CN109726515B - Cell satellite adsorption type non-cooperative target capturing method - Google Patents
Cell satellite adsorption type non-cooperative target capturing method Download PDFInfo
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Abstract
The invention discloses a cell satellite adsorption type non-cooperative target capturing method. Firstly, a cell satellite adsorption type capturing mechanism is designed, wherein the adsorption mechanism is designed to be a square sucker which is distributed on one surface of a cell satellite and has a structure similar to a tiger claw, and a butt joint mechanism which is used for coordinating a non-cooperative target after adsorption is used for the subsequent operation of the whole adsorption body. A physical model is established during adsorption, namely a two-body hinged connecting rod mechanism, and the situation that single-point or single-side contact and the like can not be stably adsorbed during adsorption is mainly considered. And (3) mathematical model construction during adsorption, namely establishing a multi-body model by using a D-H expression method and a Lagrange equation, and theoretically carrying out modeling analysis on the equivalent physical model. The cell satellite adsorption mechanism provided by the invention is used for directly adsorbing the non-cooperative target, and has the advantages of simplicity, reliability and economy.
Description
Technical Field
The invention relates to the technical field of space docking, in particular to a cell satellite adsorption type non-cooperative target capturing method.
Background
A space non-cooperative target refers to any spacecraft that is not designed for docking or capturing, i.e. any spacecraft on which the target is not equipped with gripping means (handles) for robotic arm capture and cooperative markers and feature blocks for aiding measurements, or which is not capable of attitude control, free rolling in space. Existing in-orbit spacecraft are basically non-cooperative targets. In view of the current development situation, the capture technology for the space cooperation target is relatively mature and is successfully applied to the on-orbit service. However, the capture of spatially non-cooperative targets is still in the process of exploration and development. Mainly utilizes catching tools such as a fly claw, a fly net and a paw, and has the problems of high catching difficulty and more key technologies to be solved. The existing catching mechanism has the problems of complex mechanism, high cost, high catching difficulty and the like, and a simple and reliable catching mechanism is urgently needed to be designed.
Disclosure of Invention
The technical problems to be solved by the invention are as follows: the invention provides a method for capturing a non-cooperative target by using a cell satellite adsorption type mechanism, aiming at solving the problems of high capturing difficulty, low reliability and the like of the existing non-cooperative target. Firstly, a non-cooperative target catching mechanism design-a cell satellite adsorption type catching mechanism is carried out, namely an adhesion mechanism similar to a tiger claw or a fish fork is designed on a cell satellite, and is directly attached to the surface of the non-cooperative target by using the adhesion mechanism, ideally, the specific surfaces of the two can be stably attached together, but unilateral or single-point contact is likely to occur, so that the specific surfaces cannot be adhered to cause adhesion failure. Then, modeling of the capture process is performed. The invention provides an equivalent model-a physical model of a two-body hinged connecting rod mechanism for the condition of single-point or single-side contact, and can perform theoretical analysis by utilizing a multi-body model established by a D-H representation method and a Lagrange equation.
In order to achieve the purpose, the technical scheme adopted by the invention for solving the technical problem is as follows:
a cell satellite adsorption type non-cooperative target capturing method comprises the following steps:
1) designing a cell satellite adsorption type catching mechanism and establishing a model thereof: the cell satellite adsorption type capturing mechanism is a cell satellite and comprises a cell satellite main body, a docking mechanism and an adhesion mechanism, wherein the docking mechanism is arranged on one surface of the cell satellite main body and used for subsequent operation, and the adhesion mechanism is used for adhesion;
2) constructing a physical model of a two-body hinged connecting rod mechanism for capturing a non-cooperative target process by a cell satellite adsorption type capturing mechanism;
3) establishing a mathematical model when the cell satellite adsorption type catching mechanism catches, firstly modeling a connecting rod and a joint by using a D-H expression method, determining a transformation matrix between any two adjacent coordinate systems, and further obtaining a total transformation matrix; then, defining a Lagrangian function by calculating the kinetic energy and the potential energy of the connecting rod and the joint; finally, solving a kinetic equation by deriving joint variables through a Lagrange function; further, each joint variable was solved, and adsorption stability was quantitatively analyzed.
