CN109397249A - The two dimensional code positioning crawl robot system algorithm of view-based access control model identification - Google Patents
The two dimensional code positioning crawl robot system algorithm of view-based access control model identification Download PDFInfo
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- CN109397249A CN109397249A CN201910011866.5A CN201910011866A CN109397249A CN 109397249 A CN109397249 A CN 109397249A CN 201910011866 A CN201910011866 A CN 201910011866A CN 109397249 A CN109397249 A CN 109397249A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J5/00—Manipulators mounted on wheels or on carriages
- B25J5/007—Manipulators mounted on wheels or on carriages mounted on wheels
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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
- B25J9/10—Programme-controlled manipulators characterised by positioning means for manipulator elements
- B25J9/106—Programme-controlled manipulators characterised by positioning means for manipulator elements with articulated links
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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
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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
- B25J9/1694—Programme controls characterised by use of sensors other than normal servo-feedback from position, speed or acceleration sensors, perception control, multi-sensor controlled systems, sensor fusion
- B25J9/1697—Vision controlled systems
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Abstract
The invention discloses a kind of two dimensional code positioning crawl robot system algorithms of view-based access control model identification, comprising the following steps: s1. identification is crawled object equipped with two dimensional code；S2. the posture information of the two dimensional code geometric center is extracted；S3. it is set to the static target value of the two dimensional code relative pose；The deviation between current time two dimensional code pose and the pose target of setting is calculated, and the threshold value of the deviation and setting is compared；If deviation is more than threshold value, combine pid algorithm, convert velocity information for deviation information, and according to the velocity information control wheat take turns platform move to it is static after pose target；If deviation is less than threshold value, keep wheat wheel platform static；S4. the inverse kinematics that mechanical arm is carried out using the two dimensional code posture information, make the central clamp position of mechanical arm tail end manipulator reach two dimensional code center；By coordinate transform, the corner of mechanical arm driving motor is solved；Driving motor export the corner drive robot arm end effector move to be crawled object after complete holding action.
Description
Technical field
The present invention relates to multi-freedom robot control algolithm field, in particular to a kind of view-based access control model identification two dimensional code
The running fix of Omni-mobile platform and four-degree-of-freedom mechanical arm grasping algorithm.
Background technique
The mobile robot autonomous navigation of view-based access control model refers to that the image capturing system of mobile robot platform obtains machine
Environmental information under people's current state determines the position of environmental objects and robot in the environment by analyzing ambient image.
Since image has high-resolution, environmental information is complete, meets the cognition habit of the mankind, therefore, in recent years, view-based access control model
Mobile robot autonomous navigation is obtained extensive concern and approval, and obtained in terms of theory and practice it is considerable at
Fruit.In the prior art, the algorithm that moving trolley positioning is realized based on two dimensional code is had existed, for controlling moving trolley to mesh
It is mobile to mark two dimensional code.In addition, in the prior art, researcher combines machine vision and mechanical arm, increase for mechanical arm
" eyes " of intelligence, can greatly increase the environment sensing ability and intelligent decision ability of mechanical arm, keep mechanical arm light
Pine nut shows the movement such as crawl and placement of article.But the vision for combining mechanical arm with mobile platform is found no at present and is known
Other grasping algorithm；
Therefore, it is necessary to a kind of two dimensional code positioning crawl robot system algorithm of view-based access control model identification, algorithm combination PID
The mobile platform location algorithm and mechanical arm inverse kinematics of algorithm improve the solution efficiency of the inverse solution of mechanical arm, more traditional
The fixed mechanical arm of pedestal, is used in combination mechanical arm and mobile platform, increases the opereating specification and dexterity of action of mechanical arm, adopt
It is positioned with two dimensional code, promotes crawl success rate.
Summary of the invention
In view of this, the present invention in view of the drawbacks of the prior art, provides a kind of two dimensional code positioning of view-based access control model identification
Robot system algorithm is grabbed, which realizes the running fix grasping movement of view-based access control model identification two dimensional code, is able to quickly complete
At the crawl of distant object, increase the crawl range of conventional base solid mechanical arm, the flexibility of hoisting machine people.
