Method and device for determining static stiffness of cable parallel drive system for deep space exploration

Abstract

The application discloses a kind of static stiffness determination method and device for cable parallel drive system of deep space exploration.The method comprises the following steps: constructing system mechanics model based on initial structure parameter and operating state parameter, to obtain initial system state data;Based on initial system state data, the tension direction parameter and the action position parameter of each cable are calculated, and the generalized force data of the system is calculated based on the tension direction parameter and the action position parameter;Based on the change of generalized force data and platform pose parameter, the system stiffness matrix is calculated, and the system stiffness matrix is decomposed into passive stiffness component and active stiffness component, to obtain stiffness decomposition result;Based on stiffness decomposition result and tension parameter, the system stiffness distribution state is evaluated, target stiffness adjustment parameter is generated, and the tension parameter is adjusted and controlled based on target stiffness adjustment parameter, to obtain optimized static stiffness.The application solves the technical problem that static stiffness cannot be accurately determined.

Description

Technical Field

[0001] This invention relates to the field of deep space exploration, and more specifically, to a method and apparatus for determining the static stiffness of a cable parallel drive system for deep space exploration. Background Technology

[0002] To meet the needs of extraterrestrial object exploration for low-gravity simulation experiments, facilities such as [examples of such simulations] have been constructed. Figure 1 The low-gravity simulation platform for extraterrestrial bodies shown provides a low-gravity simulation environment for hovering, obstacle avoidance, ignition, and landing experiments of Mars, Moon, and asteroid probes. The system employs a suspension method, connecting the probe to a suspension cable. During the experiment, the cable moves with the probe, maintaining verticality and constant tension to simulate the low-gravity environment of extraterrestrial bodies. The entire system consists of... Figure 2 The system consists of a parallel cable drive system and a rapid servo system. The parallel cable drive system performs a wide range of movements and tracking, while the rapid servo system achieves precise hybrid control of tension and position tracking. By employing a hierarchical control design method, the technical difficulty and cost of design and manufacturing can be reduced, while simultaneously improving the system's control accuracy and speed.

[0003] The cable-driven parallel drive system provides the workspace and primary speed and acceleration for the rapid servo system. However, the cable system's unidirectional load-bearing capacity and susceptibility to elastic deformation reduce the system's stiffness and positioning accuracy, limiting response speed and operational precision. In particular, the low-gravity simulation test platform has a large workspace span, with the maximum span of the steel cable reaching 140 meters. Under the influence of gravity, it exhibits a catenary shape, further reducing the system's stiffness and positioning accuracy. This platform requires that, within a 74m × 20m × 20m workspace, when a 20-ton disc accelerates upwards at 2.6 m / s², the positional deviation be controlled within 100 mm.

[0004] Therefore, it is necessary to determine the stiffness of the cable parallel system in order to clarify its elastic deformation and positioning accuracy under a certain load, thereby providing a theoretical basis and implementation method for improving the system stiffness. Summary of the Invention

[0005] This invention provides a method and apparatus for determining the static stiffness of a cable-parallel drive system for deep space exploration, thereby at least solving the technical problem of inaccurate determination of static stiffness.

[0006] According to one aspect of the present invention, a method for determining the static stiffness of a cable-driven parallel system for deep space exploration is provided, comprising: acquiring initial structural parameters and operating state parameters of the cable-driven parallel system, and constructing a system mechanical model based on the initial structural parameters and the operating state parameters to obtain initial system state data, wherein the structural parameters include connection position parameters and length parameters of each cable, and the operating state parameters include platform pose parameters and tension parameters of each cable; calculating the tension direction parameters and action position parameters of each cable based on the initial system state data, and calculating generalized force data of the system based on the tension direction parameters and action position parameters; calculating the system stiffness matrix based on the generalized force data and the change in the platform pose parameters, and decomposing the system stiffness matrix into passive stiffness components and active stiffness components to obtain stiffness decomposition results; evaluating the system stiffness distribution state based on the stiffness decomposition results and the tension parameters, generating target stiffness adjustment parameters, and adjusting and controlling the tension parameters based on the target stiffness adjustment parameters to obtain optimized static stiffness.

[0007] According to another aspect of the present invention, a static stiffness determination device for a cable-parallel drive system for deep space exploration is also provided, comprising: a state determination module configured to acquire initial structural parameters and operating state parameters of the cable-parallel drive system, and construct a system mechanical model based on the initial structural parameters and the operating state parameters to obtain initial system state data, wherein the structural parameters include connection position parameters and length parameters of each cable, and the operating state parameters include platform pose parameters and tension parameters of each cable; and a generalized force calculation module configured to calculate the tension direction parameters of each cable based on the initial system state data. The system includes a generalized force data calculation module, configured to calculate the system stiffness matrix based on the generalized force data and the changes in the platform pose parameters, and decompose the system stiffness matrix into passive stiffness components and active stiffness components to obtain stiffness decomposition results; and a static stiffness calculation module, configured to evaluate the system stiffness distribution state based on the stiffness decomposition results and the tension parameters, generate target stiffness adjustment parameters, and adjust and control the tension parameters based on the target stiffness adjustment parameters to obtain optimized static stiffness.