As a further improvement of the invention, the adhesion mechanism is a suction cup.
As a further improvement of the invention, the sucker comprises a square sucker body and claw structures distributed around the square sucker body.
As a further improvement of the invention, the cell satellite main body is of a cubic structure.
As a further improvement of the present invention, the physical model of the two-body hinge linkage in step 2) refers to:
and establishing a model in which the cell satellite and the target satellite are connected through two orthogonal rotating pairs, and realizing the rotation of the cell satellite adsorption type capturing mechanism relative to the non-cooperative target in any direction.
As a further improvement of the invention, the specific steps of the step 3) are as follows:
establishing a model in which a cell satellite adsorption type capturing mechanism and a non-cooperative target are connected through two orthogonal rotating pairs to realize the rotation of the cell satellite in any direction relative to a target satellite;
the two-body hinged linkage mechanism is quantitatively expressed by using a D-H expression method: the angle θ represents the rotation angle around the z-axis, d represents the distance between two adjacent common perpendicular lines on the z-axis, a represents the length of each common perpendicular line, and the angle α represents the angle between two adjacent z-axes; the transformation between adjacent coordinate systems is realized by utilizing alpha, a, d and theta, and the local coordinate system xn+1-zn+1To xn-znThe transformation matrix of (a) is:
for the transformation of a plurality of coordinate systems, there arenTR＝1TR 2T1 3T2…nTn-1(ii) a Therefore, the coordinate transformation matrix represented by the D-H parameters of the two-body hinge linkage is as follows:
re-establishing non-cooperative targets relative to the inertial systemEquations of motion, i.e. establishing a coordinate system Tx of the non-cooperative target specimenbybzbRelative to the transformation matrix of the inertial system, the corresponding coordinate transformation matrix is:
the kinetic energy of the non-cooperative target specimen coordinate system is as follows:
wherein, UijIs a transformation matrix to a joint variable qjIs expressed as
Represents
Is rewritten as a pseudo inertia matrix
The inertia matrix is independent of joint angular velocity and velocity; bringing the above into the kinetic energy expression, there are:
the potential energy of the system is the sum of the potential energy of each connecting rod, and the gravity is not considered, so that the potential energy of the system is 0, namely P is 0; therefore, the system lagrangian function is:
derivation of the lagrange function yields the kinetic equation:
wherein the content of the first and second substances,nis the system degree of freedom, n is 8; q. q.sj(j is less than or equal to n) is a generalized coordinate, specifically referring to the 6 degrees of freedom x, y, z, alpha, beta, gamma and two rotation angles theta of the target spacecraft1And theta2，
And
are respectively generalized coordinates qjThe corresponding first and second derivatives; dijAnd DijkIs defined as:
each joint variable is solved by a model (8).
The invention has the beneficial effects that:
the invention provides a cell satellite adsorption mechanism for directly adsorbing a non-cooperative target to capture the non-cooperative target, wherein the cell satellite adsorption type capture mechanism is distributed on one surface of a cell satellite and is provided with a square sucker with a structure similar to a tiger claw, and a docking mechanism for cooperating the non-cooperative target after adsorption is used for the subsequent operation of the whole adsorption body. The structure has the advantages of simplicity, reliability and economy, and particularly, the equivalent processing method of the contact structure during adsorption has the characteristics of simplicity, convenience and intuition on the premise of ensuring that the movement form is not changed, and the stability of the adsorption process can be theoretically analyzed.
The modeling method of the invention provides an equivalent model, namely a physical model of a two-body hinged connecting rod mechanism, for the condition of single-point or unilateral contact, and can perform theoretical analysis by using a multi-body model established by a D-H representation method and a Lagrange equation. The modeling method is simple, utilizes the cell satellite adsorption mechanism to directly adsorb the non-cooperative target, and has the advantages of simplicity, reliability and economy.
