CN105773609A  Robot kinematics calibration method based on vision measurement and distance error model  Google Patents
Robot kinematics calibration method based on vision measurement and distance error model Download PDFInfo
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 CN105773609A CN105773609A CN201610157552.2A CN201610157552A CN105773609A CN 105773609 A CN105773609 A CN 105773609A CN 201610157552 A CN201610157552 A CN 201610157552A CN 105773609 A CN105773609 A CN 105773609A
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Classifications

 B—PERFORMING OPERATIONS; TRANSPORTING
 B25—HAND TOOLS; PORTABLE POWERDRIVEN TOOLS; MANIPULATORS
 B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
 B25J9/00—Programmecontrolled manipulators
 B25J9/02—Programmecontrolled manipulators characterised by movement of the arms, e.g. cartesian coordinate type
 B25J9/04—Programmecontrolled manipulators characterised by movement of the arms, e.g. cartesian coordinate type by rotating at least one arm, excluding the head movement itself, e.g. cylindrical coordinate type or polar coordinate type
 B25J9/046—Revolute coordinate type

 B—PERFORMING OPERATIONS; TRANSPORTING
 B25—HAND TOOLS; PORTABLE POWERDRIVEN TOOLS; MANIPULATORS
 B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
 B25J9/00—Programmecontrolled manipulators
 B25J9/16—Programme controls
 B25J9/1602—Programme controls characterised by the control system, structure, architecture
 B25J9/1605—Simulation of manipulator layout, design, modelling of manipulator

 B—PERFORMING OPERATIONS; TRANSPORTING
 B25—HAND TOOLS; PORTABLE POWERDRIVEN TOOLS; MANIPULATORS
 B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
 B25J9/00—Programmecontrolled manipulators
 B25J9/16—Programme controls
 B25J9/1628—Programme controls characterised by the control loop
 B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis

 B—PERFORMING OPERATIONS; TRANSPORTING
 B25—HAND TOOLS; PORTABLE POWERDRIVEN TOOLS; MANIPULATORS
 B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
 B25J9/00—Programmecontrolled manipulators
 B25J9/16—Programme controls
 B25J9/1694—Programme controls characterised by use of sensors other than normal servofeedback from position, speed or acceleration sensors, perception control, multisensor controlled systems, sensor fusion
 B25J9/1697—Vision controlled systems
Abstract
The invention discloses a robot kinematics calibration method based on vision measurement and a distance error model. The method includes the steps that a corrected robot DH model is established; the distance error model is established; a robot kinematics calibration model is established; simultaneous calibration of a handeye relation and kinematics parameters is performed; measurement of an actual coordinate position of a tail end is performed; robot DH parameters are corrected; and experimental verification is conducted. The robot kinematics calibration method based on vision measurement and the distance error model and provided by the invention has the advantages of being simple, efficient and fast; a noncontact measurement mode of vision detection is adopted; meanwhile, repetitive errors of handeye calibration are considered, and the calibration model is simplified through a mode of an equidistance model; and accordingly, the positioning precision and distance precision of an industrial robot can be greatly improved, the robot kinematics calibration method is universally suitable for series connection jointtype robots, and certain practical significance is achieved.
Description
Technical field
The present invention relates to robot kinematics calibration technical field, particularly relate to a kind of viewbased access control model and measure and apart from by mistake
The industrial robot kinematics scaling method of differential mode type.
Background technology
Since in the world first robot produces, robot plays increasingly at life and the production field of people
Important effect.In real work, by controlling robot end's pose and the reality of robot end's arrival that software obtains
Error is there is between the pose on border.In general, the repetitive positioning accuracy of robot is the highest, and the absolute fix of robot is smart
Spend the highest.The reason causing robot absolute fix precision the highest have production, carry, the error assembled and joint transmission by mistake
Difference etc..But, in many fields of robot application, such as Complex Assembly, keep in repair, welding etc., due to the spy of themselves
Point, it is desirable to robot allows for reaching enough precision.Therefore, how to overcome the impact of various factors and improve as much as possible
The absolute fix precision of robot becomes a crucial part in Robotics.