The two dimensional code positioning crawl robot system algorithm of view-based access control model identification of the invention, comprising the following steps:
S1. identification is crawled object equipped with two dimensional code；S2. the posture information of the two dimensional code geometric center is extracted；s3.
It is set to the static target value of the two dimensional code relative pose；Calculate current time two dimensional code pose and setting pose target it
Between deviation, and the threshold value of the deviation and setting is compared；If deviation is more than threshold value, in conjunction with pid algorithm, by deviation information
Be converted into velocity information, and according to the velocity information control wheat wheel platform move to it is static after pose target；If deviation is less than
Threshold value then keeps wheat wheel platform static；S4. the inverse kinematics that mechanical arm is carried out using the two dimensional code posture information, are made
The central clamp position of mechanical arm tail end manipulator reaches two dimensional code center；By coordinate transform, mechanical arm driving electricity is solved
The corner of machine；Driving motor export the corner drive robot arm end effector move to be crawled object after to complete clamping dynamic
Make；
Further, it in step s2, using open source two dimensional code recognizer software package ar_track_alvar or visp, mentions
Take the posture information [x of two dimensional code geometric centercurrent ycurrent zcurrent]TAnd four element [qxcurrent qycurrent
qzcurrent qwcurrent]T；
Further, step s3 includes:
S31. pass through the four elements [qxcurrent qycurrent qzcurrent qwcurrent]TObtain two dimensional code geometric center
Yaw angle yawcurrent,
S32. [x is setgoal ygoal yawgoal]TObject pose between camera and two dimensional code；Set [xthreshold
ythreshold yawthreshold]TDifference threshold limit value between current two-dimension pose and the object pose of setting；Setting
[xoffset yoffset yawoffset]T (t)For the deviation between current time two dimensional code pose and the object pose of setting；Set [vx
vy wz]T (t)For camera coordinates system OcameraUnder XYZ, current time wheat takes turns the speed of mobile platform geometric center；
S33. deviation [the x between current time two dimensional code pose and the object pose of setting is calculatedoffset yoffset
yawoffset]T (t), its calculation formula is:
If deviation [the x s34. between current time two dimensional code pose and the object pose of settingoffset yoffset
yawoffset]T (t)More than the threshold value [xoffset yoffset yawoffset]T (t), then the speed of mobile platform geometric center is taken turns according to wheat
Spend [vx vy wz]T (t)Wheat wheel platform movement is controlled, in conjunction with pid algorithm, takes turns platform to target point movement, the wheat to accelerate wheat
Take turns the speed [v of mobile platform geometric centerx vy wz]T (t)Calculation formula it is as follows
If deviation [the x between current time two dimensional code pose and the object pose of settingoffset yoffset yawoffset]T (t)
Less than the threshold value [xoffset yoffset yawoffset]T (t), then wheat wheel platform remain stationary state, i.e.,
S35. by camera coordinates system OcameraThe velocity information of XYZ transforms to wheat wheel platform coordinate system Omecanum_baseXYZ becomes
Change formula are as follows:
Wherein,Indicate O under camera coordinates systemcameraThe speed that XYZ is acquired；
Indicate O under wheat wheel platform coordinate systemmecanum_baseXYZ, wheat take turns the speed in the platform centre of motion.
S36. according to the velocity information of obtained wheat wheel platform geometric centerBe converted to each Mecanum wheel
Angular speed [w0 w1 w2 w3]T, conversion formula are as follows:
Wherein, a is the width that wheat takes turns platform, and b is the length that wheat takes turns platform, and R is the radius that wheat takes turns bull wheel.