Drawings
FIG. 1 is a flow chart of a method for catching a non-cooperative target mechanism by a cell satellite adsorption type catching mechanism;
FIG. 2 is a schematic view of the whole cell satellite adsorption type catching mechanism;
FIG. 3 is an enlarged view of the suction cup of FIG. 2;
FIG. 4 is a model view of a two-body articulated linkage;
fig. 5 is a motion transformation diagram of the target spacecraft body coordinate system.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
As shown in figure 1, the cell satellite adsorption type capture non-cooperative target method comprises the steps of designing and modeling a cell satellite adsorption type capture mechanism, building a physical model of a capture process, namely a two-body hinged link mechanism, building a mathematical model of the capture process, and building a multi-body model by using a Debavit-Hartenberg (D-H) expression method and a Lagrange equation.
(1) The design and modeling of the cell satellite adsorption type capturing mechanism comprise three parts: the cell satellite main body is designed into a cube, the adsorption mechanism is designed into square suckers 3 which are distributed on one surface of the cell satellite and have structures similar to gecko claws, and the butt joint mechanism is used for collaborating non-cooperative targets after adsorption and is used for subsequent operation on the adsorption whole body.
(2) Establishing a physical model of a capturing process, considering that a non-cooperative target rolls freely around the mass center of the non-cooperative target, and the non-cooperative target has 3 rotational degrees of freedom and 3 moving degrees of freedom; the cell satellite adsorption type capture mechanism can be considered to freely rotate around an adhesion point in space, and theoretically has 3 rotational degrees of freedom. Then the system will have 9 degrees of freedom. On the premise of ensuring that the movement is not influenced, in order to simplify the analysis, the spherical hinge can be equivalent to 2 orthogonal revolute pairs, and at the moment, the system has 8 degrees of freedom. The physical model of the two-body articulated linkage is the basis for mathematical modeling.
(3) Establishing a mathematical model of a capturing process, firstly, modeling a connecting rod and a joint by using a D-H expression method, determining a transformation matrix between any two adjacent coordinate systems, and further obtaining a total transformation matrix; then, defining a Lagrangian function by calculating the kinetic energy and the potential energy of the connecting rod and the joint; and finally, solving a kinetic equation by deriving the joint variable by the Lagrangian function. Furthermore, each joint variable can be solved, and the adsorption stability can be quantitatively analyzed.
As shown in figure 2, the cell satellite adsorption type catching mechanism comprises 20 multiplied by 20cm3A cell satellite body 1, a docking mechanism 2 for subsequent operations on one surface of the cell satellite, and a suction cup 3 having a gecko-like claw structure.
The cell satellite main body 1 has the characteristic of small volume and is easy to launch, and meanwhile, the cell satellite has a communication function and can be used as a cooperative mark after being absorbed into a whole with a non-cooperative target, namely, the cell satellite main body is equivalent to cooperative transformation of the non-cooperative target; the docking mechanism 2 for subsequent operation is prepared for further operation in consideration of the limitation of functions of the cell satellite body 1 and the limitation of operations which can be carried out on non-cooperative targets; the concrete structure of the sucker 3 with the gecko-like claw structure is shown in figure 3, and 8 claw structures 5 with the gecko-like structure are distributed around a square sucker body 4 and play a role in adhesion.
Ideally, the specific surfaces are stably attached together during adsorption, but a single-side or single-point contact is likely to occur, which may cause the specific surfaces to fail to adhere and cause adsorption failure. Therefore, an equivalent model, namely a physical model of the two-body hinged connecting rod mechanism, which is necessary to be provided for the condition of single-point or single-side contact can be theoretically analyzed by utilizing a multi-body model established by a D-H (Debavit-Hartenberg) representation method and a Lagrange equation.
Assuming that the non-cooperative target is eastern red satellite number one, the eastern red satellite number one is an approximately spherical 72-sided body, with a diameter of about 1m and a mass of about 173 kg. The running orbit is a large elliptical orbit, the height of the orbit at the near place is 439km, the height of the orbit at the far place is 2384km, the orbit period is 114min, and the inclination angle of the orbit is 68.44 degrees; the tracking spacecraft was a square with a profile parameter of 400 x 400mm and a mass of about 40 kg.
