An assembly body cognitive reasoning method fusing a space-time world model

Abstract

The application discloses a method for assembling body cognitive reasoning of fusion space-time world model, comprising: constructing an assembly hypergraph by constructing a hypergraph to explicitly encode part contact and multi-body assembly constraints, and using SE(3) isomer implicit neural simulator to extract assembly state hidden space representation containing physical law; at the same time, a retrieval enhanced hierarchical space-time cognitive memory network is introduced to extract historical context from the structured memory bank by sparse associative retrieval attention mechanism to overcome time drift; on this basis, a cognitive-physical collaborative internal optimization closed loop is established, the preliminary task intention hidden vector is input into the differentiable simulator for forward deduction, and the intention is iteratively corrected in a guided manner of physical compliance cost gradient, and the optimal action is generated which is physically feasible and semantically consistent. The application improves the accuracy and reliability of intention recognition and execution in long sequence human-machine collaborative assembly task.

Description

Technical Field

[0001] This invention relates to the field of embodied intelligence and robot collaboration technology, and in particular to an assembly-based embodied cognitive reasoning method that integrates a spatiotemporal world model. Background Technology

[0002] As industrial manufacturing evolves towards greater flexibility and intelligence, human-robot collaborative assembly has become a key technological path for improving production efficiency and product consistency. In such scenarios, robots not only need to execute pre-programmed fixed actions, but also need to understand the assembly intentions of human operators in real time and proactively provide compliant tool delivery, part positioning, or collaborative fastening assistance. The emergence of Visual Language Models (VLMs) has provided a new solution to this need, with its powerful cross-modal alignment capabilities enabling robots to perform semantic reasoning and decision generation based on visual scenes and natural language instructions. However, directly applying general VLMs to long-sequence, high-precision assembly scenarios exposes several structural defects.

[0003] First, existing Virtual Models (VLMs) largely rely on statistical correlations between 2D image features and text tags for perception and reasoning, lacking a deep understanding of the rigid structure of parts, spatial pose constraints, and contact dynamics in the 3D physical world. This leads to model outputs that, while semantically plausible, may contain errors such as penetration, slippage, or constraint conflicts that are physically impossible to execute, severely impacting assembly success rates. Second, long-sequence assembly tasks require models to maintain coherent contextual awareness across hundreds of steps. However, the context window of a pure attention mechanism suffers from information decay and retrieval bottlenecks, easily causing temporal drift and forgetting of early key information, resulting in subsequent decisions lacking reliable historical basis. Third, existing methods treat physical plausibility verification as an external filtering step after the VLM output. This "generate first, then verify" approach can only passively reject infeasible outputs, failing to actively correct the intent to the physically feasible domain during reasoning. When faced with continuous deviations, it easily falls into an inefficient cycle of repeated rejection and regeneration.

[0004] Therefore, there is an urgent need for an embodied intelligence method that can integrate the structured prior nature of the physical world into the entire cognitive reasoning process, in order to overcome the current technological bottlenecks of physical infeasibility, contextual forgetting, and shallow coupling in long-sequence precision assembly. Summary of the Invention

[0005] The purpose of this invention is to provide an assembly-based embodied cognitive reasoning method that integrates a spatiotemporal world model, in order to solve at least some of the problems existing in the prior art.

[0006] The technical solution, an assembly-based embodied cognitive reasoning method integrating a spatiotemporal world model, includes the following steps:

[0007] Acquire multimodal observation data of the assembly scenario and construct an assembly hypergraph that characterizes parts, physical contact between parts, and assembly constraint relationships;

[0008] Based on the assembly hypergraph, the hidden states of the current assembly state are extracted by an isovariant hidden neural simulator and used as the current state layer for understanding.

[0009] Based on the historical action sequence, a structured memory bank is constructed; using the current state layer understanding as the query, historical context is retrieved from the structured memory bank through sparse associative retrieval attention, and then fused with the current state layer understanding to generate a fused representation;

[0010] Based on the fusion representation and task instructions, a preliminary task intent latent vector is generated;

[0011] The initial task intent latent vector is input into a differentiable, isovariant latent neural simulator for forward simulation and deduction. Based on the deduction results, a physical compliance cost is constructed. The initial task intent latent vector is iteratively corrected online through gradient-guided projection to generate a physically feasible optimal task intent latent vector.

