CN112621802A - Robot end effector and structure optimization method thereof - Google Patents

Robot end effector and structure optimization method thereof Download PDF

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Publication number
CN112621802A
CN112621802A CN202011408245.XA CN202011408245A CN112621802A CN 112621802 A CN112621802 A CN 112621802A CN 202011408245 A CN202011408245 A CN 202011408245A CN 112621802 A CN112621802 A CN 112621802A
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knuckle
rod
end effector
connecting rod
clamping
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CN112621802B (en
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袁明新
张全兵
申一虎
孙宏伟
张人杰
陈伟浩
缪海鹏
王强
戴现令
何淑婷
阮文涛
申燚
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Jiangsu University of Science and Technology
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Jiangsu University of Science and Technology
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Priority to PCT/CN2021/130033 priority patent/WO2022116788A1/en
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J15/00—Gripping heads and other end effectors
    • B25J15/08—Gripping heads and other end effectors having finger members
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J15/00—Gripping heads and other end effectors
    • B25J15/0023—Gripper surfaces directly activated by a fluid
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J17/00—Joints
    • B25J17/02—Wrist joints
    • B25J17/0258—Two-dimensional joints

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
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Abstract

The invention discloses a robot end effector and a structure optimization method thereof. The robot end effector provided by the invention can realize the self-adaption and enveloping clamping work of hubs with multiple shapes and sizes. The structural optimization method of the robot end effector realizes the global optimal optimization of the structural parameters of the end effector, effectively ensures the balance and stability of the clamping force of each knuckle when the end effector grabs a hub, and solves the difficult problems that the balance of joint contact force and the stable grabbing are difficult to ensure in the empirical design of the end effector.

Description

Robot end effector and structure optimization method thereof
Technical Field
The invention belongs to the technical field of industrial robots, and particularly relates to an end effector for a forging robot and a structure optimization method thereof.
Background
The wheel hub is an important part of an automobile and is mainly manufactured through a forging process. The forging environment of the forge piece has high temperature, vibration and noise, and the working environment is poor, the danger is high and the labor intensity is high. With the development of manufacturing industry, the automatic production line formed by forging robots is used for replacing manual operation in a high-temperature environment, the consistency of the quality of forgings can be improved, the production efficiency is improved, the cost is reduced, and the forging robot becomes the first choice in forging production.
However, the existing forging robot end effector for clamping the hub forging mainly adopts a special clamp with a single form, when the appearance and the size of the hub forging are changed, the clamp needs to be replaced in time, and the self-adaptive clamping of the multi-appearance and multi-size hub forging cannot be realized, so that the workload is increased, and the working efficiency is reduced. The under-rank mechanism is a new mechanism discovered in recent years, and is also called as an under-actuated mechanism because the number of driven members is less than the degree of freedom of the mechanism, and has the advantage of gripping objects with different shapes and sizes in an adaptive envelope manner, so that the under-rank mechanism is widely concerned. Therefore, the novel end effector designed based on the principle of the under-rank mechanism is helpful for solving the clamping requirement of the robot on the multi-appearance and multi-size wheel hub forging in the wheel hub forging process. The under-rank mechanism is usually multi-joint, the length, the angle and other constraints exist among structures, the existing design is usually based on an empirical method, the structural parameters of the under-rank mechanism are not optimized under the condition of stabilizing a clamping target, and the balance of joint contact force and the grabbing stability are difficult to guarantee, so that the design of a corresponding structure optimization method is developed on the basis of the design of the end pick-up of the hub forging robot based on the under-rank mechanism principle, and the effectiveness and the stability of the robot for clamping the hub are improved.
Disclosure of Invention
The invention aims to break through the self-adaptive, stable and accurate clamping technology of a forging robot for multi-appearance and multi-size hub forgings, and provides a robot end effector and an optimization method thereof based on the principle of an under-rank mechanism.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a robot end effector comprises a flange frame arranged at the end part of a robot arm, wherein a driving mechanism is arranged on the flange frame, a clamping mechanism is arranged on the driving mechanism, the clamping mechanism comprises clamping jaws arranged in mirror symmetry, and the clamping jaws are formed by connecting a head knuckle assembly, a middle knuckle assembly and a tail knuckle assembly from bottom to top;
the driving mechanism comprises a driving piece, two sliding blocks are arranged on the driving piece, the two sliding blocks can slide oppositely or reversely along the driving piece, and the driving piece is connected with the flange frame;
the first knuckle assembly comprises a first knuckle triangular connecting block, a driving connecting rod is hinged to one corner of the first knuckle triangular connecting block, a first knuckle transmission folding connecting rod and a first knuckle spring coupling connecting rod are respectively hinged to the other two corners of the first knuckle triangular connecting block, a supporting arm is further hinged to a hinge point of the first knuckle triangular connecting block and the first knuckle spring coupling connecting rod, the other end of the supporting arm is fixed to the driving piece, and the other end of the driving connecting rod is hinged to the sliding block;
the middle knuckle assembly comprises a middle knuckle triangular connecting block, one corner of the middle knuckle triangular connecting block is hinged with the first knuckle transmission folding connecting rod and the first knuckle spring coupling connecting rod, the other two corners of the middle knuckle triangular connecting block are respectively hinged with a middle knuckle transmission folding connecting rod and a middle knuckle spring coupling connecting rod, and a first knuckle supporting rod is further hinged between the hinged point of the middle knuckle triangular connecting block and the middle knuckle spring coupling connecting rod and the hinged point of the first knuckle triangular connecting block and the first knuckle spring coupling connecting rod;
the last knuckle subassembly includes the last knuckle bracing piece, last knuckle bracing piece with well knuckle transmission is rolled over the connecting rod and is articulated mutually with well knuckle spring coupling connecting rod, well knuckle triangle connecting block with the articulated point of well knuckle spring coupling connecting rod with still articulated between the last knuckle bracing piece have well knuckle bracing piece.
Further, the driving piece is a cylinder, the cylinder comprises two piston rods which can extend out of the back of the body and retract back of the body in opposite directions, the two sliding blocks are connected with the two piston rods respectively, the piston rods drive the sliding blocks to slide in opposite directions or in opposite directions, each sliding block comprises a sliding block body, a mounting seat fixed on the sliding block body and a cylinder heat insulation gasket arranged between the mounting seat and the sliding block body, and the driving connecting rod is hinged to the mounting seat.
