CN116108701B - FAST novel feed cabin mechanism kinematics positive solution solving and control method - Google Patents

FAST novel feed cabin mechanism kinematics positive solution solving and control method Download PDF

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CN116108701B
CN116108701B CN202310375061.5A CN202310375061A CN116108701B CN 116108701 B CN116108701 B CN 116108701B CN 202310375061 A CN202310375061 A CN 202310375061A CN 116108701 B CN116108701 B CN 116108701B
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lower platform
cable
pose
rope
solving
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CN116108701A (en
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尚伟伟
马逸凡
高新宇
张彬
王晓燕
李朝阳
张飞
姚蕊
殷家宁
李辉
杨清阁
李庆伟
朱文白
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University of Science and Technology of China USTC
National Astronomical Observatories of CAS
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University of Science and Technology of China USTC
National Astronomical Observatories of CAS
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    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/04—Constraint-based CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention discloses a method for solving and controlling kinematic positive solutions of a FAST novel feed cabin mechanism, and belongs to the field of astronomical equipment control. The solving method comprises the following steps: step S1, establishing a local coordinate system to describe the pose of a lower platform; s2, determining geometric parameters and structural parameters of the parallel flexible cable mechanism; step S3, defining a rope length constraint equation; step S4, establishing a kinematic model of the parallel flexible cable mechanism based on increment; and S5, setting a kinematic forward solution optimization objective function and solving. The control method comprises the following steps: calculating expected cable force and expected rope length through the expected pose of the lower platform by using an offline planning module based on a kinematic positive solution solving equation and a dynamic model; the rope length of the 6-set upper inhaul cable mechanism and the rope force of the 3-set lower inhaul cable mechanism are respectively controlled. The invention can realize the control of the FAST feed cabin mechanism under the maximum zenith angle of 50 degrees, meet the control precision of the pose of the lower platform, effectively adjust the internal force of the parallel flexible cable mechanism, improve the cable force performance and improve the anti-interference capability.

Description

FAST novel feed cabin mechanism kinematics positive solution solving and control method
Technical Field
The invention relates to the field of astronomical equipment control, in particular to a FAST novel feed cabin mechanism kinematics positive solution solving method and a lower platform pose force-position hybrid control method.
Background
500 m caliber spherical radio telescope (Five-handred-meter Aperture Spherical radioTelescope, FAST) is currently the single caliber radio telescope with the largest caliber and highest sensitivity in the world. The FAST system mainly comprises a deformable active reflecting surface, a six-cable parallel driving mechanism, a central feed cabin and the like. The feed cabin is internally provided with a star-shaped frame, an AB rotating shaft mechanism, a Stewart platform and other auxiliary mechanisms. The Stewart platform consists of an upper platform, a lower platform and 6 telescopic rods connected with each other, wherein the upper platform is connected with an AB rotating shaft, and the lower platform is used for installing a feed source receiver; the pose change of the lower platform relative to the upper platform is realized by controlling the lengths of 6 telescopic rods. The multi-beam feed source receiver is arranged on the lower platform, and the high-precision directional tracking observation of the feed source receiver on the celestial body is realized through fine adjustment control on the pose and the angle of the lower platform.
In order to effectively reduce the weight of the feed cabin, the observation angle of the telescope is improved to 50 degrees, and a flexible cable driving mechanism is used for replacing a Stewart rigid parallel platform and an AB rotary shaft mechanism. The method for the kinematic forward solution of the Stewart platform mainly comprises an analysis method, a numerical method and the like, but the kinematic forward solution solving method using the Stewart parallel platform in the prior art is not applicable to a parallel flexible cable mechanism because of the unique working mode and redundancy characteristics of the flexible cable driving mechanism, and the instantaneity and the solving precision of the kinematic forward solution cannot be ensured.
For the lower platform pose control of the novel feed cabin mechanism, only a kinematic control scheme for controlling the length of the rope is considered, and under the conditions that the dynamic model and the actual model are uncertain and the system is subject to external disturbance, the tension on the rope can not be ensured to be kept within the rope force limiting range required by the system at any time, and the feedback and control on the internal force of the system are required in the complete control scheme. Therefore, how to accurately model and solve the kinematic positive solution of the flexible cable-driven FAST novel feed cabin mechanism and a control scheme meeting the pose control precision requirement are problems to be solved in FAST engineering.
In view of this, the present invention has been made.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a method for solving and controlling the kinematic positive solution of a FAST novel feed cabin mechanism, which realizes the solution of the kinematic positive solution of the FAST novel feed cabin mechanism through an incremental kinematic positive solution modeling and an optimization objective function based on complete rope length constraint; on the other hand, the control precision of the pose of the lower platform of the FAST novel feed cabin mechanism is met by performing kinematic control on each upper inhaul cable mechanism and performing force and position hybrid control on each lower inhaul cable mechanism, so that the problems in the prior art are solved.
The invention aims at realizing the following technical scheme:
a method for solving a novel FAST feed cabin mechanism kinematics positive solution comprises the following steps:
step S1, establishing a local coordinate system C system, a P system and an M system for describing the pose of a lower platform according to the connection relation between an outer cable mechanism of a FAST novel feed cabin mechanism and a feed cabin;
s2, determining geometric parameters and structural parameters of a parallel flexible cable mechanism serving as an inner cable mechanism of the FAST novel feed cabin mechanism according to the local coordinate system C system, the local coordinate system P system and the local coordinate system M system established in the step S1;
step S3, determining a rope length constraint equation met by the current pose of the lower platform according to the local coordinate systems C, P and M established in the step S1 and the geometric parameters and the structural parameters of the parallel flexible cable mechanism determined in the step S2;
step S4, establishing an incremental parallel flexible cable mechanism kinematics forward solution model according to the rope length constraint equation met by the current pose of the lower platform determined in the step S3, establishing a kinematics forward solution optimization objective function according to the incremental parallel flexible cable mechanism kinematics forward solution model, and establishing an incremental parallel flexible cable mechanism kinematics forward solution equation according to the kinematics forward solution optimization objective function;
and S5, solving an incremental parallel flexible cable mechanism kinematics positive solution solving equation constructed in the step S4 to obtain the current pose of the lower platform of the FAST novel feed cabin mechanism.
A FAST novel feed cabin mechanism control method comprises the following steps:
a1, before a FAST novel feed cabin mechanism operates, receiving a lower platform expected pose of the FAST novel feed cabin mechanism planned out of line;
a2, when the system runs, the lower platform of the FAST novel feed cabin mechanism is controlled in a force and position mixed control mode according to the received expected pose of the lower platform, and in the control process, the current pose of the lower platform is monitored through a visual tracking system until the control process is finished;
step A3, judging whether the visual tracking system fails or not in the process of monitoring the current pose of the lower platform through the visual tracking system, if so, executing the step A4, and if not, repeatedly executing the step A2;
and step A4, solving the current pose of the lower platform of the FAST novel feed cabin mechanism by adopting the method for solving the kinematic positive solution of the FAST novel feed cabin mechanism, re-planning the expected pose of the lower platform according to the current pose of the lower platform, and re-executing the step A2 according to the re-planned expected pose of the lower platform to perform force-position hybrid control on the lower platform.
Compared with the prior art, the FAST novel feed cabin mechanism kinematics positive solution solving and controlling method provided by the invention has the beneficial effects that:
Through solving and force position hybrid control based on incremental parallel flexible cable mechanism kinematics positive solution, the control under the maximum 50 zenith angle of the novel FAST feed cabin mechanism can be realized, the control precision of the platform pose under the novel FAST feed cabin mechanism is met, the internal force of the parallel flexible cable mechanism of the novel FAST feed cabin mechanism can be effectively regulated, the cable force performance of the parallel flexible cable mechanism is improved, and the anti-interference capability is improved.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a FAST novel feed cabin mechanism kinematic forward solution solving method.
Fig. 2 is a schematic coordinate diagram of a FAST novel feed cabin mechanism provided by the invention.
Fig. 3 is a top view of the FAST novel feed cabin mechanism and a representation diagram of the anchor point coordinates.
Fig. 4 is a side view of the FAST novel feed cabin mechanism and a representation diagram of geometric parameters.
Fig. 5 is an overall schematic diagram of the FAST novel feed cabin mechanism provided by the invention.
Fig. 6 is a flowchart of a FAST novel feed cabin mechanism control method provided by the invention.
