Manufacturing path planning method and device based on multi-gate hybrid expert network, equipment and medium

Abstract

The invention provides a manufacturing path planning method and device based on a multi-gate hybrid expert network, equipment and a medium, and relates to the technical field of path planning. The method comprises the following steps: converting Cartesian coordinates of a plurality of processing points into joint angle vectors through inverse kinematics operation; wherein the joint angle vector comprises a plurality of joint angle components, and each joint angle component is the angle of one joint of the multi-joint machining robot; aiming at each joint angle vector, multiplying each joint angle component in the joint angle vector by the weight of the corresponding joint to obtain a plurality of weighted joint angle vectors; and constructing a TSP map based on the plurality of weighted joint angle vectors, inputting the TSP map into the trained multi-gate hybrid expert network, and determining a manufacturing path of the plurality of processing points. According to the method, the manufacturing sequence with the highly approximate optimal energy consumption can be quickly generated for any given number of machining points, and the operation energy consumption of the industrial robot and the cost of model development are remarkably reduced.

Description

Technical Field

[0001] This invention relates to the field of path planning technology, and in particular to a manufacturing path planning method, apparatus, equipment and medium based on a multi-gate hybrid expert network. Background Technology

[0002] In industrial automated production, when robots complete multi-point processing tasks (such as drilling, spot welding, and component assembly), they need to traverse all processing points sequentially and optimize their motion trajectory. The core objective is to minimize energy consumption, time, and path redundancy. This type of task can be abstracted as the Traveling Salesman Problem (TSP).

[0003] However, existing technical solutions have several inherent limitations. First, most studies directly plan paths within the Cartesian space (i.e., the two-dimensional or three-dimensional workspace) of the robot's end effector, using Euclidean geometric distance as a cost metric. This approach ignores the robot's actual motion mechanism—its motion is achieved through the rotation of multiple joints, and the angular displacement of the joint space is directly related to the driving energy consumption. This means that the "shortest path" planned in Cartesian space is not necessarily the most energy-efficient joint motion path. Second, even when planning in joint space, existing methods typically treat the motion of each joint equally, ignoring the uneven energy consumption caused by differences in physical characteristics such as load and torque among different joints. This leads to a discrepancy between the optimization objective and actual energy consumption. Furthermore, although some studies in recent years have attempted to solve TSP using deep learning models such as graph neural networks, these models are often trained and deployed for specific problem scales (fixed number of nodes). In actual production, the number of processing points changes dynamically with the task, requiring the training and maintenance of multiple models for different scales. This results in wasted computing resources, complex deployment, and difficulty in flexibly adapting to changing production scenarios. Summary of the Invention

[0004] This invention provides a manufacturing path planning method, apparatus, equipment, and medium based on a multi-gate hybrid expert network to solve the problems of large energy consumption control deviation and high optimization cost in multi-point processing task path planning.

[0005] In a first aspect, embodiments of the present invention provide a manufacturing path planning method based on a multi-gate hybrid expert network, comprising: Through inverse kinematics operations, the Cartesian coordinates of multiple processing points are transformed into joint angle vectors; where the joint angle vectors include multiple joint angle components, each of which is the angle of one joint of the multi-joint processing robot. For each joint angle vector, each joint angle component in the vector is multiplied by the weight of the corresponding joint to obtain multiple weighted joint angle vectors; where the weight of each joint is determined based on the mechanical characteristics of each joint, including torque. A TSP graph is constructed based on multiple weighted joint angle vectors and input into a trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points.

[0006] In one possible implementation, the multi-gate hybrid expert network includes a shared bottom layer, multiple expert networks, multiple gating networks, and multiple tower networks; a TSP graph is constructed based on multiple weighted joint angle vectors and input into the trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points, including: Construct a TSP graph by using weighted joint angle vectors as nodes and Manhattan distances between adjacent weighted joint angle vectors as edge distances; Based on the maximum scale of the multi-gate hybrid expert network, the TSP graph is filled and input into the shared bottom layer to obtain the TSP graph with feature embedding. Multiple expert networks are used to extract structural features from the TSP graph with embedded features in parallel, resulting in multiple weighted graph structural features. Based on the scale of multiple processing points, each weighted graph structural feature is sliced ​​to obtain multiple slice features; Multiple slice features are input into a gating network corresponding to the scale of multiple processing points, and the multiple slice features are weighted and summed to obtain the fused features; By inputting the fused features into a tower network corresponding to the scale of multiple processing points, a path probability heatmap of multiple processing points is obtained. By using Beam search to filter the path with the smallest total edge distance on the path probability heatmap, manufacturing paths for multiple processing points are obtained.

[0007] In one possible implementation, the shared underlying layer is a batch normalization layer, each expert network is a GAT network, and each tower network is a fully connected network.

[0008] In one possible implementation, before constructing the TSP graph based on multiple weighted joint angle vectors and inputting it into a trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points, the following steps are also included: Construct a multi-point processing scenario dataset; the multi-point processing scenario dataset includes multiple multi-point processing scenarios, each with a different processing point scale; Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-gate hybrid expert network is trained to obtain the trained multi-gate hybrid expert network.

[0009] In one possible implementation, an initial multi-level hybrid expert network is trained based on a multi-point processing scenario dataset and an uncertainty-weighted loss function to obtain a trained multi-level hybrid expert network, including: Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-level hybrid expert network is trained in multiple rounds to obtain the trained multi-level hybrid expert network. For each round of training, perform the following steps: Based on the maximum scale of a multi-gate hybrid expert network, multiple random instances are generated through spatial sampling, and each random instance is sliced ​​and filled based on different processing point scales to obtain multiple subtasks with different processing point scales. Multiple subtasks of different processing point scales are input into a multi-gate hybrid expert network, and shared features of each subtask of processing point scale are generated by sharing the underlying layer and each expert network. The shared features of subtasks at each processing point scale are input into the gating network and tower network corresponding to that processing point scale to obtain the path probability heatmap of the subtasks at that processing point scale, and the loss at that processing point scale is calculated based on the path probability heatmap and the uncertainty weighted loss function. Based on the loss at each processing point, perform a backpropagation to update all trainable parameters of the multi-gate hybrid expert network.