[0012] The optimal task intent latent vector is decoded into robot control instructions and executed.

[0013] Beneficial effects: By constructing an assembly hypergraph-like implicit neural simulator and a cognitive-physical collaborative internal optimization closed loop, this invention deeply internalizes physical feasibility constraints into the intention reasoning gradient correction process of the visual language model, solving the problems of physical infeasibility and contextual forgetting in long-sequence precision assembly, and improving the robot's intention understanding accuracy and task execution success rate in industrial human-robot collaboration scenarios. Attached Figure Description

[0014] Figure 1 This is a flowchart of the overall solution of the present invention. Detailed Implementation

[0015] 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.

[0016] like Figure 1 As shown, this embodiment describes in detail the data processing flow of an assembly-based embodied cognitive reasoning method that integrates a spatiotemporal world model, specifically including:

[0017] S1: Acquire multimodal observation data of the assembly scenario and construct an assembly hypergraph representing parts, physical contacts between parts, and assembly constraints, including:

[0018] S1.1 Multimodal observation data acquisition and part pose estimation.

[0019] In real or simulated industrial assembly scenarios, multi-view RGB-D cameras and torque sensor networks are deployed to simultaneously capture multimodal observation data containing rich spatiotemporal information. Specifically, the RGB-D cameras simultaneously acquire color and depth image streams at a frame rate of 30Hz. After stereo correction and registration, these streams generate dense point clouds with spatial 3D information. Simultaneously, torque sensors installed on each joint of the collaborative robot record force signals from the interaction between the end effector and the environment during operation at a high frequency. According to one aspect of this application, to extract structured information from these raw observations, a pre-trained part-level six-DOF pose estimation network is applied to each frame of point cloud data. This network first separates individual part point cloud clusters from the complex background using a semantic segmentation module. Then, a regressor based on template matching and point cloud registration is applied to each point cloud cluster to accurately estimate the six-DOF pose of each part in the camera coordinate system, including three translational components and three rotational components represented by quaternions. This process provides continuous, high-fidelity part motion trajectory data for subsequent graph-structured representation.

[0020] S1.2 Definition of part nodes and physical contact edges.

[0021] Based on the estimated poses of each part, the assembly scene is formally represented as an assembly hypergraph with a dynamic topology. In this hypergraph, each physically independent and identifiable rigid part, such as a screw, a bearing, or a base, is abstractly defined as a basic node, and each node is assigned a globally unique numerical identifier. Furthermore, the definition of physical contact edges is dynamically determined based on the spatial proximity between adjacent parts. For example, the spatial proximity rule calculates the Euclidean distance between the nearest faces or point clouds of two parts and compares this distance with a preset dynamic threshold. If the distance is less than the threshold, it is determined that there is potential physical contact between the two parts, and a connecting edge is created for this pair of nodes in the hypergraph. This edge not only represents the possibility of contact but is also initialized with a state vector for subsequent message passing. This data-driven graph construction method allows the model to dynamically perceive the evolution of the assembly structure during the assembly process without pre-defining all possible contact pairs.

[0022] S1.3 Construction of constraint hyperedges for multibody assembly.

[0023] Unlike ordinary edges, hyperedges are designed to explicitly encode structured multibody assembly constraints that go beyond simple contact. In a preferred embodiment, these constraints, such as a three-body coaxial fastening constraint consisting of a shaft-hole-circlip, or a face-to-face fit constraint between two planar parts, are derived from digital annotations in the assembly process manual. A hyperedge connects all part nodes involved in the constraint, and its semantic information is encoded as a parameterized latent vector of the constraint equation. Specifically, this latent vector is generated by a small autoencoder, whose input is the known constraint type and tolerance, and whose output is a fixed-length low-dimensional latent vector whose position in high-dimensional space represents the geometric type of the constraint (e.g., coaxial, coplanar, parallel, perpendicular) and its tightness. In the physical simulation, this latent vector is decoded to drive the motion of the part group to always remain above the manifold defined by the constraints.

[0024] S2: Based on the assembly hypergraph, the hidden states of the current assembly state are extracted using an isovariant implicit neural simulator as the current state layer for understanding, including:

[0025] S2.1 SE(3) - Equivalent Message Passing and State Iteration.