Absolute fix precision is mainly affected by link parameters precision in robot kinematics's model, and calibration technique can
By the correction of robot kinematics's parameter being improved the absolute fix precision of robot.Therefore, need before robot uses
It is demarcated.The method of robot kinematics calibration mainly has two kinds at present: kinematics loop method and shaft centerline measurement method.
Kinematics loop method is the pose being obtained robot end by measurement apparatus, obtains by solving the kinematical equation of robot
The method of joint of robot parameter.Compared with shaft centerline measurement method, kinematics loop method process is simple, and workable, precision is more
High.
In tradition scaling method, when obtaining robot end's pose, generally use laser measuring apparatus, threecoordinates measuring machine
Etc. measurement apparatus, expensive, operation complexity.Vision measurement is used to have the advantages such as fast, the noncpntact measurement of measuring speed.But
When carrying out vision hand and eye calibrating, owing to employing the nominal value of the kinematics parameters of robot, so causing the position demarcating out
There is repetitive error in appearance.
Summary of the invention
The present invention is directed to the problems referred to above of the prior art, it is proposed that a kind of viewbased access control model is measured and range error model
Robot kinematics calibration method, is effectively increased the absolute fix precision of industrial robot.
To achieve these goals, the technical scheme that the embodiment of the present invention provides is as follows:
A kind of viewbased access control model is measured and the robot kinematics calibration method of range error model, and described method includes following
Step:
The robot DH model that S1, foundation are revised；
S2, range error model；
S3, set up robot kinematics calibration model；
S4, trick relation are demarcated with kinematics parameters simultaneously；
S5, end real coordinate position are measured；
S6, correction robot DH parameter and trick relation；
S7, experimental verification, it may be judged whether meet required precision, if meeting, then demarcate and terminate, if it is not, chosen position again
Point, by experimental result iteration, carries out calibration experiment again.
As a further improvement on the present invention, described step S1 is set up in the robot DH kinematics model revised, tradition
DH model adjacent segment coordinate system homogeneous transformation relational matrix is:
When the rotary shaft less parallel in adjacent two joints, need the rotation amount β introduced on the y axis to represent, constitute
The DH model revised, i.e. MDH model, then the transition matrix of adjacent segment coordinate system is:
Wherein, a is length of connecting rod, and α is connecting rod corner, and d is connecting rod offset distance, and θ is joint angle, and β is around the yaxis anglec of rotation.
As a further improvement on the present invention, described step S2 is set up range error model and is specifically included: robot end
Measured point coordinate in base coordinate system is P_{R}I (), the coordinate in measuring coordinate system is P_{RW}(i), the distance of any two points
Error can be expressed as:
Δ d (i+1)= I_{R}(i+1)I_{RW}(i+1)
Here,  I_{R}(i+1)  represent and on robot actual path, put P_{R}I () arrives P_{R}(i+1) distance；I_{RW}(i+1)  represent
P is put on robot instruction's track_{RW}I () arrives P_{RW}(i+1) distance.
The range error of adjacent pointtopoint transmission and the relation of site error can be expressed as:
d_{p}I () is certain point position deviation vector in base coordinate system, d_{p}(i)=P_{R}(i)P_{RW}(i)。
Under the influence of connecting rod geometric parameter error, the homogeneous transform matrix of adjacent links coordinate systemTo become
Differential disturbance homogeneous matrix is:
Then robot end's connecting rod relative to the transformation matrix of base coordinate system is:
Wherein,
Calculating abbreviation acquisition error matrix is:
Wherein the first three items of the 4th row is robot localization error dp [d_{x} d_{y} d_{z}]^{T}。
As a further improvement on the present invention, in described step S3, the formula of robot kinematics calibration model is:
Here, Δ d (i+1) is range error, and Δ q is robot kinematics's parameter error.
