Multi-agent trajectory prediction method and system based on rotation isovariant diffusion model

Abstract

The invention discloses a multi-agent trajectory prediction method and system based on a rotation isovariant diffusion model, and the method comprises the steps: carrying out the dimension reduction of a historical observation trajectory and a future real trajectory of an agent through SVD, and mapping the trajectories into a low-rank space; based on the future trajectory in the low-rank space, a K-means clustering algorithm is adopted to generate trajectory anchor points; a rotation equivariant Transform module is adopted to extract future real trajectory features in the low-rank space; a cosine noise scheduling table is introduced into the features extracted by the Transform module; and outputting a future trajectory based on the future real trajectory features introduced into the noise table, and adjusting the generated future trajectory by using the trajectory anchor points to complete multi-agent trajectory prediction. According to the method, the low-rank potential space is designed, and the agent trajectory data is mapped into the potential space, so that the calculation complexity is reduced, and the model reasoning time and time cost are reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of trajectory prediction of autonomous driving agents, in particular to a multi-agent trajectory prediction method and system based on a rotation equivariant diffusion model. BACKGROUND

[0002] Trajectory prediction of multi-agent systems has wide application in the field of autonomous driving. Existing multi-modal trajectory prediction based on diffusion models still has the following problems: first, the time cost and model representation ability are difficult to balance. In order to ensure the ability of the model to represent the distribution of future trajectories, enough denoising steps are needed, which will greatly increase the inference time of the model and the time cost is high; second, the complexity and diversity of trajectory data lead to low precision. The trajectory data of different agents in different scenarios are different, and there are noises or redundancies in the data, if not processed, it will lead to high computational complexity of the model and low prediction accuracy; third, the physical characteristics of rotation equivariance of agent trajectories are not fully utilized. SUMMARY

[0003] To solve the technical problems in the above background, the present application proposes a multi-agent trajectory prediction method and system based on a rotation equivariant diffusion model. By introducing low-rank latent space, rotation equivariant Transformer, and designing noise scheduling table, the accuracy and computational efficiency of prediction are significantly improved.

[0004] To achieve the above purpose, the present application provides a multi-agent trajectory prediction method based on a rotation equivariant diffusion model, comprising the following steps:

[0005] Dimensionality reduction is performed on the historical observation trajectory and the future real trajectory of the agent by using SVD decomposition, and the trajectory is mapped into a low-rank space;

[0006] Based on the future real trajectory in the low-rank space, a K-means clustering algorithm is used to generate trajectory anchor points;

[0007] A rotation equivariant Transformer module is used to extract the features of the future real trajectory in the low-rank space;

[0008] A cosine noise scheduling table is introduced in the features extracted by the Transformer module;

[0009] Based on the future real trajectory features with the introduced noise table, the future trajectory is output, and the trajectory anchor points are used to adjust the generated future trajectory, and the multi-agent trajectory prediction is completed.

[0010] Preferably, the method of mapping trajectories into a low-rank space includes: stacking historical observation trajectories and future real trajectories in a pre-constructed dataset, normalizing the trajectories by translation, rotation, and scaling to obtain a normalized trajectory matrix, then performing truncated SVD decomposition to construct a coordinate system of the low-rank space, and then constructing a transformation matrix using a B-spline algorithm, mapping the historical observation trajectories through eigenvectors, and mapping agent trajectories of different lengths in different datasets into the low-rank space.

[0011] Preferably, the method of generating the trajectory anchor points includes: using the future real trajectories Ψ mapped into the low-rank space, clustering Ψ into N s center points using a K-means clustering algorithm, each center point representing a motion mode of the multi-modal future trajectory; and regarding the N s center points as different trajectory anchors

[0012] Preferably, the framework of the rotation equivariant Transformer module is the same as the encoder of the traditional Transformer, and all operations in the rotation equivariant Transformer module are replaced by rotation equivariant operations; a vector neuron VN is introduced into the rotation equivariant Transformer module to construct a VN multi-head attention mechanism, a VN layer normalization, a VN multi-layer perceptron, and a VN linear layer expression including:

[0013]

[0014] wherein, represents the input; represents a learnable weight parameter, C represents the number of output channels, and T represents the number of input vectors.