Fig. 7 is a block diagram of a control system corresponding to the FAST novel feed cabin mechanism control method provided by the invention.
The component names corresponding to the marks in the figures are as follows: 1-a lower platform; a 2-PAF beam receiver; a 3-19 beam receiver; 4-a pull-up rope mechanism; a 5-connecting ring; 6-a pull-down cable mechanism; 7-a winding mechanism of a lower inhaul cable mechanism; 8-a winding mechanism of a pull-up rope mechanism; 9-an anchor point of the stay rope mechanism; 10-a stay rope mechanism anchoring point; 11-star frame.
Detailed Description
The following description of the embodiments of the present invention will be made in detail, but clearly understood to mean a portion of the embodiments, not all of the embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention. What is not described in detail in the embodiments of the present invention belongs to the prior art known to those skilled in the art.
The terms that may be used herein will first be described as follows:
the term "and/or" is intended to mean that either or both may be implemented, e.g., X and/or Y are intended to include both the cases of "X" or "Y" and the cases of "X and Y".
The terms "comprises," "comprising," "includes," "including," "has," "having" or other similar referents are to be construed to cover a non-exclusive inclusion. For example: including a particular feature (e.g., a starting material, component, ingredient, carrier, formulation, material, dimension, part, means, mechanism, apparatus, step, procedure, method, reaction condition, processing condition, parameter, algorithm, signal, data, product or article of manufacture, etc.), should be construed as including not only a particular feature but also other features known in the art that are not explicitly recited.
The term "consisting of … …" is meant to exclude any technical feature element not explicitly listed. If such term is used in a claim, the term will cause the claim to be closed, such that it does not include technical features other than those specifically listed, except for conventional impurities associated therewith. If the term is intended to appear in only a clause of a claim, it is intended to limit only the elements explicitly recited in that clause, and the elements recited in other clauses are not excluded from the overall claim.
Unless specifically stated or limited otherwise, the terms "mounted," "connected," "secured," and the like should be construed broadly to include, for example: the connecting device can be fixedly connected, detachably connected or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the terms herein above will be understood by those of ordinary skill in the art as the case may be.
The terms "center," "longitudinal," "transverse," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," etc. refer to an orientation or positional relationship based on that shown in the drawings, merely for ease of description and to simplify the description, and do not explicitly or implicitly indicate that the apparatus or element in question must have a particular orientation, be constructed and operated in a particular orientation, and therefore should not be construed as limiting the present disclosure.
The method for solving and controlling the kinematic positive solution of the FAST novel feed cabin mechanism provided by the invention is described in detail below. What is not described in detail in the embodiments of the present invention belongs to the prior art known to those skilled in the art. The specific conditions are not noted in the examples of the present invention and are carried out according to the conditions conventional in the art or suggested by the manufacturer. The reagents or apparatus used in the examples of the present invention were conventional products commercially available without the manufacturer's knowledge.
The embodiment of the invention provides a method for solving a kinematic positive solution of a FAST novel feed cabin mechanism, which comprises the following steps:
step S1, establishing a local coordinate system C system, a P system and an M system for describing the pose of a lower platform according to the connection relation between an outer cable mechanism of a FAST novel feed cabin mechanism and a feed cabin;
s2, determining geometric parameters and structural parameters of a parallel flexible cable mechanism serving as an inner cable mechanism of the FAST novel feed cabin mechanism according to the local coordinate system C system, the local coordinate system P system and the local coordinate system M system established in the step S1;
step S3, determining a rope length constraint equation met by the current pose of the lower platform according to the local coordinate systems C, P and M established in the step S1 and the geometric parameters and the structural parameters of the parallel flexible cable mechanism determined in the step S2;
Step S4, establishing an incremental parallel flexible cable mechanism kinematics forward solution model according to the rope length constraint equation met by the current pose of the lower platform determined in the step S3, establishing a kinematics forward solution optimization objective function according to the incremental parallel flexible cable mechanism kinematics forward solution model, and establishing an incremental parallel flexible cable mechanism kinematics forward solution equation according to the kinematics forward solution optimization objective function;
and S5, solving an incremental parallel flexible cable mechanism kinematics positive solution solving equation constructed in the step S4 to obtain the current pose of the lower platform of the FAST novel feed cabin mechanism.
Referring to fig. 5, preferably, in the above method, the parallel flexible cable mechanism serving as the inner cable mechanism of the FAST new feed cabin mechanism comprises 9 sets of cable mechanisms, wherein the split cable arrangement is formed by 6 sets of upper cable mechanisms and 3 sets of lower cable mechanisms, the 6 sets of upper cable mechanisms are divided into 3 pairs, each pair of upper cable mechanisms are uniformly arranged at intervals of 120 degrees, and the 3 sets of lower cable mechanisms are uniformly arranged at intervals of 120 degrees and are staggered with each pair of upper cable mechanisms at intervals of 60 degrees; 6 sets of upper inhaul cable mechanisms are used for controlling the kinematics of the lower platform pose of the feed cabin, and 3 sets of lower inhaul cable mechanisms are used for controlling the kinematics of the lower platform pose;
The upper inhaul cable mechanisms and the lower inhaul cable mechanisms are identical in composition and comprise a hoisting mechanism, a steel wire rope, a servo motor, an encoder and rope anchoring points.
Preferably, in step S1 of the above method, a local coordinate system C, P and M describing the pose of the lower platform is established according to the connection relationship between the outer cable mechanism of the FAST new feed cabin mechanism and the feed cabin, including:
anchoring point S of external cable mechanism on feed cabin i Establishing a local coordinate system C of the feed cabin by taking the plane center as an origin C;
the upper surface of the following platform is anchored with point A i The method comprises the steps of establishing a local coordinate system P system of a lower platform by taking the plane center as an origin P;
establishing a centroid coordinate system M of the lower platform by taking a centroid position M of the lower platform as an origin, wherein the directions of coordinate axes of the M system are parallel to the P system;
when the lower platform is kept horizontal relative to the feed deck, the P, M and C systems are completely parallel.
Preferably, in the above method, in the step S2, the geometric parameters and structural parameters of the parallel flexible cable mechanism serving as the inner cable mechanism of the FAST new feed cabin mechanism are determined according to the local coordinate system C-system, P-system and M-system established in the step S1 in the following manner, including:
in the local coordinate system C, the anchor point B on the feed cabin i For the corresponding anchoring point of the ith stay rope on the star-shaped frame, D j Anchoring point B for j-th stay rope on star-shaped frame i And D j The distribution radius of (2) is r B Stay cable anchorage point D j Is of a fixed distribution height H D Stay cable anchor point B i Is distributed with the height of H Bi ；
Anchor point A of upper stay rope on lower platform i Is of distribution radius r A ；
In the local coordinate system P, the anchor point C of the lower stay rope on the lower platform j Are all fixed on the connecting ring of the lower platform, and the distribution radius is r C The distribution height is H C The method comprises the steps of carrying out a first treatment on the surface of the Anchor point B i 、D j 、A i 、C j Position coordinates of (a) C B i 、 C D j 、 P A i 、 P C j The method comprises the following steps of:
Figure SMS_1
(1)；
Figure SMS_2
(2) ；
Figure SMS_3
(3) ；
Figure SMS_4
(4) ；
in the above formulae (1) to (4), T represents a transposed matrix; i is the number of upper guy wires, i=1, …,6; j is the number of down-cables, j=1, …,3;
anchoring point A in local coordinate systems M and C i 、C j Coordinates of (c) M A i 、 M C j 、 C A i 、 C C j The method comprises the following steps of:
Figure SMS_5
(5)；
Figure SMS_6
(6)；
in the above formulas (5) and (6), P A i is the anchorage point A under the local coordinate system P system i Coordinates of (c); P C j is the anchoring point C under the local coordinate system P system j Coordinates of (c);
Figure SMS_9
an offset vector from the M origin of the lower M center to the P origin, i.e. +.>
Figure SMS_11
；/>
Figure SMS_14
Is the position vector of the origin of the M line under the C line, i.e. +.>
Figure SMS_8
；/>
Figure SMS_12
For the rotation matrix of M-series versus C-series, < >>
Figure SMS_15
，
Figure SMS_16
For being in charge of the rotation matrix>
Figure SMS_7
Corresponding Euler angle vectors represent the attitude angles of the lower platform; M A i is an anchor point A under a local coordinate system M system i Coordinates of (c); />
Figure SMS_10
The P-series and M-series rotation matrices are fixed on the lower platform and parallel to each other, so +.>
Figure SMS_13
Is a unit matrix; M C j is the anchoring point C under the local coordinate system M system j Is defined by the coordinates of (a).