As a further improvement on the present invention, in described step S4, trick relation is demarcated with kinematics parameters simultaneously and is included:
Actual range d between the location point that robot actual motion is arrived_{W}(i+1) with use the error of having demarcating out
Distance d ' between the point of the position that the robot actual motion that trick relational matrix X calculates is arrived_{W}(i+1) relational expression is:
Distance d of point on robot instruction's track_{R}(i+1) distance and between the point of position that arrives of robot actual motion
d_{W}(i+1) relational expression between is:
Trick relation and kinematics parameters calibration formula simultaneously is:
As a further improvement on the present invention, described step S5 particularly as follows:
In robot working space, take any n point, record the coordinate value of each point, i.e. described instruction tracing point
P_{RW}(i).Utilize CCD camera to obtain the outer parameter matrix M of every width picture simultaneously, then obtain hand and eye calibrating matrix X.Then robot
End effector coordinate system is A=M relative to the position autocontrol of world coordinate system^{1}*X^{1}, first three is individual for the 4th row of position autocontrol A
Element is the world coordinates of end effector of robot, i.e. described actual path point P_{R}(i)。
In order to reduce calculating rounding error, use equidistant peg model when taking, make on robot motion's track adjacent
Distance between 2 is equal, then range error peg model is reduced to:
As a further improvement on the present invention, described step S6 particularly as follows:
By being measured by CCD camera of instruction trajectory coordinates value corresponding for each specified point in step S5 and correspondence thereof
To the Robot Handeye relation that is updated in step S4 of the actual path coordinate value of robot end with kinematics parameters simultaneously
Calibration formula, forms an equation group, and equation group is rewritten into matrix form, uses the basic theories of generalized inverse matrix to try to achieve
A young waiter in a wineshop or an inn takes advantage of solution, i.e. robot each connecting rod geometric parameter error amount Δ a_{i1}, Δ α_{i1}, Δ d_{i}, Δ θ_{i}, Δ β_{i}, and trick relation ginseng
Number error.Bring connecting rod geometric parameter error into each connecting rod to be modified, bring trick parameter error into trick matrix and repair
Just.
As a further improvement on the present invention, described step S7 is:
The trick relational matrix using connecting rod geometric parameter and the correction revised obtains corrected range error, carries out reality
Checking, is analyzed calculating to the result after experiment, it may be judged whether meet required precision, the most then demarcate and terminate, if it is not,
The most again chosen position point, carries out calibration experiment again.
Accompanying drawing explanation
Fig. 1 is the idiographic flow of the robot kinematics calibration method of viewbased access control model of the present invention measurement and range error model
Figure；
Fig. 2 is the DH kinematics model figure of sixshaft industrial robot in the specific embodiment of the invention；
Fig. 3 is the range error model schematic of robot in the specific embodiment of the invention；
Fig. 4 is that in the specific embodiment of the invention, robotic vision measures process schematic；
Equidistant model schematic when Fig. 5 is robot vision sampling site in the specific embodiment of the invention；
Detailed description of the invention
It is illustrated in figure 1 the flow chart element of the robot kinematics calibration method of viewbased access control model measurement and range error model
Figure, is described further the enforcement of the present invention below according to accompanying drawing and instantiation:
The robot DH model that S1, foundation are revised；
DH model is most basic robot kinematics's model, and it is to describe how to enter connecting rod and the joint of robot
The method of row modeling, is widely used in the configuration of any robot.Fig. 2 show the DH kinematics model figure of 6 axle robots,
Comprise 4 geometric parameters: length of connecting rod a, connecting rod corner α, connecting rod offset distance d, joint angle θ.Tradition DH model connecting rod i1 and company
Shown in following (1) formula of the adjacent segment coordinate system homogeneous transformation relational matrix of bar i:
But when the rotary shaft less parallel in adjacent two joints, certain error can be there is, absolute parallel in ideal
It is not exist in practice, even if two joint rotary shaft is the least from absolute parallel deviation, all can cause their common vertical line and reason
Think absolute parallel time the common vertical line that arbitrarily takes between there is great error.So needing to introduce rotation amount β on the y axis
Representing, constitute the DH model revised, i.e. MDH model, then the transition matrix of adjacent segment coordinate system is as follows shown in (2) formula:
Wherein, a is length of connecting rod, and α is connecting rod corner, and d is connecting rod offset distance, and θ is joint angle, and β is around the yaxis anglec of rotation.