Further, first knuckle antiskid grip block is installed to the inboard of first knuckle bracing piece, first knuckle bracing piece with be equipped with first knuckle heat insulating gasket between the first knuckle antiskid grip block, first knuckle antiskid grip block is spill and the concave part inboard is the arc shape.
Furthermore, well knuckle antiskid grip block is installed to the inboard of well knuckle bracing piece, well knuckle bracing piece with be equipped with well knuckle heat insulating gasket between the antiskid of well knuckle adds the grip block, well knuckle antiskid grip block is spill and the concave part inboard is the arc shape.
Further, last knuckle antiskid grip block is installed to the inboard of last knuckle bracing piece, last knuckle bracing piece with be equipped with last knuckle heat insulating gasket between the antiskid grip block of last knuckle, last knuckle antiskid grip block is spill and the concave part inboard is the arc shape.
In order to achieve the purpose, the invention adopts another technical scheme to realize:
a structure optimization method of a robot end effector comprises an end effector clamping contact force model establishment, an end effector structure parameter optimization method and an end effector structure parameter optimization process;
the method for establishing the clamping contact force model of the end pick-up comprises the following steps:
(1) establishing a geometric model and a statics analysis model according to the structure of the end effector;
the geometric model mainly enables the driving connecting rod in the driving mechanism to be equivalent to an AB rod, and enables the first knuckle triangular connecting block in the first knuckle assembly to be equivalent to an O rod1BC triangle and O1Side length of C is a2The first knuckle transmission folding connecting rod is equivalent to a CD rod, and the first knuckle spring coupling connecting rod is equivalent to an O rod1D spring for making the first knuckle supporting rod be equivalent to O1O2A rod having a length d1Equating the middle knuckle triangular connecting block in the middle knuckle assembly to be O2DE triangle, and O2Side length of D is a3，O2E side length is a4The middle knuckle transmission folding connecting rod is equivalent to an EH rod, and the side length is b2The middle knuckle spring coupling connecting rod is equivalent to O2H spring, the middle knuckle supporting rod is equivalent to O2O3The length of the side of the rod is d2Equating the last knuckle component to O3HG triangle, the end knuckle support bar is equivalent to O3G side, O3Side length of H is a5，O3Side length of G is d3；
The statics analysis model defines mainly O1BC triangle middle O1C is bound with O1An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line1Definition of O1O2The rod is connected with1The included angle between the counterclockwise direction as a fulcrum and the horizontal line is beta1Define DO1SpringReverse time needle with D as fulcrum and O2DO in DE triangle2Included angle of side being epsilon2Defining the angle between the CD lever and the horizontal line in the counterclockwise direction by taking C as a fulcrum as alpha4Definition of O2In DE triangle O2D is defined by O2As a pivot, clockwise forms an included angle with the horizontal line
Figure BDA0002818009680000031
Definition of O2In DE triangle O2E is defined by O2An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line2Definition of O2In DE triangle O2E is defined by O2Clockwise and O as a fulcrum1O2The angle of extension of the rod is gamma1Defining the angle between the E as a pivot point of the EH rod and the horizontal line as alpha5Definition of O2O3The rod is connected with2Counter-clockwise and O as a fulcrum1O2The angle of extension of the rod is beta2Definition of O3H rod with O3An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line3Definition of O3H rod with O3As a fulcrum clockwise and O2O3The angle of extension of the rod is gamma2Definition of O3G rod with O3Counter-clockwise and O as a fulcrum2O3The angle of extension line of the rod is beta3Define spring HO2Counterclockwise and HO with H as fulcrum3The angle of the rod being epsilon3Defining the drive input torque of the drive link 12 as T1Define a spring DO1Input torque of T2Define spring HO2Input torque of T3Definition of perpendicular action on O1O2Force at the midpoint of the rod is F1And F is1Point of action and O1Distance between points is h1Definition of perpendicular action on O2O3Force at the midpoint of the rod is F2And F is2Point of action and O2Distance between points is h2Definition of perpendicular action on O3Force at mid-point of the G-bar is F3And F is3Point of action and O3Distance between points is h3；
(2) Establishing an end pickup according to the virtual work principleVirtual work balance equation of input torque and output torque, TI·VM＝FT·VVWherein, TIFor input of a torque vector, VMAs imaginary motion vectors, FTAs contact force vector, VVVirtual velocity at the point of contact for gripping an object by an end effector, and TI＝[T1 T2 T3]，VM＝[ωα1 vl1 vl2]T，FT＝[F1 F2 F3]，VV＝[vd1 vd2 vd3]T，
Wherein, ω isα1For applying driving torque to O1Virtual angular velocity, v, on C-barl1，vl2Are each O1D spring and O2H virtual velocity of spring; v. ofd1,vd2,vd3Respectively acting on the gripping contact points O of the end effector1O2Rod, O2O3A rod and O3G virtual speed of the rod;
(3) respectively obtaining the virtual velocity v of the contact point of the object clamped by the end effector according to the rigid body motion velocity principled1，vd2，vd3，
vd1＝Δβ1·h1
vd2＝Δβ2·h2+Δβ1·(d1·cosβ2·h2+h2)
vd3＝Δβ3·h3+Δβ2(d2·cosβ2+h3)+Δβ1[d1·cos(β2+β3)+d2·cosβ3+h3]
In the formula,. DELTA.beta.1Is O1O2Angular velocity of rotation of the lever relative to the horizontal, Δ β2Is O2O3Rod relative to O1O2Angular velocity of rotation of the rod, Δ β3Is O3G rod relative to O2O3Angular velocity of rotation of the lever, and order deltaβ＝[Δβ1 Δβ2 Δβ3]T；
(4) Writing the virtual speed in the step (3) into a Jacobian matrix form VV＝Jvδβ，JvIs a virtual velocity jacobian matrix, and
Figure BDA0002818009680000041
(5) considering the influence of the spring coupling connecting rod in the first knuckle and the middle knuckle on the clamping stability, converting the virtual work balance into the static balance of the spring coupling connecting rod, and according to a plane four-connecting-rod vector closed equation:
Figure BDA0002818009680000042
finding imaginary motion vector VMExpression VM＝Jωδβ，JωIs a virtual angular velocity jacobian matrix, and
Figure BDA0002818009680000043
in the formula (I), the compound is shown in the specification,
Figure BDA0002818009680000044
(6) the virtual speed V in the step (4) is comparedVAnd the virtual motion vector V in step (5)MSubstituting into the balance equation in the step (2) to obtain TI·Jω＝FT·JvThen, then
Figure BDA0002818009680000045
In practice, the input moment T of the spring is ignored because the force of the end effector clamping the hub is much greater than the spring coupling link force2、T3Thus, a contact force model for the end effector clamped condition can be obtained:
Figure BDA0002818009680000046
the optimization method of the structural parameters of the end pick-up comprises an adaptive small world optimization algorithm, wherein the adaptive small world optimization algorithm comprises a local short link search operator psi, a random long link search operator T and a global long link probability PLAn adaptive policy Θ;
the local area short-link search operator Ψ is a method for searching node information from si(k) To Ri(k) Intermediate distance target solution nearest node si' (k) wherein si(k) Given a node for the k generation, there exists a neighborhood space