[0008] In this embodiment of the invention, the above method solves the technical problem that static stiffness cannot be accurately determined. Attached Figure Description

[0009] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0010] Figure 1 This is a schematic diagram of a low-gravity simulation test platform for extraterrestrial bodies based on existing technology;

[0011] Figure 2 This is a schematic diagram of a parallel drive for a rapidly moving follower disk based on existing technology.

[0012] Figure 3 This is a flowchart of a method for determining the static stiffness of a cable-parallel drive system for deep space exploration, according to an embodiment of this application.

[0013] Figure 4 This is a flowchart of another method for determining the static stiffness of a cable-parallel drive system for deep space exploration according to an embodiment of this application.

[0014] Figure 5 This is a schematic diagram of an optional cable parallel drive system according to an embodiment of the present invention;

[0015] Figure 6 This is a schematic diagram of an optional coordinate system according to an embodiment of the present invention;

[0016] Figure 7 This is a flowchart of a method for establishing a quantitative relationship between pose perturbation and force response according to an embodiment of the present invention;

[0017] Figure 8 This is a structural schematic diagram of a static stiffness determination device for a cable parallel drive system for deep space exploration according to an embodiment of this application.

[0018] Figure 9 A schematic diagram of the structure of a computer device suitable for implementing embodiments of the present disclosure is shown. Detailed Implementation

[0019] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] According to an embodiment of the present invention, a method embodiment for determining the static stiffness of a cable-parallel drive system for deep space exploration is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0022] Figure 3 This application discloses a method for determining the static stiffness of a cable-parallel drive system for deep space exploration, as described in an embodiment of this application. Figure 3 As shown, the method includes:

[0023] Step S302: Obtain the initial structural parameters and operating state parameters of the cable parallel drive system, and construct a system mechanical model based on the initial structural parameters and the operating state parameters to obtain initial system state data;

[0024] For example, a global coordinate system is established based on the cable connection position parameters in the initial structural parameters, and the platform spatial position is determined in the global coordinate system based on the platform pose parameters in the operating state parameters, thus obtaining pose expression data; based on the length parameters in the initial structural parameters and the pose expression data, the spatial geometric relationship of each cable is calculated, thus obtaining cable geometric relationship data; based on the tension parameters in the operating state parameters and the cable geometric relationship data, the mechanical equilibrium relationship in the system mechanical model is constructed, thus obtaining the initial system state data. The structural parameters include the connection position parameters and length parameters of each cable, and the operating state parameters include the platform pose parameters and the tension parameters of each cable.

[0025] Step S304: Based on the initial system state data, calculate the tension direction parameters and action position parameters of each cable, and calculate the generalized force data of the system based on the tension direction parameters and action position parameters;

[0026] For example, based on the cable geometric relationship data in the initial system state data, the unit direction vector of each cable is calculated to obtain the tension direction parameter; based on the connection position parameters in the initial structural parameters and the platform pose parameters, the position of the action point of each cable on the platform is determined to obtain the action position parameter; based on the tension direction parameter and the action position parameter, a system Jacobian matrix is ​​constructed, and calculations are performed based on the Jacobian matrix and the tension parameter to obtain the generalized force data.

[0027] Step S306: Based on the generalized force data and the change in the platform pose parameters, calculate the system stiffness matrix, and decompose the system stiffness matrix into passive stiffness components and active stiffness components to obtain the stiffness decomposition result.

[0028] For example, based on the changes in the platform pose parameters, the generalized force data is analyzed to obtain the system stiffness matrix; based on the system stiffness matrix and the tension parameters, the passive stiffness components caused by the tension characteristics of each cable are calculated, and based on the system stiffness matrix and the platform pose parameters, the active stiffness components caused by changes in system configuration are calculated; based on the passive stiffness components and the active stiffness components, the stiffness decomposition result is obtained.

[0029] Step S308: Based on the stiffness decomposition results and the tension parameters, evaluate the stiffness distribution state of the system, generate target stiffness adjustment parameters, and adjust and control the tension parameters based on the target stiffness adjustment parameters to obtain optimized static stiffness.

[0030] First, target stiffness adjustment parameters are generated. For example, based on the stiffness decomposition results, stiffness components of the system in different directions are extracted to obtain stiffness distribution data. The stiffness distribution data is compared with preset stiffness distribution requirements to obtain stiffness deviation data. A mapping relationship is established between the tension parameters and the stiffness distribution data. Based on the mapping relationship, the stiffness deviation data is converted into a tension adjustment amount, and the tension adjustment amount is constrained to obtain the target stiffness adjustment parameters.