Preferably, in step S3 of the above method, the determining the rope length constraint equation satisfied by the current pose of the lower platform according to the local coordinate systems C, P and M established in step S1 and the geometric parameters and structural parameters of the parallel flexible cable mechanism determined in step S2 includes:
the rope of the parallel flexible rope mechanism comprises an upper inhaul cable and a lower inhaul cable, and the length of the upper inhaul cable
Figure SMS_17
And rope length of the lower dragline->
Figure SMS_18
The method comprises the following steps of:
Figure SMS_19
(7)；
Figure SMS_20
(8)；
in the above formulas (7) and (8), the formula (I) is represented by
Figure SMS_21
The length vector of the upper guy rope mechanism is
Figure SMS_22
The method comprises the steps of carrying out a first treatment on the surface of the By->
Figure SMS_23
The length vector of the obtained down-cable mechanism is +.>
Figure SMS_24
；
Figure SMS_25
(9)；
Figure SMS_26
(10)；
In the above formulas (9) and (10), T represents a transposed matrix; M C j is the anchoring point C under the local coordinate system M system j Coordinates of (c);
lower platform current pose
Figure SMS_27
Represented by the position and attitude angle of the M-line relative to the C-line, wherein>
Figure SMS_28
For Euler angle vector of current pose of lower platform in C system, determining current pose of lower platform according to Euler angle vector>
Figure SMS_29
The satisfied rope length constraint equation is:
Figure SMS_30
(11)；
Figure SMS_31
(12)；
in the above formulas (11) and (12),
Figure SMS_32
、/>
Figure SMS_33
the rope length of the upper inhaul cable and the rope length of the lower inhaul cable at the previous moment are respectively; p (P) 0 An initial position vector expressed as the origin of the M system under the C system; />
Figure SMS_34
For being in charge of the rotation matrix>
Figure SMS_35
Corresponding initial euler angle vectors; C B i is an anchor point B under a local coordinate system C system i Coordinates of (c); C D j is the anchorage point D under the local coordinate system C system j Is defined by the coordinates of (a).
Preferably, in the above method, in step S4, an incremental parallel flexible cable mechanism kinematic forward solution model is established according to a rope length constraint equation satisfied by the current pose of the lower platform determined in step S3, including:
the rope length constraint equations of (11), (12) are set in the previous pose of the lower platform
Figure SMS_36
Performing Taylor expansion, and reserving until a second order term to obtain an incremental parallel flexible rope mechanism kinematic forward model of the following formula (13):
Figure SMS_37
(13)；
in the previous pose formula of the lower platform and (13),
Figure SMS_39
is the position vector of the previous moment; />
Figure SMS_49
Is the Euler angle vector of the previous moment; t is a transposed matrix; />
Figure SMS_56
、/>
Figure SMS_38
The length of the upper inhaul cable and the length of the lower inhaul cable at the current moment are respectively,
Figure SMS_50
、/>
Figure SMS_57
the rope length of the upper inhaul cable and the rope length of the lower inhaul cable at the previous moment are respectively; />
Figure SMS_63
For the increment of the lower platform pose->
Figure SMS_40
And->
Figure SMS_46
The position increment of the lower platform and the attitude angle increment of the lower platform are respectively;
Figure SMS_53
indicating the length of the upper guy cable at the current time>
Figure SMS_60
Before the lower platform, the position X P Partial derivative of lower platform position vector P, < >>
Figure SMS_41
Representing the partial derivative; />
Figure SMS_45
Indicating the length of the upper guy cable at the current time>
Figure SMS_52
In the position of the next previous platform X P Pair and rotation matrix->
Figure SMS_59
Partial derivatives of the corresponding euler angle vectors Φ;
Figure SMS_42
indicating the length of the upper guy cable at the current time>
Figure SMS_47
Before the lower platform, the position X P Position vector P and rotation matrix of the lower platform>
Figure SMS_54
The second partial derivative of the corresponding euler angle vector Φ;
Figure SMS_61
indicating the length of the downcable at the current time>
Figure SMS_44
Before the lower platform, the position X P Partial derivative of the pair with the lower platform position vector P; />
Figure SMS_48
Indicating the length of the downcable at the current time>
Figure SMS_55
Before the lower platform, the position X P Pair and rotation matrix->
Figure SMS_62
Partial derivatives of the corresponding euler angle vectors Φ;
Figure SMS_43
indicating the length of the downcable at the current time>
Figure SMS_51
Before the lower platform, the position X P Position vector P and rotation matrix of the lower platform>
Figure SMS_58
The second partial derivative of the corresponding euler angle vector Φ.
Preferably, in step S4 of the above method, the establishing a kinematic forward solution optimization objective function according to the kinematic forward solution model of the incremental parallel flexible cable mechanism, and the establishing an incremental kinematic forward solution equation of the parallel flexible cable mechanism according to the kinematic forward solution optimization objective function includes:
In the running process of the FAST novel feed cabin mechanism, the initial pose of the lower platform is accurately measured by an external sensor, and when the kinematic correct solution is solved each time, the previous pose of the lower platform is obtained
Figure SMS_64
Is a known value, the rope length corresponding to the previous pose of the lower platform is +.>
Figure SMS_65
Calculated by the above formulas (11) and (12); solving the current pose of the lower platform through kinematic positive solution according to the following mode: measuring rope length +.>
Figure SMS_66
Calculating the pose increment of the lower platform by using the rope length at the current moment>
Figure SMS_67
The current pose X of the lower platform is obtained through calculation of a formula (14):
Figure SMS_68
(14)；
in the above-mentioned formula (14),
Figure SMS_69
and->
Figure SMS_70
The position increment of the lower platform and the attitude angle increment of the lower platform are respectively, and according to the rope length constraint equations of the formulas (11) and (12), the kinematic positive solution optimization objective function of the following formula (15) is obtained as follows:
Figure SMS_71
(15)；
establishing an incremental parallel flexible cable mechanism kinematic positive solution solving equation of the following formula (16) based on the kinematic positive solution optimizing objective function of the formula (15):
Figure SMS_72
(16)；
the parameters in the above formula (16) have the same meanings as the corresponding parameters in the above formula (13).
Preferably, in the above method, the method reduces the solution error of the solution equation of the kinematic positive solution of the incremental parallel flexible cable mechanism by the following method, including:
in the previous pose of the same lower platform
Figure SMS_73
When Taylor expansion is carried out on the position, the current pose of the lower platform obtained by solving each positive solution is used for +.>
Figure SMS_74
Carrying out Taylor expansion again, and carrying out next solving again in the updating mode (16);
in the method, the solution speed of the kinematic forward solution equation of the incremental parallel flexible cable mechanism is accelerated by the following steps:
solving to obtain the current pose of the lower platform in each positive solution
Figure SMS_75
Performing Taylor expansion again according to formula (16), and introducing the matrix of formula (16)>
Figure SMS_76
、/>
Figure SMS_77
Storing; when updating Taylor expansion each time, the current actual pose of the lower platform is +.>
Figure SMS_78
Carry to->
Figure SMS_79
、/>
Figure SMS_80
。
As shown in fig. 6, the embodiment of the present invention further provides a FAST novel feed cabin mechanism control method, including:
a1, before a FAST novel feed cabin mechanism operates, receiving a lower platform expected pose of the FAST novel feed cabin mechanism planned out of line;
a2, when the system runs, the lower platform of the FAST novel feed cabin mechanism is controlled in a force and position mixed control mode according to the received expected pose of the lower platform, and in the control process, the current pose of the lower platform is monitored through a visual tracking system until the control process is finished;
step A3, judging whether the visual tracking system fails or not in the process of monitoring the current pose of the lower platform through the visual tracking system, if so, executing the step A4, and if not, repeatedly executing the step A2;
And A4, solving the current pose of the lower platform of the FAST novel feed cabin mechanism by adopting the FAST novel feed cabin mechanism kinematics positive solution solving method, re-planning the expected pose of the lower platform according to the current pose of the lower platform, and re-executing the step A2 according to the re-planned expected pose of the lower platform to perform force-position hybrid control on the lower platform.