S37. angular speed [the w that will be solved0 w1 w2 w3]TIt is respectively transmitted the motor taken turns to control wheat, driving wheat takes turns platform
Movement；
Further, step s4 includes:
S41. H point is solved in camera coordinates system OcameraThe position of XYZ, solution formula are as follows:
cameraH=[cameraxcurrent-LGH cameraycurrent camerazcurrent]T；
H point is solved in mechanical arm pedestal rotating coordinate system Oarm_baseThe position of XYZ:
Mechanical arm local coordinate system MlocalThe X-axis and mechanical arm pedestal rotating coordinate system O of XYZarm_baseThe folder of the y-axis of XYZ
Angle
S42. solution point H is in mechanical arm local coordinate system MlocalThe position of XYZ:
localHy=0；
localHz=arm_baseHz-la_l；
Wherein, da_lFor mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalBoth XYZ Z axis it
Between distance；
la_lFor mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalThe X0Y plane of both XYZ exists
Distance in Z-direction；
S43. L is solved1In mechanical arm local coordinate system MlocalThe angle of XYZ and X-axis1,
Solve L2In mechanical arm local coordinate system MlocalThe angle of XYZ and X-axis2,
Wherein,
Beneficial effects of the present invention: the two dimensional code positioning crawl robot system identified using view-based access control model of the invention is calculated
Method increases range, efficiency and the flexibility of mechanical arm crawl, simultaneously by the coordinated between mobile platform and mechanical arm
It is lower compared with industrial mechanical arm cost.
Detailed description of the invention
The invention will be further described with reference to the accompanying drawings and examples.
Fig. 1 is mobile crawl robot structural schematic diagram of the invention；
Fig. 2 is the pose schematic diagram of two dimensional code of the invention under camera coordinates system；
Fig. 3 is that camera of the invention-wheat takes turns platform coordinate relation schematic diagram；
Fig. 4 is that wheat of the invention takes turns platform structure schematic diagram；
Fig. 5 is mechanical arm mechanism schematic diagram of the invention；
Fig. 6 is mechanical arm pedestal rotating coordinate system O in the present inventionarm_baseXYZ and its local coordinate system MlocalXYZ relationship
Schematic diagram；
Fig. 7 is mechanical arm part the computation of inverse- kinematics schematic diagram of the invention；
Fig. 8 is algorithm flow chart of the invention.
Specific embodiment
1 mobile crawl robot structural schematic diagram
As shown in Figure 1, robot obtains image in 2 D code by the camera being fixed on wheat wheel platform, and is known by related
Other algorithm extracts posture information, and then controls the movement of wheat wheel platform and the movement of mechanical arm, is finally completed and posts two dimensional code mark
The crawl task of the object of label.Mainly include 3 parts in Fig. 1: (hereinafter wheat wheel is flat for 1. Mecanum wheel Omni-mobile platforms
Platform)；2. camera；3. four-degree-of-freedom mechanical arm.
2 two dimensional code position auto―controls obtain
By ar_track_alvar or VISP open source algorithm packet, the position auto―control of two dimensional code can be calculated in real time, is had
Body is as follows: as shown in Fig. 2,
[xcurrent ycurrent zcurrent]T: spatial position of the two dimensional code geometric center under camera coordinates system；
[qxcurrent qycurrent qzcurrent qwcurrent]T: four elements of the two dimensional code geometric center under camera coordinates system
(angle).
3 wheats take turns platform running fix
When wheat wheel platform apart from two dimensional code farther out when, need the relative positional relationship of the two being converted to velocity information, with
Control wheat wheel platform is moved to the target position of relative two dimensional code.