Figure BDA0002818009680000051
The local short join search operator Ψ can be defined as:
Figure BDA0002818009680000052
the random long join search operator f is at a global long join probability PLNext, at the kth generation node si(k) Is not adjacent
Figure BDA0002818009680000053
Internally randomly selecting a point si"(k) for remote information transfer;
the random long join search operator f can be defined as:
Figure BDA0002818009680000054
the global long connection probability PlAdaptive strategy Θ, includes the following for PLThe adaptive model of (2):
Figure BDA0002818009680000055
in the formula: pL1，PL2Respectively minimum and maximum long connection probability, k being the current evolution algebramaxFor maximum evolution algebra, faveThe average target value of all individuals of the population of the current generation is f, and the target value of the individual of the population of the current generation is f;
thirdly, the optimization process of the structural parameters of the end effector comprises the following steps:
(1) based on the end effector clamping contact force model, and with the contact force as uniform and equal as possible during the clamping of the end effector as a target, establishing an objective function of parameter optimization under the stable clamping state of the end effector:
Figure BDA0002818009680000056
wherein Fi(X) is the contact force at the clamping contact point of the end effector, X is the structural parameter variable set of the less rank end effector
Figure BDA0002818009680000057
Figure BDA0002818009680000058
(2) Setting a constraint range of an end effector structure parameter variable set X;
(3) initializing parameters of the adaptive small-world optimization algorithm, including the number n of algorithm population and the maximum iteration number k of the algorithmmax、PL1、 PL2Initial value, initial population x (k), etc., k ← 0;
(4) for global long connection probability PLAdaptive operation Θ, PL′←Θ(PL)；
(5) Performing local area short concatenation search operation Ψ, X' (k) ← Ψ (X (k));
(6) according to PL'performing a global long join operation Γ, X "(k) ← Γ (X' (k));
(7) updating the population information;
(8) and (5) judging the termination condition. If k is equal to kmaxIf so, the algorithm is terminated and the variable X corresponding to the optimal target value is output*Namely the structural parameters of the under-rank end pickup; otherwise, updating the iteration algebra, k being k +1, and returning to the step (a)4)。
Advantageous effects
The invention has the following beneficial effects:
1. compared with the special fixture for the existing hub forging robot with a single form, the end picker designed based on the rank lacking principle can realize the self-adaption and enveloping clamping work of hubs with multiple shapes and sizes. The self-adaptive clamping avoids the requirement of replacing a special clamp on a production line due to the change of the appearance and the size of the hub, reduces the workload of manual replacement and improves the production efficiency; and enveloping and clamping improve the stability of clamping the wheel hub forging by the robot in a high-temperature and vibration forging environment.
2. The invention provides a method for establishing a clamping contact force model of an end effector, which is mainly used for carrying out statics analysis based on the virtual power theorem so as to establish a contact force model in a three-finger self-adaptive grabbing state. The establishment of the model provides an optimization basis for the selection of the structural parameters of the robot end effector, and the randomness of the selection of the structural parameters in the current end effector experience design can be effectively avoided.
3. Aiming at optimization of end-effector structure parameters, the invention provides an improved self-adaptive small-world algorithm, which aims at the global long connection probability P on the basis of an original local short connection search operator psi and a random long connection search operator TLSelf-adaptive adjustment is carried out, and the search efficiency is accelerated in the early stage of algorithm evolution; the premature population trapping is prevented from being locally minimum in the middle stage of algorithm evolution; the algorithm not only helps the population jump out of local minimum in the late evolution stage, but also avoids the algorithm from falling into random search.
4. The invention provides an end effector structure parameter optimization process, which is based on an end effector clamping contact force model, and realizes the establishment of an optimization function with the aim of uniformly and equally distributing contact force as much as possible when the end effector clamps; meanwhile, the overall optimal optimization of the structural parameters of the end effector is realized by combining a self-adaptive small-world optimization algorithm, and the balance and stability of the clamping force of each knuckle when the end effector grabs the hub are effectively ensured.
Drawings
FIG. 1: the overall structure schematic diagram of the robot end effector in the embodiment of the invention;
FIG. 2: the robot end effector driving module in the embodiment of the invention has a schematic structure;
FIG. 3: the robot end effector in the embodiment of the invention has a schematic structure diagram of a first knuckle assembly;
FIG. 4: the embodiment of the invention is a schematic structural diagram of a first knuckle anti-slip clamping block;
FIG. 5: the robot end effector in the embodiment of the invention is structurally schematic diagram of a knuckle assembly and a tail knuckle assembly;
FIG. 6: in the embodiment of the invention, the robot end effector is used for grabbing a front schematic view of a hub forging;
FIG. 7: in the embodiment of the invention, the robot end effector envelopes and grabs the hub forging and then schematically illustrates the hub forging;
FIG. 8: the invention discloses a flow chart of an optimization method of a robot end effector;
FIG. 9: the geometric model diagram of the structure of the robot end picking device in the embodiment of the invention;
FIG. 10: in the embodiment of the invention, the structure of the robot end effector is a statics model diagram;
FIG. 11: a global long connection probability variation curve graph along with an iteration process;
FIG. 12: the embodiment of the invention is a schematic diagram of a robot for completely clamping a hub forging;
the reference numbers in the figures are: 1. a flange frame; 2. a robot arm end; 3. a drive mechanism; 4. a head knuckle assembly; 5. a middle knuckle assembly; 6. a distal knuckle assembly; 7. a drive member; 8. a cylinder head; 9. a slider; 10. a cylinder heat insulation gasket; 11. a mounting seat; 12. a drive link; 13. an air valve; 14. a support arm; 15. a first knuckle triangular connecting block; 16. the first knuckle drives the folding connecting rod; 17. a first knuckle spring coupled link; 18. a first knuckle support bar; 19. a first knuckle heat insulation pad; 20. a first knuckle anti-slip clamping block; 21. a middle knuckle triangular connecting block; 22. the middle knuckle drives the folding connecting rod; 23. a middle knuckle spring coupling link; 24. a middle knuckle support bar; 25. a middle knuckle heat insulating spacer; 26, a middle knuckle antiskid clamping block; 27. a distal knuckle support bar; 28. a distal knuckle heat insulating spacer; 29. a distal knuckle anti-slip clamping block; 30. a hub forging; 31. a robot.