[0026] The constructed assembly hypergraph is fed into an equivariant implicit neural simulator for physical encoding. The core of the simulator is an SE(3)-equivariant message passing network, whose node state update mechanism is equivariant to rigid body motion groups (SE(3)). This means that regardless of whether the entire assembly is rigidly translated or rotated, the node update vector calculated by the network will be covariant, ensuring the independence of the reference frame for physical feature extraction. In each message passing iteration, ordinary edges act as information channels for potential contact forces, encoding the current motion state (pose and velocity) of the node into collision force messages for transmission. At the same time, the hyperedge calculates the correction force that pulls the associated node back to the constraint manifold in real time based on its stored constraint implicit vector, and broadcasts this information as a hyperedge message to all nodes it connects to. After receiving messages from all adjacent edges and hyperedges, the node integrates the context information and updates its own implicit state through a gated recurrent unit mechanism. This mechanism enables the network to handle both dynamic collision dynamics between parts and precise geometric constraints simultaneously.

[0027] S2.2 Variable Topology Event Detection and God's Frequent Differential Equations Driven.

[0028] According to a further improvement in this application, the evolution of the assembly state is not a discrete inter-frame jump, but a smooth flow dominated by a continuous neural ordinary differential equation. This neural ordinary differential equation parameterizes the rate of change of the node states as a deep neural network function of the current state. To simulate the topologically variable physical process of "from separation to contact" or "from contact to fastening" in assembly, a set of learnable discrete contact event detection gates are integrated into the network. These detection gates continuously monitor the relative distance, relative velocity, and degree of violation of constraint hyperedges between nodes. Once a critical event (such as the first contact between two parts) is determined to be about to occur or has already occurred, the detection gate outputs a trigger signal, causing a smooth but rapid switch in the parameter set of the neural network's dynamic equations. This mechanism endows the implicit neural simulator with the ability to capture discontinuous physical events. Finally, the node hidden state vector obtained by integrating over a continuous time point, which integrates all interaction history and constraint information, represents a deep spatiotemporal understanding of the current assembly state.

[0029] S3: Based on the historical action sequence, construct a structured memory bank; using the current state layer understanding as the query, retrieve historical context from the structured memory bank through sparse associative retrieval attention, and fuse it with the current state layer understanding to generate a fused representation, including:

[0030] S3.1 Construction of a structured memory bank for historical actions.

[0031] Before generating the initial task intent latent vector, historical information needs to be effectively organized. After the robot completes an assembly subtask (such as "inserting the shaft"), a dedicated memory encoder packages the current step into a memory slot. Preferably, each memory slot is a composite vector composed of three parts: ① the global latent state after the operation is completed; ② the hypergraph substructure of the parts involved in the operation, represented by a local graph obtained through graph pooling; ③ an action description vector encoded by a small language model, such as embedding semantic actions like "grasp," "horizontal movement," and "tightening." This memory slot is stored in a structured external memory bank, using the semantic tag of the "assembly subtask" as the retrieval key. The memory bank uses a key-value pair storage structure and dynamically grows as the assembly process progresses, forming a quickly accessible externalized cognitive memory that solves the problem of information being forgotten or confused in long-sequence tasks.

[0032] S3.2 Contextual Retrieval and Fusion Based on Sparse Associative Attention

[0033] In the current assembly step, to integrate historical experience, the system employs a sparse associative retrieval attention mechanism. Specifically, the current state understanding is first used as the query vector, and the similarity score between the query and all stored keys in the memory bank is calculated. Unlike traditional attention, this scheme only retains the top K memory slots with the highest similarity (K is a small integer), forcing the remaining attention weights to zero to achieve sparsity and filter out massive amounts of irrelevant information. Based on the attention weights of these selected memory slots, their value vectors are weighted and summed to aggregate into a condensed historical context vector. This historical context vector contains key information about "what operations were taken in the past and their results under similar assembly states." Finally, the process of generating the fused representation is a gated fusion module that accepts the current state understanding and the historical context vector as input. Through a learnable gating signal, it dynamically determines which information needs to be emphasized or suppressed at the element-wise level, thereby outputting a unified cognitive representation that understands the present and connects to the past.