Preferably, in step A2 of the above control method, the control of the lower platform of the FAST new feed cabin mechanism by the hybrid control method of the received desired pose of the lower platform includes:
solving equations and dynamic models through kinematic positive solutions of incremental parallel flexible cable mechanisms, and utilizing received expected pose of lower platform
Figure SMS_81
Respectively calculating and obtaining expected rope length L of parallel flexible rope mechanisms of the platform under the drive of the FAST novel feed cabin mechanism d And the expected cable force T d ；
According to the obtained expected rope length L d Controlling the rope length of the 6-set upper stay rope mechanism of the parallel flexible rope mechanism and according to the obtained expected rope force T d And controlling the cable force of the 3 sets of lower cable mechanisms of the parallel flexible cable mechanism.
Preferably, in the control method, the received desired pose of the lower platform is utilized by solving an equation through kinematic positive solutions of incremental parallel-flexible-rope mechanisms in the following manner
Figure SMS_82
Calculating to obtain expected rope length L of parallel flexible rope mechanism of FAST novel feed cabin mechanism d Comprising:
the kinematic positive solution equation of the incremental parallel flexible cable mechanism is expressed as formula (16):
Figure SMS_83
(16);
the meaning of each parameter in the formula (16) is the same as that of each corresponding parameter in the formula (16) in the FAST novel feed cabin mechanism kinematics positive solution method;
according to the length of the rope at the previous moment
Figure SMS_84
Solving and calculating the pose increment of the lower platform
Figure SMS_85
Then combine the former pose of the lower platform>
Figure SMS_86
Solving the current pose of the lower platform
Figure SMS_87
The expected rope length L is obtained according to the current pose of the lower platform d ；
Utilizing the received lower platform desired pose by parallel-flex mechanism dynamics model in the following manner
Figure SMS_88
Calculated to obtainThe expected cable force T of the parallel flexible cable mechanism is obtained d Comprising:
the parallel flexible rope mechanism dynamic model is (17):
Figure SMS_89
(17);
determining expected cable force T of parallel flexible cable mechanism through dynamic model of parallel flexible cable mechanism of (17) d A cable force optimization function satisfying the following equation (18):
Figure SMS_90
(18);
in the above formulae (17) and (18),
Figure SMS_93
the pose is expected for the lower platform; />
Figure SMS_96
A first order derivative of the expected pose of the lower platform is used for representing the speed variable of the lower platform; />
Figure SMS_100
A second derivative of the expected pose of the lower platform is used for representing the acceleration variable of the lower platform; / >
Figure SMS_94
；/>
Figure SMS_98
；/>
Figure SMS_101
；J d The matrix is a jacobian matrix corresponding to the parallel flexible cable mechanism; j (J) dT The device is a transpose of a jacobian matrix corresponding to the parallel flexible cable mechanism; m is m P For the lower platform quality, I 3×3 Is a unitary matrix, 0 3×3 Is an all-zero matrix, 0 3×1 Is an all-zero vector, g is a gravitational acceleration vector, < ->
Figure SMS_103
For a rotation matrix of the local coordinate system C system to the global coordinate system G system,/for>
Figure SMS_91
For an antisymmetric matrix corresponding to the angular velocity omega, C I n for the inertia matrix of the lower platform in C series, < >>
Figure SMS_95
， M I n For the inertia matrix of the lower platform in the M system, < >>
Figure SMS_99
For the rotation matrix of M-series versus C-series, < >>
Figure SMS_102
A transposed matrix of the rotation matrix of the M system relative to the C system; parameters corresponding to the subscript S and the subscript U are parameters corresponding to 6 sets of upper inhaul cable mechanisms and parameters corresponding to 3 sets of lower inhaul cable mechanisms respectively; />
Figure SMS_92
The matrix is a jacobian matrix corresponding to the upper inhaul cable mechanism; />
Figure SMS_97
The matrix is a jacobian matrix corresponding to the lower guy cable mechanism;
based on the expected pose of the lower platform through the determined cable force optimization function
Figure SMS_104
Desired cable force T for a given parallel flex cable mechanism d ；
Determining the expected cable force of the down cable mechanism according to the redundancy of the parallel flexible cable mechanism
Figure SMS_105
After that, the desired cable force of the cable-up mechanism +.>
Figure SMS_106
The unique determination is as follows:
Figure SMS_107
(19);
in the above-mentioned formula (19),
Figure SMS_108
the cable-lifting mechanism corresponds to the transposition of the jacobian matrix; / >
Figure SMS_109
The device is a transposition of a jacobian matrix corresponding to the lower inhaul cable mechanism; the other parameters have the same meanings as those of the corresponding parameters in the above formulas (17) and (18).
In actual control, when the expected pose of the lower platform is given, the expected rope length is obtained by solving an equation through kinematic positive solution of an incremental parallel flexible rope mechanism
Figure SMS_110
Actual rope length +.>
Figure SMS_111
Feeding back through an encoder;
tracking 6 the desired rope length of the pull-up rope mechanism 4 by control law in the position mode of the drive
Figure SMS_112
For the current pose of the lower platform +.>
Figure SMS_113
Performing control;
the motor of the 6-set stay rope mechanism 4 works in a position mode, and controls the rope length by using a PID controller, and a position increment signal sent to a motor driver of the stay rope mechanism 4 is as follows:
Figure SMS_114
(21)；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_115
、/>
Figure SMS_116
、/>
Figure SMS_117
diagonal coefficient matrixes of proportional term, integral term and differential term of the controller respectively;
real-time feedback of actual cable force through cable force sensor
Figure SMS_118
When the expected pose of the lower platform is given, the dynamics model and the cable force optimization function are combined, and the expected cable force of 3 sets of lower cable mechanisms 6 is calculated>
Figure SMS_119
And converts the torque signal into a motor which sends the torque signal to the 3 sets of lower guy rope mechanisms 6, and the cable force of the 3 sets of lower guy rope mechanisms 6 is +.>
Figure SMS_120
Control is carried out to realize the rope force of all the inhaul ropes of the parallel flexible rope mechanism >
Figure SMS_121
Is controlled by (a); />
The motor of the 3 sets of down-cable mechanisms 6 is arranged to work in a position mode, the force-position hybrid controller is used for controlling the length and the force of the rope respectively, and the position increment signals sent to the motor driver of the down-cable mechanisms 6 are as follows:
Figure SMS_122
(22)；
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_123
、/>
Figure SMS_124
、/>
Figure SMS_125
diagonal coefficient matrixes of proportional term, integral term and differential term corresponding to the rope length error respectively; />
Figure SMS_126
And the diagonal coefficient matrix is a proportional term corresponding to the cable force error.
According to the invention, through incremental type parallel flexible cable mechanism kinematic forward solution and force position hybrid control, control of the FAST feed cabin mechanism under the maximum zenith angle of 50 degrees can be realized, the control precision of the lower platform pose of the FAST feed cabin mechanism is met, the internal force of the parallel flexible cable mechanism can be effectively regulated, the cable force performance of the parallel flexible cable mechanism is improved, and the anti-interference capability is improved.
In order to clearly show the technical scheme and the technical effects, the method for solving and controlling the positive kinematics of the novel FAST feed cabin mechanism provided by the embodiment of the invention is described in detail in the following by using a specific embodiment.
Example 1
The embodiment provides a method for solving kinematic positive solutions of a FAST novel feed cabin mechanism, which comprises the following steps:
Step S1, establishing a local coordinate system C, P and M to describe the pose of a lower platform of the FAST novel feed cabin mechanism, wherein as shown in FIG. 2, an external cable mechanism anchors a point S on the feed cabin i Establishing a local coordinate system C, y of a feed source cabin by taking the plane center as an origin C C The axis is S 5 Point to the direction of origin C, z C The axis is perpendicular to the feed cabin anchoring point S i Plane up, x C The axis being perpendicular to C-y C z C A plane; p-x of local coordinate P system of lower platform P y P Built on the upper surface of the lower platform 1 to anchor the point A i The center of the plane is the origin P, x P 、y P The direction of the axis is shown in FIG. 2, z P Anchor point A of inhaul cable mechanism with shaft perpendicular to feed cabin i The plane is upward, a centroid coordinate system M system of the lower platform 1 is established, an origin M of the M system is positioned at the centroid position of the lower platform 1, directions of coordinate axes of the M system are parallel to the P system, and when the lower platform 1 keeps horizontal relative to the feed cabin, the P system, the M system and the C system are completely parallel. In the following, when the kinematic analysis in the feed cabin is performed, the coordinate system of the position and attitude angle references of the lower platform is selected as the coordinate system C.