[0010] In one possible implementation, the uncertainty-weighted loss function is:

[0011]

[0012] in, for gradient, For all trainable parameters of a multi-gate hybrid expert network, For parameters and multi-point processing scenarios The total loss during a single round of training. For learnable parameters, For the first Total edge distance error for each processing point The total number of processing points. For batch size, For the first The length of a Bernoulli sampling path at the scale of a processing point. For the first The length of the greedy sampling path at the scale of each processing point. For the first The average performance difference of sampling paths at the scale of each processing point. For parameters The path to be generated The probability of.

[0013] In one possible implementation, before multiplying each joint angle component in each joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors, the following steps are also included: The weight of each joint is determined based on the mechanical characteristics of each joint of the multi-joint machining robot.

[0014] Secondly, embodiments of the present invention provide a manufacturing path planning device based on a multi-gate hybrid expert network, comprising: The conversion module is used to convert the Cartesian coordinates of multiple processing points into joint angle vectors through inverse kinematics operations; wherein, the joint angle vector includes multiple joint angle components, and each joint angle component is the angle of one joint of the multi-joint processing robot. The weighting module is used to multiply each joint angle component in each joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors; wherein, the weight of each joint is determined based on the mechanical characteristics of each joint, including torque. The planning module is used to construct a TSP graph based on multiple weighted joint angle vectors and input it into a trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points.

[0015] Thirdly, embodiments of the present invention provide an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described in the first aspect or any possible implementation thereof.

[0016] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in the first aspect or any possible implementation thereof.

[0017] The manufacturing path planning method, apparatus, equipment, and medium based on a multi-gate hybrid expert network provided in this invention transforms the coordinates of processing points into joint angle vectors through inverse kinematics. This establishes the planning problem at its source within the joint space, directly related to the robot's drive energy consumption. Weights are introduced for each joint angle component and weighted processing is performed. Physical characteristics such as torque differences between different joints are incorporated into the optimization model, ensuring that subsequent path cost calculations accurately reflect the actual energy consumption contribution of each joint's movement. This achieves a fundamental improvement from "minimizing geometric distance" to "minimizing actual energy consumption." The trained multi-gate hybrid expert network directly processes the weighted TSP graph. This network possesses powerful feature learning and reasoning capabilities, automatically learning complex energy-saving path patterns from data and, crucially, exhibiting inherent flexibility in handling problems of different scales. Therefore, this method can quickly generate a manufacturing sequence that closely approximates energy-optimal for any given number of processing points, significantly reducing the operating energy consumption of industrial robots while avoiding the cost of repeatedly developing models for tasks of different scales, thus improving the versatility and practicality of the planning system. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating the implementation of a manufacturing path planning method based on a multi-gate hybrid expert network according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating the implementation of a manufacturing path planning method based on a multi-gate hybrid expert network, provided in another embodiment of the present invention. Figure 3 This is a schematic diagram of the structure of an MMOE network provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of a GAT network provided in an embodiment of the present invention; Figure 5 This is a comparison chart of the performance gap between the manufacturing path planning method based on a multi-gate hybrid expert network provided in an embodiment of the present invention and the optimal path on nine different TSP scales; Figure 6 This is a performance comparison chart of the manufacturing path planning method based on a multi-gate hybrid expert network provided in an embodiment of the present invention on 9 different TSP scales and 91 different TSP scales. Figure 7A This is a diagram showing the effect of the Gurobi method provided in an embodiment of the present invention on the planning path of workpiece 1; Figure 7B This is a diagram showing the effect of the MTL4TSP method provided in an embodiment of the present invention on the planning path of workpiece 1; Figure 7C This is a diagram showing the effect of the NAR4TSP method provided in an embodiment of the present invention on the planning path of workpiece 1; Figure 7D This is a diagram showing the effect of the Gurobi method provided in an embodiment of the present invention on the planning path of workpiece 2; Figure 7E This is a diagram showing the effect of the MTL4TSP method provided in an embodiment of the present invention on the planning path of workpiece 2; Figure 7F This is a diagram showing the effect of the NAR4TSP method provided in an embodiment of the present invention on the planning path of workpiece 2; Figure 8 This is a schematic diagram of the manufacturing path planning device based on a multi-gate hybrid expert network provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0019] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0020] See Figure 1 The flowchart illustrating the implementation of the manufacturing path planning method based on a multi-gate hybrid expert network provided in this embodiment of the invention is described in detail below: Step 101: Through inverse kinematics operation, the Cartesian coordinates of multiple processing points are converted into joint angle vectors; wherein, the joint angle vector includes multiple joint angle components, and each joint angle component is the angle of one joint of the multi-joint processing robot.

[0021] In this embodiment, the method is applied to multi-joint machining robots, such as six-axis industrial robots used for spot welding in automobile manufacturing or for drilling holes in the fuselage in the aerospace field. Figure 2 The complete process of "Cartesian coordinates → original joint angles → weighted joint angles → equivalent unweighted TSP" in this embodiment is shown below, and will be described in detail below.

[0022] The initial step of this method is to obtain the Cartesian coordinates of multiple processing points that the robot needs to access sequentially in a three-dimensional workspace. Since the robot's motion is achieved by the rotation of its joints, directly optimizing the linear distance in space does not reflect the actual energy consumption; therefore, the problem must be transformed into joint space. This transformation is accomplished through inverse kinematics operations.