Detailed Description
In order to make the purpose and technical solution of the embodiments of the present invention clearer, the technical solution of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only some of the embodiments of the invention, and not all of them. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention without any invasive work, are within the scope of protection of the invention.
The meaning of "front and back" in the present invention means that when the reader is facing the drawings, the direction from the drawing sheet to the reader is front and the direction from the drawing sheet to the back, and is not a specific limitation of the end effector apparatus of the present invention.
The meaning of "left and right" in the present invention means that the reader is facing the drawings, with the left side of the drawing sheet being left and the right side of the drawing sheet being right, and is not a specific limitation of the end effector apparatus of the present invention.
The meaning of "up and down" in the present invention means that when the reader is facing the drawings, the upper side of the drawing sheet is up and the right side of the drawing sheet is right, and is not a specific limitation of the end effector apparatus of the present invention.
The terms "inside, outside" as used herein, and inside means the side of the gripper jaw opposite to the side of the gripper jaw, and vice versa, and is not intended to limit the end effector assembly of the present invention specifically.
As shown in fig. 1, the robot end effector of the present invention includes a flange frame 1 mounted on an end portion 2 of a robot arm, a driving mechanism 3 is mounted on the flange frame 1, a clamping mechanism is mounted on the driving mechanism 3, the clamping mechanism includes clamping jaws arranged in mirror symmetry, and the clamping jaws are formed by connecting a first knuckle assembly 4, a middle knuckle assembly 5 and a last knuckle assembly 6 from bottom to top.
As shown in fig. 2, the driving mechanism 3 includes a driving member 7, two sliding blocks 9 are disposed on the driving member 7, the two sliding blocks 9 can slide along the driving member 7 in opposite directions or in opposite directions, and the driving member 7 is connected to the flange frame 1; the driving piece 7 is a cylinder, the cylinder includes two piston rods that can simultaneously stretch out dorsad and withdraw simultaneously in opposite directions, install cylinder cover 8 on the cylinder, the cylinder passes through cylinder cover 8 with flange frame 1 is connected, bilateral symmetry's pneumatic valve 13 is equipped with to the front end of cylinder, pneumatic valve 13 control two piston rods of cylinder stretch out and withdraw, two the slider 9 is respectively with two the piston rod is connected, by the piston rod drives and slides in opposite directions or dorsad, slider 9 includes the slider body and fixes mount pad 11 on the slider body and sets up mount pad 11 with cylinder heat insulating gasket 10 between the slider body.
As shown in fig. 3, the first knuckle assembly 4 includes a first knuckle triangular connecting block 15, a driving connecting rod 12 is hinged to one corner of the first knuckle triangular connecting block 15, the other two corners of the first knuckle triangular connecting block 15 are respectively hinged to a first knuckle transmission folding connecting rod 16 and a first knuckle spring coupling connecting rod 17, a supporting arm 14 is hinged to a hinge point of the first knuckle triangular connecting block 15 and the first knuckle spring coupling connecting rod 17, the other end of the supporting arm 14 is fixed to the driving member 7, and the driving connecting rod 12 is hinged to the mounting base 11.
As shown in fig. 3 and 5, the middle knuckle assembly 5 includes a middle knuckle triangular connecting block 21, one corner of the middle knuckle triangular connecting block 21 is hinged to the first knuckle transmission folding connecting rod 16 and the first knuckle spring coupling connecting rod 17, the other two corners of the middle knuckle triangular connecting block 21 are respectively hinged to a middle knuckle transmission folding connecting rod 22 and a middle knuckle spring coupling connecting rod 23, and a first knuckle supporting rod 18 is further hinged between the hinge point of the middle knuckle triangular connecting block 21 and the middle knuckle spring coupling connecting rod 23 and the hinge point of the first knuckle triangular connecting block 15 and the first knuckle spring coupling connecting rod 17; the last knuckle assembly 6 comprises a last knuckle supporting rod 27, the last knuckle supporting rod 27 is hinged to the middle knuckle transmission folding connecting rod 22 and the middle knuckle spring coupling connecting rod 23, and a middle knuckle supporting rod 24 is hinged between the hinge point of the middle knuckle triangle connecting rod 21 and the middle knuckle spring coupling connecting rod 23 and the last knuckle supporting rod 27.
As shown in fig. 3, 4 and 5, a first knuckle anti-slip clamping block 20 is installed on the inner side of the first knuckle support rod 18, a first knuckle heat insulation gasket 19 is arranged between the first knuckle support rod 18 and the first knuckle anti-slip clamping block 20, and the first knuckle anti-slip clamping block 20 is concave and the inner side of the concave part is arc-shaped. Middle knuckle anti-skidding clamping blocks 26 are installed on the inner sides of the middle knuckle supporting rods 24, middle knuckle heat-insulating gaskets 25 are arranged between the middle knuckle supporting rods 24 and the middle knuckle anti-skidding clamping blocks 26, and the inner sides of the concave parts of the middle knuckle anti-skidding clamping blocks 26 are arc-shaped and concave parts are concave. Last knuckle antiskid grip block 29 is installed to the inboard of last knuckle bracing piece 27, last knuckle bracing piece 27 with be equipped with the thermal-insulated gasket 28 of last knuckle between the antiskid grip block 29 of last knuckle, last knuckle antiskid grip block 29 is the spill and the concave part inboard is the arc form.
