CN114714346A - Mechanical arm control strategy and optimization method for microwave far-field and near-field scanning and imaging tasks - Google Patents

Mechanical arm control strategy and optimization method for microwave far-field and near-field scanning and imaging tasks Download PDF

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CN114714346A
CN114714346A CN202210245617.4A CN202210245617A CN114714346A CN 114714346 A CN114714346 A CN 114714346A CN 202210245617 A CN202210245617 A CN 202210245617A CN 114714346 A CN114714346 A CN 114714346A
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sampling
joint
mechanical arm
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牛富金
张德慷
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Qingdao University
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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
    • 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
    • B25J9/1628—Programme controls characterised by the control loop
    • 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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Abstract

The invention discloses a mechanical arm control strategy and optimization method for a microwave far-field and near-field scanning and imaging task, which comprises the steps of firstly obtaining an actual inaccessible working area of a mechanical arm according to the limit angle constraint of a joint of a 6-joint mechanical arm and the limit of a plane sampling surface of an antenna polarization direction of an end effector, then obtaining a microwave source near-field imaging maximum sampling surface according to the condition that no intersection exists between a tail end sampling point and the inaccessible area on a space sampling surface, and finally obtaining the optimal path planning of the joint displacement of the 6-joint mechanical arm based on the shortest path principle under a Cartesian coordinate system and the principle that the change amplitude of a front five-axis joint under a joint space is the lowest. The maximum scanning cylindrical surface and the optimal motion control strategy in the constrained space can be rapidly solved, the problem that an inaccessible area can occur in the smart working space of the mechanical arm is solved, and then the optimal realization of microwave imaging scanning is achieved in the constrained range.

Description

Mechanical arm control strategy and optimization method for microwave far-field and near-field scanning and imaging tasks
Technical Field
The invention belongs to the electromagnetic compatibility technology, and automatic detection and positioning of a target radiation source are completed by holding a detection antenna by a robot. According to the technical scheme, a multi-joint mechanical arm is combined with a microwave far-field-near-field conversion and imaging (ESM) technology, and a control strategy for the mechanical arm in a cylindrical scanning microwave Source near-field imaging task is researched in an important mode. Through a control strategy, a corresponding maximum scanning surface and a mechanical arm motion path can be quickly generated under the condition of giving detection antenna characteristics and mechanical arm configuration parameters, and high-precision quick scanning and field-entering imaging of a first-measurement microwave source are realized.
Background
With the development of the electronic industry, particularly the emergence of 5G or terahertz technology, higher and higher requirements are put on the requirements of electromagnetic Compatibility (EMC) and electromagnetic Interference (EMI) detection of electronic devices. The current popular 3/5m darkroom detection standard faces upward compatibility challenges. In this context, the microwave far-field-near-field transformation and imaging technology based on the synthetic aperture radar imaging principle gradually draws attention. On the other hand, due to the maturity of robotics and its positive role in electromagnetic detection, various institutions are actively applying automated detection techniques such as robots to electromagnetic detection tasks. Although the robot has higher positioning accuracy and operation efficiency, the compatibility problem still exists between the robot and diversified electromagnetic compatibility detection technologies, and the control strategy needs to consider multiple constraints from self or external. Taking the microwave far-field-near-field imaging scan as an example, the detection technology requires a multi-joint mechanical arm to hold a detection antenna or probe to point at a specific angle to a microwave radiation source, which requires that the tail joint of the mechanical arm keeps a constant pointing direction (i.e. tail joint axial direction) in the whole scanning process. Because the shaft joint of the mechanical arm has the rotation angle limitation and the axial direction of the tail end joint needs to be locked forcibly, an inaccessible area can appear in the smart working space of the mechanical arm which is originally complete, and the inaccessible area is contradictory to a continuous large-scale scanning surface required by microwave imaging scanning. Based on the above problems and requirements, the motion planning and control strategy of the robot under specific multi-dimensional constraints needs to be studied, so as to optimally implement microwave imaging scanning within the constraint range.