The two dimensional code geometric center posture information extracted by above-mentioned open source algorithm packet, is converted into two dimensional code by four elements
The yaw angle yaw of geometric centercurrent, calculation formula is as follows:
By two dimensional code with respect to camera pose parameter [x y yaw]T, it is translated into velocity information and is sent to wheat wheel movement
Platform, such as Fig. 3, specific conversion process are as follows:
Setting: [xgoal ygoal yawgoal]T: indicate the position for being finally reached balance (static) between camera and two dimensional code
Appearance target value (needs to set reasonable value in a program)；
[xthreshold ythreshold yawthreshold]T: it indicates between current two-dimension pose and the pose target value of setting
Difference threshold limit value (needs to set reasonable value in a program)；
[xoffset yoffset yawoffset]T (t): it indicates between current time two dimensional code pose and the pose target value of setting
Deviation；
[vx vy wz]T (t): O under camera coordinates systemcameraXYZ, current time wheat take turns the speed of mobile platform geometric center；
Calculate t moment, the deviation of target value and current value (the current pose of two dimensional code),
That is:
If threshold value (wheat take turns platform apart from two dimensional code too far) of the deviation beyond setting,
That is:
Wheat wheel platform movement is then controlled, in conjunction with pid algorithm, takes turns platform to target point movement to accelerate wheat, calculation formula is such as
Under (by pid regulator parameters, to reach optimum efficiency):
Otherwise wheat wheel platform remain stationary state,
That is:
Camera coordinates system OcameraXYZ and wheat take turns platform coordinate system Omecanum_baseXYZ is different, needs to be coordinately transformed,
By camera coordinates system OcameraThe velocity information of XYZ is transformed into wheat wheel platform coordinate system Omecanum_baseXYZ, it is as follows
Indicate O under camera coordinates systemcameraThe speed that XYZ is acquired
Indicate O under wheat wheel platform coordinate systemmecanum_baseXYZ, wheat take turns the speed in the platform centre of motion
The coordinate of velocity information between the two is transformed to
4 wheats take turns platform inverse kinematics equation
The velocity information that wheat is taken turns to the wheat wheel platform geometric center solved in platform running fix is converted to each wheat
The angular speed of Ke Namu wheel, detailed process is as follows
As shown in figure 4, wheat takes turns platform according to " interior eight " mode is arranged four wheats wheel, and O is establishedmecanum_baseXYZ coordinate system,
Four wheat wheels, marked as 0,1,2,3, platform geometric center O are defined counterclockwisemecanum_baseMovement velocity indicate are as follows:
[Vc w]T
Vc: geometric center Omecanum_baseLinear velocity；
W: geometric center Omecanum_baseAngular speed；
A: the width of wheat wheel platform；
B: the length of wheat wheel platform；
R: the radius of wheat wheel bull wheel；
[V0 V1 V2 V3]: respectively represent the velocity vector of four wheats wheel.
As can be seen from Figure 4, by resolution of velocity method, the speed general formula of single wheat wheel can be by following calculating:
Further solve the rotational angular velocity of single wheat wheel:
Equation is solved in the speed of t moment are as follows:
Angular speed [the w that will be solved in above formula0 w1 w2 w3]TIt is respectively transmitted the motor taken turns to control wheat, realizes that wheat wheel is flat
The movement of platform.
5 four-degree-of-freedom mechanical arm inverse kinematics
Target position ([x is moved in wheat wheel platformgoal ygoal yawgoal]T) after, it just controls mechanical arm crawl and posts two
The object of code label is tieed up, specific grasping algorithm is as follows:
Mechanical arm configuration uses the structure of the four-degree-of-freedom (including mechanical paw) of the DOBOT and UARM mechanical arm of open source,
Have many advantages, such as that kinematic accuracy is high, load capacity is strong, but presently, there are document in, nearly all using DH method come calculating machine arm
Inverse kinematics equation, solution procedure speed is compared with slow, method is more complex, thus the ingenious geometrical constraint using its structure of this algorithm
Relationship solves the movement angle in three joints of mechanical arm.
As shown in figure 5, including three coordinate systems: camera coordinates system OcameraXYZ, mechanical arm pedestal rotating coordinate system
Oarm_baseXYZ and mechanical arm local coordinate system MlocalXYZ, G indicate " tiger's jaw " center of mechanical paw, that is to say that two dimensional code is several
What center position, mechanical paw HG remain horizontal attitude (geometrical constraint: α1=α2+α3), the structure ginseng of mechanical arm
Relative positional relationship and G point between number, above three coordinate system is in camera coordinates system OcameraThe position of XYZ be it is known,
To solve Inverse Kinematics Solution [θ1 θ2 θ3]T。
Each parameter is following (in conjunction with Fig. 5 and Fig. 6):
θ1: indicate L1In mechanical arm local coordinate system MlocalThe angle of XYZ and X-axis；
θ2: indicate L2In mechanical arm local coordinate system MlocalThe angle of XYZ and X-axis；
θ3: indicate mechanical arm local coordinate system MlocalThe X-axis and mechanical arm pedestal rotating coordinate system O of XYZarm_baseThe y of XYZ
The angle (such as Fig. 6) of axis.