And S2, determining geometric parameters and structural parameters of the parallel flexible cable mechanism. As shown in fig. 3, 4 and 5, the anchor point B on the feed deck is in the local coordinate system C i For the corresponding anchoring point of the ith strand upper stay rope mechanism on the star-shaped frame 11, D j Is the anchoring point of the j-th strand lower inhaul cable mechanism 6 on the star-shaped frame 11, and the distribution radius is r B The method comprises the steps of carrying out a first treatment on the surface of the When the structure reconstruction of the parallel flexible cable mechanism according to the task scene is considered, the anchoring point B i D because of the difference of the control distribution heights of the sliding rails j The distribution heights are fixed, and are respectively H Bi 、H D . Anchor point A of upper inhaul cable mechanism on lower platform i 9 has a distribution radius r A The method comprises the steps of carrying out a first treatment on the surface of the In the local coordinate system P, the anchor point C of the lower guy rope mechanism 6 on the lower platform i 10 are all fixed on the circumference of the upper part of the round table, and the distribution radius is r C The distribution height is H C . The position coordinates of these anchor points are expressed as:
Figure SMS_127
(1)；
Figure SMS_128
(2)；
Figure SMS_129
(3)；
Figure SMS_130
(4)；
Figure SMS_131
；/>
in the above formulas, the upper left letter indicates a coordinate system to which the coordinates or vectors refer, for example: P A i is the anchoring point A of the lower platform 1 in the P system i Is used for the purpose of determining the coordinates of (a), C B i is the anchor point B of the upper stay rope mechanism in the C system i Coordinates of (c);
by using
Figure SMS_132
、/>
Figure SMS_133
The rotation matrices of the P-series relative to the M-series and the M-series relative to the C-series are respectively shown. Since the P-series and M-series are fixed on the lower platform 1 and parallel to each other, the two systems are +.>
Figure SMS_134
Is an identity matrix. Anchor point a in local coordinates M and C i 、C i The coordinates of (2) are:
Figure SMS_135
(5)；
Figure SMS_136
(6)；
in the above-mentioned description of the invention,
Figure SMS_137
an offset vector from the M origin of the lower M centroid to the P origin, i.e. +.>
Figure SMS_138
;/>
Figure SMS_139
Is the position vector of the origin of the M line under the C line, i.e. +. >
Figure SMS_140
；/>
Figure SMS_141
For being in charge of the rotation matrix>
Figure SMS_142
Corresponding Euler angle vector
Figure SMS_143
。
And S3, defining a rope length constraint equation, and analyzing rope length constraints satisfied by the rope. As shown in fig. 3, the parallel flexible cable mechanism is divided into an upper cable mechanism 4 and a lower cable mechanism 6, namely a in fig. 3 respectively i B i And C j D j Their rope lengths are respectively:
Figure SMS_144
(7)；
Figure SMS_145
(8)；
in the above formulas (7) and (8),
Figure SMS_146
(9)；
Figure SMS_147
(10)；
at this time, the length vector of the parallel flexible rope mechanism can be recorded as
Figure SMS_148
，
Figure SMS_149
、/>
Figure SMS_150
The length vectors of the upper inhaul cable mechanism and the lower inhaul cable mechanism are respectively.
The current pose of the lower platform is represented by the position and the attitude angle of the M system relative to the C system, and the pose is recorded as
Figure SMS_152
Wherein->
Figure SMS_154
The Euler angle vector in the coordinate system C is the lower platform attitude. Anchor point B i Height H of (2) Bi Can be formed by a sensor arranged on a sliding railDirect readout, anchoring point D j Height H of (2) D Is a fixed parameter. I.e. each time a kinematic forward solution is performed, C B i 、 C D j the coordinates are known, at this time the theoretical value of rope length +.>
Figure SMS_156
Given by the above formulas (5) - (10); rope length vector of upper stay rope mechanism>
Figure SMS_153
And the rope length vector of the lower inhaul cable mechanism>
Figure SMS_155
Actual value of the total length of the rope
Figure SMS_157
Can initiate the pose through the lower platform>
Figure SMS_158
And (5) combining the motor encoder readings. [0024]At this time, the current pose of the lower platform +.>
Figure SMS_151
The satisfied rope length constraint equation is as follows: / >
Figure SMS_159
(11)；
Figure SMS_160
(12)。
And S4, establishing an incremental parallel flexible rope mechanism kinematic forward model. As the parallel flexible rope mechanism moves slowly in actual operation, the maximum traction speed of the feed cabin is 24mm/s, and the maximum rotation speed of the pitch angle is 1.2 multiplied by 10 -3 rad/s. Based on the hypothesized rope length constraint equation, the position of the lower platform in front of the previous position
Figure SMS_161
Taylor expansion is performed at the position and retained until the second order term is obtained to obtain the following formula (13)Incremental parallel flexible cable mechanism kinematic forward model:
Figure SMS_162
(13)；
the meaning of each parameter in the above formula (13) is the same as that of each parameter in the above formula (13), and is not repeated here.
In the actual process, the initial pose of the lower platform 1 can be accurately measured through an external sensor. Therefore, each time the kinematic positive solution is solved, the previous pose of the lower platform
Figure SMS_163
The corresponding rope length is known
Figure SMS_164
Calculated by formulas (11) and (12) in the step S3; the current pose of the lower platform is obtained through kinematic positive solution according to the following mode: measuring rope length +.>
Figure SMS_165
Calculating the pose increment of the lower platform by using the rope length at the current moment>
Figure SMS_166
The current pose X of the lower platform is calculated according to the following formula (14):
Figure SMS_167
(14)。
step S5, establishing an optimization problem according to a rope length constraint equation to solve the kinematic positive solution, and obtaining the following kinematic positive solution optimization objective function according to constraint conditions of formulas (11) and (12):
Figure SMS_168
(15)；
The meaning of each parameter in the above formula (15) is the same as that of each corresponding parameter in the above formula (13), and is not repeated here;
based on the kinematic positive solution optimization objective function of the formula (15), constructing an incremental parallel flexible cable mechanism kinematic positive solution solving equation of the following formula (16):
Figure SMS_169
(16);
the meaning of each parameter in the above formula (16) is the same as that of each corresponding parameter in the above formula (13), and is not repeated here.
The solving method can adopt the following mode (1) to reduce solving errors and adopts the following mode (2) to accelerate solving speed:
(1) In the previous pose of the same lower platform
Figure SMS_170
When Taylor expansion is carried out, along with +.>
Figure SMS_171
、
Figure SMS_172
The errors of the kinematic positive solution are obviously accumulated. Therefore, the current pose of the lower platform obtained by solving through each positive solution is +.>
Figure SMS_173
The Taylor expansion is carried out again, and the next solving is carried out again by the updating (16).
(2) Lower platform current pose obtained by solving at each time of positive solution
Figure SMS_174
The Taylor expansion is carried out again, so that the solving precision of the incremental kinematic algorithm can be effectively improved; however, the additional calculation of Taylor expansion causes the algorithm time to increase dramatically, so that the sign form of Taylor expansion can be stored, that is, the matrix +. >
Figure SMS_175
、/>
Figure SMS_176
Storing; when updating Taylor expansion each time, only the current pose of the lower platform is required to be +.>
Figure SMS_177
Carry to->
Figure SMS_178
、/>
Figure SMS_179
Thereby reducing computation time.
Example 2
The embodiment provides a control method of a FAST novel feed cabin mechanism, which is a force-position hybrid control method for kinematics-dynamics of parallel flexible cable mechanisms of the FAST novel feed cabin mechanism, wherein the lower platform pose is kinematically controlled by 6 sets of upper cable mechanisms, and the dynamics is controlled by 3 sets of lower cable mechanisms 6, so that the internal force of the parallel flexible cable mechanisms can be effectively regulated, the cable force performance is improved, and the anti-interference capability is improved.