[0023] Specifically, for the coordinates of a processing point in space, using the robot's known geometric parameters such as link lengths and joint offsets, a set of joint angles that allow the robot's end effector to reach that position can be solved analytically or numerically. For a robot with m joints, each processing point corresponds to an m-dimensional joint angle vector. Each component represents the rotation angle of a joint relative to its zero position. For example, for a typical six-axis robot, its joint angle vector is six-dimensional, corresponding to the angles of the six degrees of freedom: base rotation, upper arm, forearm, etc. This step transforms the intuitive spatial position planning problem into a joint motion planning problem directly related to the actuator's energy consumption.

[0024] Step 102: For each joint angle vector, multiply each joint angle component in the joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors; wherein, the weight of each joint is determined based on the mechanical characteristics of each joint, including torque.

[0025] In this embodiment, the physical characteristics of the robot's joints are not the same. The joint motors driving the upper arm movement typically require a larger torque output to overcome gravity, while the joints driving the rotation of the end effector wrist have a lighter load. This means that different joints consume different amounts of energy to rotate the same angle. To accurately reflect this difference in the planning, this method introduces a joint weighting factor.

[0026] The weighting factors are determined directly based on the robot's physical characteristics. The most straightforward method is to use the rated torque or maximum continuous torque of each joint motor. The principle is that the work done (energy consumption) W by the motor equals the torque T multiplied by the angular displacement. The product of these components. Therefore, multiplying each joint angle component by the torque weight of that joint yields a weighted joint angle component. This vector represents the node of the TSP, and its physical meaning is directly proportional to energy consumption. For example, if the torque of joint A1 is 187 Nm and the torque of joint A6 is 7 Nm, then the energy consumption for rotating 1 radian is approximately 26.7 times that of joint A1. The space in which they reside can be called the energy-normalized joint configuration space.

[0027] Furthermore, to ensure consistency in data distribution between the training and inference phases, the weighted joint angle vectors need to be normalized using Max-Min Scale. Mapping to the [0,1] interval, the formula is as follows:

[0028] Normalized vector As the final TSP node.

[0029] Step 103: Construct a TSP graph based on multiple weighted joint angle vectors and input it into a trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points.

[0030] In this embodiment, a complete graph, i.e., a traveling salesman problem graph, is constructed based on these weighted joint angle vectors. The weighted joint angle vectors corresponding to adjacent processing points are then... and The Manhattan distance between two points is defined as the "edge distance" of the TSP, i.e. At this point, the edge distance has been integrated with the joint weight information, and the path optimization objective of "minimizing the total edge distance" is equivalent to "minimizing the robot's actual motion energy consumption", ultimately forming an equivalent unweighted multidimensional TSP problem.

[0031] To solve this TSP, this method employs a pre-trained multi-gate hybrid expert network. This network is designed to handle problems of variable scale. The constructed TSP graph is input into this network, which, through complex internal feature extraction and inference, ultimately obtains a sequence of node visits. This sequence is the desired manufacturing path, indicating the order in which the robot visits processing points to minimize the total weighted joint movement distance (i.e., total energy consumption).

[0032] This invention transforms the coordinates of processing points into joint angle vectors through inverse kinematics, fundamentally establishing the planning problem within the joint space, which is directly related to the robot's driving energy consumption. Weights are introduced for each joint angle component and weighted processing is performed, incorporating physical characteristics such as torque differences between different joints into the optimization model. This ensures that subsequent path cost calculations accurately reflect the actual energy consumption contribution of each joint's movement, achieving a fundamental improvement from "minimizing geometric distance" to "minimizing actual energy consumption." A trained multi-disciplinary hybrid expert network is used to directly process the weighted TSP graph. This network possesses powerful feature learning and reasoning capabilities, automatically learning complex energy-saving path patterns from data and, crucially, exhibiting inherent flexibility in handling problems of varying scales. Therefore, this method can quickly generate highly approximate energy-optimal manufacturing sequences for any given number of processing points, significantly reducing the operating energy consumption of industrial robots while avoiding the cost of repeatedly developing models for tasks of different scales, thus improving the versatility and practicality of the planning system.

[0033] In one possible implementation, the multi-gate hybrid expert network includes a shared bottom layer, multiple expert networks, multiple gating networks, and multiple tower networks; a TSP graph is constructed based on multiple weighted joint angle vectors and input into the trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points, including: Construct a TSP graph by using weighted joint angle vectors as nodes and Manhattan distances between adjacent weighted joint angle vectors as edge distances; Based on the maximum scale of the multi-gate hybrid expert network, the TSP graph is filled and input into the shared bottom layer to obtain the TSP graph with feature embedding. Multiple expert networks are used to extract structural features from the TSP graph with embedded features in parallel, resulting in multiple weighted graph structural features. Based on the scale of multiple processing points, each weighted graph structural feature is sliced ​​to obtain multiple slice features; Multiple slice features are input into a gating network corresponding to the scale of multiple processing points, and the multiple slice features are weighted and summed to obtain the fused features; By inputting the fused features into a tower network corresponding to the scale of multiple processing points, a path probability heatmap of multiple processing points is obtained. By using Beam search to filter the path with the smallest total edge distance on the path probability heatmap, manufacturing paths for multiple processing points are obtained.

[0034] In this embodiment, considering the dynamic changes in the scale of processing points, the Multi-gate Mixture-of-Experts (MMOE) network is modified for specific scenarios to achieve single-model coverage of multiple processing point scales. The structure of the MMOE network is as follows: Figure 3 As shown in Table 1, the core modules and functions of the architecture are as follows: Table 1

[0035] As shown in Table 1, the MMOE network is an integrated multi-task learning system. In the inference phase, the weighted joint angle vectors (normalized joint angle vectors) obtained in the previous steps are first used as node coordinates, and the Manhattan distance between all node pairs is calculated as the edge weights to construct the initial TSP graph.

[0036] Since a trained network has a preset maximum processing size N_max (e.g., 100), for practical problems with a size n smaller than N_max, graph padding is required. Padding typically involves expanding the node and edge feature matrices of the original graph to N_max size by copying or adding virtual nodes to ensure compatibility between the input dimension and the network.