[0031] Next, the optimized static stiffness is obtained. For example, based on the target stiffness adjustment parameter, the tension adjustment amount corresponding to each cable is determined, and the tension adjustment amount is applied to each cable drive mechanism to adjust the tension parameter; based on the adjusted tension parameter, the system stiffness matrix is ​​recalculated and the stiffness decomposition result is updated. When the updated stiffness decomposition result meets the preset stiffness condition, the optimized static stiffness is obtained.

[0032] In ground-based simulation systems related to deep space exploration, cable-driven parallel systems typically undertake the dual tasks of supporting large-scale motion and simulating low-gravity environments. From existing engineering practice, a significant characteristic of such systems is their enormous scale and considerable flexibility, especially when cable lengths reach tens or even hundreds of meters, where the cable's self-weight effect becomes non-negligible. Further analysis reveals that in this situation, the actual force path and geometry of the cable are no longer approximately straight, but rather exhibit a typical catenary distribution. This change directly affects the system's force transmission path and stiffness distribution. Therefore, if the ideal straight-line assumption is still used when establishing the system model, it will inevitably lead to stiffness estimation errors, which will amplify the errors in subsequent control processes. Based on these issues, this embodiment, while maintaining computational feasibility, couples the cable's geometric relationships, tension states, and self-weight effects.

[0033] Figure 4 This is another method for determining the static stiffness of a cable-parallel drive system for deep space exploration according to an embodiment of this application, such as... Figure 4 As shown, the method includes:

[0034] Step S402: Construct a system mechanical model.

[0035] In practical applications, cable parallel drive systems, such as Figure 5 The system consists of multiple fixed support structures and a moving platform. One end of each cable is fixed to a tower or support structure, and the other end is connected to different positions on the moving platform. To provide a unified description of the system, a unified coordinate system needs to be established first.

[0036] In this embodiment, as Figure 6 As shown, the geometric center of the test site is selected as the reference point to establish a global fixed coordinate system. , where the coordinate axes Pointing in a vertically upward direction. and They are arranged horizontally. Simultaneously, a local coordinate system is defined on the motion platform. Its origin is set at the geometric center of the platform, and the coordinate system moves with the platform.

[0037] For the The fixed-end connection position of the root cable is expressed in the global coordinate system as follows:

[0038]

[0039] In the above expression, Indicates the first The position vector of the fixed end of the root cable. , , These represent the coordinates of the point along the three coordinate axes of the global coordinate system; these parameters are structural parameters.

[0040] Correspondingly, the first The connection position of the root cable in the platform's local coordinate system is represented as follows:

[0041]

[0042] in, This represents the position vector of the connection point of the cable on the platform. , , These are the coordinate components in the local coordinate system.

[0043] To describe the platform's state in space, a pose parameter vector is introduced:

[0044]

[0045] In this expression, This represents the position vector of the platform's centroid in the global coordinate system, while These represent the platform's attitude angles around the three coordinate axes. These six parameters together constitute the platform's operational status parameters.

[0046] When the platform moves, points in its local coordinate system need to be mapped to the global coordinate system through rigid body transformation. For the first... The connection point of the roots, its position in the global coordinate system can be represented as:

[0047]

[0048] In this formula, This indicates the position of the platform-side connection point in the global coordinate system. This represents a rotation matrix composed of attitude angles, which is used to transform local coordinates to global coordinates.

[0049] In engineering implementation, when the attitude angle is small, the following approximation can be used:

[0050]

[0051] in, Represents the identity matrix. The antisymmetric matrix constructed from the attitude angles has the following form:

[0052]

[0053] This matrix is ​​used to describe the effect of small-angle rotation on the vector, where , , These represent the rotation angles around the three coordinate axes, respectively.

[0054] Based on the above positional relationships, we can obtain the first... The spatial vector of the root:

[0055]

[0056] This vector represents the direction from the fixed end to the platform end, and its magnitude is the geometric length of the cable:

[0057]

[0058] in, Indicates the first The straight length of the root cable, Representing vectors respectively Components in three directions.

[0059] In traditional models, this length is usually directly used in stiffness calculations. However, under large-span conditions, this approach ignores the influence of the cable's self-weight. Therefore, this embodiment corrects the cable length and uses an equivalent length expression:

[0060]

[0061] In this formula, This indicates the corrected equivalent length. This represents the gravitational load per unit length of the cable. Indicates the first Tension of the root cord, This is an empirical correction factor used to adjust the weight of the effect of self-weight. To prevent small constants with a denominator of zero.

[0062] Furthermore, after obtaining the geometric relationships, the mechanical equilibrium relationships of the system are established by combining them with the tension parameters. Let there be a total of [number missing] in the system. If the roots are fixed, then the force balance of the system can be expressed as:

[0063]

[0064] in, This represents the external load vector acting on the platform. Indicates the first Tension of the root cord, This represents the unit direction vector of the cable.

