A movable docking mechanism multi-parallel constraint assembly pose prediction method

Abstract

This invention provides a method for predicting the assembly pose of a movable docking mechanism with multiple parallel constraints, belonging to the field of mechanical engineering and robotics assembly accuracy technology. The method includes: identifying multiple parallel assembly transfer paths of the docking mechanism; overcoming the limitations of traditional Jacobi parallel methods in handling complex symmetrical constraints by introducing an additional geometric error variation model of the assembly surface based on symmetrical positioning features; accurately defining the constraint boundaries of the symmetrical tolerance domain for the translation of the assembly and small rotations around the normal direction of the assembly surface, and generating six-degree-of-freedom small displacement screw parameters; combining the Jacobi matrix, transferring each feature deviation to the global coordinate system for cumulative calculation, and performing intersection calculations of the screws of multiple dimension chains to obtain high-precision assembly pose prediction results. This invention solves the problem of difficult accurate modeling of over-positioning features in complex parallel dimension chains, improving the assembly success rate and accuracy of movable docking mechanisms under multi-constraint environments.

Description

Technical Field

[0001] This invention relates to the fields of mechanical engineering and assembly accuracy modeling technology, specifically to a method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism. Background Technology

[0002] With the rapid development of aerospace rendezvous and docking, deep-sea submersible docking, automatic charging connector locking for automated guided vehicles, and quick-change devices for high-end industrial robots, movable docking mechanisms play a crucial role in precision manufacturing and automation. When performing docking and assembly tasks, movable docking mechanisms typically involve large-scale spatial pose searches and multi-point concurrent physical contacts at close range. To ensure docking rigidity and guiding accuracy, the docking flange surface is often designed with multi-point array guide pins, positioning holes, and large contact surfaces. The manufacturing tolerances, assembly clearances, and form and position errors of these docking features couple and accumulate along multiple assembly transmission paths. Especially at the moment when the movable mechanism is about to achieve rigid physical locking, the concurrent accumulation of errors from multiple paths can lead to a serious deviation between the assembly end pose and the ideal state, easily causing guide pin interference, jamming, or even damage and scrapping of the docking mechanism.

[0003] In engineering practice and theoretical research, the Jacobi screw model is widely used in assembly error analysis because it can transform the tolerance domain into a six-degree-of-freedom small displacement screw in three-dimensional space and express the spatial geometric transfer relationship of deviations through the Jacobi matrix. However, for the special working scenario of movable docking mechanisms, the traditional Jacobi screw multi-dimensional chain parallel analysis method has obvious theoretical limitations. First, when dealing with multiple parallel assembly transfer paths, traditional methods often forcibly simplify the local parallel dimensional chains into a single serial dimensional chain for calculation, or use simple algebraic linear superposition at the end. For movable docking mechanisms, the geometric boundary at the moment of docking is a physical closed loop composed of multiple unrelated dimensional chains. Simple mathematical superposition completely ignores the nonlinear characteristics and physical interference constraints in the over-positioning system, resulting in a serious "expansion divergence" of the predicted tolerance range.

[0004] Secondly, existing parallel Jacobi methods typically employ linear mapping when characterizing highly representative symmetrical features in movable docking mechanisms (such as locating pins or groups of locating holes arranged symmetrically on the docking end faces). This simplified approach severely neglects the special nonlinear constraints arising from the mutual constraints within the tolerance domain of symmetrical features (especially the small anti-rotation constraints around the docking axis, such as the Z-axis). This problem, caused by the lack of applicability of the basic variation model, is amplified as the Jacobi matrix of the spatial links of the docking mechanism is passed through multiple levels. Ultimately, this leads to significant uncertainty in the online pose inference of the host computer in automated dynamic docking environments with few samples and large initial positioning deviations, making it impossible to reliably guarantee the assembly success rate of movable docking mechanisms. Therefore, there is an urgent need to propose a multi-parallel constraint assembly pose prediction method for movable docking mechanisms to address the technical pain points of inaccurate modeling of multi-dimensional parallel dimensional chain errors and distortion in the handling of symmetrical locking constraints in existing technologies. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for predicting the assembly pose of a movable docking mechanism with multiple parallel constraints. This method solves the problems in existing technologies where inaccurate modeling of multi-dimensional parallel dimensional chain errors in complex assemblies and distortion of symmetric constraint processing lead to insufficient assembly pose prediction accuracy and an inability to guarantee the success rate of automated assembly.