As shown in fig. 6 and 7, the driving link 12 connected to the slider 9 realizes a linkage driving the first knuckle assembly 4, the middle knuckle assembly 5, and the last knuckle assembly 6, and realizes underactuation based on the principle of an underrank mechanism, and fig. 6 shows a state where the first knuckle assembly 4, the middle knuckle assembly 5, and the last knuckle assembly 6 are fully opened when the slider 9 is located inside the cylinder. Fig. 7 shows the state in which the leading knuckle assembly 4, the middle knuckle assembly 5 and the trailing knuckle assembly 6 are fully self-adaptively envelope gripping the hub forging 30 when the slide block 9 is outside the cylinder. Compared with a single-form special hub clamp, the end picking device can also be used for grabbing in a self-adaptive enveloping mode when the size of a hub forging piece is increased, and can also be used for clamping when the forging piece is not round and comprises an oval shape, so that the special hub clamp has the advantage of self-adaptive clamping.
Referring to fig. 8, 9 and 10, a method for optimizing a robotic end effector according to the present invention includes a method for establishing a model of a gripping contact force of an end effector, a method for optimizing structural parameters of an end effector, and a process for optimizing structural parameters of an end effector,
firstly, establishing a contact force model of the end effector, which comprises the following specific contents and steps:
(1) establishing a geometric model and a statics analysis model according to the structure of the end effector;
the geometric model mainly makes the driving connecting rod 12 in the driving mechanism 3 equivalent to an AB rod, and the first knuckle triangular connecting block 15 in the first knuckle assembly 4 equivalent to an O rod1BC triangle and O1Side length of C is a2The first knuckle transmission folding connecting rod 16 is equivalent to a CD rod, and the first knuckle spring coupling connecting rod 17 is equivalent to an O rod1D spring, which is equivalent to the first knuckle support rod 18 as O1O2A rod having a length d1The middle knuckle triangular connecting block 21 in the middle knuckle assembly 5 is equivalent to O2DE triangle, and O2Side length of D is a3，O2E side length is a4The middle knuckle transmission folding connecting rod 22 is equivalent to an EH rod and has a side length of b2The middle knuckle spring coupling connecting rod 23 is equivalent to O2H spring, equivalent said middle knuckle support rod 24 to O2O3The length of the side of the rod is d2Equating the distal knuckle assembly 6 to O3HG triangle, the end knuckle strut 27 is equivalent to O3G side, O3Side length of H is a5，O3Side length of G is d3；
The statics analysis model defines mainly O1BC triangle middle O1C is bound with O1An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line1Definition of O1O2The rod is connected with1The included angle between the counterclockwise direction as a fulcrum and the horizontal line is beta1Define DO1Spring reverse time needle with D as fulcrum and O2DO in DE triangle2Included angle of side being epsilon2Defining the angle between the CD lever and the horizontal line in the counterclockwise direction by taking C as a fulcrum as alpha4Definition of O2In DE triangle O2D is defined by O2As a pivot, clockwise forms an included angle with the horizontal line
Figure BDA0002818009680000091
Definition of O2In DE triangle O2E is defined by O2An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line2Definition of O2In DE triangle O2E is defined by O2Clockwise and O as a fulcrum1O2The angle of extension of the rod is gamma1Defining the angle between the E as a pivot point of the EH rod and the horizontal line as alpha5Definition of O2O3The rod is connected with2Counter-clockwise and O as a fulcrum1O2The angle of extension of the rod is beta2Definition of O3H rod with O3An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line3Definition of O3H rod with O3As a fulcrum clockwise and O2O3The angle of extension of the rod is gamma2Definition of O3G rod with O3Counter-clockwise and O as a fulcrum2O3The angle of extension line of the rod is beta3Define spring HO2Counterclockwise and HO with H as fulcrum3The angle of the rod being epsilon3Defining the drive input torque of the drive link 12 as T1Define a spring DO1Input torque of T2Define spring HO2Input torque of T3Definition of perpendicular action on O1O2Force at the midpoint of the rod is F1And F is1Point of action and O1Distance between points is h1Definition of perpendicular action on O2O3Force at the midpoint of the rod is F2And F is2Point of action and O2Distance between points is h2Definition of perpendicular action on O3Force at mid-point of the G-bar is F3And F is3Point of action and O3Distance between points is h3；
(2) Establishing a virtual work balance equation T of the input torque and the output torque of the end effector according to the virtual work principleI·VM＝FT·VVWherein, TIFor input of a torque vector, VMAs imaginary motion vectors, FTAs contact force vector, VVVirtual velocity at the point of contact for gripping an object by an end effector, and TI＝[T1 T2 T3]，VM＝[ωα1 vl1 vl2]T，FT＝[F1 F2 F3]，VV＝[vd1 vd2 vd3]T，
Wherein, ω isα1For applying driving torque to O1Virtual angular velocity, v, on C-barl1，vl2Are each O1D spring and O2H virtual velocity of spring; v. ofd1,vd2,vd3Respectively acting on the gripping contact points O of the end effector1O2Rod, O2O3A rod and O3G virtual speed of the rod;
(3) respectively obtaining the virtual velocity v of the contact point of the object clamped by the end effector according to the rigid body motion velocity principled1，vd2，vd3，
vd1＝Δβ1·h1
vd2＝Δβ2·h2+Δβ1·(d1·cosβ2·h2+h2)
vd3＝Δβ3·h3+Δβ2(d2·cosβ2+h3)+Δβ1[d1·cos(β2+β3)+d2·cosβ3+h3]
In the formula,. DELTA.beta.1Is O1O2Angular velocity of rotation of the lever relative to the horizontal, Δ β2Is O2O3Rod relative to O1O2Angular velocity of rotation of the rod, Δ β3Is O3G rod relative to O2O3Angular velocity of rotation of the lever, and order deltaβ＝[Δβ1 Δβ2 Δβ3]T；
(4) Writing the virtual speed in the step (3) into a Jacobian matrix form VV＝Jvδβ，JvIs a virtual velocity jacobian matrix, and
Figure BDA0002818009680000101
(5) and considering the influence of the spring coupling connecting rod in the first knuckle and the middle knuckle on the clamping stability, and converting the virtual work balance into the static balance of the spring coupling connecting rod. The influence of the spring coupling connecting rod on the clamping stability is considered, and the static force of the spring coupling connecting rod is considered. According to the synthesis and decomposition of rigid motion velocity vectors, there are:
Figure BDA0002818009680000102
wherein the content of the first and second substances,
Figure BDA0002818009680000103
Figure BDA0002818009680000104
because node O1 is on the chassis, so
Figure BDA0002818009680000105
And because of alpha2+γ1＝β1，α3+γ2＝β1+β2Therefore, it is
νl2＝(Δβ1+Δβ2)·d2·sin(ε3-γ2)+(Δβ1+Δβ2-Δγ2)·a5·sin(ε3-γ2)
＝Δβ1·(d2+a5)·sin(ε3-γ2)+Δβ2·(d2+a5)·sin(ε3-γ2)-Δγ2·a5·sin(ε3-γ2)