[0015] Preferably, the expression of the VN multi-head attention mechanism includes:

[0016]

[0017] wherein, respectively represent the projection matrix of the query, key, and value of the hth head; W O represents the output change matrix; Q represents the query, K represents the key, Z represents the value, and H represents the total number of check heads.

[0018] Preferably, the expression of the VN layer normalization includes:

[0019]

[0020] wherein, ⊙ represents an element-wise product; Z (n) represents a matrix composed of all input vectors of the nth sample, and Z (n，t) represents a matrix composed of all input vectors of the nth sample.(n) the tth two-dimensional vector in the set.

[0021] Preferably, the VN multi-layer perceptron is composed of the VN linear layer and VN-ReLU, wherein the expression of the VN-ReLU comprises:

[0022]

[0023] The application also provides a multi-agent trajectory prediction system based on a rotation isomorphic diffusion model, which is used to implement the above method and comprises a mapping module, a clustering module, an extraction module, an introduction module and a prediction module.

[0024] The mapping module is used to reduce the dimensionality of the historical observation trajectory and the future real trajectory of the agent by SVD decomposition, and map the trajectory into a low-rank space.

[0025] The clustering module is used to generate trajectory anchor points by using a K-means clustering algorithm based on the future real trajectory in the low-rank space.

[0026] The extraction module is used to extract the feature of the future real trajectory in the low-rank space by using a rotation isomorphic Transformer module.

[0027] The introduction module is used to introduce a cosine noise schedule table into the feature extracted by the Transformer module.

[0028] The prediction module is used to output a future trajectory based on the future real trajectory feature with the noise table, and adjust the generated future trajectory by using the trajectory anchor points, to complete the multi-agent trajectory prediction.

[0029] Compared with the prior art, the application has the following beneficial effects:

[0030] The application maps the agent trajectory data into a latent space by designing a low-rank latent space, reduces the computational complexity, reduces the model inference time and time cost, and introduces trajectory anchor points to improve the ability of the model to model the multi-modal trajectory. At the same time, the rotation isomorphic Transformer is innovatively introduced to model the vector in the latent space, fully utilizes the physical property of the rotation isomorphic of the agent trajectory, improves the generalization ability of the model, and makes the model more robust to noise interference in the data. Finally, a noise schedule table for trajectory prediction tasks is designed to increase the effective information learned by the diffusion model in the forward process, and to generate multi-modal predicted trajectories. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings described below only show some of the embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0032] Figure 1 Structure diagram of the VN linear layer of the embodiment of the present application;

[0033] Figure 2 Structure diagram of the rotating equivariant Transformer module of the embodiment of the present application;

[0034] Figure 3 Structure diagram of the trajectory prediction model of the embodiment of the present application. DETAILED DESCRIPTION

[0035] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0036] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0037] Embodiment one

[0038] The embodiment provides a multi-agent trajectory prediction method based on a rotating equivariant diffusion model, and the steps include:

[0039] S1. Dimensionality reduction is performed on the historical observed trajectory and the future real trajectory of the agent by using SVD decomposition, and the trajectory is mapped into a low-rank space.

[0040] The historical observed trajectory and the future trajectory of the agent are dimensionality reduced by using truncated singular value decomposition (SVD decomposition), and the trajectory is mapped into a low-rank latent space. The historical observed trajectory and the future real trajectory in the pre-constructed data set are stacked, and the trajectory is normalized by translation, rotation and scaling to obtain a normalized trajectory matrix. Then, truncated SVD decomposition is performed to construct a coordinate system of the low-rank space, and then a transformation matrix is constructed by using a B-spline algorithm, so that the eigenvector can map the historical observed trajectory. Through the above operation, the agent trajectories of different lengths in different data sets can be mapped into a low-rank space, and the generalization ability and the stability of the prediction of the model can be improved.

