Make error
Figure DEST_PATH_IMAGE047
Reach default precision:
Figure DEST_PATH_IMAGE048
, wherein
Figure DEST_PATH_IMAGE049
,
Figure DEST_PATH_IMAGE050
With
Figure DEST_PATH_IMAGE051
Be defined as respectively
Figure DEST_PATH_IMAGE052
,
Figure DEST_PATH_IMAGE053
,, obtain piecewise linearity projection equation by the continuous iteration of algorithm Separate, thereby obtain the optimal solution of redundancy mechanical arm error-tolerance type motion planning.
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