[0006] To achieve the above objectives, the present invention provides a method for predicting the pose of a multi-parallel constraint assembly of a movable docking mechanism, comprising: S1: Based on the assembly task to be executed, obtain the characteristic parameters and accuracy information of the movable docking mechanism, and identify multiple parallel assembly and transfer paths of the docking mechanism; S2: To address the limitations of the traditional Jacobi parallel method in handling symmetrical constraints, an assembly surface geometric error variation model based on symmetrical positioning features is additionally introduced into the parallel assembly transfer path. S3: Based on the assembly surface geometric error variation model of the symmetrical positioning features, analyze the constraint relationship of the symmetrical tolerance domain on translation and small rotation, and construct a six-degree-of-freedom small displacement screw parameter; S4: For each of the parallel assembly transfer paths, combined with the Jacobian screw model, construct the Jacobian matrix based on the relative position between the local coordinate system where a single assembly feature is located and the global coordinate system where the target assembly feature is located; S5: Combine the small displacement screw parameters output by the assembly surface geometric error variation model based on symmetric positioning features with the corresponding Jacobian matrix to describe the transmission and accumulation of the assembly features in the global coordinate system, and obtain the target assembly pose prediction result. S6: Based on the predicted target assembly pose, perform parameter compensation on the assembly target pose of the movable docking mechanism to complete the assembly task.

[0007] Preferably, in step S1, the three-dimensional model data includes at least the design dimensions, geometric tolerances, geometric parameters, fit types, and fit accuracy levels of each part of the movable docking mechanism and the target assembly; the parallel assembly transfer path is constructed with the final docking pose at the end of the assembly as a closed loop and the fit relationships of each key assembly feature as transfer nodes, and all independent assembly error transfer paths are fully preserved during the construction process without serial simplification or merging.

[0008] Preferably, in step S1, the key assembly features identified include at least the mating end face, locating pin hole, fastening bolt hole, mating journal, and mating hole surface, which are geometric features that directly participate in the assembly fit. At the same time, the design datum, tolerance range, and local coordinate system of each assembly feature are marked.

[0009] Preferably, in step S2, the introduction of the assembly surface geometric error variation model based on symmetrical positioning features specifically includes: when the docking surface between the docking mechanism and the target assembly has symmetrically arranged positioning holes, establishing an assembly surface geometric error variation model based on symmetrical positioning features; the model, under the constraints of two symmetrical tolerance domains, simultaneously limits the small translations of the assembly along the X and Y axes, as well as the small rotations around the Z axis. The constraint range of the small rotations around the Z axis is jointly determined by the tolerance parameters of the symmetrical positioning holes, the additional tolerance parameters of the fit, and the base circle radius of the positioning holes.

[0010] Preferably, in step S3, the small displacement spinor parameter of the six degrees of freedom is expressed in the form of a combination of a small displacement vector and a small rotation vector in three-dimensional space.

[0011] Preferably, in step S3, the construction process of the six-degree-of-freedom small displacement screw parameters specifically includes: based on the geometric error variation model of the assembly surface with symmetrical positioning features, solving for the limit variation range of the small translation along the X-axis and Y-axis of the assembly under the constraint of the symmetrical tolerance domain, and the limit variation range of the small rotation around the Z-axis; combined with the axial fit constraint of the assembly feature, determining the limit range of the small translation along the Z-axis and the limit range of the small rotation around the X-axis and Y-axis of the assembly feature; and mapping the limit variation range of the six degrees of freedom to the six-degree-of-freedom small displacement screw parameters to form the error variation boundary of the corresponding assembly feature.