Disclosure of Invention
The invention aims to combine a multi-joint mechanical arm with a microwave far-field-near-field transformation and imaging (ESM) technology, quickly generate a corresponding maximum scanning surface and a mechanical arm movement path under the condition of setting detection antenna characteristics and mechanical arm configuration parameters, and realize high-precision quick scanning and field-entering imaging of a first-measurement microwave Source.
According to the method, firstly, constraint conditions such as a mechanical arm structure, a polarization characteristic of a detection antenna, a space sampling surface and the like are modeled aiming at the microwave imaging scanning task characteristic, and the maximum area of a near-field imaging sampling cylindrical surface of a microwave source is obtained through nonlinear programming of sampling points. On the premise of giving a scanning cylindrical surface, based on the path and the principle of minimum five-axis rotation angle before the mechanical arm, a smooth joint angle inverse solution sequence is generated before and after a Hamilton path through an RRT algorithm improved based on a joint search strategy, and then the optimal motion planning and control strategy of the joint position state of the mechanical arm is solved. By the calculation method provided by the invention, the maximum scanning cylindrical surface and the optimal motion control strategy in the constrained space can be rapidly solved under the constraint condition of the given mechanical arm and the given detection antenna type, so that a theoretical basis and a technical guarantee are provided for the combination of the mechanical arm and a microwave imaging scanning task.
In order to achieve the above object, the present invention relates to a mechanical arm control strategy and optimization method for microwave far-field and near-field scanning and imaging tasks, which specifically comprises the following steps:
(1) obtaining an actual inaccessible working area of the mechanical arm according to the joint limiting angle constraint of the 6-joint mechanical arm and the limit of the end effector antenna polarization direction plane sampling surface;
end effector grasping inaccessible area of antenna midpoint
Figure BDA0003544269050000021
The corresponding cartesian closed boundary parameter equation is shown in the following formula:
Figure BDA0003544269050000022
wherein,
Figure BDA0003544269050000023
is an inaccessible area
Figure BDA0003544269050000024
Any point (x, y, z), R on the boundaryi、RoTo represent
Figure BDA0003544269050000025
The inner diameter and the outer diameter of the pipe,
Figure BDA0003544269050000026
representing a parametric angle of a parametric equation;
(2) then, according to the fact that intersection does not exist between the tail end sampling point and the unreachable area on the space sampling surface, a microwave source near-field imaging maximum sampling surface is obtained;
Figure BDA0003544269050000027
is a sampling point on the sampling plane C,
Figure BDA0003544269050000028
for the end antenna at the point
Figure BDA0003544269050000029
Is a vector of the orthogonal constraint of
Figure BDA00035442690500000210
Different heights have the same constraint effect, will
Figure BDA00035442690500000211
To x0oy0Projecting the plane to obtain sx，yAll s on the sampling plane Cx，yForming a set S, and searching a dynamic constraint area omega meeting the single mapping of the sampling points based on the sampling point set S6，Ω6Generating cylinder of the scan with preference given to a single mapping f relationship, i.e.