[0041] Specifically, the observed trajectories and the future real trajectories in the dataset are stacked and normalized by translation, rotation and scaling to obtain a normalized trajectory matrix where L past , L pred represent the number of observed trajectories and future real trajectories, respectively, T past , T pred represent the time steps of observation and prediction, respectively. The truncated SVD decomposition of Y can be obtained as follows:

[0042]

[0043] where K0represents using the first K0singular values and their corresponding eigenvectors, K0 where is composed of K0trajectory eigenvectors , and v pred，k are orthogonal to each other, so they can be regarded as an orthogonal basis in the latent low-rank space, and a coordinate system of the low-rank space is constructed; Transpose represents the transpose operation.

[0044] Since there is a difference between the observation time of the agent's historical observed trajectory and the future real trajectory, a transformation matrix is constructed using the B-spline algorithm pred，k , so that the eigenvectors v can map the historical observed trajectory, and the observed trajectory

[0045]

[0046] where Similarly, the future real trajectory can be mapped to by After the above operations, the agent trajectories of different lengths in different datasets can be mapped to the low-rank space, which can improve the generalization ability of the model and the stability of the prediction.

[0047] S2. Based on the future trajectory in the low-rank space, a K-means clustering algorithm is used to generate trajectory anchor points.

[0048] The K-means clustering algorithm is used to generate trajectory anchor points, and each anchor point represents a potential future trajectory pattern, which can improve the model's ability to capture local features and assist the model in modeling the multi-modal trajectory of the agent in the denoising process, while making the predicted trajectory more socially acceptable.

[0049] Specifically, the future real trajectory Ψ mapped to the low-rank space is used to cluster Ψ into Ns center points, each of which represents a motion pattern of the multi-modal future trajectory. In the low-rank space, the N s center points can be regarded as different trajectory anchors To assist the model in modeling the multi-modal trajectory of the agent in the denoising process, while making the predicted trajectory have higher social acceptability.

[0050] S3. Adopting a rotation equivariant Transformer module to extract the features of the future real trajectory in the low-rank space.

[0051] In order to make full use of the rotation equivariant characteristics of the trajectory, a rotation equivariant Transformer is introduced for the interaction feature extraction between agents. The framework of the rotation equivariant Transformer module is the same as that of the encoder of the traditional Transformer, and all the operations therein are replaced by rotation equivariant operations. First, the vector neuron (VN) is introduced to construct the VN multi-head attention mechanism, VN layer normalization, and VN multi-layer perceptron. Through this module, the model can better capture the relative motion features between agents and enhance the generalization ability of the model.

[0052] Specifically, first, the concept of vector neuron (VN) is introduced. Unlike traditional neurons (such as multi-layer perceptron), the input of the vector neuron architecture is a vector, as shown in Figure 1 For example, for the input , there is:

[0053]

[0054] wherein is a learnable parameter. At the same time, the VN linear layer has the property of rotation equivariance, that is:

[0055] Linear VN (xR, W) = WxR = (Wx)R = Linear VN (x, W)R.

[0056] The overall framework of the rotation equivariant Transformer module is shown in Figure 2 , which mainly consists of VN multi-head attention mechanism, VN layer normalization, and VN multi-layer perceptron, and all operations are rotation equivariant.

[0057] (1) VN multi-head attention mechanism

[0058] This part calculates the attention score using the Frobenius inner product (matrix inner product). For the query and key and The attention matrix Attn(Q, K) between the two is as follows:

[0059]

[0060] where <Q (n) , K (m) > F denotes the Frobenius inner product between the two, which is rotationally invariant; M denotes the batch size of the key vectors.

[0061] Then for the tensor we have:

[0062]

[0063] where m denotes the m-th sample in the key-value pair; n denotes the n-th sample in the query.

[0064] For the simultaneously rotated input tensors, Atten VN (·) is rotationally equivariant, i.e.:

[0065]

[0066] R denotes a rotation matrix; <·,·> F denotes the Frobenius inner product (element-wise inner product of matrices).

[0067] The extension to multi-head attention mechanisms can be obtained as:

[0068]

[0069] where denote the projection matrices for the query, key, and value of the h-th head, respectively; W O denotes the output transformation matrix; Q denotes the query, K denotes the key, Z denotes the value; H denotes the total number of heads.

[0070] (2) VN layer normalization

[0071] The modification can be obtained on the basis of the original layer normalization as:

[0072]

[0073] where ⊙ denotes the element-wise product; T denotes the number of input vectors; Z (n) denotes the matrix composed of all input vectors of the n-th sample, Z (n，t) denotes the t-th two-dimensional vector in the matrix Z (n) .