[0034] S4: Based on the fusion representation and task instructions, generate a preliminary task intent latent vector; input the preliminary task intent latent vector into a differentiable, isovariant implicit neural simulator for forward simulation and deduction, including:

[0035] S4.1 Generate the initial hidden vector of the task intent.

[0036] First, a vision-language model acts as an intent generator, receiving a fused representation and a high-level task instruction described in natural language (e.g., "complete the pre-tightening assembly of the rotor"). This vision-language model consists of an encoder-decoder architecture based on a Transformer, whose cross-modal attention mechanism deeply interacts the fused vision-physical representation with the semantic features of the language instruction. Its output layer does not directly generate explicit robot action instructions, but rather generates a low-dimensional latent intent vector residing in a semantic-physical shared latent space. This vector can be interpreted as an abstract intent encoding "smoothly move the currently manipulated part in a specific direction and velocity to approximate its dual part." In this way, the model decouples high-level semantic understanding from low-level physical operations, providing a flexible operational space for subsequent physical verification and correction.

[0037] S4.2 Differentiable computation graph construction and physical compliance cost assessment.

[0038] To verify and optimize this initial intent, this scheme constructs a differentiable computational graph that combines a joint vision-language model and a world model. In a preferred embodiment, the generated latent vector of the initial task intent is set as an optimizable variable node in the computational graph. This vector is fed into an isovariant latent neural simulator, which acts as the world model, and its action decoder decodes it into an explicit sequence of physical forces and trajectories for several future time steps. The simulator performs a fast forward simulation to predict the future six-DOF pose sequence of each node in the assembly hypergraph after the intent sequence is applied. Based on this predicted sequence, a physical compliance cost function is calculated. This cost includes at least two items: one is the penetration depth between parts efficiently calculated using a signed distance field, used to penalize physical interfering; the other is the projection error of the part group deviating from the constraint manifold for all active assembly hyperedges, i.e., the constraint satisfaction error. Finally, these two items are weighted and summed to form a scalar physical compliance cost value, used to quantify the potential physical infeasibility of the intent.

[0039] S5: Based on the deduction results, construct the physical compliance cost, and perform online iterative correction on the initial task intent latent vector through gradient-guided projection to generate the physically feasible optimal task intent latent vector, including:

[0040] S5.1 Construction of the total loss and gradient calculation for joint optimization.

[0041] After obtaining the physical compliance cost, the process doesn't simply reject physically infeasible intentions; instead, it initiates an internal optimization correction process. First, a joint optimization total loss function is constructed. This total loss consists of a weighted sum of the physical compliance cost and a semantic consistency constraint term. The semantic consistency constraint term is defined as the cosine or Euclidean distance between the latent vector of the intention being optimized and the original initial task intention latent vector. Its function is to constrain the corrected intention from deviating excessively from the original task objective. For example, the Lagrange multiplier method or a simple weighted method is used, setting a weight coefficient λ to balance physical feasibility and semantic fidelity. Subsequently, automatic differentiation is performed throughout the differentiable computational graph. Starting from the total loss, it propagates backward along the computational graph to calculate the precise gradient of the total loss with respect to the initial task intention latent vector. This gradient vector indicates in the latent space in which direction the intention should be modified to most quickly reduce physical violations while maintaining semantic invariance.

[0042] S5.2 Online gradient descent iteration and optimal intent generation.

[0043] Within millisecond-level time slices of the inference phase, such as a 100-millisecond control period, the calculated gradient is used to perform a specified number of online gradient descent iterations on the initial task intent latent vector, typically requiring only three to five steps. In each iteration, the intent latent vector is updated with small steps along the negative gradient direction, and after each update, it is mapped back to the effective semantic manifold defined by the prior distribution of the training data through a projection function. This projective gradient descent process is equivalent to allowing the initial intent to "slide" to a local optimum in a field with a physical cost as the potential energy gradient. After several iterations, the intent latent vector converges or reaches the maximum number of iterations. The final latent vector obtained is the optimal task intent latent vector that is physically feasible and highly consistent with the original task instruction within the semantic-physical shared latent space. This process intrinsically "magnetizes" the output of the cognitive model with physical knowledge.

[0044] S6: Decode the optimal task intent latent vector into robot control commands and execute them, including:

[0045] S6.1 Motion decoding and robot control command mapping.