S2, range error model；
Fig. 3 show range error model schematic, and robot end measured point coordinate in basis coordinates system is P_{R}
I (), the coordinate in measuring coordinate system is P_{RW}(i), formula (3) is the range error model of any two points:
Δ d (i+1)= I_{R}(i+1)I_{RW}(i+1) (3)
Here,  I_{R}(i+1)  represent and on robot actual path, put P_{R}I () arrives P_{R}(i+1) distance；I_{RW}(i+1)  represent
P is put on robot instruction's track_{RW}I () arrives P_{RW}(i+1) distance.
Shown in the range error of adjacent pointtopoint transmission and following (4) formula of the relation of site error:
d_{p}I () is certain point position deviation vector in base coordinate system, d_{p}(i)=P_{R}(i)P_{RW}(i)。
Owing to manufacturing and installation process exist partially between actual geometric parameter and the theoretical parameter value of joint of robot
Difference, the homogeneous transform matrix of adjacent links coordinate systemTo becomeFormula (5) is that the differential of adjacent links is disturbed
Dynamic homogeneous matrix:
Here,
Robot end's connecting rod is relative to shown in following (6) formula of the transformation matrix of base coordinate system:
Wherein,
Calculate abbreviation and obtain shown in following (7) formula of error matrix:
Wherein the first three items of the 4th row is robot localization error dp=[d_{x} d_{y} d_{z}]^{T}
S3, set up robot kinematics calibration model；
It is illustrated in figure 3 robot range error model schematic, for robot any two points in three dimensions, though
So they are different in basis coordinates system of robot and the coordinate values measured in coordinate system, but these 2 in robot basis coordinates
Distance in system and the distance in measuring coordinate system are identical.Utilize this feature, establish robot range error mark
Cover half type, shown in formula following (8):
Here, Δ d (i+1) is range error, and Δ q is robot kinematics's parameter error, B_{i}For coefficient matrix, can pass through
S2 solves.
S4, trick relation are demarcated with kinematics parameters simultaneously；
When carrying out vision measurement hand and eye calibrating, owing to employing the nominal value of robot kinematics's parameter, so causing
Demarcate pose out and there is repetitive error, right with the point on instruction track on the end effector of robot actual path tried to achieve
The world coordinates of the point of the position that the robot actual motion answered is arrived inaccuracy, it is necessary to this error is taken into account.In reality
Actual range d between robot two positions point in the motion of border_{W}(i+1) the trick relation square having error demarcating out with use
Distance d ' between the point of the position that the robot actual motion that battle array X calculates is arrived_{W}(i+1) relational expression is:
Distance d of point on robot instruction's track_{R}(i+1) distance and between the point of position that arrives of robot actual motion
d_{W}(i+1) relational expression between is:
Then shown in following (9) formula of trick relation and kinematics parameters calibration formula simultaneously:
S5, end real coordinate position are measured；
In robot working space, arbitrarily choose n point, record the coordinate value of each point, i.e. described instruction track
Point P_{RW}(i).Utilize CCD camera to obtain the outer parameter matrix M of every width picture simultaneously, then obtain hand and eye calibrating result X.Then machine
Robot end actuator coordinate system is A=M relative to the position autocontrol of world coordinate system^{1}*X^{1}, the 4th of position autocontrol A arranges first three
Individual element is the world coordinates of end effector of robot, i.e. described actual path point P_{R}I (), Fig. 4 is robot vision
Instrumentation plan.