[0074] This operation is also rotationally equivariant, i.e.:

[0075]

[0076] (3) VN multi-layer perceptron

[0077] This part is composed of the VN linear layer and the VN-ReLU introduced above. For the VN-ReLU, let the input be First, calculate the query and the key where are square matrices, which are learnable parameters; T represents the number of input vectors. Then, the VN-ReLU operation is:

[0078]

[0079] This operation is also rotation equivariant, that is:

[0080]

[0081] Using the rotation equivariant Transformer module can take advantage of the SO(2) equivariance of the agent trajectory to better extract the social interaction features f context (Ξ) between agents, improving the generalization ability of the model in different scenarios. Before this, the historical observation trajectory mapped to the low-rank space is first encoded, which can further increase the historical information in the social interaction features.

[0082] S4. Introduce a cosine noise scheduling table in the features extracted by the Transformer module.

[0083] The embodiment designs a cosine noise scheduling table suitable for the trajectory prediction task. A limiting parameter is added to the cosine noise scheduling table to make it suitable for the trajectory prediction task, so that the noise gradually increases in the forward process of the diffusion model, avoiding the loss of effective information caused by the rapid introduction of noise, thereby improving the denoising effect of the model.

[0084] Specifically, a cosine noise scheduling table is introduced, and a limiting parameter is added to the cosine noise scheduling table to make it suitable for the trajectory prediction task. The cosine noise scheduling table is as follows:

[0085]

[0086] where b represents the bias, which prevents the noise added near t = 0 from being too small, and b = 0.008; c = 20 is a limiting parameter, which can be adjusted according to different trajectory prediction tasks; denotes the cosine noise scheduling factor at the t-th time step; β t denotes the limiting factor at the t-th time step.

[0087] The cosine noise scheduling is in the middle step of the forward process, is linearly decreasing, and the change near t=0 and t=T is small, preventing sudden changes in noise.

[0088] S5. Based on the future real trajectory feature table introduced noise, the future trajectory is output, and the generated future trajectory is adjusted by using the trajectory anchor point, and the multi-agent trajectory prediction is completed.

[0089] Combined with the future real interaction feature extracted by the rotation invariant Transformer and the trajectory anchor point, the diffusion model is used to generate the multi-modal future trajectory, so that the model can provide multiple possible future trajectory predictions for each agent.

[0090] The step-by-step prediction method is used to remove noise to generate future trajectories. The historical observation trajectory information Ξ and the interaction f context (Ξ) are encoded as conditions in the denoising process to guide the model to generate trajectories. First, the β t learning time embedding is learned, which is connected with f context (Ξ) and encoded to obtain a feature vector; then, the above conditions are input into the denoising module, that is:

[0091]

[0092] In the formula, z~N(z;O,I) represents noise, t represents the denoising process at the tth time step, represents the noise added in the model prediction . The denoising module outputs the future trajectory The generated trajectory anchor point Π is used to adjust the generated future trajectory, so that the generated multi-modal trajectory is more accurate and reliable; finally, the predicted multi-modal trajectory is mapped back to the Euclidean space to obtain the final reconstructed trajectory The flow of the embodiment is shown in Figure 3 .

[0093] Example two

[0094] The embodiment also provides a multi-agent trajectory prediction system based on a rotation isometric diffusion model, comprising a mapping module, a clustering module, an extraction module, an introduction module and a prediction module; the mapping module is used for dimension reduction on historical observation trajectories and future real trajectories of agents by SVD decomposition, and the trajectories are mapped into a low-rank space; the clustering module is used for generating trajectory anchor points by a K-means clustering algorithm based on future trajectories in the low-rank space; the extraction module is used for extracting future real trajectory features in the low-rank space by a rotation isometric Transformer module; the introduction module is used for introducing a cosine noise schedule table into the features extracted by the Transformer module; and the prediction module is used for outputting future trajectories based on the future real trajectory features with the noise table introduced, and adjusting the generated future trajectories by the trajectory anchor points to complete multi-agent trajectory prediction.