[0065] In this embodiment, a global fixed coordinate system and a local coordinate system that moves with the motion platform are established. Based on the fixed end connection position parameters of each cable in the global fixed coordinate system, the platform end connection position parameters in the local coordinate system, and the platform pose parameters, the coordinates of the platform end connection positions of each cable in the global fixed coordinate system are obtained through rigid body transformation. Based on the coordinates of the fixed ends and platform ends of each cable in the global fixed coordinate system, the geometric length of each cable is calculated, and the geometric length is corrected using the equivalent length correction formula to obtain the equivalent length of each cable. Combining the equivalent length of each cable, tension parameters, and external loads, the force balance relationship of the system is established to construct the system mechanical model. The equivalent length correction method involves adjusting the geometric length of each cable based on its geometric length, combined with the gravitational load per unit length of the cable, the tension of the corresponding cable, empirical correction coefficients, and small constants to prevent the denominator from being zero, to obtain the equivalent length of each cable. The rigid body transformation is implemented using a rotation matrix. When the platform attitude angle is small, this rotation matrix can be approximated as the sum of the identity matrix and an antisymmetric matrix constructed from the attitude angles. The attitude angles are the rotation angles of the platform around the three coordinate axes of the global fixed coordinate system in the platform's pose parameters, and the antisymmetric matrix is ​​constructed from the aforementioned attitude angles. This method accurately compensates for the influence of cable self-weight, simplifies calculations, improves the modeling accuracy of the system's mechanical model, and better reflects actual engineering scenarios.

[0066] Step S404: Calculate the generalized force data.

[0067] Based on the spatial vector obtained in step S402 , can calculate the first The unit direction vector of the root:

[0068]

[0069] In this expression, Indicates the first The direction of the root cable is a unit vector, and its physical meaning is the direction of the tension. This represents the magnitude of the vector, i.e., the geometric length of the cable.

[0070] At the same time, the The position vector of the root's point of action on the platform can be represented as:

[0071]

[0072] in, Indicates the position of the point of action relative to the platform's center of mass. Let be a rotation matrix. These are local coordinates.

[0073] Considering that the platform is subjected to not only forces but also torques, a unified generalized force expression is needed. The generalized force of the system is defined as:

[0074]

[0075] in, Represents the resultant force vector. This represents the resultant moment vector.

[0076] Based on the principle of superposition of force and torque, the Jacobian matrix of the system can be constructed:

[0077]

[0078] In this matrix, the upper part represents the force direction mapping, and the lower part represents the torque mapping. Furthermore, the relationship between the generalized forces and tensions of the system can be obtained:

[0079]

[0080] in, This represents the tension vector.

[0081] In redundant drive systems, the tension solution is not unique. To introduce adjustability, the tension is expressed as:

[0082]

[0083] in, This represents the fundamental tension solution that satisfies the equilibrium condition. Describe the zero-space basis of the Jacobian matrix. This represents the adjustment parameter vector.

[0084] In this embodiment, based on the cable geometry data in the initial system state data, the unit direction vector of each cable is calculated by dividing its spatial vector by its magnitude. This unit direction vector represents the direction of tension, thus yielding the tension direction parameter. Based on the connection position parameters and platform pose parameters in the initial structural parameters, a rotation matrix is ​​used to map the connection positions of each cable in the platform's local coordinate system to their positions relative to the platform's center of mass, determining the position of each cable's point of action on the platform, thus obtaining the position parameter. A system Jacobian matrix is ​​constructed based on the tension direction parameter and the position parameter. The upper half of this Jacobian matrix maps the direction of force, and the lower half maps the direction of torque. Through the corresponding operation between this Jacobian matrix and the tension parameters, generalized force data containing the resultant force vector and resultant torque vector is obtained. This method improves the accuracy of generalized force calculation.

[0085] Step S406: Establish a quantitative relationship between pose perturbation and force response.

[0086] like Figure 7 As shown, the method for establishing a quantitative relationship between pose perturbation and force response includes the following steps:

[0087] Step S4062: Calculate the system stiffness matrix.

[0088] In classical mechanics, system stiffness is usually defined as the derivative of force with respect to displacement. In this embodiment, since the system involves both translation and rotation, the stiffness matrix is ​​defined in a generalized coordinate form.

[0089] The system stiffness matrix is ​​defined as follows:

[0090]

[0091] In this expression, Represents the system stiffness matrix. Represents the generalized force vector of the system. This represents the generalized pose vector of the platform. The rate of change of the generalized force generated within the system when the platform's pose undergoes a small change is called stiffness.

[0092] To facilitate the derivation, the expression for the generalized force is substituted into the above definition. From step S404, we know that:

[0093]

[0094] Therefore, differentiating the pose, we have:

[0095]

[0096] This formula is a superposition of two parts. One part comes from the Jacobian matrix changing with pose, and the other part comes from the tension changing with pose.

[0097] The stiffness matrix is ​​further written as:

[0098]

[0099] in,

[0100]

[0101]

[0102] In the above expression, The stiffness component caused by changes in the structure's geometry is usually called active stiffness; This represents the stiffness component caused by the elastic properties of the cable itself, and is usually called passive stiffness.