As shown in fig. 5, the parallel flexible cable mechanism is divided into 9 sets of cable mechanisms, and comprises 6 sets of upper cable mechanisms 4 and 3 sets of lower cable mechanisms 6 which form a pair-pull type layout to drive the lower platform 1; the upper inhaul cable mechanisms 4 are divided into 3 pairs, each pair is evenly arranged at an interval of 120 degrees, and 3 sets of lower inhaul cable mechanisms 6 are equally spaced at an interval of 120 degrees and are staggered with each pair of upper inhaul cable mechanisms 4 at an interval of 60 degrees; the 6 sets of the cable-pulling mechanisms 4 consist of cable-pulling mechanism hoisting mechanisms 8, cable-pulling mechanism steel wires and cable-pulling mechanism anchoring points 9; the 3 sets of lower inhaul cable mechanisms 6 consist of lower inhaul cable mechanism hoisting mechanisms 7, lower inhaul cable mechanism steel wire ropes and lower inhaul cable mechanism anchoring points 10; the hoisting mechanisms of the upper inhaul cable mechanism 4 and the lower inhaul cable mechanism 6 are composed of a servo motor, an encoder, a winding drum and the like.
In the control system of the lower platform pose shown in fig. 7, the offline planning module is responsible for solving equations and dynamic models based on kinematic positive solutions, and calculating expected cable force through the lower platform expected pose
Figure SMS_180
Desired rope length +.>
Figure SMS_181
The method comprises the steps of carrying out a first treatment on the surface of the The kinematic control module and the dynamic control module respectively realize the rope length control of the 6-set upper inhaul cable mechanism 4 and the rope force control of the 3-set lower inhaul cable mechanism 6, and concretely realize the following:
solving an equation based on the kinematic positive solution of the formula (16), and according to the length of the rope at the current moment
Figure SMS_182
Solving the pose increment of the lower platform>
Figure SMS_183
Then combine the former pose of the lower platform>
Figure SMS_184
Solving the current pose of the lower platform>
Figure SMS_185
Solving the expected rope length according to the current pose of the lower platform>
Figure SMS_186
；
The kinematic positive solution equation of formula (16) is identical to the kinematic positive solution equation of the incremental parallel-flexible-wire mechanism of formula (16) of embodiment 1, and the corresponding parameters have the same meaning and are not repeated here.
Determining the expected rope force of the rope based on the parallel flexible rope mechanism dynamics model of (17)
Figure SMS_187
Satisfy formula (18):
Figure SMS_188
(17);
Figure SMS_189
(18);
the meaning of each parameter in the above formulae (17) and (18) is the same as the meaning of each parameter corresponding to the above formulae (17) and (18), and is not repeated here;
by means of a given cable force optimization function, the expected cable force T of the cable is given based on the expected pose of the lower platform d The method comprises the steps of carrying out a first treatment on the surface of the Due to the redundancy of the parallel flexible cable mechanisms, a cable force is expected for a given down cable mechanism 6
Figure SMS_190
After that, the cable force is desired by the cable-up mechanism 4>
Figure SMS_191
The unique determination is as follows:
Figure SMS_192
(19);
in the above-mentioned formula (19),
Figure SMS_193
the cable-lifting mechanism corresponds to the transposition of the jacobian matrix; />
Figure SMS_194
The device is a transposition of a jacobian matrix corresponding to the lower inhaul cable mechanism; the other parameters have the same meanings as those of the corresponding parameters in the above formulas (17) and (18), and are not repeated here.
The kinematics control of the upper inhaul cable mechanism can obtain the expected rope length and the actual rope length based on the incremental parallel flexible cable mechanism kinematics positive solution solving equation when the expected pose of the lower platform is given
Figure SMS_195
Feedback can be provided by the encoder; in the position mode of the drive, the desired rope length of the 6-set pull-up rope mechanism is tracked by means of a control law>
Figure SMS_196
Thereby realizing the current pose of the lower platform>
Figure SMS_197
Is controlled by the rope length. The motor of the 6-set stay rope mechanism is arranged to work in a position mode and a PID controller is usedThe rope length is controlled, and the position increment signal sent to the motor driver of the upper inhaul cable mechanism is:
Figure SMS_198
(20);
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_199
、/>
Figure SMS_200
、/>
Figure SMS_201
the diagonal coefficient matrix is the proportional term, integral term and differential term of the controller. On the basis of the kinematic control of the 6-set upper inhaul cable mechanism 4, the rope force of the 3-set lower inhaul cable mechanism 6 is controlled to be +. >
Figure SMS_202
Tracking desired cable force +.>
Figure SMS_203
Can effectively regulate and control 4 cable force of the upper cable mechanism of the parallel flexible cable mechanism>
Figure SMS_204
Improving the cable force of the parallel flexible cable mechanism>
Figure SMS_205
Thereby improving the anti-interference capability.
The dynamics control of the lower inhaul cable mechanism 6 and the actual cable force
Figure SMS_206
By means of real-time feedback of the cable force sensor, for the expected pose of a given lower platform, the expected cable force ++of 3 sets of lower cable mechanisms 4 can be calculated by combining the dynamic model and the cable force distribution function>
Figure SMS_207
And converts the torque signal into a torque signal to be sent to a motor, and controls 3 sets of ropes of the lower inhaul cable mechanism 6 in real timeForce->
Figure SMS_208
Thereby realizing the rope force of the parallel flexible rope mechanism>
Figure SMS_209
Is controlled by the control system. The motor of the 3 sets of lower inhaul cable mechanisms 6 is arranged to work in a position mode, the force and position mixed control controller is used for controlling the rope length and the rope force respectively, and the position increment signals sent to the motor driver of the lower inhaul cable mechanisms 6 are as follows: />
Figure SMS_210
(21)；
Wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure SMS_211
、/>
Figure SMS_212
、/>
Figure SMS_213
the diagonal coefficient matrix of the proportional term, the integral term and the differential term corresponding to the rope length error; />
Figure SMS_214
And the diagonal coefficient matrix is a proportional term corresponding to the cable force error.
Those of ordinary skill in the art will appreciate that: all or part of the flow of the method implementing the above embodiments may be implemented by a program to instruct related hardware, where the program may be stored in a computer readable storage medium, and the program may include the flow of the embodiment of each method as described above when executed. The storage medium may be a magnetic disk, an optical disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), or the like.
The above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (10)

1. The method for solving the positive kinematics solution of the FAST feed cabin mechanism is characterized by comprising the following steps of:
step S1, establishing a local coordinate system C system, a P system and an M system for describing the pose of a lower platform according to the connection relation between an outer cable mechanism of a FAST feed cabin mechanism and a feed cabin;
s2, determining geometric parameters and structural parameters of a parallel flexible cable mechanism serving as an inner cable mechanism of the FAST feed cabin mechanism according to the local coordinate system C system, the local coordinate system P system and the local coordinate system M system established in the step S1;
step S3, determining a rope length constraint equation met by the current pose of the lower platform according to the local coordinate systems C, P and M established in the step S1 and the geometric parameters and the structural parameters of the parallel flexible cable mechanism determined in the step S2;
Step S4, establishing an incremental parallel flexible cable mechanism kinematics forward solution model according to the rope length constraint equation met by the current pose of the lower platform determined in the step S3, establishing a kinematics forward solution optimization objective function according to the incremental parallel flexible cable mechanism kinematics forward solution model, and establishing an incremental parallel flexible cable mechanism kinematics forward solution equation according to the kinematics forward solution optimization objective function;
and S5, solving an incremental parallel flexible cable mechanism kinematics positive solution solving equation constructed in the step S4 to obtain the current pose of the lower platform of the FAST feed cabin mechanism.
2. The method for solving the positive kinematics solution of the FAST feed deck mechanism according to claim 1, wherein the parallel flexible cable mechanism serving as an inner cable mechanism of the FAST feed deck mechanism comprises 9 sets of cable mechanisms, wherein the cable mechanisms are formed by 6 sets of upper cable mechanisms and 3 sets of lower cable mechanisms in a pair-pull type layout, the 6 sets of upper cable mechanisms are divided into 3 pairs, each pair of upper cable mechanisms are uniformly arranged at an interval of 120 degrees, and the 3 sets of lower cable mechanisms are uniformly arranged at an interval of 120 degrees and are staggered with each pair of upper cable mechanisms at an interval of 60 degrees; 6 sets of upper inhaul cable mechanisms are used for controlling the kinematics of the lower platform pose of the feed cabin, and 3 sets of lower inhaul cable mechanisms are used for controlling the kinematics of the lower platform pose;
The upper inhaul cable mechanisms and the lower inhaul cable mechanisms are identical in composition and comprise a hoisting mechanism, a steel wire rope, a servo motor, an encoder and rope anchoring points.