[0095] The application will be described in detail below with reference to the embodiment, and how the application solves the technical problems in actual work will be described in detail.

[0096] Firstly, the mapping module performs dimension reduction on historical observation trajectories and future real trajectories of agents by SVD decomposition, and maps the trajectories into a low-rank space.

[0097] The historical observation trajectories and future trajectories of agents are dimension reduced by truncated singular value decomposition (SVD decomposition), and the trajectories are mapped into a low-rank latent space. The observation trajectories and future real trajectories in the data set are stacked, and the trajectories are normalized by translation, rotation and scaling to obtain a normalized trajectory matrix, and then truncated SVD decomposition is performed, a coordinate system of the low-rank space is constructed, and then a transformation matrix is constructed by using a B-spline algorithm, so that the feature vector can map the historical observation trajectories. Through the above operations, the agent trajectories of different lengths in different data sets can be mapped into a low-rank space, and the generalization ability and the stability of prediction of the model can be improved.

[0098] Specifically, the observation trajectories and future real trajectories in the data set are stacked, and the trajectories are normalized by translation, rotation and scaling to obtain a normalized trajectory matrix wherein, L past , L pred respectively represent the number of observation trajectories and future real trajectories, T past , T pred respectively represent the time steps of observation and prediction. Truncated SVD decomposition is performed on Y to obtain:

[0099]

[0100] wherein, K0 represents that the first K0 singular values and the corresponding feature vectors are used, and K0 < r (r is the rank of the matrix Y); the truncated matrix is wherein, is composed of K0trajectory feature vectors , and v pred，k are orthogonal to each other, so they can be regarded as an orthogonal basis in the potential low-rank space, constructing a coordinate system of the low-rank space; Transpose represents the transpose operation.

[0101] Since there is a difference between the observation time of the agent historical observation trajectory and the future real trajectory, the B-spline algorithm is used to construct the transformation matrix , so that the feature vector v pred，k can be mapped to the historical observation trajectory, and the observation trajectory in the low-rank space is as follows:

[0102]

[0103] , where Similarly, the future real trajectory can be mapped to by After the above operation, the agent trajectories of different lengths in different data sets can be mapped to the low-rank space, which can improve the generalization ability and stability of the prediction of the model.

[0104] Then, the clustering module generates trajectory anchor points based on the future trajectory in the low-rank space using the K-means clustering algorithm.

[0105] The trajectory anchor points are generated by the K-means clustering algorithm, and each anchor point represents a potential future trajectory pattern, which can improve the ability of the model to capture local features and assist the model in modeling the multi-modal trajectory of the agent in the denoising process, while making the predicted trajectory have higher social acceptability.

[0106] Specifically, using the above-mentioned future real trajectory Ψ mapped to the low-rank space, the K-means clustering algorithm is used to cluster Ψ into N s center points, each of which represents a motion pattern of a multi-modal future trajectory. In the low-rank space, the N s center points can be regarded as different trajectory anchors to assist the model in modeling the multi-modal trajectory of the agent in the denoising process, while making the predicted trajectory have higher social acceptability.

[0107] The extraction module uses the rotation-invariant Transformer module to extract the features of the future real trajectory in the low-rank space.

[0108] To fully utilize the rotational equivariance of trajectories, we introduce a rotational equivariant Transformer to extract interaction features between agents. The framework of the rotational equivariant Transformer module is the same as the encoder of the traditional Transformer, and all operations in it are replaced by rotational equivariant operations. First, we introduce vector neurons (VNs) to construct VN multi-head attention mechanisms, VN layer normalization, and VN multi-layer perceptrons. Through this module, the model can better capture the relative motion features between agents and enhance the generalization ability of the model.

[0109] Specifically, first, we introduce the concept of vector neurons (VNs). Unlike traditional neurons (such as multi-layer perceptrons), the input of a vector neuron architecture is a vector, as shown in Figure 1 For example, for the input we have:

[0110]

[0111] where are learnable parameters. At the same time, the VN linear layer is rotational equivariant, i.e.,

[0112] Linear VN (xR, W) = WxR = (Wx)R = Linear VN (x, W)R.