Figure BDA00035442690500000212
By setting the radius R, the height H and the offset D of the sampling cylinderoffsetGenerating different point sets S and taking the actual sampling area A of the sampling surface as the maximum targetAnd (3) performing nonlinear programming on the standard function to generate a scanning cylindrical surface maximally, wherein the sampling area and the constraint condition are shown as the following formula:
max A＝πRH
Figure BDA00035442690500000213
wherein,
Figure BDA0003544269050000031
Figure BDA0003544269050000032
Figure BDA0003544269050000033
is | q3|＝qlimThe coordinates of the end of the time axis joint 4,
Figure BDA0003544269050000034
representing the general case i.e. | q3|≠qlimTime of flight
Figure BDA0003544269050000035
The actual space of (a) is,
Figure BDA0003544269050000036
represents | q3| take qlimOf the hour
Figure BDA0003544269050000037
Actual space of (A), RreachIs composed of
Figure BDA0003544269050000038
Z is z, D in coordinates (x, y, z)offsetIs the sampling plane C and omega6The shortest Euclidean distance between the two groups,
Figure BDA0003544269050000039
is an empty set;
(3) finally, based on the shortest path principle under a Cartesian coordinate system and the lowest principle of the change amplitude of the front five-axis joint under the joint space, the optimal path planning of the joint displacement of the 6-joint mechanical arm is obtained;
selecting Christofides algorithm and target loss function to finally obtain the shortest sampling sequence Q trace path and the distance thereof,
target loss function: min { ∑ w (i, j) | vj∈V-{vi}}
Wherein w (i, j) is an endpoint viAnd a rear endpoint vjWeights of constituent edges, V is the line between sample points, { ViThe cost function is used as the cost function;
end effector middle position matrix without considering orthogonal constraint under base coordinate system0T6Specifically, the transformation is as follows:
0T6＝0T1 1T2 2T3 3T4 4T5 5T6Rx(α)Ry(β)
Figure BDA00035442690500000310
wherein,i-1Tirepresentative coordinate system xi-1oyi-1Transformation into coordinate system xioyiBy a homogeneous transformation matrix, rotation angle
Figure BDA0003544269050000041
Wherein
Figure BDA0003544269050000042
Represents the circle center coordinate of the bottom surface of the sampling surface C, (p)x，py，pz) As gripper coordinates, Rx(α)，Ry(β) is a rotation matrix;
the shortest sampling sequence Q and0T6input RRT algorithmAnd obtaining a path with the minimum change amplitude of the adjacent joint angles on the sequence.
Compared with the prior art, the invention has the following beneficial effects: the electromagnetic compatibility and electromagnetic interference detection technology of the electronic system by the mechanical arm control strategy and the optimization method can efficiently complete the tasks of microwave far-field-near-field transformation and imaging (ESM) based on cylindrical scanning. Compared with the traditional 3/5m microwave darkroom detection method, the method provided by the invention realizes inversion and imaging of the EMI radiation intensity distribution on the surface of the tested equipment, and can directly guide development enterprises or developers to carry out optimization and modification on the EMI performance of the equipment. In addition, by the calculation method provided by the invention, the maximum scanning cylindrical surface and the optimal motion control strategy in the constrained space can be rapidly solved, the problem that an inaccessible area occurs in the smart working space of the mechanical arm is solved, and the optimal realization of microwave imaging scanning is further realized in the constrained range.
Drawings
Fig. 1 is a diagram showing a 6-degree-of-freedom robot arm.
Fig. 2 is a 6-degree-of-freedom robot arm structure diagram (labeled link angle).
Fig. 3 is a schematic diagram of spatial cylindrical surface sampling of a 6-joint mechanical arm.
FIG. 4 is a view of link a without consideration of end effector constraints2Schematic representation of inaccessible area at the end.
Fig. 5 is a schematic view of an unreachable area under the constraint of an end effector of a 6-joint robot arm.
FIG. 6 shows x0oy0Under the view
Figure BDA0003544269050000043
Is arranged at
Figure BDA0003544269050000044
The impact of constraints on reachable regions.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention belong to the protection scope of the present invention.
Examples
In the embodiment, a 6-joint mechanical arm is taken as an object, only two orthogonal/vertical antenna polarization directions are considered, and a control strategy of the 6-joint mechanical arm in a cylindrical scanning microwave source near-field imaging task is mainly researched. In order to obtain the maximum sampling area of the sampling surface in the reachable working area of the mechanical arm and the path of the tail end of the mechanical arm, the mechanical arm control strategy and optimization method for the microwave far-field and near-field scanning and imaging task comprises the following steps:
(1) obtaining an actual inaccessible working area of the mechanical arm according to the joint limiting angle constraint of the 6-joint mechanical arm and the limit of the end effector antenna polarization direction plane sampling surface;
(2) then, according to the fact that intersection does not exist between the tail end sampling point and the unreachable area on the space sampling surface, a microwave source near-field imaging maximum sampling surface is obtained;
(3) and finally, obtaining the optimal path planning of the joint displacement of the 6-joint mechanical arm based on a path shortest principle under a Cartesian coordinate system and a front five-axis joint variation amplitude lowest principle under a joint space.