The inverse solution calculating process of specific mechanical arm and as follows:
1. the central clamp position of end manipulator known to is G (namely two dimensional code center) in camera coordinates system
OcameraCoordinate under XYZ iscameraG=[cameraxcurrent cameraycurrent camerazcurrent]T, the length table of each connecting rod
It is shown as L1、L5、L6, solve two steering engine corner [θ1 θ2]TWith pedestal stepper motor rotational angle theta3；
2. due to camera coordinates system OcameraXYZ, mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and mechanical arm are locally sat
Mark system MlocalXYZ (as shown in Figure 5), the translation transformation relationship between three coordinate systems are as follows:
1)Camera coordinates system OcameraXYZ is revolved relative to mechanical arm pedestal
Turn coordinate system Oarm_baseThe positional relationship of XYZ；
2) as shown in Figure 5 and Figure 6, mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and mechanical arm local coordinate system
MlocalRelationship between XYZ
3. pedestal stepper motor rotational angle theta3
As shown in Figure 5 and Figure 6, H point is calculated first in camera coordinates system OcameraPosition under XYZ, then calculate H point
In mechanical arm pedestal rotating coordinate system Oarm_baseSpatial position under XYZ, finally projects to Oarm_baseXYZ plane calculates, tool
Body process is as follows:
Ask H point in camera coordinates system OcameraThe position of XYZ:
LGH=L5 cos α3
cameraH=[cameraxcurrent-LGH cameraycurrent camerazcurrent]T
Ask H point in mechanical arm pedestal rotating coordinate system Oarm_baseThe position of XYZ:
It is obtained from Fig. 6
4. solving rotational angle theta1And θ2
1) as shown in fig. 6, solution point H is in mechanical arm local coordinate system MlocalThe position of XYZ
localHy=0
localHz=arm_baseHz-la_l
da_l: indicate mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalBetween both XYZ Z axis
Distance
la_l: indicate mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalBoth XYZ XOY plane
Distance in the Z-axis direction；
2) as shown in fig. 7,
3) Δ θ=θ is calculated2-θ1,
In Δ MHG, obtained by the cosine law,
Finally, it is stated that the above examples are only used to illustrate the technical scheme of the present invention and are not limiting, although referring to compared with
Good embodiment describes the invention in detail, those skilled in the art should understand that, it can be to skill of the invention
Art scheme is modified or replaced equivalently, and without departing from the objective and range of technical solution of the present invention, should all be covered at this
In the scope of the claims of invention.
Claims (4)
1. a kind of two dimensional code positioning crawl robot system algorithm of view-based access control model identification, which comprises the following steps:
S1. identification is crawled object equipped with two dimensional code；
S2. the posture information of the two dimensional code geometric center is extracted；
S3. it is set to the static target value of the two dimensional code relative pose；Calculate the position of current time two dimensional code pose and setting
Deviation between appearance target, and the threshold value of the deviation and setting is compared；It, will in conjunction with pid algorithm if deviation is more than threshold value
Deviation information is converted into velocity information, and according to the velocity information control wheat wheel platform move to it is static after pose target；If partially
Difference is less than threshold value, then keeps wheat wheel platform static；
S4. the inverse kinematics that mechanical arm is carried out using the two dimensional code posture information, are made in mechanical arm tail end manipulator
Heart clip position reaches two dimensional code center；By coordinate transform, the corner of mechanical arm driving motor is solved；Driving motor output
The corner drive robot arm end effector move to be crawled object after complete holding action.