In order to reduce calculating rounding error, using equidistant peg model when taking, Fig. 5 is the signal of equidistant sampling site model
Figure, makes on robot motion's track the distance between adjacent 2 equal, then range error peg model can be reduced to formula
(10):
S6, correction robot DH parameter and trick relation；
By being measured by CCD camera of instruction trajectory coordinates value corresponding for each specified point in step S5 and correspondence thereof
To the Robot Handeye relation that is updated in step S4 of the actual path coordinate value of robot end with kinematics parameters simultaneously
Calibration formula.
Obtained n1 equation by n point, form an equation group；
Equation group is rewritten into matrix form, uses the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. machine
People each connecting rod geometric parameter error amount Δ a_{i1}, Δ α_{i1}, Δ d_{i}, Δ θ_{i}, Δ β_{i}, and trick Relation Parameters error.Connecting rod is several
What parameter error is brought each connecting rod into and is modified, and brings trick parameter error into trick matrix and is modified.
S7, experimental verification
The trick relational matrix using connecting rod geometric parameter and the correction revised obtains corrected range error, carries out reality
Checking, is analyzed calculating to the result after experiment, and whether range error meets requirement, it is judged that whether robot meets precision
Requirement, the most then demarcate and terminate, if it is not, return step S5, ask for other experimental data point, again carry out calibration experiment, directly
Reach required precision.
Abovementioned viewbased access control model is measured and the robot kinematics calibration method of range error model, corrected by building
5 parameter DH models, make kinematics model more accurate.Have employed kinematics loop method build robot inaccuracy model, simply,
Efficiently, highly versatile.Asking for actual point position coordinates when, have employed the mode of vision measurement, have measuring speed fast,
The advantages such as noncpntact measurement.Mode that trick relation and kinematics parameters are demarcated simultaneously, it is to avoid repetitive error, substantially increases
The precision demarcated.
In sum, the viewbased access control model that the present invention provides is measured and the robot kinematics calibration method of range error model
Have simple, practical, efficiently, advantage efficiently, be generally applicable to the revolute robot that connects, be greatly improved industrial robot
Positioning precision and range accuracy.
The foregoing is only the preferred embodiments of the present invention, be not limited to the present invention；Skill for this area
For art personnel, the present invention can have various modifications and variations.All within the spirit and principles in the present invention, that is made any repaiies
Change, equivalent, improvement etc., should be included within the scope of the present invention.
Claims (8)
1. a viewbased access control model is measured and the robot kinematics calibration method of range error model, it is characterised in that described side
Method includes step:
The robot DH model that S1, foundation are revised；
S2, range error model；
S3, set up robot kinematics calibration model；
S4, trick relation are demarcated with kinematics parameters simultaneously；
S5, end real coordinate position are measured；
S6, correction robot DH parameter and trick relation；
S7, experimental verification, it may be judged whether meet required precision, if meeting, then demarcate and terminate, if it is not, chosen position point the most again,
Again carry out calibration experiment.
Method the most according to claim 1, it is characterised in that described step S1 sets up the robot DH kinematics revised
In model, in tradition DH model, adjacent segment coordinate system homogeneous transformation relational matrix is:
When the rotary shaft less parallel in adjacent two joints, need the rotation amount β introduced on the y axis to represent, constitute and revise
DH model, i.e. MDH model, then the transition matrix of adjacent segment coordinate system is:
Wherein, a is length of connecting rod, and α is connecting rod corner, and d is connecting rod offset distance, and θ is joint angle, and β is around the yaxis anglec of rotation.
Method the most according to claim 1, it is characterised in that described step S2 is set up range error model and specifically included:
Robot end measured point coordinate in base coordinate system is P_{R}I (), the coordinate in measuring coordinate system is P_{RW}(i), arbitrarily
The range error of 2 can be expressed as:
Δ d (i+1)= I_{R}(i+1)I_{RW}(i+1)
Here,  I_{R}(i+1)  represent and on robot actual path, put P_{R}I () arrives P_{R}(i+1) distance.I_{RW}(i+1)  represent machine
People instructs some P on track_{RW}I () arrives P_{RW}(i+1) distance.