(1) Microwave imaging detection task and constraint condition modeling
In the embodiment, a multi-degree-of-freedom redundant rigid mechanical arm is selected to collect the complex amplitude and phase distribution information of the electromagnetic field on the spatial sampling plane. The technical experiment object is a 6-degree-of-freedom mechanical arm which comprises an axial joint 1, an axial joint 2, an axial joint 3, an axial joint 4, an axial joint 5 and an axial joint 6, and the mechanical structure is shown in figures 1 and 2. Wherein z isiIndicating the direction of the joint axis, the base coordinate system xiyiziSatisfy the right hand screw rule and the connecting rod rotation angle qiRepresents a winding ziAngle of rotation of the shaft, distance d of the connecting rodiIs shown along ziAxial translation distance, aiRepresents an edge xiDistance of translation of shaft, angle of torsion alpha of connecting rodiDenotes ziAround xi+1Angle of rotation of the shaft, θiThe angle of each joint which can freely rotate is represented, and i is more than or equal to 1 and less than or equal to 6. Q when the mechanical arm actually operates2、q3∈[-qlim，qlim]As a physical constraint, take qlim＝3/4π。
The present invention assumes that the joint envelope lengths are ignored. Then, taking a point which meets the condition that a mechanical arm on a space sampling surface C has a kinematic inverse solution
Figure BDA0003544269050000051
The point set and the unreachable area
Figure BDA0003544269050000052
The complementary sets of D are taken to obtain the intersection, namely, the condition of random
Figure BDA0003544269050000053
And then under the condition of dynamic orthogonal constraint, generating different sampling points through the radius R and the height H of different sampling cylindrical surfaces
Figure BDA0003544269050000054
And different offset distances DoffsetNon-linear programming is achieved, maximizing the generation of the scan cylinder (as shown in fig. 3). Finally passes through RRT*And (3) an algorithm is used for converting the sampling points from the Cartesian space to the joint space and exploring a path with the minimum joint angle change amplitude in the joint space.
(2) Unreachable workspace analysis under end effector constraints
In practical application, the rotation angle of the mechanical arm shaft joint is limited, and the invention combines the mechanical arm joint limit constraint and the terminal antenna polarization direction constraint and solves the practical inaccessible working area of the mechanical arm when designing a microwave far-field-near-field transformation scanning system. The method applies terminal attitude constraint in steps, and analyzes the accessibility of the mechanical arm before and after the constraint is applied.
First, the end positions, i.e., the axis joints 5 and 6, are not considered, and only q needs to be arbitrarily selected because the axis joint 1 has isotropy1And rotating the two-dimensional unreachable area under the special case to obtain the unreachable area under the corresponding Cartesian coordinate system, wherein the corresponding relation is shown in FIG. 4.
For the robot arm base coordinate system x0y0z0The following arbitrary coordinate points p: (x, y, z),
Figure BDA0003544269050000055
γ∈[-qlim，qlim]if there is no inverse kinematics solution at p at the end of the mechanical arm shaft joint 4, the point p is called an unreachable point at the end of the shaft joint 4
Figure BDA0003544269050000056
And set of points
Figure BDA0003544269050000057
It is called the inaccessible area of the end of the shaft joint 4
Figure BDA0003544269050000058
Traversal gamma is in [ -q [ ]lim，qlim]All unreachable regions fetched in are called a set
Figure BDA0003544269050000061
So far, the inaccessible area of the tail end of the shaft joint 4 under the limit angle can be obtained
Figure BDA0003544269050000062
γ∈[-qlim，qlim]That is, γ is the intersection of the set of unreachable regions obtained from all angles under the constraint of the limit angle. To pair
Figure BDA0003544269050000063
Rotating around the axis joint 1 as a fixed axis to obtain an inaccessible area
Figure BDA0003544269050000064
The closed boundary equation (equation 1). Wherein R isuntouchRadius of inaccessible sphere ═ d2sin(π/4)。
Figure BDA0003544269050000065
I.e. inaccessible area
Figure BDA0003544269050000066
Is (0, 0, a) as the center of a circle1) Radius RuntouchThe spherical surface of (2).