[0037] The padded TSP graph is fed into the shared bottom layer of the MMOE network, which is essentially a feature embedding module. It typically consists of a linear transformation layer, a batch normalization layer, and a ReLU activation function, and is responsible for projecting the original node coordinates and edge distance data into a high-dimensional, unified feature space to generate initial node feature embeddings and edge feature embeddings.

[0038] Subsequently, multiple expert networks process these initial features in parallel. Each expert network is a powerful graph neural network, with a multi-layer graph attention network at its core. The GAT layer dynamically calculates the association strength between nodes in the graph through an attention mechanism and aggregates neighbor information to update the node representation.

[0039] Considering the scale n of the real-world problem, it's necessary to extract the parts relevant to the actual n nodes from the features calculated for the N_max scale graph; this process is called slicing. The sliced ​​features are then fed into a gating network corresponding to scale n. The gating network is a lightweight neural network that receives the sliced ​​node features and outputs a set of weights. These weights are used to perform a weighted summation of the features output by multiple expert networks. Its purpose is to dynamically fuse the opinions of different experts for the specific task scale, forming a task-specific fused feature representation.

[0040] This fused feature is then fed into a tower network corresponding to the same size n. The tower network, typically composed of several fully connected layers, decodes the high-dimensional fused feature into an n×n real-valued matrix called a path probability heatmap. The value in the i-th row and j-th column of this heatmap visually reflects the tendency score of choosing node j as the next access point after node i when planning the path.

[0041] Finally, the decoding process uses beam search on this heatmap. The search begins with a node selected based on the probability of the starting node. At each step, the heatmap is masked based on the set of currently visited nodes, and then several partial path candidates with the highest total scores are retained until all nodes have been visited and the process returns to the starting point. Ultimately, the complete path with the highest total score (corresponding to the smallest total edge distance) is determined as the optimal manufacturing path. The entire process achieves end-to-end efficient computation from physical coordinates to the energy-saving operation sequence.

[0042] In one possible implementation, the shared underlying layer is a batch normalization layer, each expert network is a GAT network, and each tower network is a fully connected network.

[0043] In this embodiment, the batch normalization layer in the shared bottom layer is crucial. It normalizes the features of each batch of data during training and inference, ensuring a mean of 0 and a variance of 1. This significantly accelerates the training convergence process of deep networks and improves the model's generalization ability. Specifically, the shared bottom layer normalizes the input node coordinates... and edge distance Mapped to respectively 3D feature vector:

[0044]

[0045] in, , The weight matrix is ​​a learnable matrix. , Here, BN represents the batch normalization operation, and ReLU is the activation function. This embedding layer ensures consistent feature representations for TSP problems of different scales. The GAT network used in each expert network is the feature extraction engine of this scheme, and its specific structure is as follows: Figure 4 As shown. The network includes There are stacked graph attention modules, each consisting of a graph attention layer and an edge feature transformation layer. The data flow is as follows: (1) Graph Attention Layer - Node Feature Update First, the first Layer node embedding , With edge embedding The features are concatenated and then generated by linear transformation and LeakyReLU activation:

[0046] in, This represents a vector concatenation operation. , , For a learnable projection matrix, This is a feature vector that integrates node pair information and edge cost. Then, the attention coefficients are calculated using masked Softmax:

[0047] in, This represents element-wise multiplication. Let the neighborhood mask matrix be defined as:

[0048] For nodes The neighbor set is specifically defined as the distance from the node. Recent Each node. This mask ensures that each node only focuses on its own nodes. Nearest neighbor nodes (in this embodiment) This reduces computational complexity and enhances the ability to perceive local structures.

[0049] Finally, the node embedding is updated by weighted aggregation of neighbor features and combined with residual connections:

[0050] Residual connections preserve the original node information, effectively mitigating the gradient vanishing problem in deep networks.

[0051] (2) Edge feature transformation layer - edge feature update The edge feature update utilizes the updated node features to capture the associations between node pairs. First, the node features are projected onto different dimensional spaces through two independent linear transformations:

[0052]

[0053] Then, the interaction feature matrix of the node pairs is generated by broadcast addition:

[0054] in, This indicates a broadcast addition operation, which converts the shape to... and The tensor expansions are added together to obtain The interaction matrix is ​​designed to explicitly model the feature relationships between each pair of nodes. Finally, historical edge features are fused and edge features are updated using Sigmoid activation and residual connections:

[0055] The Sigmoid function compresses eigenvalues ​​to... The interval, combined with residual connections to preserve historical edge information, enables the network to refine the transition probability representation of edges layer by layer. Standard GAT calculates attention based solely on node features, while this embodiment further utilizes enhanced GAT, incorporating edge feature terms into the attention scoring function. This allows the network to fully understand the cost of connecting nodes when learning node relationships, thus learning a more energy-efficient relational representation. Each tower network is implemented using a fully connected network, which has a simple structure but a clearly defined function. For the task... The tower network will use the gated weighted edge features Layer-by-layer transformation:

[0056] in, and For the first The tower network Layer weights and biases. For example, a two-layer tower network ( The first layer will The first layer maps the 1D input features to an intermediate layer and introduces non-linearity using the ReLU activation function; the second layer maps the intermediate features to a single scalar output, and finally the outputs of all node pairs are reshaped to... heatmap matrix In this matrix The larger the value, the more likely it is to originate from the node. Transfer to node The higher the probability, the better. This combination ensures that the model has both strong graph structure modeling capabilities and can efficiently output interpretable planning results.

[0057] In one possible implementation, before constructing the TSP graph based on multiple weighted joint angle vectors and inputting it into a trained multi-gate hybrid expert network to determine the manufacturing path for multiple processing points, the following steps are also included: Construct a multi-point processing scenario dataset; the multi-point processing scenario dataset includes multiple multi-point processing scenarios, each with a different processing point scale; Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-gate hybrid expert network is trained to obtain the trained multi-gate hybrid expert network.