[0103] It needs to be specifically noted here that... The Jacobian matrix represents the rate of change of pose, reflecting the influence of changes in the system's geometric configuration on the force transmission path. This reflects the response characteristics of tension to pose disturbances.

[0104] Step S4064: Determine the passive stiffness components.

[0105] For the passive stiffness component, the core lies in determining the relationship between tension changes and length changes. Consider the first... The tension change of the root can be expressed as:

[0106]

[0107] in, This represents the change in tension. This indicates the tangential stiffness of the cable. This indicates the change in cable length.

[0108] Furthermore, the change in length can be expressed as:

[0109]

[0110] in, It is a unit direction vector. This indicates the displacement change at the platform-side connection point.

[0111] Substituting the above expression, we get:

[0112]

[0113] By combining all the cables, we can obtain a matrix form of the tension change:

[0114]

[0115] in:

[0116]

[0117] In this expression, This represents the tangent stiffness matrix, which is a diagonal matrix with diagonal elements representing the tangent stiffness of each cable.

[0118] Substituting into the passive stiffness expression, we get:

[0119]

[0120] This formula shows that the passive stiffness is determined by the directional distribution of the cables and the stiffness of each cable.

[0121] Step S4066: Determine the active stiffness components.

[0122] Active stiffness originates from changes in the system's geometry, specifically the effect of the Jacobian matrix changing with pose. For the ... The derivative of the direction vector of a root vector with respect to pose can be expressed as:

[0123]

[0124] in, Represents the identity matrix. This represents the directional projection matrix.

[0125] This expression reflects that the change in direction is only related to the component perpendicular to the original direction.

[0126] Furthermore, we can obtain:

[0127]

[0128] in, Indicates the first The geometric stiffness matrix corresponding to the root cable.

[0129] As can be seen from the above, passive stiffness is highly dependent on tangential stiffness. Traditional models typically employ:

[0130]

[0131] in, Indicates the elastic modulus of a material. Represents the cross-sectional area. Indicates the length of the cable.

[0132] However, this expression has significant limitations under long-span conditions. Actual testing shows that as the cable span increases, the stiffness decreases significantly faster than predicted by the linear model. The essence of this phenomenon lies in the change in the spatial shape of the cable; its force path is no longer along a straight line but rather distributed along a curve.

[0133] Based on this observation, this embodiment proposes an improved model.

[0134] Define curvature factor:

[0135]

[0136] In this expression, Indicates the first The equivalent curvature parameter of the rootstock, This represents gravity per unit length. Indicates the length of the cable. Indicates tension, It is a small constant. Indicates the height difference between the two ends. This is the adjustment coefficient.

[0137] Further construct a nonlinear correction function:

[0138]

[0139] in, Indicates the stiffness attenuation coefficient. This is a non-linear adjustment parameter.

[0140] The improved tangential stiffness is finally obtained:

[0141]

[0142] In this expression, This indicates the corrected tangent stiffness. This is the equivalent length.

[0143] When the tension is large As the tension decreases, the exponential term approaches 1, and the model degenerates into a traditional linear stiffness; when the tension is small or the span is large... The increase in stiffness significantly reduces the stiffness, which is more consistent with actual test results.

[0144] The final system stiffness can be expressed as:

[0145]

[0146] in:

[0147]

[0148]

[0149] In this embodiment, the system stiffness matrix is ​​constructed by differentiating the generalized force with respect to pose. When determining the passive stiffness components, the tangential stiffness matrix is ​​constructed by combining the tangential stiffness of each cable, the unit direction vector, and the displacement change of the platform end connection point, thus obtaining the passive stiffness components. When determining the active stiffness components, the geometric stiffness matrices of each cable are obtained based on the rate of change of the unit direction vector with pose and the corresponding tension, and then superimposed to obtain the active stiffness components. In addition, a nonlinear tangential stiffness correction model based on curvature factor is introduced to correct the tangential stiffness of the cables. The passive stiffness components are updated based on the corrected tangential stiffness, and finally the system stiffness decomposition result is obtained, establishing a quantitative relationship between pose perturbation and force response. This embodiment can accurately capture the stiffness characteristics of long-span cable systems and improve the modeling accuracy of the quantitative relationship between pose perturbation and force response using the above method.

[0150] Step S408: Evaluate the stiffness distribution based on the stiffness decomposition results and generate target stiffness adjustment parameters.

[0151] After constructing and decomposing the system stiffness matrix, the overall stiffness distribution of the system under the current pose and tension state can be obtained. However, in engineering practice, simply obtaining the stiffness values ​​is not enough to support system operation. The more critical issue is whether the stiffness distribution meets the mission requirements, and if not, how to adjust the cable tension to achieve the target stiffness.

[0152] The system stiffness matrix has been obtained in step S406:

[0153]

[0154] in, This represents the corrected passive stiffness matrix. This represents the active stiffness matrix.