Due to the middle finger joint O2EHO3For a four-bar linkage, a plane four-bar vector closed equation can be obtained:
Figure BDA0002818009680000106
then:
Figure BDA0002818009680000107
for gamma1+β2、γ2Respectively calculating partial derivatives, and sorting to obtain:
Figure BDA0002818009680000108
from the same component angular velocity transformation relationship, it can be obtained:
Figure BDA0002818009680000111
thus:
Figure BDA0002818009680000112
and is
Figure BDA0002818009680000113
Similarly, for the four-bar linkage O in the first joint1CDO2Is provided with
Figure BDA0002818009680000114
Then:
Figure BDA0002818009680000115
to pair
Figure BDA0002818009680000116
And beta1-α1Respectively calculating partial derivatives, and sorting to obtain:
Figure BDA0002818009680000117
note the book
Figure BDA0002818009680000118
The following can be obtained:
Figure BDA0002818009680000119
finally, the imaginary motion vector V is obtainedMExpression VM＝Jωδβ，JωIs a virtual angular velocity jacobian matrix, and
Figure BDA00028180096800001110
(6) the virtual speed V in the step (4) is comparedVAnd the virtual motion vector V in step (5)MSubstituting into the balance equation in the step (2) to obtain TI·Jω＝FT·JvThen, then
Figure BDA00028180096800001111
In practice, the input moment T of the spring is ignored because the force of the end effector clamping the hub is much greater than the spring coupling link force2、T3Thus, a contact force model for the end effector clamped condition can be obtained:
Figure BDA00028180096800001112
secondly, the optimization method of the structural parameters of the end effector comprises a self-adaptive small world optimization algorithm, wherein the self-adaptive small world optimization algorithm comprises a local short connection search operator psi, a random long connection search operator T and a global long connection probability PLSelf-adapting strategy theta;
the local area short-link search operator Ψ is a method for searching node information from si(k) To Ri(k) Intermediate distance target solution nearest node si' (k) wherein si(k) Given a node for the k generation, there exists a neighborhood space
Figure BDA0002818009680000121
The local short join search operator Ψ can be defined as:
Figure BDA0002818009680000122
the random long join search operator f is at a global long join probability PLNext, at the kth generation node si(k) Is not adjacent
Figure BDA0002818009680000123
Internally randomly selecting a point si"(k) for remote information transfer;
the random long join search operator f can be defined as:
Figure BDA0002818009680000124
the global long connection probability PlAdaptive strategy Θ, includes the following for PLThe adaptive model of (2):
Figure BDA0002818009680000125
in the formula: pL1，PL2Respectively minimum and maximum long connection probability, k being the current evolution algebramaxFor maximum evolution algebra, faveThe average target value of all individuals of the population of the current generation is f, and the target value of the individual of the population of the current generation is f;
thirdly, the optimization process of the structural parameters of the end effector comprises the following steps:
(1) based on the end effector clamping contact force model, and with the contact force as uniform and equal as possible during the clamping of the end effector as a target, establishing an objective function of parameter optimization under the stable clamping state of the end effector:
Figure BDA0002818009680000126
wherein Fi(X) is the contact force at the clamping contact point of the end effector, and X is the structure of the end effector with less rankA set of parameter variables and
Figure BDA0002818009680000127
Figure BDA0002818009680000128
(2) setting a constraint range of an end effector structure parameter variable set X;
(3) initializing parameters of the adaptive small-world optimization algorithm, including the number n of algorithm population and the maximum iteration number k of the algorithmmax、PL1、 PL2Initial value, initial population x (k), etc., k ← 0;
(4) for global long connection probability PLAdaptive operation Θ, PL′←Θ(PL)；
(5) Performing local area short concatenation search operation Ψ, X' (k) ← Ψ (X (k));
(6) according to PL'performing a global long join operation Γ, X "(k) ← Γ (X' (k));
(7) updating the population information;
(8) and (5) judging the termination condition. If k is equal to kmaxIf so, the algorithm is terminated and the variable X corresponding to the optimal target value is output*Namely the structural parameters of the under-rank end pickup; otherwise, updating the iteration algebra, and returning to the step (4), wherein k is k + 1.
As shown in fig. 11, is a global long connection probability PLThe curve is changed along with the optimization process. As can be seen from the figure: at the initial stage of population evolution, the global long join probability PLThe value is small, and for the initial population, local search of each point can be completed by highlighting local short connection, so that the algorithm search efficiency is improved; as population evolution progresses, PLThe increase is accelerated, mainly preventing the population from falling into local minimum early and reaching the later stage of population evolution, PLAnd the algorithm is slowly increased, and the algorithm is prevented from being trapped in random search mainly when the algorithm is helped to jump out of a local minimum. Global long connection probability PLThe adaptive adjustment of the optical head structure can help to improve the optimization efficiency and the global optimization precision of the structural parameters of the optical head.
Taking grabbing a wheel hub with a minimum diameter of 70mm as an example, aiming at a wheel hub forging robot end picker scheme designed based on an under-rank mechanism principle, empirical method design and optimization design based on an Fmcon Optimization Function (FOF), a Genetic Algorithm (GA), a basic Small World Algorithm (SWA) and an Adaptive Small World Algorithm (ASWA) in the invention are respectively adopted, and considering the probability optimization of the optimization design, each optimization design is respectively subjected to 30 independent tests. As can be seen from the data in Table I, after the optimization design is performed by FOF, GA, SWA and ASWA, no matter the average objective function or the optimal objective function value is smaller than the objective function subjected to the empirical method, which indicates that the optimization design of the structure of the end effector is very important. In the four optimization results, it is obvious that the average objective function and the optimal objective function value of the ASWA of the present invention are also the minimum, thereby verifying the effectiveness and superiority of the optimization method proposed by the present invention.
Table one:
Figure BDA0002818009680000131
fig. 12 is a schematic view of a robot 31 for completely clamping a hub forging 30 by using an end effector designed according to an embodiment of the present invention.