The model schematic diagram of the two-body hinged linkage mechanism is shown in figure 4, wherein T represents a target satellite, and C represents a cell satellite adsorption type catching mechanism; the cell satellite and the non-cooperative target are connected through two orthogonal rotating pairs, and the cell satellite rotates in any direction relative to the non-cooperative target.
The two-body hinged link mechanism is quantitatively expressed by using a D-H expression method, and the D-H parameter table is shown in a table 1.
TABLE 1 TWO-BODY HINGED LINKAGE D-H PARAMETER TABLE
Wherein the content of the first and second substances,
the two-body articulated link mechanism is represented quantitatively by using a D-H representation method: angle θ represents the angle of rotation about the z-axis, d represents the distance between two adjacent common perpendicular lines on the z-axis, a represents the length of each common perpendicular line (also called joint offset), and angle α represents the angle between two adjacent z-axes (also called joint twist); the transformation between adjacent coordinate systems is realized by utilizing alpha, a, d and theta, and a local coordinate system xn+1-zn+1To xn-znThe transformation matrix of (a) is:
for the transformation of a plurality of coordinate systems, there arenTR＝1TR 2T1 3T2…nTn-1. Therefore, the coordinate transformation matrix represented by the D-H parameters in Table 1 is:
wherein the 0 system is a transition coordinate system introduced for convenience of transformation.
Considering that the non-cooperative target itself is also moving, it is obvious that the non-cooperative target object coordinate system TxbybzbNot an inertial system, it is necessary to establish the equation of motion of the non-cooperative target with respect to the inertial system, i.e., to establish the non-cooperative target specimen coordinate system TxbybzbA transformation matrix with respect to the inertial frame. Referring to FIG. 5, the D-H parameter table is:
TABLE 2 target spacecraft D-H parameterTable
The corresponding coordinate transformation matrix is:
wherein the 0 system is a transition coordinate system introduced for convenience of transformation.
The kinetic energy of the system is:
wherein, UijIs a transformation matrix to a joint variable qjIs expressed as
Represents
Can be rewritten as
The inertia matrix is independent of joint angular velocity and velocity, so it only needs to be calculated once. Bringing the above into the kinetic energy expression, there are:
the potential energy of the system is the sum of the potential energy of each connecting rod, and the gravity is not considered, so the potential energy of the system is 0, namely P is 0. Therefore, the system Lagrangian function is
Deriving a Lagrange function to obtain a kinetic equation
Wherein n is a system degree of freedom, where n is 8; q. q.sj(j is less than or equal to n) is a generalized coordinate, specifically referring to the 6 degrees of freedom x, y, z, alpha, beta, gamma and two rotation angles theta of the target spacecraft1And theta2，
And
are respectively generalized coordinates qjThe corresponding first and second derivatives; dijAnd DijkIs defined as:
the model (8) is used to solve for the individual joint variables.
In a word, the invention relates to the technical field of space docking and provides a method for capturing a non-cooperative target by using a cell satellite adsorption type capturing mechanism. Firstly, designing a cellular satellite adsorption type catching mechanism, wherein the cellular satellite is designed to be 20 multiplied by 20cm3The adsorption mechanism is designed to be distributed on a certain surface of the cell satelliteThere are square suction cups with a structure similar to a gecko's claw, and a docking mechanism for collaborating non-cooperative targets after adsorption for subsequent operation of the adsorption entity. A physical model building-two-body hinged connecting rod mechanism in a capturing process mainly considers the situation that adsorption may not be stable due to single-point or single-side contact and the like during adsorption. And (3) mathematical model construction during adsorption, namely establishing a multi-body model by using a D-H expression method and a Lagrange equation, and theoretically carrying out modeling analysis on the equivalent physical model. The cell satellite adsorption mechanism provided by the invention is used for directly adsorbing the non-cooperative target, and has the advantages of simplicity, reliability and economy.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention, and all equivalent changes and modifications made within the scope of the present invention should be considered as the technical scope of the present invention.