The reachable region is the complement of the unreachable region, and the reachable region omega without considering the tail end posture can be obtained according to the formula (1)4。
Followed by applying the end poses, i.e. the axial joints, 5-6 pairs omega4The influence of (c). Traversing all the conditions of orthogonal constraint to finally obtain an inaccessible area of the middle point of the holding antenna of the end effector
Figure BDA0003544269050000067
(as shown in fig. 5). The corresponding cartesian closed boundary parameter equation is shown in equation (2).
Figure BDA0003544269050000068
Wherein,
Figure BDA0003544269050000069
is an inaccessible area
Figure BDA00035442690500000610
Any point (x, y, z), R on the boundaryi、RoTo represent
Figure BDA00035442690500000611
The inner diameter and the outer diameter of the pipe,
Figure BDA00035442690500000612
representing the parametric angle of the parametric equation.
(3) Method for generating microwave source near-field imaging maximum scanning surface under six-degree-of-freedom mechanical arm
The previously inaccessible area under end effector constraint for a 6 joint robotic arm
Figure BDA00035442690500000613
And analyzing, and then further researching the selection of the microwave source near-field imaging maximum sampling cylindrical parameter. It is assumed that the sampling plane C under the base coordinate system satisfies the condition of equation (3).
Figure BDA00035442690500000614
Wherein D isoffsetIs the sampling plane C and omega6The shortest Euclidean distance between the two groups,
Figure BDA00035442690500000615
is an empty set.
Figure BDA00035442690500000616
Is a sampling point on the sampling plane C,
Figure BDA00035442690500000617
for the end antenna at the point
Figure BDA00035442690500000618
The orthogonal constraint vector of (b). Due to the fact that
Figure BDA00035442690500000619
Having the same constraining effect at different heights, the invention only needs to study x0oz0Points under view projection
Figure BDA0003544269050000071
Constrained vector of antenna
Figure BDA0003544269050000072
The influence on the selection of the sampling surface is only needed. As shown in particular in fig. 6.
Due to the fact that
Figure BDA0003544269050000073
With the same constraint effect at different heights, the invention will
Figure BDA0003544269050000074
To x0oy0Projecting the plane to obtain sx，yAll s on the sampling plane Cx，yA set S is formed. At point sx，yOf
Figure BDA0003544269050000075
Omega under offset constraint4With and corresponding to only the accessible region at the end of the single-axis joint 6
Figure BDA0003544269050000076
Is called single mapping
Figure BDA0003544269050000077
If only in a single static constraint region omega6Inner part
Figure BDA0003544269050000078
Maximizing the generation of the cylinder of the scan, obviously limited by Ω6Each sx，yCorresponding to
Figure BDA0003544269050000079
The section is not fully utilized and the resulting scanned cylinder is not maximal.
In order to solve the problem, the invention provides a method for searching a dynamic constraint area omega meeting the single mapping of sampling points based on a sampling point set S6。Ω6Generating cylinder scans with priority given to a single mapping f relationship, i.e.
Figure BDA00035442690500000710
And preferably satisfies omega6F(s), wherein
Figure BDA00035442690500000711
The specific reachable region is shown in equations (4) and (5).
Figure BDA00035442690500000712
Figure BDA00035442690500000713
Wherein,
Figure BDA00035442690500000714
is | q3|＝qlimThe coordinates of the end of the hour axis joint 4,
Figure BDA00035442690500000715
representing the general case i.e. | q3|≠qlimTime of flight
Figure BDA00035442690500000716
The actual space of (a) is,
Figure BDA00035442690500000717
represents | q3| take qlimWhen it is used
Figure BDA00035442690500000718
Actual space of (A), RreachIs composed of
Figure BDA00035442690500000719
Z is z in coordinates (x, y, z).