[0113] The overall framework of the rotational equivariant Transformer module is shown in Figure 2 It mainly consists of VN multi-head attention mechanisms, VN layer normalization, and VN multi-layer perceptrons, and all operations are rotational equivariant.

[0114] (1) VN multi-head attention mechanism

[0115] This part uses the Frobenius inner product (matrix inner product) to calculate the attention score. For the query and key and the attention matrix Attn(Q, K) is as follows:

[0116]

[0117] In the formula, <Q (n) , K (m) > F represents the Frobenius inner product between the two, which has rotational invariance; M represents the batch size of the key vector.

[0118] Then for the tensor we have:

[0119]

[0120] where m denotes the m-th sample in the key-value pair; n denotes the n-th sample in the query.

[0121] For the simultaneously rotated input tensors, Atten VN (·) is rotation equivariant, i.e.

[0122]

[0123] R denotes the rotation matrix; <·,·> F denotes the Frobenius inner product (element-wise inner product of matrices).

[0124] Extended to multi-head attention mechanism, we have:

[0125]

[0126] where, denote the projection matrices of the query, key, value of the h-th head, respectively; W O denotes the output transformation matrix; Q denotes the query, K denotes the key, Z denotes the tensor; H denotes the total number of checking heads.

[0127] (2) VN layer normalization

[0128] Based on the original layer normalization, we can modify it as:

[0129]

[0130] where ⊙ denotes the element-wise product; T denotes the number of input vectors; Z (n) denotes the matrix composed of all input vectors of the n-th sample; Z (n,t) denotes the t-th two-dimensional vector in the matrix Z (n) .

[0131] This operation is also rotation equivariant, i.e.

[0132]

[0133] (3) VN multi-layer perceptron

[0134] This part is composed of the VN linear layer and VN-ReLU introduced above. For VN-ReLU, let the input be First, calculate the query and the key where, are square matrices, which are learnable parameters; T denotes the number of input vectors. Then, the VN-ReLU operation is:

[0135]

[0136] The operation is also rotationally equivariant, i.e.:

[0137]

[0138] The rotationally equivariant Transformer module can better extract social interaction features f between agents by using the SO(2) equivariance of agent trajectories context (Ξ), improving the generalization ability of the model in different scenarios. Before this, the historical observation trajectories mapped to the low-rank space are encoded, which can further increase the historical information in the social interaction features.

[0139] The introduction module introduces a cosine noise schedule table into the features extracted by the Transformer module.

[0140] The embodiment designs a cosine noise schedule table suitable for trajectory prediction tasks, adds a limiting parameter to the cosine noise schedule table, so that it is suitable for trajectory prediction tasks, and gradually increases the noise in the forward process of the diffusion model, avoiding the loss of effective information caused by the rapid introduction of noise, thereby improving the denoising effect of the model.

[0141] Specifically, the cosine noise schedule table is introduced, and a limiting parameter is added to the cosine noise schedule table to make it suitable for trajectory prediction tasks. The cosine noise schedule table is as follows:

[0142]

[0143] Where b represents the bias, preventing the noise added near t = 0 from being too small, and b = 0.008; c = 20 is a limiting parameter, which can be adjusted according to different trajectory prediction tasks; represents the cosine noise scheduling factor at the t-th time step; β t represents the limiting factor at the t-th time step.

[0144] The cosine noise schedule is linearly decreasing in the middle steps of the forward process, and the change near t = 0 and t = T is very small, preventing sudden changes in noise.

[0145] Finally, the future trajectory is output based on the future real trajectory feature of the introduced noise table, and the generated future trajectory is adjusted using the trajectory anchor point to complete the multi-agent trajectory prediction.

[0146] The future real interaction features extracted by the rotationally equivariant Transformer and the trajectory anchor point are combined to generate multi-modal future trajectories using the diffusion model, ensuring that the model can provide multiple possible future trajectory predictions for each agent.