[0012] Preferably, in step S4, the construction process of the Jacobian matrix specifically includes: for each independent parallel assembly transfer path, taking the coordinate system where the final docking pose of the assembly task is located as the global coordinate system and the design reference coordinate system where each assembly feature in the path is located as the local coordinate system, solving the homogeneous transformation matrix between each local coordinate system and the global coordinate system; based on the principle of differential kinematics and combined with the relative positional relationship between each local coordinate system and the global coordinate system, constructing the Jacobian matrix sub-block corresponding to each assembly feature; according to the error transmission order of the assembly transfer path, cascading and combining each Jacobian matrix sub-block to form the complete Jacobian matrix corresponding to the assembly transfer path.

[0013] Preferably, in step S5, the process of obtaining the target assembly pose prediction result further includes the screw intersection operation of multiple parallel dimensional chains, specifically including: for each parallel assembly transfer path, solving for the six-degree-of-freedom deviation vector and limit variation range of the assembly end pose in the global coordinate system under the action of a single path; extracting the vector offset range of each parallel assembly transfer path on the six degrees of freedom of the Jacobi screw model, and performing an intersection operation on the vector offset range to obtain the worst physical constraint boundary of each dimensional chain under the joint action, which is taken as the final variation range of the multi-dimensional chain parallel assembly error, i.e., the target assembly pose prediction result.

[0014] Preferably, in step S6, the parameter compensation specifically includes: determining the parameter compensation target value of the assembly end pose based on the final variation range of the six-degree-of-freedom pose deviation in the target assembly pose prediction result; Compared with the prior art, the present invention has the following advantages and technical effects: This invention introduces a geometric error variation model for assembly surfaces based on symmetrical positioning features. During the screw generation stage, it accurately characterizes the constraint effect of the symmetrical tolerance domain on the geometric displacement of the assembly, especially the small rotation around the Z-axis. From the error modeling perspective, it ensures the consistency between the model input boundary and the actual physical constraints of the assembly. This solves the modeling distortion problem caused by the neglect of the nonlinear constraints of the mutual constraints of the symmetrical tolerance domain when dealing with symmetrically distributed positioning features in the traditional Jacobi screw method. It fills the theoretical gap in error modeling of over-constrained symmetrical features.

[0015] This invention constructs a Jacobian matrix for each independent parallel assembly transmission path, thus fully preserving the independent constraint characteristics of the parallel assembly paths. It abandons the traditional method of forcibly simplifying parallel dimension chains into serial dimension chains and blindly linearly superimposing error results. This fundamentally avoids the error prediction divergence problem caused by oversimplification of parallel constraints and accurately restores the transmission and accumulation characteristics of errors in multiple parallel transmission paths.

[0016] This invention introduces an independent screw intersection operation mechanism for each degree of freedom in the coupling analysis of multiple parallel dimensional chains. Based on the physical essence that "the actual pose at the end of the assembly must simultaneously meet the constraints of all parallel assembly transmission paths", it accurately fits the extreme constraint state when multiple structures are in physical contact, which greatly improves the accuracy and confidence of pose prediction in multi-parallel constrained assembly scenarios. It solves the problem that the calculation results of traditional methods deviate too much from the actual assembly conditions and cannot provide a reliable basis for automated assembly.

[0017] This invention constructs a complete closed-loop process from assembly path identification, refined modeling of symmetric constraints, error propagation mapping, pose prediction to assembly parameter compensation. It can directly feed back high-precision pose prediction results to the movable docking mechanism, realize pose compensation before assembly, significantly reduce the physical interference rate and jamming risk in the automated assembly process, and improve the success rate and assembly accuracy stability of the movable docking mechanism under multiple parallel constraints. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Appendix Figure 1 This is a flowchart of a method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism provided in an embodiment of the present invention. Appendix Figure 2 A schematic diagram of the error accuracy source of the movable docking mechanism provided in an embodiment of the present invention; Appendix Figure 3 A schematic diagram of the assembly and transfer path of the movable docking mechanism provided in an embodiment of the present invention; Appendix Figure 4 A schematic diagram of a geometric error variation model for symmetrical positioning features on a circular surface provided in an embodiment of the present invention; Appendix Figure 5 A schematic diagram of a geometric error variation model for symmetrical positioning features on a plane provided in an embodiment of the present invention; Appendix Figure 6 A schematic diagram of the target pose simulation error results of the movable docking mechanism provided in an embodiment of the present invention; Detailed Implementation

[0019] The present invention will be further illustrated below with reference to the accompanying drawings, which clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention.