Claims (5)
1. A cell satellite adsorption type non-cooperative target capturing method is characterized by comprising the following steps:
1) designing a cell satellite adsorption type catching mechanism and establishing a model thereof: the cell satellite adsorption type capturing mechanism is a cell satellite and comprises a cell satellite main body (1), a docking mechanism (2) and an adhesion mechanism, wherein the docking mechanism is used for subsequent operation on one surface of the cell satellite main body (1);
2) constructing a physical model of a two-body hinged link mechanism for capturing a non-cooperative target process by a cell satellite adsorption type capturing mechanism;
3) establishing a mathematical model when the cell satellite adsorption type catching mechanism catches, firstly modeling a connecting rod and a joint by using a D-H expression method, determining a transformation matrix between any two adjacent coordinate systems, and further obtaining a total transformation matrix; then, defining a Lagrangian function by calculating the kinetic energy and the potential energy of the connecting rod and the joint; finally, solving a kinetic equation by deriving joint variables through a Lagrange function; then, solving each joint variable, and quantitatively analyzing the adsorption stability;
step 3) comprises the following steps:
establishing a model in which a cell satellite adsorption type capturing mechanism and a non-cooperative target are connected through two orthogonal rotating pairs to realize the rotation of the cell satellite in any direction relative to a target satellite;
the two-body hinged linkage mechanism is quantitatively expressed by using a D-H expression method: the angle θ represents the rotation angle around the z-axis, d represents the distance between two adjacent common perpendicular lines on the z-axis, a represents the length of each common perpendicular line, and the angle α represents the angle between two adjacent z-axes; the transformation between adjacent coordinate systems is realized by utilizing alpha, a, d and theta, and the local coordinate system xn+1-zn+1To xn-znThe transformation matrix of (a) is:
for the transformation of a plurality of coordinate systems, there arenTR＝1TR 2T1 3T2…nTn-1(ii) a Therefore, the coordinate transformation matrix represented by the D-H parameters of the two-body articulated linkage is:
then, an equation of motion of the non-cooperative target relative to the inertial system is established, namely, a coordinate system Tx of the non-cooperative target specimen is establishedbybzbRelative to the transformation matrix of the inertial system, the corresponding coordinate transformation matrix is:
the kinetic energy of the non-cooperative target specimen coordinate system is as follows:
wherein, UijIs a transformation matrix to a joint variable qjIs expressed as
Represents
Is rewritten as a pseudo inertia matrix
The inertia matrix is independent of joint angular velocity and velocity; bringing the above into the kinetic energy expression, there are:
the potential energy of the system is the sum of the potential energies of all the connecting rods, and the gravity is not considered, so that the potential energy of the system is 0, namely P is 0; therefore, the system lagrangian function is:
deriving a Lagrange function to obtain a kinetic equation:
wherein n is a system degree of freedom, and n is 8; q. q.sjIs a generalized coordinate, j is less than or equal to n, and specifically refers to 6 degrees of freedom x, y, z, alpha, beta, gamma and two rotation angles theta of the target spacecraft1And theta2，
And
are respectively generalized coordinates qjThe corresponding first and second derivatives; dijAnd DijkIs defined as:
the model (8) is used to solve for each joint variable.
2. The method for capturing non-cooperative targets by cell satellite adsorption according to claim 1, wherein: the adhesion mechanism is a sucker (3).
3. The method of claim 2, wherein the method comprises: the sucker (3) comprises a square sucker main body (4) and claw structures (5) distributed around the square sucker main body (4).
4. The method for capturing non-cooperative targets by cell satellite adsorption according to claim 1, wherein: the cell satellite main body (1) is of a cubic structure.
5. The method for capturing non-cooperative targets by cell satellite adsorption according to claim 1, wherein: the physical model of the two-body hinged link mechanism in the step 2) refers to:
and establishing a model in which the cell satellite and the target satellite are connected through two orthogonal rotating pairs, and realizing the rotation of the cell satellite adsorption type catching mechanism relative to the non-cooperative target in any direction.
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| WO2017000396A1 (en) * | 2015-06-30 | 2017-01-05 | 中国空间技术研究院 | Truss antenna reflector deployment dynamics modelling method based on multi-body analysis test |
| CN106628275A (en) * | 2016-09-30 | 2017-05-10 | 西北工业大学 | Space rapid rotation fragment despun capture system based on double-tethered satellite |
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