[0147] The method of step-by-step prediction and noise removal is used to generate future trajectories. For the historical observation trajectory information Ξ, the interaction between agents f context (Ξ) is encoded as a condition in the denoising process to guide the model to generate trajectories. First, use β t Learn temporal embeddings and combine them with f context (Ξ) and encode to obtain a feature vector; then, the above conditions are input into the denoising module, that is:

[0148]

[0149] Where z~N(z;0,I) represents the noise, t represents the denoising process at the t-th time step, Represents model predictions The noise added in the denoising module outputs the future trajectory The generated trajectory anchor point π is used to adjust the generated future trajectory to make the generated multimodal trajectory more accurate and reliable; finally, the predicted multimodal trajectory is mapped back to the Euclidean space to obtain the final reconstructed trajectory The process of this embodiment is as follows Figure 3 shown.

[0150] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by persons skilled in the art should fall within the scope of protection defined by the claims of the present invention.

Claims

1. A multi-agent trajectory prediction method based on a rotational equivariant diffusion model, characterized in that the steps include: Use SVD decomposition to reduce the dimension of the agent's historical observation trajectory and future real trajectory, and map the trajectory into a low-rank space; Based on the future real trajectory in the low-rank space, the K-means clustering algorithm is used to generate trajectory anchor points; The rotation equivariant Transformer module is used to extract the future real trajectory features in the low-rank space; Introducing a cosine noise schedule into the features extracted by the Transformer module; The future trajectory is output based on the future real trajectory features introduced into the noise table, and the generated future trajectory is adjusted using the trajectory anchor point to complete the multi-agent trajectory prediction.

2. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 1 is characterized in that: The method of mapping trajectories into low-rank space includes: stacking the historical observation trajectories and future real trajectories in a pre-constructed dataset, and normalizing the trajectories through translation, rotation, and scaling to obtain a normalized trajectory matrix, followed by truncated SVD decomposition to construct a coordinate system in the low-rank space, and then using the B-spline algorithm to construct a transformation matrix, mapping the historical observation trajectories through eigenvectors, and mapping the trajectories of agents of different lengths in different datasets into the low-rank space.

3. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 1 is characterized in that: The method for generating the trajectory anchor point includes: using the future real trajectory Ψ mapped to the low-rank space, clustering Ψ into N s Center points, each center point represents a motion mode of the multimodal future trajectory; at the same time, in the low-rank space, N s Treated as different trajectory anchors 4. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 1 is characterized in that: The framework of the rotation-equivariant Transformer module is the same as that of the traditional Transformer encoder, and all operations therein are replaced with rotation-equivariant operations. Vector neurons VN are introduced into the rotation-equivariant Transformer module to construct a VN multi-head attention mechanism, VN layer normalization, and VN multi-layer perceptron. The expression of the VN linear layer includes: in, Represents input; Represents the learnable weight parameter, C represents the number of output channels; T represents the number of input vectors.

5. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 4 is characterized in that: The expression of the VN multi-head attention mechanism includes: in, Represents the projection matrix of query, key, and value of the h-th head respectively; W O represents the output change matrix; Q represents query, K represents key, Z represents value; H represents the total number of check heads.

6. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 5 is characterized in that: The VN layer normalization expression includes: Among them, ⊙ represents the element-by-element product; Z (n) Represents the matrix composed of all input vectors of the nth sample, Z (n，t) Represents the matrix Z (n) The t-th two-dimensional vector in .

7. The multi-agent trajectory prediction method based on the rotational equivariant diffusion model according to claim 6 is characterized in that: The VN multi-layer perceptron is composed of the VN linear layer and VN-ReLU, where the expression of VN-ReLU includes:

8. A multi-agent trajectory prediction system based on a rotational equivariant diffusion model, the system being used to implement the method according to any one of claims 1 to 7, characterized in that: include: Mapping module, clustering module, extraction module, introduction module and prediction module; The mapping module is used to reduce the dimension of the historical observation trajectory and future real trajectory of the intelligent agent by using SVD decomposition, and map the trajectory into a low-rank space; The clustering module is used to generate trajectory anchor points based on the future real trajectory in the low-rank space using the K-means clustering algorithm; The extraction module is used to extract future real trajectory features in the low-rank space using a rotational equivariant Transformer module; The introduction module is used to introduce a cosine noise schedule into the features extracted by the Transformer module; The prediction module is used to output a future trajectory based on the future real trajectory features introduced into the noise table, and use the trajectory anchor point to adjust the generated future trajectory to complete the multi-agent trajectory prediction.

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