[0155] To analyze the stiffness characteristics of the system in different directions, the stiffness matrix needs to be eigenvalued, i.e.:

[0156]

[0157] In this expression, This represents the eigenvector matrix, whose column vectors correspond to the principal stiffness directions; It is a diagonal matrix, and its diagonal elements are eigenvalues, which reflect the stiffness of the system in each principal direction.

[0158] Furthermore, the stiffness distribution can be expressed as:

[0159]

[0160] in, Indicates the system at the 1st The stiffness component in a principal direction, which corresponds to a translational direction or a rotational direction.

[0161] In practical applications, the target stiffness distribution is usually pre-defined according to task requirements:

[0162]

[0163] in, Indicates the first The desired stiffness value in each direction.

[0164] Based on this, stiffness deviation can be defined as follows:

[0165]

[0166] This deviation reflects the difference between the current system stiffness and the target stiffness.

[0167] To further convert stiffness deviation into an executable tension adjustment, a mapping relationship between tension and stiffness needs to be established. For this purpose, a sensitivity matrix is ​​introduced:

[0168]

[0169] in, This indicates the sensitivity of the stiffness eigenvalue to changes in tension, and its first... The element represents the first element. The stiffness component for the first Rate of change of root cable tension.

[0170] In numerical implementation, this matrix can be approximated using finite difference methods:

[0171]

[0172] in, Represents the elements of the sensitivity matrix. Indicates the first Small-amplitude tension disturbance applied to the root cord.

[0173] After obtaining the sensitivity matrix, a tension adjustment model can be constructed:

[0174]

[0175] in, This represents the tension adjustment vector. This indicates the adjustment step size coefficient. This represents the generalized inverse of the sensitivity matrix.

[0176] The reason for using the generalized inverse here is that the system is usually a redundant driven structure, that is, the number of keys is greater than the number of degrees of freedom, which makes the matrix non-invertible.

[0177] To ensure the safety of system operation, tension also needs to be constrained.

[0178]

[0179] in, Indicates the first The minimum allowable tension of the root cable is typically used to prevent cable slack. This indicates the maximum permissible tension, used to prevent material failure.

[0180] Furthermore, to improve the stability of the adjustment, this embodiment introduces a regularization term to smooth the adjustment amount:

[0181]

[0182] in, This is the regularization coefficient, used to suppress excessive tension changes.

[0183] In engineering practice, it can be observed that directly adjusting the stiffness based on the deviation often leads to drastic fluctuations in the tension distribution, thereby affecting system stability. Introducing the aforementioned regularization process can satisfy the stiffness optimization objective while avoiding overly aggressive tension adjustments.

[0184] This embodiment extracts directional stiffness components by performing eigenvalue decomposition on the system stiffness matrix and establishing a sensitivity mapping relationship between tension and stiffness. It converts stiffness deviation into tension adjustment amount and performs constraint and regularization processing to obtain target stiffness adjustment parameters, thereby realizing the quantification and stabilization of stiffness adjustment and improving the system control accuracy and reliability.

[0185] In this embodiment, the system stiffness matrix from the stiffness decomposition result is used as input to perform eigenvalue decomposition, yielding an eigenvector matrix and a diagonal eigenvalue matrix. The column vectors of the eigenvector matrix correspond to the principal stiffness directions, and the diagonal elements of the diagonal eigenvalue matrix correspond to the stiffness components of each principal direction, thereby extracting the current system stiffness distribution. Using the current system stiffness distribution and a preset target stiffness distribution as input, the difference between the two is calculated to obtain the stiffness deviation, reflecting the difference between the current and target stiffness. Finally, using the current system stiffness distribution and the tension of each cable as input, a finite difference method is employed... The method calculates the rate of change of stiffness eigenvalues ​​with respect to changes in cable tension, constructs a sensitivity matrix characterizing the sensitivity of stiffness components to changes in cable tension, and then uses this sensitivity matrix and stiffness deviation as inputs to convert the stiffness deviation into cable tension adjustment amount through matrix operations. Using the cable tension adjustment amount, the minimum allowable tension of each cable, the maximum allowable tension of each cable, and the regularization coefficient as inputs, the tension adjustment amount is first constrained to ensure that the adjusted cable tension is within the allowable range, and then a regularization term is introduced to smooth the tension adjustment amount, finally obtaining the target stiffness adjustment parameter, thus realizing the quantification and stabilization of stiffness adjustment.

[0186] Step S410: Adjust the tension based on the target stiffness adjustment parameters and optimize the static stiffness.

[0187] First, based on the adjustment amount obtained in step S408, update the tension of each cable:

[0188]

[0189] in, This indicates the updated tension value. This represents the tension adjustment amount after constraint and regularization processing.

[0190] After the tension is updated, the system stiffness matrix needs to be recalculated:

[0191]

[0192] in, This represents the updated stiffness matrix. This indicates the stiffness in step S406.

[0193] Furthermore, the updated stiffness is subjected to eigenvalue decomposition:

[0194]

[0195] in, This represents the updated stiffness distribution.