3. The method for solving the positive kinematics solution of the FAST feed cabin mechanism according to claim 1 or 2, wherein in the step S1, a local coordinate system C, P and M describing the pose of the lower platform is established according to the connection relationship between the outer cable mechanism of the FAST feed cabin mechanism and the feed cabin in the following manner, and the method comprises the following steps:
anchoring point S of external cable mechanism on feed cabin i Establishing a local coordinate system C of the feed cabin by taking the plane center as an origin C;
the upper surface of the following platform is anchored with point A i The method comprises the steps of establishing a local coordinate system P system of a lower platform by taking the plane center as an origin P;
establishing a centroid coordinate system M of the lower platform by taking a centroid position M of the lower platform as an origin, wherein the directions of coordinate axes of the M system are parallel to the P system;
when the lower platform is kept horizontal relative to the feed deck, the P, M and C systems are completely parallel.
4. The method according to claim 1 or 2, wherein in the step S2, the geometric parameters and the structural parameters of the parallel flexible cable mechanism serving as the internal cable mechanism of the FAST feed cabin mechanism are determined according to the local coordinate systems C-system, P-system and M-system established in the step S1 in the following manner, and the method comprises the following steps:
In the local coordinate system C, the anchor point B on the feed cabin i For the corresponding anchoring point of the ith stay rope on the star-shaped frame, D j Anchoring point B for j-th stay rope on star-shaped frame i And D j The distribution radius of (2) is r B Stay cable anchorage point D j Is of a fixed distribution height H D Stay cable anchor point B i Is distributed with the height of H Bi ；
Anchor point A of upper stay rope on lower platform i Is of distribution radius r A ；
In the local coordinate system P, the anchor point C of the lower stay rope on the lower platform j Are all fixed on the connecting ring of the lower platform, and the distribution radius is r C The distribution height is H C The method comprises the steps of carrying out a first treatment on the surface of the Anchor point B i 、D j 、A i 、C j Position coordinates of (a) C B i 、 C D j 、 P A i 、 P C j The method comprises the following steps of:
Figure QLYQS_1
(1)；
Figure QLYQS_2
(2) ；
Figure QLYQS_3
(3) ；
Figure QLYQS_4
(4) ；
in the above formulae (1) to (4), T represents a transposed matrix; i is the number of upper guy wires, i=1, …,6; j is the number of down-cables, j=1, …,3;
anchoring point A in local coordinate systems M and C i 、C j Coordinates of (c) M A i 、 M C j 、 C A i 、 C C j The method comprises the following steps of:
Figure QLYQS_5
(5)；
Figure QLYQS_6
(6)；
in the above formulas (5) and (6), P A i is the anchorage point A under the local coordinate system P system i Coordinates of (c); P C j is the anchoring point C under the local coordinate system P system j Coordinates of (c);
Figure QLYQS_7
an offset vector from the M origin of the lower M center to the P origin, i.e. +.>
Figure QLYQS_8
；/>
Figure QLYQS_9
Is the position vector of the origin of the M line under the C line, i.e. +.>
Figure QLYQS_10
；/>
Figure QLYQS_11
For the rotation matrix of M-series versus C-series, < >>
Figure QLYQS_12
，/>
Figure QLYQS_13
The Euler angle vector of the current pose of the lower platform in the C system represents the pose angle of the lower platform; M A i Is an anchor point A under a local coordinate system M system i Coordinates of (c); M C j is the anchoring point C under the local coordinate system M system j Coordinates of (c);
in the step S3, a rope length constraint equation satisfied by the current pose of the lower platform is determined according to the local coordinate systems C, P and M established in the step S1 and the geometric parameters and structural parameters of the parallel flexible cable mechanism determined in the step S2, and the method includes:
the rope of the parallel flexible rope mechanism comprises a top stay ropeAnd a lower stay rope, a length of the upper stay rope
Figure QLYQS_14
And rope length of the lower dragline->
Figure QLYQS_15
The method comprises the following steps of:
Figure QLYQS_16
(7)；
Figure QLYQS_17
(8)；
in the above formulas (7) and (8), the formula (I) is represented by
Figure QLYQS_18
The length vector of the upper guy rope mechanism is
Figure QLYQS_19
The method comprises the steps of carrying out a first treatment on the surface of the By->
Figure QLYQS_20
The length vector of the obtained down-cable mechanism is +.>
Figure QLYQS_21
；
Figure QLYQS_22
(9)；
Figure QLYQS_23
(10)；
In the above formulas (9) and (10), T represents a transposed matrix; M C j is the anchoring point C under the local coordinate system M system j Coordinates of (c);
lower platform current pose
Figure QLYQS_24
Represented by the position and attitude angle of the M-line relative to the C-line, wherein>
Figure QLYQS_25
For Euler angle vector of current pose of lower platform in C system, representing pose angle of lower platform, determining current pose of lower platform according to the Euler angle vector
Figure QLYQS_26
The satisfied rope length constraint equation is:
Figure QLYQS_27
(11)；
Figure QLYQS_28
(12)；
in the above formulas (11) and (12),
Figure QLYQS_29
、/>
Figure QLYQS_30
the rope length of the upper inhaul cable and the rope length of the lower inhaul cable at the previous moment are respectively; p (P) 0 An initial position vector expressed as the origin of the M system under the C system; / >
Figure QLYQS_31
For being in charge of the rotation matrix>
Figure QLYQS_32
Corresponding initial euler angle vectors; C B i is an anchor point B under a local coordinate system C system i Coordinates of (c); C D j is the anchorage point D under the local coordinate system C system j Is defined by the coordinates of (a).
5. The FAST feed cabin mechanism kinematic forward solution method according to claim 4, wherein in the step S4, an incremental parallel flexible cable mechanism kinematic forward solution model is established according to a rope length constraint equation satisfied by the current pose of the lower platform determined in the step S3, and the method comprises the following steps:
the rope length constraint equations of (11), (12) are set in the previous pose of the lower platform
Figure QLYQS_33
Performing Taylor expansion, and reserving until a second order term to obtain an incremental parallel flexible rope mechanism kinematic forward model of the following formula (13):
Figure QLYQS_34
(13)；
in the previous pose formula of the lower platform and (13),
Figure QLYQS_41
is the position vector of the previous moment; />
Figure QLYQS_42
Is the Euler angle vector of the previous moment; t is a transposed matrix; />
Figure QLYQS_53
、/>
Figure QLYQS_38
The rope length of the upper inhaul cable and the rope length of the lower inhaul cable at the current moment are respectively +.>
Figure QLYQS_46
、/>
Figure QLYQS_50
The rope length of the upper inhaul cable and the rope length of the lower inhaul cable at the previous moment are respectively; />
Figure QLYQS_56
For the increment of the lower platform pose->
Figure QLYQS_40
And->
Figure QLYQS_54
The position increment of the lower platform and the attitude angle increment of the lower platform are respectively;
Figure QLYQS_59
indicating the length of the upper guy cable at the current time >
Figure QLYQS_60
Before the lower platform, the position X P Partial derivative of lower platform position vector P, < >>
Figure QLYQS_37
Representing the partial derivative; />
Figure QLYQS_48
Indicating the length of the upper guy cable at the current time>
Figure QLYQS_55
In the position of the next previous platform X P Pair and rotation matrix->
Figure QLYQS_58
Partial derivatives of the corresponding euler angle vectors Φ;
Figure QLYQS_36
indicating the length of the upper guy cable at the current time>
Figure QLYQS_43
Before the lower platform, the position X P Position vector P and rotation matrix of the lower platform>
Figure QLYQS_47
The second partial derivative of the corresponding euler angle vector Φ;
Figure QLYQS_52
indicating the length of the downcable at the current time>
Figure QLYQS_35
Before the lower platform, the position X P Partial derivative of the pair with the lower platform position vector P; />
Figure QLYQS_44
Indicating the length of the downcable at the current time>
Figure QLYQS_49
Before the lower platform, the position X P Pair and rotation matrix->
Figure QLYQS_57
Partial derivatives of the corresponding euler angle vectors Φ;
Figure QLYQS_39
indicating the length of the downcable at the current time>
Figure QLYQS_45
Before the lower platform, the position X P Position vector P and rotation matrix of the lower platform>
Figure QLYQS_51
The second partial derivative of the corresponding euler angle vector Φ.