[0058] In this embodiment, before training the MMOE network, a multi-point processing scenario dataset needs to be constructed: to meet the requirements of model training and performance evaluation, the training set needs to cover TSP instances with the number of nodes (corresponding to the processing point scale) ranging from 20 to 100, with a node interval of 10 between adjacent scales (i.e., including TSP instances with 20, 30, 40, ..., 100 nodes).

[0059] Specifically, this embodiment employs an efficient simulation method to construct a multi-point machining scenario dataset: uniform random sampling is performed within the robot's joint space (an m-dimensional unit hypercube, where m is the number of joints) to generate a large set of random weighted joint angle vectors. These sets are organized into problem instances of different sizes, such as containing 20, 50, or 100 nodes, thus forming a synthetic dataset covering various task complexities. For example, in each training epoch, by sampling from the six-dimensional space [0,1]... 6 Using the internal sampling node method, 12,800 TSP100 instances (i.e., 100 TSP instances per node) are generated.

[0060] Then, a shared training process is introduced: multiple scale TSP instances are input in a single round of training, shared features are generated by sharing the underlying layer and expert network, and the corresponding gating and tower networks calculate the loss at each scale. Finally, all parameters are updated through a backpropagation, so that a single round of training can cover multiple processing point scales, which greatly reduces the training time.

[0061] In one possible implementation, an initial multi-level hybrid expert network is trained based on a multi-point processing scenario dataset and an uncertainty-weighted loss function to obtain a trained multi-level hybrid expert network, including: Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-level hybrid expert network is trained in multiple rounds to obtain the trained multi-level hybrid expert network. For each round of training, perform the following steps: Based on the maximum scale of a multi-gate hybrid expert network, multiple random instances are generated through spatial sampling, and each random instance is sliced ​​and filled based on different processing point scales to obtain multiple subtasks with different processing point scales. Multiple subtasks of different processing point scales are input into a multi-gate hybrid expert network, and shared features of each subtask of processing point scale are generated by sharing the underlying layer and each expert network. The shared features of subtasks at each processing point scale are input into the gating network and tower network corresponding to that processing point scale to obtain the path probability heatmap of the subtasks at that processing point scale, and the loss at that processing point scale is calculated based on the path probability heatmap and the uncertainty weighted loss function. Based on the loss at each processing point, perform a backpropagation to update all trainable parameters of the multi-gate hybrid expert network.

[0062] In this embodiment, in each training round, a batch of TSP instances is first randomly generated based on the maximum scale supported by the network. This batch of data undergoes a forward propagation through the network's shared underlying layers and all expert networks, resulting in a set of basic graph features. Then, for each target scale (e.g., 20, 50, ..., 100) that the network needs to learn, the training process initiates an independent "task branch": extracting slices of the corresponding scale from the basic features; feeding these slices into gated networks and tower networks specific to that scale to generate a prediction heatmap; decoding two paths from the heatmap using Bernoulli sampling (exploration) and greedy search (exploitation), and calculating their lengths (costs). Based on these costs, combined with an adaptive baseline (typically an exponential moving average of historical performance), the current gradient loss for this task is calculated.

[0063] After calculating the losses for all task branches, a crucial step is applying an uncertainty-weighted mechanism. The loss for each task is multiplied by the reciprocal of its uncertainty weight, then summed using weighted averages, and a regularization term for the uncertainty parameter is added to form the final total loss. Subsequently, a backpropagation is performed based on this total loss, simultaneously updating the parameters of the shared underlying layers, all expert networks, all gating networks, and all tower networks. This "one forward pass - multi-task evaluation - one backpropagation" paradigm is the core of the model's ability to efficiently learn multi-task knowledge. It makes the time required to train a model handling nine different task sizes comparable to the time required to train a single, high-scale model, significantly improving training efficiency.

[0064] In one possible implementation, the uncertainty-weighted loss function is:

[0065]

[0066] in, for gradient, For all trainable parameters of a multi-gate hybrid expert network, For parameters and multi-point processing scenarios The total loss during a single round of training. For learnable parameters, For the first Total edge distance error for each processing point The total number of processing points. For batch size, For the first The length of a Bernoulli sampling path at the scale of a processing point. For the first The length of the greedy sampling path at the scale of each processing point. For the first The average performance difference of sampling paths at the scale of each processing point. For parameters The path to be generated The probability of.

[0067] In this embodiment, the loss function is divided into two layers: the inner layer is for each task. Policy gradient loss gradient .in, It is the batch size, used to average the gradient noise within a single batch and increase stability. and represents the path length of the k-th scale task obtained through random sampling and greedy search, respectively, and their difference reflects the advantage of the current stochastic policy over the deterministic baseline policy.

[0068] This advantage is the average value across the batch, used to further reduce the variance of the gradient estimate, and is calculated as follows:

[0069] It is the policy gradient, which specifies how to adjust the network parameters θ to increase the generation of the current sampling path. The probability of is the bridge that transmits path performance feedback to the neural network parameters, and its calculation formula is:

[0070] in, To select the starting node The probability, To select a node in step i The probability, This refers to the node size.

[0071] The outer layer is the total loss gradient. It applies to all The loss gradients of each task are summed using weighted averages. The weights are determined by learnable parameters. pass Decide, Characterize the inherent uncertainty of task k. When a task is difficult to learn and its predictions are highly volatile ( When the probability of a task is high (e.g., large), its weight will automatically decrease to prevent it from interfering with the learning of other tasks; conversely, the weight of tasks with high determinism will increase. Additional The term is used as a regularization to prevent The weights are increased indefinitely until zero. This mechanism allows the model to intelligently allocate learning attention to tasks of different scales without human intervention during training, providing a theoretical guarantee for achieving robust multi-task performance.