[0196] Define convergence criterion:

[0197]

[0198] in, This represents the stiffness error norm.

[0199] The optimization is considered complete when the following conditions are met:

[0200]

[0201] in, This indicates the preset tolerance error.

[0202] If the condition is not met, update the tension and repeat the above process:

[0203]

[0204] In this expression, Indicates the number of iterations.

[0205] To improve the convergence speed, this embodiment further introduces an adaptive step size mechanism:

[0206]

[0207] in, This represents the step size adjustment factor.

[0208] In practical tests, it can be found that when the system approaches the target stiffness state, appropriately reducing the step size helps to avoid oscillations; while increasing the step size in the initial stage can accelerate the convergence speed. The above adaptive mechanism is proposed based on this observation.

[0209] Finally, when the system meets the stiffness requirements, the optimized tension parameters and corresponding stiffness distribution can be output.

[0210] In this embodiment, the tension adjustment amount in the target stiffness adjustment parameters and the current tension of each cable are used as inputs. The current tension of each cable is added to the corresponding tension adjustment amount to obtain the updated tension value of each cable. The updated tension value and platform pose parameters are used as inputs to recalculate the system stiffness matrix according to the preset stiffness calculation method to obtain the updated system stiffness matrix. The updated system stiffness matrix is ​​subjected to eigenvalue decomposition to obtain the updated stiffness distribution. The updated stiffness distribution and the preset target stiffness distribution are used as inputs to calculate the stiffness error norm of the two as a convergence criterion and compare it with the preset allowable error. If the stiffness error norm is less than the preset allowable error, the optimization is completed, and the optimized tension parameters and corresponding stiffness distribution are output. If not, the tension is updated and the above tension update, stiffness matrix recalculation, eigenvalue decomposition and convergence judgment steps are repeated. At the same time, an adaptive step size mechanism is introduced to adjust the adjustment step size to improve the convergence speed until the convergence criterion is met, thus realizing static stiffness optimization.

[0211] This application also provides a device for determining the static stiffness of a cable-parallel drive system for deep space exploration, such as... Figure 8 As shown, the system includes: a state determination module 82, configured to acquire the initial structural parameters and operating state parameters of the cable parallel drive system, and construct a system mechanical model based on the initial structural parameters and the operating state parameters to obtain initial system state data, wherein the structural parameters include the connection position parameters and length parameters of each cable, and the operating state parameters include the platform pose parameters and tension parameters of each cable; a generalized force calculation module 84, configured to calculate the tension direction parameters and action position parameters of each cable based on the initial system state data, and calculate the generalized force data of the system based on the tension direction parameters and action position parameters; a stiffness decomposition module 86, configured to calculate the system stiffness matrix based on the generalized force data and the change in the platform pose parameters, and decompose the system stiffness matrix into passive stiffness components and active stiffness components to obtain stiffness decomposition results; and a static stiffness calculation module 88, configured to evaluate the system stiffness distribution state based on the stiffness decomposition results and the tension parameters, generate target stiffness adjustment parameters, and adjust and control the tension parameters based on the target stiffness adjustment parameters to obtain optimized static stiffness.

[0212] It should be noted that the static stiffness determination device for a cable-parallel drive system for deep space exploration provided in the above embodiments is only an example of the division of the above functional modules. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the static stiffness determination device for a cable-parallel drive system for deep space exploration provided in the above embodiments and the static stiffness determination method embodiment for a cable-parallel drive system for deep space exploration belong to the same concept. The specific implementation process is detailed in the method embodiment and will not be repeated here.

[0213] Figure 9 A schematic diagram of a computer device suitable for implementing embodiments of the present disclosure is shown. It should be noted that... Figure 9 The computer device shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments disclosed herein.

[0214] like Figure 9 As shown, the computer device includes a central processing unit (CPU) 1001, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1002 or a program loaded from a storage section 1008 into a random access memory (RAM) 1003. The RAM 1003 also stores various programs and data required for system operation. The CPU 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An input / output (I / O) interface 1005 is also connected to the bus 1004.

[0215] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 1010 as needed so that computer programs read from it can be installed into storage section 1008 as needed.

[0216] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

Claims

1. A method for determining the static stiffness of a cable-driven parallel system for deep space exploration, characterized in that, include: The initial structural parameters and operating state parameters of the cable parallel drive system are obtained, and a system mechanical model is constructed based on the initial structural parameters and the operating state parameters to obtain initial system state data. The structural parameters include the connection position parameters and length parameters of each cable, and the operating state parameters include the platform pose parameters and tension parameters of each cable. Based on the initial system state data, calculate the tension direction parameters and the position parameters of each cable, and calculate the generalized force data of the system based on the tension direction parameters and the position parameters of the cable. Based on the generalized force data and the changes in the platform pose parameters, the system stiffness matrix is ​​calculated, and the system stiffness matrix is ​​decomposed into passive stiffness components and active stiffness components to obtain the stiffness decomposition result. Based on the stiffness decomposition results and the tension parameters, the stiffness distribution state of the system is evaluated, a target stiffness adjustment parameter is generated, and the tension parameter is adjusted and controlled based on the target stiffness adjustment parameter to obtain the optimized static stiffness.