[0020] A method for predicting the assembly pose of a movable docking mechanism with multiple parallel constraints is presented. This method, based on multi-path parallel transmission identification, refined modeling of symmetrical physical constraints, and global error space accumulation calculation, ultimately achieves high-precision prediction and parameter compensation of the assembly pose throughout the entire process. Specifically, the method includes the following steps: S1: Based on the assembly task to be performed, obtain the characteristic parameters and accuracy information of the movable docking mechanism, and identify multiple parallel assembly transfer paths of the docking mechanism. Specifically, the core of obtaining the feature parameters and accuracy information of the movable docking mechanism lies in the deep analysis of the manufacturing and assembly semantics of the 3D model of the assembly (such as files based on STEP, IGES, or specific CAD source formats). The extracted feature parameters and accuracy information include at least: the nominal design dimensions and geometric tolerances (such as flatness, perpendicularity, coaxiality, and positional tolerances) of each part of the movable docking mechanism and the target assembly; the geometric parameters of the assembly mating features (such as the nominal diameter of the guide pin and the nominal diameter of the locating hole); the mating type (such as clearance fit, transition fit, and interference fit); and the mating accuracy level. Simultaneously, it is also necessary to calibrate the design datum, tolerance range, and local coordinate system of each key geometric feature involved in the assembly mating (such as the mating end face, locating pin hole, fastening bolt hole, mating journal, and mating hole surface). The error accuracy source of the movable docking mechanism is shown in the attached figure. Figure 2 As shown. Furthermore, in order to accurately identify multiple parallel assembly transfer paths of the docking mechanism from a complex mechanical assembly, this embodiment uses a graph theory method based on constraint information to construct an undirected graph G=(V,E) of the assembly.

[0021] In this undirected graph, the node set V represents the assembly feature surface (such as the mating end plane, the guide pin cylindrical surface, the positioning hole inner cylindrical surface, etc.); the edge set W represents the internal pair relationship (i.e. the geometric dimension and tolerance constraint relationship between different features within the same part, reflecting the manufacturing error of the part itself) or the assembly pair relationship (i.e. the kinematic contact and fit clearance constraint between mating features of different parts, reflecting the clearance error in the assembly process).

[0022] After constructing the undirected graph of the high-dimensional assembly, the movable docking mechanism typically employs a multi-point array distribution (such as multiple guide pins and positioning holes evenly distributed around a flange) to ensure rigid locking and torque resistance, which constitutes a typical multi-parallel closed-dimensional chain in physical space. To accurately identify these intricate paths, this step introduces the Dijkstra algorithm for intelligent search of the assembly path: First, the reference coordinate system node of the docking mechanism (usually set as the base coordinate system of the robot end flange or fixed base) is used as the starting point (source node) for the algorithm search. Second, the weights of each edge (constraint relationship) are calculated. To overcome the shortcomings of the traditional Dijkstra algorithm, which suffers from non-negative weighted undirected graphs and unweighted undirected graphs, thus failing to form the actual optimal physical path, this invention uses assembly features or intersections as vertices in the Dijkstra algorithm and dynamically determines the weights using a weighted average algorithm of weights and distances from an additional Kalman filter model. This weighting not only considers spatial geometric distance but also integrates the constraint stiffness matrix and tolerance sensitivity, enabling the weights to truly reflect the physical "resistance" of error propagation. Finally, based on the determined weights, the improved Dijkstra algorithm is used to search for the set of shortest paths to the target assembly feature node (i.e., the final assembly mating surface or locking feature). This set represents multiple parallel assembly transfer paths. For the movable docking mechanism in this implementation, its assembly transfer paths are shown in the appendix. Figure 3 As shown, IFE represents internal manufacturing error propagation and CFE represents external connection error propagation.