[0072] In one possible implementation, before multiplying each joint angle component in each joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors, the following steps are also included: The weight of each joint is determined based on the mechanical characteristics of each joint of the multi-joint machining robot.

[0073] In this embodiment, the determination of joint weights is the linchpin connecting the physical energy consumption model and the mathematical optimization model. These weights are not arbitrarily set, but are directly derived from the mechanical power parameters of the multi-joint machining robot itself. The most direct and effective way to determine the weights is to use the rated output torque of the drive motors for each joint. This information can be directly obtained from the product technical specification manual or motor data sheet provided by the robot manufacturer. For example, for the KUKA KR6 900 model robot, the rated torques of its six joints are [187, 185, 70, 18, 15, 7] Nm.

[0074] The physical principle behind choosing torque as a weight is sound: the mechanical work W done by the motor under uniform rotation is equal to the product of its output torque T and the rotation angle θ. Therefore, multiplying the angular displacement of each joint by its torque yields a product directly proportional to the energy consumed by that joint's movement. This step allows for the embedding of a realistic physical energy consumption model within the mathematical optimization model. This ensures that the final planned path sequence mathematically minimizes the weighted distance while physically minimizing the robot system's total energy consumption, achieving a precise mapping from digital optimization to physical energy conservation.

[0075] In a specific embodiment, the method provided by the present invention is implemented as follows: (a) Hardware environment Processor: Intel Core i5-12400F; Graphics card: NVIDIA RTX 4070 Ti SUPER (supports CUDA 12.0, meeting the requirements for parallel computing); Robot: KUKA KR6 900 six-degree-of-freedom robotic arm (joint torque parameters: A1=187Nm, A2=185Nm, A3=70Nm, A4=18Nm, A5=15Nm, A6=7Nm); (ii) Software Environment Operating system: Windows 10; Deep learning framework: PyTorch 1.13.1; Simulation platform: PyBullet 3.21 (for robot kinematics simulation); Development language: Python 3.8.16; (III) Implementation Steps Step 1. Joint weight coefficient determination and TSP conversion Step 1.1: Joint weight calculation Based on the joint torque of the KUKA KR6 900 Sixx robotic arm, the weighting coefficients are determined using "torque normalization": Calculated , , , , , .

[0076] Step 1.2: Transformation of processing point coordinates Obtain the Cartesian coordinates of 49 drilling points using calipers (e.g., (100, 200, 50), (105, 200, 50)...) (adding a robot initial point to form a TSP problem of scale 50), and transform them into the original joint angle vectors through inverse kinematics (e.g. ); Step 1.3: Calculation of weighted vector and edge distance Calculate the weighted joint angle vector Adjacent vectors and edge distance This forms an equivalent unweighted TSP50 instance.

[0077] Step 2. MMOE Network Parameter Configuration Table 2

[0078] Step 3. Model Training and Inference Validation Training process: The Adam optimizer (initial learning rate 1e-4, decay coefficient 0.999) is used for 1000 epochs, each epoch contains 2560 batches (batch size 16), the validation set size is 10,000 instances, and uncertainty-weighted loss is used to balance multi-scale objectives. Reasoning verification (50 processing points): 1. Fill: Fill the TSP50 instance with 100 nodes (the fill nodes are the node coordinates in the TSP50 instance); 2. Feature processing: After the input model generates features, the slice retains the features of the first 50 nodes; 3. Path generation: Call the tower network corresponding to 50 processing points, and use Beam search (beam width B=1000) to output the optimal path; 4. Robot execution: The generated node processing sequence is sent to the robot control system to guide it in completing the actual workpiece processing.

[0079] like Figure 5 As shown, the data obtained using this method closely matches Gurobi's optimal data, with the overall discrepancy remaining within 2.55%, indicating the high performance of this method. Secondly, although the relative differences across different processing point sizes fluctuate slightly, these variations remain within acceptable limits. This cross-scale consistency validates the effectiveness of the uncertainty-based loss-weighted method in balancing multiple objectives, ensuring robust performance regardless of the processing point size.

[0080] like Figure 6 As shown, the performance of this method is compared with that of 91 different TSP scales. It can be seen that expanding to 91 TSP scales does not lead to a significant decrease in model performance.

[0081] like Figures 7A-7FAs shown, this method (MTL4TSP) is applied to workpieces 1 and 2 along with the Gurobi and NAR4TSP methods, and their planned trajectories are compared.

[0082] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0083] The following are device embodiments of the present invention. For details not described in detail, please refer to the corresponding method embodiments described above.

[0084] Figure 8 A schematic diagram of a manufacturing path planning device based on a multi-gate hybrid expert network provided in an embodiment of the present invention is shown. For ease of explanation, only the parts related to the embodiment of the present invention are shown, and are described in detail below: like Figure 8 As shown, the manufacturing path planning device 8 based on a multi-gate hybrid expert network includes: The conversion module 81 is used to convert the Cartesian coordinates of multiple processing points into joint angle vectors through inverse kinematics operations; wherein, the joint angle vector includes multiple joint angle components, and each joint angle component is the angle of one joint of the multi-joint processing robot. The weighting module 82 is used to multiply each joint angle component in the joint angle vector with the weight of the corresponding joint for each joint angle vector to obtain multiple weighted joint angle vectors; wherein, the weight of each joint is determined based on the mechanical characteristics of each joint, including torque. Planning module 83 is used to construct a TSP graph based on multiple weighted joint angle vectors and input it into a trained multi-gate hybrid expert network to determine the manufacturing path of multiple processing points.