2. The method according to claim 1, characterized in that, Based on the initial structural parameters and the operational state parameters, a system mechanical model is constructed to obtain initial system state data, including: A global coordinate system is established based on the cable connection position parameters in the initial structural parameters, and the platform spatial position is determined in the global coordinate system based on the platform pose parameters in the running state parameters, thus obtaining pose expression data. Based on the length parameter in the initial structural parameters and the pose expression data, the spatial geometric relationship of each cable is calculated to obtain cable geometric relationship data; Based on the tension parameters in the operating state parameters and the cable geometric relationship data, the mechanical equilibrium relationship in the system mechanical model is constructed to obtain the initial system state data.

3. The method according to claim 2, characterized in that, Based on the initial system state data, the tension direction parameters and application position parameters of each cable are calculated. Based on the tension direction parameters and application position parameters, the generalized force data of the system is calculated, including: Based on the cable geometric relationship data in the initial system state data, the unit direction vector of each cable is calculated to obtain the tension direction parameter; Based on the connection position parameters in the initial structural parameters and the platform pose parameters, the position of the action point of each cable on the platform is determined, and the action position parameters are obtained. The system Jacobian matrix is ​​constructed based on the tension direction parameter and the position parameter, and the generalized force data is obtained by performing calculations based on the Jacobian matrix and the tension parameter.

4. The method according to claim 1, characterized in that, Based on the generalized force data and the changes in the platform pose parameters, the system stiffness matrix is ​​calculated, and the system stiffness matrix is ​​decomposed into passive stiffness components and active stiffness components to obtain the stiffness decomposition results, including: Based on the changes in the platform pose parameters, the generalized force data is analyzed to determine the relationship between the changes and obtains the system stiffness matrix. Based on the system stiffness matrix and the tension parameters, the passive stiffness components caused by the tension characteristics of each cable are calculated, and based on the system stiffness matrix and the platform pose parameters, the active stiffness components caused by the system configuration change are calculated. The stiffness decomposition result is obtained based on the passive stiffness component and the active stiffness component.

5. The method according to claim 1, characterized in that, Based on the stiffness decomposition results and the tension parameters, the system stiffness distribution state is evaluated, and target stiffness adjustment parameters are generated, including: Based on the stiffness decomposition results, the stiffness components of the system in different directions are extracted to obtain stiffness distribution data. The stiffness distribution data is then compared with the preset stiffness distribution requirements to obtain stiffness deviation data. A mapping relationship is established between the tension parameter and the stiffness distribution data. Based on the mapping relationship, the stiffness deviation data is converted into a tension adjustment amount, and the tension adjustment amount is constrained to obtain the target stiffness adjustment parameter.

6. The method according to claim 1, characterized in that, Based on the target stiffness adjustment parameters, the tension parameters are adjusted and controlled to obtain optimized static stiffness, including: Based on the target stiffness adjustment parameters, the tension adjustment amount corresponding to each cable is determined, and the tension adjustment amount is applied to the cable drive mechanism to adjust the tension parameters. Based on the adjusted tension parameters, the system stiffness matrix is ​​recalculated and the stiffness decomposition results are updated. When the updated stiffness decomposition results meet the preset stiffness conditions, the optimized static stiffness is obtained.

7. A device for determining the static stiffness of a cable-parallel drive system for deep space exploration, characterized in that, include: The state determination module is configured to acquire the initial structural parameters and operating state parameters of the cable parallel drive system, and construct a system mechanical model based on the initial structural parameters and the operating state parameters to obtain initial system state data. The structural parameters include the connection position parameters and length parameters of each cable, and the operating state parameters include the platform pose parameters and tension parameters of each cable. The generalized force calculation module is configured to calculate the tension direction parameters and action position parameters of each cable based on the initial system state data, and to calculate the generalized force data of the system based on the tension direction parameters and action position parameters. The stiffness decomposition module is configured to calculate the system stiffness matrix based on the generalized force data and the changes in the platform pose parameters, and decompose the system stiffness matrix into passive stiffness components and active stiffness components to obtain the stiffness decomposition result. The static stiffness calculation module is configured to evaluate the system stiffness distribution state based on the stiffness decomposition results and the tension parameters, generate target stiffness adjustment parameters, and adjust and control the tension parameters based on the target stiffness adjustment parameters to obtain optimized static stiffness.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored program, wherein, when the program is executed, it controls the device on which the computer-readable storage medium is located to perform the method according to any one of claims 1 to 6.

9. A computer device, characterized in that, include: Memory and processor The memory stores computer programs; The processor is configured to execute a computer program stored in the memory, wherein when the computer program is executed, the processor performs the method according to any one of claims 1 to 6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 6.

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