The range error of adjacent pointtopoint transmission and the relation of site error are represented by:
Wherein, d_{p}I () is certain point position deviation vector in base coordinate system, d_{p}(i)=P_{R}(i)P_{RW}(i)。
Under the influence of connecting rod geometric parameter error, the homogeneous transform matrix of adjacent links coordinate systemTo become
Differential disturbance homogeneous matrix is:
Then robot end's connecting rod relative to the transformation matrix of base coordinate system is:
dT_{0} ^{i}=T_{0} ^{1}Δ_{1}T_{1} ^{i}+T_{0} ^{2}Δ_{2}T_{2} ^{i}+T_{0} ^{3}Δ_{3}T_{3} ^{i}+T_{0} ^{4}Δ_{4}T_{4} ^{i}+T_{0} ^{5}Δ_{5}T_{5} ^{i}+...+T_{0} ^{i}Δ_{i}
Here,
Calculating abbreviation acquisition error matrix is:
Wherein the first three items of the 4th row is robot localization error dp=[d_{x} d_{y} d_{z}]^{T}。
Method the most according to claim 3, it is characterised in that the public affairs of robot kinematics calibration model in described step S3
Formula is:
Here, Δ d (i+1) is range error, and Δ q is robot kinematics's parameter error.
Method the most according to claim 4, it is characterised in that in described step S4, trick relation is with kinematics parameters simultaneously
Demarcation includes: the actual range d between the location point that robot actual motion is arrived_{W}(i+1) with use demarcate out have error
The point of position that arrives of the robot actual motion that calculates of trick relational matrix X between distance d '_{W}(i+1) relational expression
For:
Distance d of point on robot instruction's track_{R}(i+1) distance d and between the point of position that arrives of robot actual motion_{W}(i+
1) relational expression between is:
Trick relation and kinematics parameters calibration formula simultaneously is:
Method the most according to claim 5, it is characterised in that described step S5 particularly as follows: in robot working space,
Choose n point, record the coordinate value of each point, i.e. described instruction tracing point P_{RW}(i).Utilize CCD camera to obtain every width simultaneously
The outer parameter matrix M of picture, then obtains hand and eye calibrating result X.Then end effector of robot coordinate system is sat relative to the world
The position autocontrol of mark system is A=M^{1}*X^{1}, the 4th first three element of row of position autocontrol A is the generation of end effector of robot
Boundary's coordinate, i.e. described actual path point P_{R}(i)。
In order to reduce calculating rounding error, use equidistant peg model when taking, make adjacent 2 points on robot motion's track
Between distance equal, then range error peg model can be reduced to:
Method the most according to claim 6, it is characterised in that described step S6 is particularly as follows: by each in step S5
Instruction trajectory coordinates value and the actual path of the robot end obtained by CCD camera measurement of correspondence thereof that specified point is corresponding are sat
The Robot Handeye relation that scale value is updated in step S4 and kinematics parameters calibration formula simultaneously, forms an equation group, will
Equation group is rewritten into matrix form, uses the basic theories of generalized inverse matrix to try to achieve least square solution, i.e. each connecting rod of robot is several
What parameter error value Δ a_{i1}, Δ α_{i1}, Δ d_{i}, Δ θ_{i}, Δ β_{i}, and trick Relation Parameters error.By connecting rod geometric parameter error
Bring each connecting rod into be modified, bring trick parameter error into trick matrix and be modified.
Method the most according to claim 7, it is characterised in that described step S7 is: use the connecting rod geometric parameter revised
Obtain corrected range error with the trick relational matrix revised, carry out experimental verification, the result after experiment is analyzed
Calculate, it may be judged whether meet required precision, the most then demarcate and terminate, if it is not, chosen position point the most again, again demarcate
Experiment.
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