[0085] In one possible implementation, the multi-gate hybrid expert network includes a shared underlying layer, multiple expert networks, multiple gated networks, and multiple tower networks; the planning module 83 is specifically used for: Construct a TSP graph by using weighted joint angle vectors as nodes and Manhattan distances between adjacent weighted joint angle vectors as edge distances; Based on the maximum scale of the multi-gate hybrid expert network, the TSP graph is filled and input into the shared bottom layer to obtain the TSP graph with feature embedding. Multiple expert networks are used to extract structural features from the TSP graph with embedded features in parallel, resulting in multiple weighted graph structural features. Based on the scale of multiple processing points, each weighted graph structural feature is sliced ​​to obtain multiple slice features; Multiple slice features are input into a gating network corresponding to the scale of multiple processing points, and the multiple slice features are weighted and summed to obtain the fused features; By inputting the fused features into a tower network corresponding to the scale of multiple processing points, a path probability heatmap of multiple processing points is obtained. By using Beam search to filter the path with the smallest total edge distance on the path probability heatmap, manufacturing paths for multiple processing points are obtained.

[0086] In one possible implementation, the shared underlying layer is a batch normalization layer, each expert network is a GAT network, and each tower network is a fully connected network.

[0087] In one possible implementation, the planning module 83 is also used for: Before constructing a TSP graph based on multiple weighted joint angle vectors and inputting it into a trained multi-gate hybrid expert network to determine the manufacturing path of multiple processing points, a multi-point processing scenario dataset is constructed. The multi-point processing scenario dataset includes multiple multi-point processing scenarios, each with a different processing point scale. Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-gate hybrid expert network is trained to obtain the trained multi-gate hybrid expert network.

[0088] In one possible implementation, the planning module 83 is specifically used to include: Based on the construction of a multi-point processing scenario dataset and an uncertainty-weighted loss function, the initial multi-level hybrid expert network is trained in multiple rounds to obtain the trained multi-level hybrid expert network. For each round of training, perform the following steps: Based on the maximum scale of a multi-gate hybrid expert network, multiple random instances are generated through spatial sampling, and each random instance is sliced ​​and filled based on different processing point scales to obtain multiple subtasks with different processing point scales. Multiple subtasks of different processing point scales are input into a multi-gate hybrid expert network, and shared features of each subtask of processing point scale are generated by sharing the underlying layer and each expert network. The shared features of subtasks at each processing point scale are input into the gating network and tower network corresponding to that processing point scale to obtain the path probability heatmap of the subtasks at that processing point scale, and the loss at that processing point scale is calculated based on the path probability heatmap and the uncertainty weighted loss function. Based on the loss at each processing point, perform a backpropagation to update all trainable parameters of the multi-gate hybrid expert network.

[0089] In one possible implementation, the uncertainty-weighted loss function is:

[0090]

[0091] in, for gradient, For all trainable parameters of a multi-gate hybrid expert network, For parameters and multi-point processing scenarios The total loss during a single round of training. For learnable parameters, For the first Total edge distance error for each processing point The total number of processing points. For batch size, For the first The length of a Bernoulli sampling path at the scale of a processing point. For the first The length of the greedy sampling path at the scale of each processing point. For the first The average performance difference of sampling paths at the scale of each processing point. For parameters The path to be generated The probability of.

[0092] In one possible implementation, the weighting module 82 is also used for: Before multiplying each joint angle component in the joint angle vector with the weight of the corresponding joint to obtain multiple weighted joint angle vectors, the weight of each joint is determined based on the mechanical characteristics of each joint of the multi-joint machining robot.

[0093] This invention transforms the coordinates of processing points into joint angle vectors through inverse kinematics, fundamentally establishing the planning problem within the joint space, which is directly related to the robot's driving energy consumption. Weights are introduced for each joint angle component and weighted processing is performed, incorporating physical characteristics such as torque differences between different joints into the optimization model. This ensures that subsequent path cost calculations accurately reflect the actual energy consumption contribution of each joint's movement, achieving a fundamental improvement from "minimizing geometric distance" to "minimizing actual energy consumption." A trained multi-disciplinary hybrid expert network is used to directly process the weighted TSP graph. This network possesses powerful feature learning and reasoning capabilities, automatically learning complex energy-saving path patterns from data and, crucially, exhibiting inherent flexibility in handling problems of varying scales. Therefore, this method can quickly generate highly approximate energy-optimal manufacturing sequences for any given number of processing points, significantly reducing the operating energy consumption of industrial robots while avoiding the cost of repeatedly developing models for tasks of different scales, thus improving the versatility and practicality of the planning system.

[0094] Figure 9 This is a schematic diagram of an electronic device provided in an embodiment of the present invention. For example... Figure 9 As shown, the electronic device 9 of this embodiment includes a processor 90 and a memory 91. The memory 91 stores a computer program 92. When the processor 90 executes the computer program 92, it implements the steps in the various method embodiments described above. Alternatively, when the processor 90 executes the computer program 92, it implements the functions of each module / unit in the various device embodiments described above.

[0095] For example, computer program 92 may be divided into one or more modules / units, which are stored in memory 91 and executed by processor 90 to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of computer program 92 in electronic device 9.

[0096] Electronic device 9 may include, but is not limited to, processor 90 and memory 91. Those skilled in the art will understand that... Figure 9 This is merely an example of electronic device 9 and does not constitute a limitation on electronic device 9. It may include more or fewer components than shown, or combine certain components, or different components. For example, electronic device 9 may also include input / output devices, network access devices, buses, etc.

[0097] The processor 90 can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor.

[0098] The memory 91 can be an internal storage unit of the electronic device 9, such as a hard disk or RAM. The memory 91 can also be an external storage device of the electronic device 9, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Furthermore, the memory 91 can include both internal and external storage units of the electronic device 9. The memory 91 is used to store the computer program 92 and other programs and data required by the electronic device 9. The memory 91 can also be used to temporarily store data that has been output or will be output.

[0099] For the sake of simplicity and clarity, only the above-described functional modules / units are used as examples. In practical applications, the functions described above can be assigned to different functional modules / units as needed. These modules / units can be implemented in hardware, software, or a combination of both.