6. The FAST feed cabin mechanism kinematic forward solution solving method according to claim 5, wherein in the step S4, a kinematic forward solution optimizing objective function is constructed according to an incremental parallel flexible cable mechanism kinematic forward solution model, and an incremental parallel flexible cable mechanism kinematic forward solution solving equation is constructed according to the kinematic forward solution optimizing objective function, including:
In the running of the FAST feed cabin mechanism, the initial pose of the lower platform is accurately measured by an external sensor, and when the kinematic correct solution is solved each time, the lower platform is arrangedFront pose of platform
Figure QLYQS_61
Is a known value, and corresponds to the previous pose of the lower platform
Figure QLYQS_62
Calculated by the above formulas (11) and (12); solving the current pose of the lower platform through kinematic positive solution according to the following mode: measuring rope length +.>
Figure QLYQS_63
Calculating the pose increment of the lower platform by using the rope length at the current moment>
Figure QLYQS_64
The current pose X of the lower platform is obtained through calculation of a formula (14):
Figure QLYQS_65
(14)；
in the above-mentioned formula (14),
Figure QLYQS_66
and->
Figure QLYQS_67
The position increment of the lower platform and the attitude angle increment of the lower platform are respectively, and according to the rope length constraint equations of the formulas (11) and (12), the kinematic positive solution optimization objective function of the following formula (15) is obtained as follows:
Figure QLYQS_68
(15)；
establishing an incremental parallel flexible cable mechanism kinematic positive solution solving equation of the following formula (16) based on the kinematic positive solution optimizing objective function of the formula (15):
Figure QLYQS_69
(16)；
each parameter in the above formula (16) has the same meaning as each corresponding parameter in the formula (13) in claim 5.
7. The method for solving the positive kinematics solution of the FAST feed cabin mechanism according to claim 6, wherein,
in the method, the solving error of the kinematic positive solution solving equation of the incremental parallel flexible cable mechanism is reduced by the following method, which comprises the following steps:
In the previous pose of the same lower platform
Figure QLYQS_70
When Taylor expansion is carried out on the position, the current pose of the lower platform obtained by solving each positive solution is used for +.>
Figure QLYQS_71
Carrying out Taylor expansion again, and carrying out next solving again in the updating mode (16);
in the method, the solution speed of the incremental parallel flexible cable mechanism kinematic forward solution equation is accelerated by the following steps:
solving to obtain the current pose of the lower platform in each positive solution
Figure QLYQS_72
Performing Taylor expansion again according to formula (16), and introducing the matrix of formula (16)>
Figure QLYQS_73
、/>
Figure QLYQS_74
Storing; when updating Taylor expansion each time, the current actual pose of the lower platform is +.>
Figure QLYQS_75
Carry to->
Figure QLYQS_76
、/>
Figure QLYQS_77
。
8. A FAST feed cabin mechanism control method, comprising:
a1, before a FAST feed cabin mechanism operates, receiving a lower platform expected pose of the FAST feed cabin mechanism planned out of line;
a2, when the system runs, the lower platform of the FAST feed cabin mechanism is controlled in a force and position mixed control mode according to the received expected pose of the lower platform, and in the control process, the current pose of the lower platform is monitored through a visual tracking system until the control process is finished;
step A3, judging whether the visual tracking system fails or not in the process of monitoring the current pose of the lower platform through the visual tracking system, if so, executing the step A4, and if not, repeatedly executing the step A2;
And step A4, solving the current pose of the lower platform of the FAST feed cabin mechanism by adopting the positive solution solving method of the kinematics of the FAST feed cabin mechanism according to any one of claims 1 to 7, re-planning the expected pose of the lower platform according to the current pose of the lower platform, and re-executing step A2 according to the re-planned expected pose of the lower platform to perform force-position hybrid control on the lower platform.
9. The method for controlling a FAST feed deck mechanism according to claim 8, wherein in the step A2, the lower platform of the FAST feed deck mechanism is controlled in a hybrid control manner according to the received desired pose of the lower platform, comprising:
solving equations and dynamic models through kinematic positive solutions of incremental parallel flexible cable mechanisms, and utilizing received expected pose of lower platform
Figure QLYQS_78
Respectively calculating and obtaining expected rope length L of parallel flexible rope mechanisms of the platform under the drive of the FAST feed cabin mechanism d And the expected cable force T d ；
According to the obtained expected rope length L d Controlling the rope length of the 6-set upper stay rope mechanism of the parallel flexible rope mechanism and according to the obtained expected rope force T d And controlling the cable force of the 3 sets of lower cable mechanisms of the parallel flexible cable mechanism.
10. The FAST feed deck mechanism control method according to claim 9, wherein in the method, the received lower platform desired pose is utilized by incremental parallel-flexible-rope mechanism kinematics positive solution equation in the following manner
Figure QLYQS_79
Calculating the expected rope length L of the parallel flexible rope mechanism of the FAST feed cabin mechanism d Comprising:
the kinematic positive solution equation of the incremental parallel flexible cable mechanism is expressed as formula (16):
Figure QLYQS_80
(16);
the meaning of each parameter in the formula (16) is the same as that of each corresponding parameter in the formula (16) in the FAST feed cabin mechanism kinematics positive solution method of claim 6;
according to the length of the rope at the previous moment
Figure QLYQS_81
Solving the pose increment of the lower platform>
Figure QLYQS_82
Then combine the former pose of the lower platform>
Figure QLYQS_83
Solving the current pose of the lower platform>
Figure QLYQS_84
The expected rope length L is obtained according to the current pose of the lower platform d ；
Utilizing the received lower platform desired pose by parallel-flex mechanism dynamics model in the following manner
Figure QLYQS_85
Calculating and obtaining expected cable force T of the parallel flexible cable mechanism d Comprising:
the parallel flexible rope mechanism dynamic model is (17):
Figure QLYQS_86
(17);
determining expected cable force T of parallel flexible cable mechanism through dynamic model of parallel flexible cable mechanism of (17) d A cable force optimization function satisfying the following equation (18):
Figure QLYQS_87
(18);
in the above formulae (17) and (18),
Figure QLYQS_91
the pose is expected for the lower platform; />
Figure QLYQS_93
A first order derivative of the expected pose of the lower platform is used for representing the speed variable of the lower platform; />
Figure QLYQS_96
A second derivative of the expected pose of the lower platform is used for representing the acceleration variable of the lower platform;
Figure QLYQS_89
；/>
Figure QLYQS_92
；/>
Figure QLYQS_97
；J d Is flexible in parallel connectionThe jacobian matrix corresponds to the cable mechanism; j (J) dT The device is a transpose of a jacobian matrix corresponding to the parallel flexible cable mechanism; m is m P For the lower platform quality, I 3×3 Is a unitary matrix, 0 3×3 Is an all-zero matrix, 0 3×1 Is an all-zero vector, g is a gravitational acceleration vector, < ->
Figure QLYQS_99
For a rotation matrix of the local coordinate system C system to the global coordinate system G system,/for>
Figure QLYQS_88
For an antisymmetric matrix corresponding to the angular velocity omega, C I n for the inertia matrix of the lower platform in C series, < >>
Figure QLYQS_94
， M I n For the inertia matrix of the lower platform in the M system, < >>
Figure QLYQS_98
For the rotation matrix of M-series versus C-series, < >>
Figure QLYQS_100
A transposed matrix of the rotation matrix of the M system relative to the C system; parameters corresponding to the subscript S and the subscript U are parameters corresponding to 6 sets of upper inhaul cable mechanisms and parameters corresponding to 3 sets of lower inhaul cable mechanisms respectively; />
Figure QLYQS_90
The matrix is a jacobian matrix corresponding to the upper inhaul cable mechanism; />
Figure QLYQS_95
The matrix is a jacobian matrix corresponding to the lower guy cable mechanism;
based on the expected pose of the lower platform through the determined cable force optimization function
Figure QLYQS_101
Desired cable force T for a given parallel flex cable mechanism d ；
Determining the expected cable force of the down cable mechanism according to the redundancy of the parallel flexible cable mechanism
Figure QLYQS_102
After that, the desired cable force of the cable-up mechanism +.>
Figure QLYQS_103
The unique determination is as follows:
Figure QLYQS_104
(19);
in the above-mentioned formula (19),
Figure QLYQS_105
the cable-lifting mechanism corresponds to the transposition of the jacobian matrix; / >
Figure QLYQS_106
The device is a transposition of a jacobian matrix corresponding to the lower inhaul cable mechanism; the other parameters have the same meanings as those of the corresponding parameters in the above formulas (17) and (18).
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