[0023] S2: To address the limitations of traditional Jacobi parallel methods in handling symmetrical constraints, an additional geometric error variation model for assembly surfaces based on symmetrical positioning features is introduced into the parallel assembly transfer path. In traditional assembly tolerance analysis and Jacobi screw modeling, it is often assumed that the variations of each assembly feature within its tolerance domain are independent and linearly algebraically superimposed. However, when the docking surfaces of the movable docking mechanism and the target assembly have symmetrically arranged positioning holes (e.g., two main positioning holes symmetrically arranged at 180° on the flange surface of a large rotating body section, or four guide holes evenly distributed at 90°), this idealized assumption of independence leads to severe "prediction divergence" and modeling distortion.

[0024] The reason is that, in the actual physical environment of assembly, the slight deflection of a locating pin within its corresponding hole is inevitably subject to the strict rigid physical constraint of another locating pin / hole wall at a symmetrical position. Traditional methods neglect the special nonlinear constraints arising from the mutual constraints of these symmetrical tolerance domains. To fundamentally solve this distortion problem, this method additionally introduces a geometric error variation model for the assembly surface based on symmetrical locating features. This model considers the independent variation of a single locating hole / pin assembly feature within its local tolerance domain (i.e., the cylindrical or polygonal variation region composed of dimensional tolerances and positional tolerances), treating multiple features symmetrically distributed on the mating surface as a coupled overall constraint system. Under the common physical constraints of two or more symmetrical tolerance domains, this variation model can strictly and accurately limit the slight translational variations (denoted as Δ) of the assembly along the X and Y axes of the mating plane (such as the XOY plane). u and Δ ν At the same time, it limits the small, anti-rotational rotation (denoted as Δ) of the assembly about the normal direction of the assembly surface (such as the Z-axis of the docking center axis). γ ).

[0025] In the assembly surface geometric error variation model based on symmetrical positioning features, the symmetrically arranged positioning features generate a mechanical anti-rotation torque, causing a small rotation Δ of the assembly around the Z-axis. γ It will be subject to geometric constraints. According to the principles of analytical geometry and tolerance, the limit constraint range of this minute rotation is strictly determined by the position tolerance t of the locating hole, the dimensional tolerance Δ of the position tolerance, and the base circle radius R of the locating hole distribution.

[0026] The geometric error variation model for symmetrical positioning features on a circular surface is shown in the appendix. Figure 4 As shown, its Δ γ The constraint range must satisfy the following inequalities:

[0027] The geometric error variation model for symmetrical positioning features on the plane is shown in the appendix. Figure 5 As shown, the constraint range of Δγ must satisfy the following inequality:

[0028] S3: Based on the assembly surface geometric error variation model based on symmetric positioning features, the constraint relationship between the symmetric tolerance domain and translation and small rotation is analyzed, and a six-degree-of-freedom small displacement screw parameter is constructed. Specifically, this step uses the Small Displacement Torsor (SDT) theory to mathematically express the tolerance domain in three-dimensional space using six degrees of freedom. Any tiny spatial geometric variation can be completely mapped to a six-degree-of-freedom small displacement screw parameter, which is expressed as a column vector combination of tiny displacement vectors and tiny rotation vectors in three-dimensional space.

[0029] Where: Δ u Δ v Δ w These represent the minute translational displacements of the assembly features along the X, Y, and Z axes of the global coordinate system; Δ α Δ β Δ γ These are the minute rotation angles (in radians) of the assembly feature around the X, Y, and Z axes of the global coordinate system.

[0030] The core of this step is to integrate the nonlinear constraints of the symmetric positioning features obtained in step S2 with the assembly surface fitting constraints, precisely limit the variation range of the above six degrees of freedom, and construct an assembly feature error screw tolerance domain that conforms to physical reality.

[0031] First, for the three degrees of freedom within the docking plane (such as the XOY plane), the symmetry constraint inequality derived in step S2 is directly applied: X-axis translation Δ u Its range of variation is determined by the dimensional tolerance, positional tolerance and fit clearance of the symmetrically arranged positioning features in the X direction, and must satisfy the geometric interference conditions of all parallel paths. Y-axis translation Δ v Its range of variation is determined by the dimensional tolerance, positional tolerance, and fit clearance of the symmetrically arranged positioning features in the Y direction. Z-axis rotation Δ γ Its limit constraint range strictly follows the inequality derived in step S2 for circular or planar positioning features. For example, for n uniformly distributed positioning features on a circular surface, its maximum allowable rotation angle is:

[0032] Where t is the position tolerance of the positioning hole, Δ is the maximum clearance between the positioning hole and the positioning pin, and R is the radius of the base circle of the positioning feature distribution.