2. the two dimensional code positioning crawl robot system algorithm of view-based access control model identification according to claim 1, feature exist
In: in step s2, using open source two dimensional code recognizer software package ar_track_alvar or visp, extract in two dimensional code geometry
Posture information [the x of the heartcurrent ycurrent zcurrent]TAnd four element [qxcurrent qycurrent qzcurrent qwcurrent]T。
3. the two dimensional code positioning crawl robot system algorithm of view-based access control model identification according to claim 2, feature exist
In step s3 includes:
S31. pass through the four elements [qxcurrent qycurrent qzcurrent qwcurrent]TObtain the inclined of two dimensional code geometric center
Navigate angle yawcurrent,
S32. [x is setgoal ygoal yawgoal]TObject pose between camera and two dimensional code；
Set [xthreshold ythreshold yawthreshold]TFor the difference between current two-dimension pose and the object pose of setting
Threshold limit value；
Set [xoffset yoffset yawoffset]T (t)It is inclined between current time two dimensional code pose and the object pose of setting
Difference；
Set [vx vy wz]T (t)For camera coordinates system OcameraUnder XYZ, current time wheat takes turns the speed of mobile platform geometric center；
S33. deviation [the x between current time two dimensional code pose and the object pose of setting is calculatedoffset yoffset yawoffset]T (t),
Its calculation formula is:
If deviation [the x s34. between current time two dimensional code pose and the object pose of settingoffset yoffset yawoffset]T (t)
More than the threshold value [xoffset yoffset yawoffset]T (t), then speed [the v of mobile platform geometric center is taken turns according to wheatx vy
wz]T (t)Wheat wheel platform movement is controlled, in conjunction with pid algorithm, takes turns platform to target point movement to accelerate wheat, the wheat takes turns mobile platform
Speed [the v of geometric centerx vy wz]T (t)Calculation formula it is as follows
If deviation [the x between current time two dimensional code pose and the object pose of settingoffset yoffset yawoffset]T (t)It is less than
Threshold value [the xoffset yoffset yawoffset]T (t), then wheat wheel platform remain stationary state, i.e.,
S35. by camera coordinates system OcameraThe velocity information of XYZ transforms to wheat wheel platform coordinate system Omecanum_baseXYZ, transformation are public
Formula are as follows:
Wherein,Indicate O under camera coordinates systemcameraThe speed that XYZ is acquired；
Indicate O under wheat wheel platform coordinate systemmecanum_baseXYZ, wheat take turns the speed in the platform centre of motion.
S36. according to the velocity information of obtained wheat wheel platform geometric centerBe converted to the angle speed of each Mecanum wheel
Spend [w0 w1 w2 w3]T, conversion formula are as follows:
Wherein, a is the width that wheat takes turns platform, and b is the length that wheat takes turns platform, and R is the radius that wheat takes turns bull wheel.
S37. angular speed [the w that will be solved0 w1 w2 w3]TIt is respectively transmitted the motor taken turns to control wheat, the fortune of driving wheat wheel platform
It is dynamic.
4. the two dimensional code positioning crawl robot system algorithm of view-based access control model identification according to claim 1, feature exist
In step s4 includes:
S41. H point is solved in camera coordinates system OcameraThe position of XYZ, solution formula are as follows:
cameraH=[cameraxcurrent-LGH cameraycurrent camerazcurrent]T；
H point is solved in mechanical arm pedestal rotating coordinate system Oarm_baseThe position of XYZ:
Mechanical arm local coordinate system MlocalThe X-axis and mechanical arm pedestal rotating coordinate system O of XYZarm_baseThe angle of the y-axis of XYZ
S42. solution point H is in mechanical arm local coordinate system MlocalThe position of XYZ:
localHy=0；
localHz=arm_baseHz-la_l；
Wherein, da_lFor mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalBetween both XYZ Z axis away from
From；
la_lFor mechanical arm pedestal rotating coordinate system Oarm_baseXYZ and local coordinate system MlocalThe XOY plane of both XYZ is in Z axis side
Upward distance；
S43. L is solved1In mechanical arm local coordinate system MlocalThe angle theta of XYZ and X-axis1,
Solve L2In mechanical arm local coordinate system MlocalThe angle theta of XYZ and X-axis2,
Wherein,
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