[0046] After obtaining the optimal task intent latent vector, a specially trained motion decoder maps it into a specific sequence of instructions that can be executed by the robot controller. In one specific implementation, the decoder outputs a dense trajectory for the next ten steps, where each trajectory point contains the target six-DOF pose of the robot's end effector, the gripper's opening and closing angles, and a six-dimensional force / torque control target. These instructions are converted into joint angles or joint torques by the robot's inverse kinematics solver and then sent to the underlying real-time motion controller or impedance controller. For example, for a seven-DOF collaborative robot, the optimal task intent latent vector is ultimately decoded into the position, velocity feedforward values, and stiffness and damping parameters of the seven joints over the next 500 milliseconds, enabling the robot to perform complex actions such as precision shaft and hole assembly in a compliant and physically precise manner.

[0047] S6.2 Post-execution prediction bias detection and online adaptive model update.

[0048] According to one aspect of this application, after each action is executed, an online learning and adaptation phase is triggered. First, the actual assembly scene state after execution is re-acquired through the perception module, and a new assembly hypergraph is constructed. The actual state transition process is quantitatively compared with the state transition predicted by the differentiable simulator, and the pose prediction error and contact state prediction error are calculated. If the norm of the deviation exceeds a preset adaptive threshold, the system determines that the model has a cognitive bias towards the current real physical environment. At this time, the current real state transition data is automatically labeled as a high-value, real-time fine-tuning sample. In a background non-blocking thread, this sample is used to perform one or more gradient descent updates with a very small learning rate on the learnable parameters in the equivalent implicit neural simulator and memory retrieval module. This extremely low-cost online adaptive update allows the entire cognition-reasoning-execution closed loop to continuously evolve, gradually adapting to unmodeled complex factors in the real world, such as friction, flexible deformation, and lighting changes, thereby continuously improving the task execution success rate over time.

[0049] This invention achieves a deep internalization and fusion of structured physical priors and visual language reasoning by constructing an assembly hypergraph-like implicit neural simulator and a retrieval-enhanced hierarchical spatiotemporal cognitive memory network. First, by explicitly encoding multi-body assembly constraints and variable topology contact dynamics through a hypergraph, the world model gains the ability to accurately depict the physical essence of parts' spatial poses, constraint manifolds, and collisions, overcoming the shortcomings of pure visual models in understanding three-dimensional physical laws. Second, by constructing an externalized cognitive memory bank through sparse associative retrieval attention, the system can proactively backtrack to key historical experiences across arbitrary time spans in tasks with hundreds of steps, overcoming the bottlenecks of contextual forgetting and temporal drift. More significantly, the designed cognitive-physical collaborative internal optimization closed loop elevates physical feasibility verification from passive posterior filtering to gradient-guided online iterative correction. This ensures that each latent vector of intent generated by reasoning undergoes "magnetization" and regularization within the semantic-physical shared latent space, resulting in output actions that naturally satisfy assembly constraints and are highly faithful to the task objective. This solution improves the accuracy of intent understanding and the reliability of action execution in long-sequence precision assembly tasks, while also possessing excellent scenario generalization capabilities and the potential for continuous online adaptive evolution.

[0050] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details of the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for embodied cognitive reasoning that integrates a spatiotemporal world model, characterized in that, include: Acquire multimodal observation data of the assembly scenario and construct an assembly hypergraph that characterizes parts, physical contact between parts, and assembly constraint relationships; Based on the assembly hypergraph, the hidden states of the current assembly state are extracted by an isovariant hidden neural simulator and used as the current state layer for understanding. Construct a structured memory bank based on historical action sequences; Using the current state layer understanding as the query, historical context is retrieved from the structured memory through sparse associative retrieval attention and fused with the current state layer understanding to generate a fused representation; Based on the fusion representation and task instructions, a preliminary task intent latent vector is generated; The initial task intent latent vector is input into a differentiable, isovariant latent neural simulator for forward simulation and deduction. Based on the deduction results, a physical compliance cost is constructed. The initial task intent latent vector is iteratively corrected online through gradient-guided projection to generate a physically feasible optimal task intent latent vector. The optimal task intent latent vector is decoded into robot control instructions and executed.