The above description is only a preferred embodiment of the present invention, and does not limit the present invention in any way. It will be understood by those skilled in the art that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (6)

1. A robot end effector, including installing flange frame (1) in robot arm end portion (2), its characterized in that: the flange frame (1) is provided with a driving mechanism (3), the driving mechanism (3) is provided with a clamping mechanism, the clamping mechanism comprises clamping jaws which are arranged in a mirror symmetry manner, and the clamping jaws are formed by connecting a first knuckle assembly (4), a middle knuckle assembly (5) and a last knuckle assembly (6) from bottom to top; wherein the content of the first and second substances,
the driving mechanism (3) comprises a driving part (7), two sliding blocks (9) are arranged on the driving part (7), the two sliding blocks (9) can slide in the opposite direction or in the opposite direction along the driving part (7), and the driving part (7) is connected with the flange frame (1);
the first knuckle assembly (4) comprises a first knuckle triangular connecting block (15), a driving connecting rod (12) is hinged to one corner of the first knuckle triangular connecting block (15), the other two corners of the first knuckle triangular connecting block (15) are respectively hinged to a first knuckle transmission folding connecting rod (16) and a first knuckle spring coupling connecting rod (17), a supporting arm (14) is hinged to a hinged point of the first knuckle triangular connecting block (15) and the first knuckle spring coupling connecting rod (17), the other end of the supporting arm (14) is fixed on the driving piece (7), and the other end of the driving connecting rod (12) is hinged to the sliding block (9);
the middle knuckle assembly (5) comprises a middle knuckle triangular connecting block (21), one corner of the middle knuckle triangular connecting block (21) is hinged with the first knuckle transmission folding connecting rod (16) and the first knuckle spring coupling connecting rod (17), the other two corners of the middle knuckle triangular connecting block (21) are respectively hinged with a middle knuckle transmission folding connecting rod (22) and a middle knuckle spring coupling connecting rod (23), and a first knuckle supporting rod (18) is further hinged between the hinged point of the middle knuckle triangular connecting block (21) and the middle knuckle spring coupling connecting rod (23) and the hinged point of the first knuckle triangular connecting block (15) and the first knuckle spring coupling connecting rod (17);
last knuckle subassembly (6) are including last knuckle bracing piece (27), last knuckle bracing piece (27) with well knuckle transmission is rolled over connecting rod (22) and well knuckle spring coupling connecting rod (23) and is articulated mutually, well knuckle triangle connecting block (21) with the articulated point of well knuckle spring coupling connecting rod (23) with still articulated between last knuckle bracing piece (27) have well knuckle bracing piece (24).
2. The robotic end effector of claim 1, wherein: the driving piece (7) is a cylinder, the cylinder comprises two piston rods which can simultaneously extend out in a back direction and retract in a back direction, the two piston rods are respectively connected with the sliding blocks (9), the piston rods drive the sliding blocks to slide in the back direction or in the back direction, the sliding blocks (9) comprise sliding block bodies and are fixed on the sliding block bodies, mounting seats (11) are arranged on the sliding block bodies, the mounting seats (11) are arranged on the sliding block bodies, cylinder heat insulation gaskets (10) are arranged between the sliding block bodies, and the driving connecting rods (12) are hinged to the mounting seats (11).
3. The robotic end effector of claim 1, wherein: first knuckle antiskid grip block (20) are installed to the inboard of first knuckle bracing piece (18), first knuckle bracing piece (18) with be equipped with first knuckle heat insulating gasket (19) between first knuckle antiskid grip block (20), first knuckle antiskid grip block (20) are spill and concave part inboard and are the arc form.
4. The robotic end effector of claim 1, wherein: well knuckle antiskid grip block (26) are installed to the inboard of well knuckle bracing piece (24), well knuckle bracing piece (24) with well knuckle antiskid adds and is equipped with well knuckle heat insulating pad (25) between holding piece (26), well knuckle antiskid grip block (26) are spill and concave part inboard and are the arc form.
5. A robotic end effector as claimed in claim 1, wherein: last knuckle antiskid grip block (29) is installed to the inboard of last knuckle bracing piece (27), last knuckle bracing piece (27) with be equipped with between last knuckle antiskid grip block (29) thermal-insulated gasket (28) of end knuckle, last knuckle antiskid grip block (29) are the spill and the concave part inboard is the arc form.
6. A method for optimizing a structure of a robot end-effector as claimed in any one of claims 1 to 5, wherein: comprises an end-effector clamping contact force model establishment, an end-effector structure parameter optimization method and an end-effector structure parameter optimization process,
firstly, establishing a contact force model of the end effector, which comprises the following steps:
(1) establishing a geometric model and a statics analysis model according to the structure of the end effector;
the geometric model mainly enables the driving connecting rod (12) in the driving mechanism (3) to be equivalent to an AB rod, and enables the first knuckle triangular connecting block (15) in the first knuckle assembly (4) to be equivalent to an O rod1BC triangle and O1Side length of C is a2The first knuckle transmission folding connecting rod (16) is equivalent to a CD rod, and the first knuckle spring coupling connecting rod (17) is equivalent to an O rod1A D spring, which is used for equivalently setting the first knuckle supporting rod (18) as O1O2A rod having a length d1Equating the middle knuckle triangular connecting block (21) in the middle knuckle assembly (5) to O2DE triangle, and O2Side length of D is a3，O2E side length is a4The middle knuckle transmission folding connecting rod (22) is equivalent to an EH rod and has the side length of b2The middle knuckle spring coupling connecting rod (23) is equivalent to O2H spring, the middle knuckle support rod (24) is equivalent to O2O3The length of the side of the rod is d2Equating the distal knuckle component (6) to O3HG triangle, the end knuckle support bar (27) is equivalent to O3G side, O3Side length of H is a5，O3Side length of G is d3；
The statics analysis model defines mainly O1BC triangle middle O1C is bound with O1An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line1Definition of O1O2The rod is connected with1The included angle between the counterclockwise direction as a fulcrum and the horizontal line is beta1Define DO1The spring takes D as a fulcrum and O in a counterclockwise direction2DO in DE triangle2Included angle of side being epsilon2Defining the angle between the CD lever and the horizontal line in the counterclockwise direction by taking C as a fulcrum as alpha4Definition of O2In DE triangle O2D is defined by O2As a pivot, clockwise forms an included angle with the horizontal line