[0033] Secondly, for the three degrees of freedom (axial direction and two deflection angles) perpendicular to the mating plane, a series constraint for the mating surface contact is introduced: Z-axis translation Δ w Its variation range is mainly determined by the flatness tolerance of the mating surfaces, the parallelism tolerance between the two mating surfaces, and the elastic deformation caused by the assembly preload. X-axis rotation Δ α Its range of variation is determined by the flatness tolerance of the mating surfaces, the parallelism tolerance between the mating surfaces, and the axial fit length between the locating pin and the hole. Y-axis rotation Δ β Its range of variation is related to Δ α Similarly, it is determined by the flatness tolerance of the mating surfaces, the parallelism tolerance between the mating surfaces, and the axial fit length of the locating pin and the hole.

[0034] It should be noted that the changes in the above six degrees of freedom are not completely independent. For example, the fit constraint of the mating surfaces will cause Δ w Δ α Δ β There is a strong coupling relationship between them: when the assembly undergoes a small rotation Δ about the X-axis α When this occurs, a corresponding displacement change will inevitably occur in the Z-axis direction, and the relationship can be accurately calculated from the geometric dimensions of the mating surfaces. This invention introduces a screw coupling matrix to describe the intrinsic relationship between these degrees of freedom, ensuring that the constructed small displacement screw parameters can truly reflect the actual error variation law of the assembly features.

[0035] Finally, by integrating all the above constraints, we obtain the six-degree-of-freedom error spinor tolerance domain of the assembly feature in its local coordinate system. T FE The tolerance domain is a closed convex polyhedron in six-dimensional space, with each face corresponding to a physical constraint. The spinor parameter integrates the series constraints of the mating surface fit on axial displacement and deflection angle, as well as the parallel interference constraints of the multi-array positioning features on radial displacement and rotation angle, forming the physical boundary of the error variation of the corresponding assembly features.

[0036] S4: For each of the parallel assembly transfer paths, a Jacobian matrix is ​​constructed based on the relative position between the local coordinate system of a single assembly feature and the global coordinate system of the target assembly feature, using the Jacobian screw model. In this step, the model constructs a spatial matrix mapping for the error transfer path based on the principle of differential kinematics. For each independent parallel assembly transfer path identified in step S1, the coordinate system of the final docking pose of the assembly task is used as the global coordinate system. O 0 The design reference coordinate system where each assembly feature in the path is located is taken as the local coordinate system.O i .

[0037] The specific process of constructing the Jacobian matrix using the Jacobian spinor model includes: First, using the rotation component of the homogeneous transformation matrix, we obtain the direction vector matrix of the i-th local coordinate system relative to the global coordinate system. R tm This matrix describes the spatial pose of the local feature reference surface.

[0038] Secondly, calculate the spatial displacement vector of the origin of the global coordinate system relative to the origin of the local coordinate system where the target feature is located, and convert it into an oblique symmetric position matrix. The introduction of this oblique symmetric matrix strictly conforms to the physical meaning of the cross product of translational and rotational moments in the spinor of a rigid body's minute motion.

[0039] Then, a block-form Jacobian matrix is ​​constructed based on the direction vector matrix and the position matrix. J FE The Jacobian matrix is ​​a 6×6 transformation matrix. Its upper left corner is the direction vector matrix, its upper right corner is the product of the oblique symmetric position matrix and the direction vector matrix, its lower left corner is a 3×3 zero matrix (because pure translation error will not cause rotational deviation at the end), and its lower right corner is the direction vector matrix.

[0040] The mathematical expression is as follows:

[0041] S5: Combine the small displacement screw parameters output by the assembly surface geometric error variation model based on symmetric positioning features with the corresponding Jacobian matrix to describe the transmission and accumulation of the assembly features in the global coordinate system, and obtain the target assembly pose prediction result; specifically, the Jacobian screw expression for the transmission and accumulation of errors in a single assembly chain is represented as the matrix composed of the Jacobian matrices transmitted by each assembly functional feature arranged in columns, and the result of matrix multiplication with the transpose of the matrix composed of the small displacement screw expressions of the corresponding assembly functional features arranged in columns.