By setting the radius R, the height H and the offset D of the sampling cylinderoffsetAnd generating different point sets S, performing nonlinear programming by taking the maximum actual sampling area A of the sampling surface as an objective function, and maximally generating a scanning cylindrical surface, wherein the sampling area and the constraint condition are shown in formula (6).
max A＝πRH
Figure BDA0003544269050000081
(4) Search strategy and path planning under terminal attitude constraint
On the basis of the obtained microwave source near-field imaging scanning surface parameters, the path planning of the mechanical arm with 6 degrees of freedom is designed, and in the process, the path length of a sampling sequence is reduced and a path with stable change of adjacent joint angles of the sequence is ensured on the basis of ensuring an inversion effect.
Firstly, rasterizing a sampling cylindrical surface, and constructing an undirected graph structure G (V, W) by the spatial relationship between sampling points and adjacent sampling points, wherein the connecting lines among the sampling points form V, and the Euclidean distance of the connecting lines forms weight W. In order to find the shortest path which does not repeatedly pass through all sampling points, the Christofides algorithm and a target loss function formula (7) are selected, and finally the shortest sampling sequence Q trace path and the distance thereof are obtained.
min{∑w(i，j)|vj∈V-{vi}} (7)
Wherein w (i, j) is an endpoint viAnd a rear endpoint vjWeights of constituent edges, V is the line between sample points, { ViThe cost function.
Assuming that the position and posture matrix of the end effector neutral position without considering the orthogonal constraint under the base coordinate system is0T6When solving the inverse solution of the mechanical arm kinematics, the orthogonal constraint condition can be met after the rotation transformation is carried out on the shaft joints 4-6.0T6The concrete transformation is shown in formulas (8) and (9).
0T6＝0T1 1T2 2T3 3T4 4T5 5T6Rx(α)Ry(β) (8)
Figure BDA0003544269050000082
Wherein,i-1Tirepresentative coordinate system xi-1oyi-1Transformation into coordinate system xioyiThe rotation angle alpha is-pi/2,
Figure BDA0003544269050000091
wherein
Figure BDA0003544269050000094
Represents the circle center coordinate of the bottom surface of the sampling surface C, (p)x，py，pz) As gripper coordinates, Rx(α)，RyAnd (beta) is a rotation matrix.
The invention relates to a method for searching sampling points by using a joint search strategy-based RRT algorithm
Figure BDA0003544269050000092
And (4) converting from the Cartesian space to the joint angle space through a kinematic inverse solution, and searching a path with the minimum change amplitude of adjacent joint angles on a sequence. Considering that the influence of the sixth joint of the six-degree-of-freedom mechanical arm on the whole motion of the six-degree-of-freedom mechanical arm is not large, the invention preferentially plans and finds a path with the minimum total change amplitude of 1-5 joint angles, and an algorithm flow chart is shown in the following table.
Figure BDA0003544269050000093
The specific execution process of the algorithm is as follows:
after the initial joint angle and the target joint angle are selected,
first, a random joint angle q is generated in the joint spacerandAnd determining qrandWhether boundary constraints and joint angle limit constraints are met.
Secondly, searching a joint angle set q with the smallest sum of the absolute values of the weighted changes of the joint angles 1-5 on the random treenearestIn a
Figure BDA0003544269050000101
Generates a set of joint angles q by vector directions ofnewAnd then updating the tree according to the joint angle searching strategy in turn.