Figure FDA0002818009670000021
Definition of O2In DE triangle O2E is on the sideO2An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line2Definition of O2In DE triangle O2E is defined by O2As a fulcrum clockwise and O1O2The angle of extension of the rod is gamma1Defining the angle between the E as a pivot point of the EH rod and the horizontal line as alpha5Definition of O2O3The rod is connected with2Counter-clockwise and O as a fulcrum1O2The angle of extension of the rod is beta2Definition of O3H rod with O3An included angle alpha is formed between the counterclockwise direction of the fulcrum and the horizontal line3Definition of O3H rod with O3As a fulcrum clockwise and O2O3The angle of extension of the rod is gamma2Definition of O3G rod with O3Counter-clockwise and O as a fulcrum2O3The angle of extension line of the rod is beta3Define spring HO2Counterclockwise and HO with H as fulcrum3The angle of the rod being epsilon3Defining the driving input torque of the driving connecting rod (12) as T1Define a spring DO1Input torque of T2Define spring HO2Input torque of T3Definition of perpendicular action on O1O2Force at the midpoint of the rod is F1And F is1Point of action and O1Distance between points is h1Definition of perpendicular action on O2O3Force at the midpoint of the rod is F2And F is2Point of action and O2Distance between points is h2Definition of perpendicular action on O3Force at mid-point of the G-bar is F3And F is3Point of action and O3Distance between points is h3；
(2) Establishing a virtual work balance equation T of the input torque and the output torque of the end effector according to the virtual work principleI·VM＝FT·VVWherein, TIFor input of a torque vector, VMAs imaginary motion vectors, FTAs contact force vector, VVVirtual velocity at the point of contact for gripping an object by an end effector, and TI＝[T1 T2 T3]，VM＝[ωα1 vl1 vl2]T，FT＝[F1 F2 F3]，VV＝[vd1 vd2 vd3]T，
Wherein, ω isα1For applying driving torque to O1Virtual angular velocity, v, on C-barl1，vl2Are each O1D spring and O2H virtual velocity of spring; v. ofd1,vd2,vd3Respectively acting on the gripping contact points O of the end effector1O2Rod, O2O3A rod and O3G virtual speed of the rod;
(3) respectively obtaining the virtual velocity v of the contact point of the object clamped by the end effector according to the rigid body motion velocity principled1，vd2，vd3，
vd1＝Δβ1·h1
vd2＝Δβ2·h2+Δβ1·(d1·cosβ2·h2+h2)
vd3＝Δβ3·h3+Δβ2(d2·cosβ2+h3)+Δβ1[d1·cos(β2+β3)+d2·cosβ3+h3]
In the formula,. DELTA.beta.1Is O1O2Angular velocity of rotation of the lever relative to the horizontal, Δ β2Is O2O3Rod relative to O1O2Angular velocity of rotation of the rod, Δ β3Is O3G rod relative to O2O3Angular velocity of rotation of the lever, and order deltaβ＝[Δβ1 Δβ2 Δβ3]T；
(4) Writing the virtual speed in the step (3) into a Jacobian matrix form VV＝Jvδβ，JvIs a virtual velocity jacobian matrix, and
Figure FDA0002818009670000031
(5) consider the first knuckle and middle fingerThe influence of the spring coupling connecting rod in the section on the clamping stability is converted into the static balance of the spring coupling connecting rod, and according to a plane four-connecting-rod vector closed equation:
Figure FDA0002818009670000032
finding imaginary motion vector VMExpression VM＝Jωδβ，JωIs a virtual angular velocity jacobian matrix, and
Figure FDA0002818009670000033
in the formula (I), the compound is shown in the specification,
Figure FDA0002818009670000034
(6) the virtual speed V in the step (4) is comparedVAnd the virtual motion vector V in step (5)MSubstituting into the balance equation in the step (2) to obtain TI·Jω＝FT·JvThen, then
Figure FDA0002818009670000035
In actual operation, the force of the end effector clamping the hub is far greater than the spring coupling link force, so the spring input torque T is ignored2、T3Thus, a contact force model for the end effector clamped condition can be obtained:
Figure FDA0002818009670000041
secondly, the optimization method of the structural parameters of the end effector comprises a self-adaptive small world optimization algorithm, wherein the self-adaptive small world optimization algorithm comprises a local short link search operator psi, a random long link search operator T and a global long link probability PLAn adaptive policy Θ;
the local short-link search operator Ψ is a method for searching node information fromsi(k) To Ri(k) Medium-distance target solution nearest node s'i(k) Wherein s isi(k) Given a node for the k generation, there exists a neighborhood space
Figure FDA0002818009670000042
The local short join search operator Ψ can be defined as:
Figure FDA0002818009670000043
the random long join search operator f is at a global long join probability PLNext, at the kth generation node si(k) Is not adjacent
Figure FDA0002818009670000044
Selecting a point s ″' at randomi(k) Carrying out long-distance information transmission;
the random long join search operator f can be defined as:
Figure FDA0002818009670000045
the global long connection probability PlAdaptive strategy Θ, includes the following for PLThe adaptive model of (2):
Figure FDA0002818009670000046
in the formula: pL1，PL2Respectively minimum and maximum long connection probability, k being the current evolution algebramaxFor maximum evolution algebra, faveThe average target value of all individuals of the population of the current generation is f, and the target value of the individual of the population of the current generation is f;
thirdly, the optimization process of the structural parameters of the end effector comprises the following steps:
(1) based on the end effector clamping contact force model, and with the aim that the contact force is distributed uniformly and equally as much as possible during the clamping of the end effector, establishing an objective function of parameter optimization under the stable clamping state of the end effector:
Figure FDA0002818009670000047
wherein Fi(X) is the contact force at the clamping contact point of the end effector, X is the structural parameter variable set of the less rank end effector
Figure FDA0002818009670000048
Figure FDA0002818009670000049
(2) Setting a constraint range of an end effector structure parameter variable set X;
(3) initializing parameters of the adaptive small-world optimization algorithm, including the number n of algorithm population and the maximum iteration number k of the algorithmmax、PL1、PL2Initial value, initial population x (k), etc., k ← 0;
(4) for global long connection probability PLAdaptive operation Θ, PL′←Θ(PL)；
(5) Performing local area short concatenation search operation Ψ, X' (k) ← Ψ (X (k));
(6) according to PL'performing a global long join operation Γ, X "(k) ← Γ (X' (k));
(7) updating the population information;
(8) determining termination condition, if k is kmaxIf so, the algorithm is terminated and the variable X corresponding to the optimal target value is output*Namely the structural parameters of the under-rank end effector; otherwise, updating the iteration algebra, and returning to the step (4), wherein k is k + 1.
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