[0042] For the k-th parallel path in the assembly system, the assembly function requirement (i.e., the relative pose change state of the end point under the single constraint of this path) transmitted by it is denoted as... T FR_k The mathematical derivation is as follows:

[0043] in, T FEiThis refers to the characteristic small displacement spinor column vector obtained after symmetric interference filtering and series-parallel parameter fusion in step S3 above. J FEi This is the Jacobian matrix obtained in step S4 above. Because multiple parallel paths act simultaneously during the locking action of a movable docking mechanism, the final physical pose of the assembly's end cannot escape the constraints of any single local pin hole; that is, it must simultaneously satisfy the spatial geometric constraints of all physical contact surfaces. Therefore, after solving for the six-degree-of-freedom deviation vector and limit variation range under the action of each single path, this method performs a screw intersection operation mechanism for multiple parallel dimensional chains.

[0044] On the six degrees of freedom of the Jacobi spinor model, extract the set of vector offset ranges mapped to the global coordinate system for each parallel assembly transfer path (assuming there are n paths in total), denoted as . S 1 ,S 2 ,...,S n Subsequently, rigorous mathematical intersection operations were performed on these vector offset ranges in the six-dimensional tolerance space. The core physical logic of this intersection operation lies in eliminating erroneous pose solutions that are within the tolerance domain in a specific dimensional chain analysis but inevitably lead to rigid collision failure and are unachievable under the constraints of another parallel dimensional chain. Through this operation, the physical constraint boundaries of each dimensional chain under their combined action are accurately obtained, serving as the final variation range of the multi-dimensional chain parallel assembly error, i.e., the high-confidence target assembly pose prediction result. Furthermore, since the form and position tolerances and dimensional errors of parts in industrial manufacturing processes inherently follow specific probabilistic statistical distributions (such as normal distributions), this embodiment uses a Monte Carlo simulation algorithm to generate batch samples that conform to the distribution characteristics during the generation of small displacement screw parameters and subsequent intersection operations. Based on the original tolerance band of the underlying features, tens of thousands (e.g., 10^5 times) of characteristic deviation screw sample groups are generated using a random number seed. These samples are then batched and substituted into the Jacobi transitivity and screw intersection model for massive parallel solving, thereby outputting the statistical distribution probability of the target assembly pose prediction result. The final results include not only the limit boundary thresholds, but also the six-degree-of-freedom error simulation results of the final target pose under a confidence interval such as 3σ (99.73%). The target pose simulation error results in this embodiment are attached. Figure 6 As shown.

[0045] S6: Based on the target assembly pose prediction result, perform parameter compensation on the assembly target pose of the movable docking mechanism to complete the assembly task. The parameter compensation mechanism includes: analyzing the final variation range of the six-degree-of-freedom pose deviation in the target assembly pose prediction result, and using this as a basis, performing parameter compensation on the end target pose of the movable docking mechanism.

[0046] It should be noted that the above specific embodiments can enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail with reference to the accompanying drawings and embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention. In short, all technical solutions and improvements that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the present invention patent.

Claims

1. A method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism, characterized in that, include: S1: Based on the assembly task to be executed, obtain the characteristic parameters and accuracy information of the movable docking mechanism, and identify multiple parallel assembly and transfer paths of the docking mechanism; S2: To address the limitations of the traditional Jacobi parallel method in handling symmetrical constraints, an assembly surface geometric error variation model based on symmetrical positioning features is additionally introduced into the parallel assembly transfer path. S3: Based on the assembly surface geometric error variation model of the symmetrical positioning features, analyze the constraint relationship of the symmetrical tolerance domain on translation and small rotation, and construct a six-degree-of-freedom small displacement screw parameter; S4: For each of the parallel assembly transfer paths, combined with the Jacobian screw model, construct the Jacobian matrix based on the relative position between the local coordinate system where a single assembly feature is located and the global coordinate system where the target assembly feature is located; S5: Combine the small displacement screw parameters output by the assembly surface geometric error variation model based on symmetric positioning features with the corresponding Jacobian matrix to describe the transmission and accumulation of the assembly features in the global coordinate system, and obtain the target assembly pose prediction result. S6: Based on the predicted target assembly pose, perform parameter compensation on the assembly target pose of the movable docking mechanism to complete the assembly task.

2. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 1, characterized in that, The additional model for geometric error variation of assembly surfaces based on symmetrical positioning features includes: When the docking surface between the docking mechanism and the assembly has symmetrically arranged positioning holes, a geometric error variation model of the assembly surface based on the symmetrical positioning features is established. Under the constraints of two symmetrical tolerance domains, the assembly is limited to make small translations along the X and Y axes, and to make small rotations about the Z axis.

3. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 2, characterized in that, The constraint range of the minute rotation around the Z-axis is determined by the relevant tolerance parameters of the positioning hole, the additional tolerance parameters, and the base circle radius of the positioning hole.

4. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 3, characterized in that, Based on the geometric error variation model of the assembly surface based on the symmetric positioning feature, a small displacement screw expression for the positioning hole assembly function feature in the parallel assembly chain is constructed. This expression is a column vector containing the X-axis translation deviation, Y-axis translation deviation, Z-axis translation deviation, and a column vector of rotational deviations around the X-axis, Y-axis, and Z-axis.

5. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 4, characterized in that, When error propagation exists simultaneously in both parallel and serial assembly chains, a geometric error variation model of the assembly surface with symmetrical positioning features is established to clarify the pose spinor parameters, specifically including: The expression for the small displacement screw of the assembly functional characteristics satisfies the union condition of the series planar characteristics and the parallel hole system characteristics; For example, on the XOY plane, the magnitude of the small rotation around the Z-axis is determined by the tolerance domain of the planar assembly functional feature. The pose screw parameters around the X and Y axes in the series features are extracted and recombined with the translation and rotation parameters around the Z-axis of the small displacement screw expression of the positioning hole assembly functional feature to obtain the final small displacement screw expression of the assembly functional feature.

6. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 1, characterized in that, The construction of the Jacobian matrix by combining the Jacobian spinor model includes: Obtain the direction vector matrix of the local coordinate system relative to the global coordinate system; Calculate the oblique-symmetric position matrix of the origin of the global coordinate system containing the target feature relative to the origin of the local coordinate system; Construct a block-form Jacobian matrix based on the direction vector matrix and the position matrix. The top left corner of the Jacobian matrix is ​​the direction vector matrix, the top right corner is the product of the oblique symmetric position matrix and the direction vector matrix, the bottom left corner is the zero matrix, and the bottom right corner is the direction vector matrix.

7. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 1, characterized in that, The Jacobian screw expression for obtaining the target assembly pose prediction result is: the result of matrix multiplication of the matrix composed of the Jacobian matrices transmitted by each assembly functional feature arranged in columns and the transpose of the matrix composed of the corresponding assembly functional feature small displacement screw expressions arranged in columns.

8. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 1, characterized in that, The obtained target assembly pose prediction result includes: On the six degrees of freedom of the Jacobi spinor model, the vector offset range of each parallel assembly transmission path is extracted, and the intersection operation is performed on the vector offset range to obtain the final variation range of the multi-size chain parallel assembly error.

9. The method for predicting the pose of a multi-parallel constrained assembly of a movable docking mechanism according to claim 1, characterized in that, Identifying multiple parallel assembly and transfer paths of the docking mechanism includes: An undirected graph of the assembly is constructed based on the constraint information of each assembly feature in the docking mechanism, where nodes represent assembly feature surfaces and edges represent internal sub-relationships or assembly sub-relationships. The Dijkstra algorithm is used to search for the shortest path set to the target assembly feature node, starting from the node of the reference coordinate system, and is determined as multiple parallel assembly transfer paths. In the process of generating the small displacement screw parameters, Monte Carlo simulation is used to generate a batch of feature deviation screw samples that conform to the normal distribution characteristics, and then the statistical distribution probability of the target assembly pose prediction result is output.

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