[0100] This invention also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the methods described in the above-described method embodiments.

[0101] This invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, it implements the methods described in the above-described method embodiments.

[0102] Computer programs include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. Computer-readable media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0103] In the above embodiments, the descriptions of each embodiment have their own emphasis. Parts not detailed or described in a particular embodiment can be referred to in the relevant descriptions of other embodiments. Unless otherwise specified or in conflict with logic, the terminology and / or descriptions between different embodiments are consistent and can be referenced interchangeably. Technical features in different embodiments can be combined to form new embodiments based on their inherent logical relationships.

[0104] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A manufacturing path planning method based on a multi-gate hybrid expert network, characterized in that, include: Through inverse kinematics operations, the Cartesian coordinates of multiple processing points are transformed into joint angle vectors; wherein, the joint angle vectors include multiple joint angle components, and each joint angle component is the angle of one joint of the multi-joint processing robot. For each joint angle vector, each joint angle component in the vector is multiplied by the weight of the corresponding joint to obtain multiple weighted joint angle vectors; where the weight of each joint is determined based on the mechanical characteristics of each joint, including torque. A TSP graph is constructed based on the multiple weighted joint angle vectors, and then input into a trained multi-gate hybrid expert network to determine the manufacturing path of the multiple processing points.

2. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 1, characterized in that, The multi-gate hybrid expert network includes a shared bottom layer, multiple expert networks, multiple gating networks, and multiple tower networks; the step of constructing a TSP graph based on the multiple weighted joint angle vectors and inputting it into the trained multi-gate hybrid expert network to determine the manufacturing path of the multiple processing points includes: Construct a TSP graph by using weighted joint angle vectors as nodes and Manhattan distances between adjacent weighted joint angle vectors as edge distances; Based on the maximum size of the multi-gate hybrid expert network, the TSP graph is filled and input into the shared bottom layer to obtain the feature-embedded TSP graph; The structural features of the TSP graph with embedded features are extracted in parallel by the multiple expert networks to obtain multiple weighted graph structural features; Based on the scale of the multiple processing points, each weighted graph structural feature is sliced ​​to obtain multiple slice features; The multiple slice features are input into a gating network corresponding to the scale of the multiple processing points, and the multiple slice features are weighted and summed to obtain the fused features; The fused features are input into a tower network corresponding to the scale of the multiple processing points to obtain a path probability heatmap of the multiple processing points. The manufacturing paths for the multiple processing points are obtained by filtering the path with the minimum total edge distance on the path probability heatmap using Beam search.

3. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 2, characterized in that, The shared underlying layer is a batch normalization layer, each expert network is a GAT network, and each tower network is a fully connected network.

4. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 2, characterized in that, Before constructing the TSP map based on the multiple weighted joint angle vectors and inputting it into a trained multi-gate hybrid expert network to determine the manufacturing path of the multiple processing points, the method further includes: Construct a multi-point processing scenario dataset; wherein the multi-point processing scenario dataset includes multiple multi-point processing scenarios, each of which has a different processing point scale; Based on the constructed multi-point processing scenario dataset and uncertainty weighted loss function, the initial multi-gate hybrid expert network is trained to obtain the trained multi-gate hybrid expert network.

5. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 4, characterized in that, The process involves training an initial multi-level hybrid expert network based on the constructed multi-point processing scenario dataset and the uncertainty-weighted loss function, resulting in a trained multi-level hybrid expert network, including: Based on the constructed multi-point processing scenario dataset and uncertainty weighted loss function, the initial multi-gate hybrid expert network is trained in multiple rounds to obtain the trained multi-gate hybrid expert network. For each round of training, perform the following steps: Based on the maximum scale of the multi-gate hybrid expert network, multiple random instances are generated through spatial sampling, and each random instance is sliced ​​and filled based on different processing point scales to obtain multiple sub-tasks with different processing point scales. The subtasks of different processing point scales are input into a multi-gate hybrid expert network, and the shared features of each subtask of processing point scale are generated by sharing the bottom layer and each expert network. The shared features of subtasks at each processing point scale are input into the gating network and tower network corresponding to that processing point scale to obtain the path probability heatmap of the subtasks at that processing point scale, and the loss at that processing point scale is calculated based on the path probability heatmap and the uncertainty weighted loss function. Based on the loss at each processing point, perform a backpropagation to update all trainable parameters of the multi-gate hybrid expert network.

6. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 4, characterized in that, The uncertainty-weighted loss function is: in, for gradient, For all trainable parameters of a multi-gate hybrid expert network, For parameters and multi-point processing scenarios The total loss during a single round of training. For learnable parameters, For the first Total edge distance error for each processing point The total number of processing points. For batch size, For the first The length of a Bernoulli sampling path at the scale of a processing point. For the first The length of the greedy sampling path at the scale of each processing point. For the first The average performance difference of sampling paths at the scale of each processing point. For parameters The path to be generated The probability of.

7. The manufacturing path planning method based on a multi-gate hybrid expert network according to claim 1, characterized in that, Before multiplying each joint angle component in each joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors, the method further includes: The weight of each joint is determined based on the mechanical characteristics of each joint of the multi-joint machining robot.

8. A manufacturing path planning device based on a multi-gate hybrid expert network, characterized in that, include: The conversion module is used to convert the Cartesian coordinates of multiple processing points into joint angle vectors through inverse kinematics operations; wherein, the joint angle vector includes multiple joint angle components, and each joint angle component is the angle of one joint of the multi-joint processing robot. The weighting module is used to multiply each joint angle component in each joint angle vector by the weight of the corresponding joint to obtain multiple weighted joint angle vectors; wherein, the weight of each joint is determined based on the mechanical characteristics of each joint, including torque. The planning module is used to construct a TSP graph based on the multiple weighted joint angle vectors and input it into a trained multi-gate hybrid expert network to determine the manufacturing path of the multiple processing points.

9. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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