Then, since the sub-sampling points on the tree are changed by weighting the absolute values of the joint anglesPath selection is performed so that for the step of reselecting a parent node and rerouting, the radius r for the reselected parent noderangeWe need to be within a proper range to ensure that the tree grows normally according to the target joint angle set, and the total variation of the joint angles is as small as possible. The number of full iterations is run until it reaches the target joint angle set qpath(x，y，z)。

Claims (1)

1. A mechanical arm control strategy and optimization method for a microwave far-field and near-field scanning and imaging task is characterized by comprising the following steps:
(1) obtaining an actual inaccessible working area of the mechanical arm according to the joint limiting angle constraint of the 6-joint mechanical arm and the limit of the plane sampling surface of the antenna polarization direction of the end effector;
end effector grasping inaccessible area of antenna midpoint
Figure FDA0003544269040000011
The corresponding cartesian closed boundary parameter equation is shown in the following formula:
Figure FDA0003544269040000012
wherein,
Figure FDA0003544269040000013
is an inaccessible area
Figure FDA0003544269040000014
Any point (x, y, z), R on the boundaryi、RoTo represent
Figure FDA0003544269040000015
The inner diameter and the outer diameter of the pipe,
Figure FDA0003544269040000016
θ∈[-π，π]representing a parametric angle of a parametric equation;
(2) then, according to the fact that intersection does not exist between the tail end sampling point and the unreachable area on the space sampling surface, a microwave source near-field imaging maximum sampling surface is obtained;
Figure FDA0003544269040000017
is a sampling point on the sampling plane C,
Figure FDA0003544269040000018
for the end antenna at the point
Figure FDA0003544269040000019
Is orthogonal to the constraint vector of (2) due to
Figure FDA00035442690400000110
Different heights have the same constraint effect, will
Figure FDA00035442690400000111
To x0ou0Projecting the plane to obtain sx，yAll s on the sampling plane Cx，yForming a set S, and searching a dynamic constraint area omega meeting the single mapping of the sampling points based on the sampling point set S6，Ω6Generating cylinder of the scan with preference given to a single mapping f relationship, i.e.
Figure FDA00035442690400000112
By setting the radius R, the height H and the offset D of the sampling cylinderoffsetGenerating different point sets S, carrying out nonlinear programming by taking the maximum actual sampling area A of a sampling surface as an objective function, and maximally generating a scanning cylindrical surface, wherein the sampling area and the constraint condition are shown in the following formula:
maxA＝πRH
Figure FDA00035442690400000113
wherein,
Figure FDA0003544269040000021
Figure FDA0003544269040000022
Figure FDA0003544269040000023
is | q3|＝qlimThe coordinates of the end of the time axis joint 4,
Figure FDA0003544269040000024
representing the general case i.e. | q3|≠qlimTime-piece
Figure FDA0003544269040000025
The actual space of (a) is,
Figure FDA0003544269040000026
represents | q3| take qlimOf the hour
Figure FDA0003544269040000027
Actual space of (A), RreachIs composed of
Figure FDA0003544269040000028
Z is z, D in coordinates (x, y, z)offsetIs the sampling plane C and omega6The shortest Euclidean distance between the two groups,
Figure FDA0003544269040000029
is an empty set;
(3) finally, based on the shortest path principle under a Cartesian coordinate system and the lowest principle of the change amplitude of the front five-axis joint under the joint space, the optimal path planning of the joint displacement of the 6-joint mechanical arm is obtained;
selecting Christofides algorithm and target loss function to finally obtain the shortest sampling sequence Q trace path and the distance thereof,
target loss function: min { ∑ w (i, j) | vj∈V-{vi}}
Wherein w (i, j) is an endpoint viAnd a rear endpoint vjWeights of constituent edges, V is the line between sample points, { ViThe cost function is used as the cost function; end effector middle position matrix without considering orthogonal constraint under base coordinate system0T6Specifically, the transformation is as follows:
0T6＝0T1 1T2 2T3 3T4 4T5 5T6Rx(α)Ry(β)
Figure FDA00035442690400000210
wherein,i-1Tirepresentative coordinate system xi-1oyi-1Transformation to coordinate system xioyiThe homogeneous transformation matrix of (a), the rotation angle α ═ pi/2,
Figure FDA0003544269040000031
wherein
Figure FDA0003544269040000032
Representing the center coordinates of the bottom surface of the sampling surface C, (p)x，py，pz) As gripper coordinates, Rx(α)，Ry(β) is a rotation matrix;
the shortest sampling sequence Q and0T6and inputting RRT algorithm to obtain a path with the minimum change amplitude of the adjacent joint angles on the sequence.
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