2. The method according to claim 1, characterized in that, The steps to extract the hidden state of the current assembly state include: Estimate the six-degree-of-freedom pose of each component from multimodal observation data; Parts are defined as nodes in the assembly hypergraph, potential physical contact pairs determined based on spatial proximity are defined as edges between nodes, and multibody assembly constraints between a pre-annotated set of parts are defined as hyperedges. Using the six-degree-of-freedom pose as the node input, the ordinary edges transmit collision forces and the super edges transmit assembly constraint correction forces based on the constraint equation parameters through the SE(3)-equal variable message passing network, and the node state is updated iteratively. The state evolution is dominated by the God constant differential equations, and at the moment when a learnable discrete contact event detection gate determines contact or constraint locking, the dynamic equations are smoothly switched to capture topological events and finally generate the hidden state of the current assembly state.

3. The method according to claim 2, characterized in that, Before generating the initial task intent latent vector, the following steps are also included: The hidden state after each operation is completed, the corresponding operation part hypergraph substructure, and the action description vector are combined into a memory slot and stored in the structured memory bank with the current assembly subtask as the key, forming an externalized cognitive memory that can be retrieved in real time. Sparse associative retrieval attention is based on the embedding of parts and constraints in the current state layer understanding. It locates and extracts the historical memory slots with the highest relevance in the structured memory bank and aggregates their implicit information into historical context.

4. The method according to claim 1, characterized in that, The process of generating the physically feasible optimal latent vector for the task intent is as follows: Construct a differentiable computational graph consisting of an isovariant implicit neural simulator and a preliminary task intent latent vector; In a differentiable computational graph, the initial task intent latent vector is decoded into an explicit sequence of physical forces, and a forward simulation is performed to obtain a predicted sequence of future states. Calculate the physical compliance cost of the future state sequence, which includes at least the part penetration depth and assembly constraint satisfaction error; The optimization direction is the gradient of the physical compliance cost with respect to the initial task intent latent vector. Under the condition of satisfying a semantic consistency constraint term to ensure that the intent does not deviate from the task objective after constraint correction, online gradient descent is performed to obtain the optimal task intent latent vector.

5. The method according to claim 4, characterized in that, The process of performing online gradient descent is as follows: Construct a joint optimization total loss, which is the weighted sum of physical compliance costs and semantic consistency constraints; Within a millisecond time slice during the inference phase, a specified number of gradient descent iterations are performed on the initial task intent latent vector to obtain the optimal task intent latent vector that is physically feasible and semantically consistent within the semantic-physical shared latent space.

6. The method according to claim 1, characterized in that, This method also includes a simulation-retrieval joint inference step for the future prediction layer: After generating the optimal task intent latent vector, the prediction head of the enhanced hierarchical spatiotemporal cognitive memory network is retrieved and combined with the current state layer understanding, historical context and the optimal task intent latent vector to infer candidate trajectories for multiple future steps in the latent space. The isovariant implicit neural simulator performs forward simulation for each candidate trajectory. At the same time, the system retrieves historical experiences similar to the simulated future state from the structured memory, performs empirical calibration on the simulation results, and generates a physically reasonable future assembly motion trajectory that conforms to historical success patterns.

7. The method according to claim 1, characterized in that, This method also includes online memory formation and model adaptation steps: After executing the robot control instructions, the actual observed state transitions are compared with the predictions of the equivalent implicit neural simulator; If the deviation exceeds the preset threshold, the current new state is used as an instant fine-tuning sample to adaptively update the parameters of the equivalent implicit neural simulator and sparse associative retrieval attention online.

8. The method according to claim 4, characterized in that, The calculation of physical compliance costs also includes: Calculate the constraint manifold projection error caused by the sequence of physical forces mapped by the implicit vector of the initial task intent, which is related to the assembly constraints. The constraint manifold projection error is included as a penalty in the physical compliance cost.

9. The method according to claim 1, characterized in that, Hyperedges in the assembly hypergraph are used to explicitly encode multi-body coaxial fastening constraints or surface-to-surface fitting constraints between a group of parts. This encoding is a parameterized implicit vector of the constraint equation.

10. The method according to claim 2, characterized in that, SE(3) - an equivariant message passing network, whose node state update function is equivariant to the translation and rotation of the six-DOF pose of the part under the action of the SE(3) group, ensuring that the state update is independent of the choice of the global reference system.

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