A hyperbolic trajectory decoupling motion generation method and system

Abstract

The application provides a hyperbolic trajectory decoupling action generation method and system, and relates to the field of artificial intelligence and robot continuous control. The method comprises the following steps: adaptively estimating the curvature of the hyperbolic manifold based on a data-driven method of an expert action sequence; incrementally scaling the robot continuous physical action sequence with time through a time geometric embedding mechanism, and projecting it to the hyperbolic space; isolating long-term prediction uncertainty by using the exponential expansion of the boundary; learning the optimal transport geodesic flow in the hyperbolic space, and optimizing the network through a loss function with conformal factor weighting; performing first-order Riemann Euler single-step integration based on the geodesic flow with zero covariant acceleration characteristics during reasoning, and finally inversely scaling and back-projecting back to the Euclidean space. The application naturally decouples the conflict trajectory by using the volume advantage of the exponential growth of the hyperbolic space, avoids the mode average problem, and realizes high-precision single-step robot action generation with extremely low delay.

Description

Technical Field

[0001] This invention relates to the field of artificial intelligence and continuous robot control, and in particular to a method and system for generating decoupled hyperbolic trajectories. Background Technology

[0002] Currently, the field of multimodal continuous control widely employs Euclidean space-based generative models (such as diffusion models and flow matching models) to map high-dimensional inputs such as vision and natural language into complex physical actions. Although these models demonstrate a certain expressive ability in capturing expert demonstration distributions, they suffer from severe "spatial capacity bottlenecks" when faced with complex real-world multimodal interactions. Real-world continuous actions typically exhibit highly branched tree-like topologies. At each decision node (such as a robot bypassing obstacles, grasping objects in different orientations, or executing uncertain commands), an effective future action distribution grows exponentially with the path. Especially in long-field-of-view, multi-step continuous control tasks, the prediction uncertainty accumulated over time exacerbates the bifurcation and expansion of this action topology. Since the volume of Euclidean space grows only polynomially with radius, attempting to fit these rapidly bifurcerating and hierarchically distributed action flows within a confined flat space inevitably leads to severe "spatial congestion" and "trajectory entanglement." When different action patterns are forced to converge, overlap, or merge in a dense Euclidean space representation, neural networks, in order to minimize regression errors during training, often output the intermediate compromise value of multiple effective paths, leading to a disastrous "pattern averaging" phenomenon. This phenomenon causes the generated trajectory to lose its clear physical meaning, manifesting as motion drift or invalid jitter at key decision points, ultimately resulting in task failure. Attempts to simply increase the size of the network model or extend the denoising iteration steps of traditional generative models cannot fundamentally overcome the limitations of the underlying flat geometry; moreover, existing research on non-Euclidean manifolds, lacking constant negative curvature, still cannot completely eradicate this trajectory conflict and aliasing problem caused by insufficient spatial capacity at the geometric level. Summary of the Invention

[0003] To address the aforementioned shortcomings in existing technologies, this invention provides a hyperbolic trajectory decoupling motion generation method and system, aiming to solve the problems of robot motion trajectory entanglement and mode averaging caused by spatial capacity bottlenecks in Euclidean space in multimodal continuous control methods in the field of robotics.

[0004] To achieve the above objectives, the technical solution adopted by this invention is: a method for generating decoupled hyperbolic trajectories, comprising the following steps: S1. During the training phase, acquire multimodal observation inputs and the robot's continuous physical action sequence corresponding to the multimodal observation inputs; S2. To address the differences in motion distribution for different robot control tasks, based on the continuous physical motion sequence of the robot, the curvature parameters of the Poincaré sphere hyperbolic manifold are adaptively calculated, and a hyperbolic space is constructed based on the curvature parameters. S3. Using a time-geometric embedding mechanism, the robot's continuous physical action sequence is scaled according to the time prediction step size, and the scaled action is projected onto the hyperbolic space through the origin exponential mapping to obtain the hyperbolic representation features. S4. Construct a hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on Riemann metric, and use hyperbolic representation features as target endpoint features to train a flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. S5. In the inference stage, starting from the prior noise, based on the optimal transmission geodesic vector field, the trained flow matching neural network is used to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. The predicted hyperbolic features are then back-projected back into Euclidean space through logarithmic mapping and inverse time scaling to obtain the final robot predicted action sequence, thus completing the generation of the decoupled hyperbolic trajectory action.

[0005] The beneficial effects of this invention are: without introducing a complex network architecture, this invention achieves geometrical decoupling of multimodal trajectories and alleviates the mode averaging phenomenon by mapping the continuous control actions of the robot to a Poincaré sphere hyperbolic manifold.

[0006] Further, S2 includes: To address the differences in motion distribution for different robot control tasks, expert teaching motion sequences are extracted from continuous physical motion sequences of the robot to construct an expert motion dataset. For zero-mean physical actions in the expert action dataset, calculate the empirical cumulative distribution function of their Euclidean norm; Extract the boundary radius of the empirical cumulative distribution function that reaches the preset percentile. ; Based on boundary radius Calculate the curvature parameters of the Poincaré spherical hyperbolic manifold. And based on the curvature parameters, a hyperbolic space matching the robot's motion distribution is constructed.

[0007] Furthermore, the curvature parameter The expression is as follows: .

[0008] The beneficial effect of the above-mentioned further solution is that, in order to enable the hyperbolic manifold to accurately match the action distribution of a specific task, this invention abandons the traditional approach of manually setting the curvature and instead adopts a data-driven adaptive estimation method. By performing zero-mean processing on the expert action dataset and calculating its Euclidean norm empirical cumulative distribution function, the boundary radius corresponding to the preset percentile is extracted from it, and then the curvature parameter is determined, thereby ensuring that most action samples can be distributed in the high-capacity region of the manifold.

[0009] Furthermore, S3 includes: The time scaling factor is calculated using a scalar function whose prediction step size increases monotonically with time. Apply a time scaling factor to the robot's continuous physical movements to obtain scaled movements; Calculate the origin exponential mapping using scaling actions; Based on the origin exponential mapping, the scaling action is projected into the hyperbolic space to obtain hyperbolic representation features. Among them, based on the increase of the time prediction step, the magnified time scalar causes the hyperbolic representation features to approach the manifold boundary of the Poincaré sphere. The exponential expansion property of the manifold boundary is used to spatially isolate and decouple the uncertainty of robot actions in the long term.

[0010] The beneficial effects of the above-mentioned further solutions are as follows: This invention designs a temporal geometry embedding mechanism based on time scaling, which can adaptively push future robot actions towards the manifold boundary for physical isolation according to the distance of different time prediction step lengths, rather than using a flat representation method in Euclidean space that is prone to trajectory entanglement, thus more accurately preserving the tree-like bifurcation structure of multimodal actions. This mechanism can directly adaptively set the curvature parameters based on the Euclidean norm distribution characteristics of the expert data itself, without the need for additional manual trial and error costs to select a better manifold space capacity.

[0011] Furthermore, the expression for the hyperbolic representation feature is as follows:

[0012]

[0013]

[0014] in, Indicates the first h Hyperbolic representation features corresponding to each time prediction step size This represents the exponential mapping at the origin. Indicates scaling action, Indicates a fixed scaling factor. Represents the hyperbolic tangent mapping. Represents the curvature parameter. Indicates the time scaling factor. This represents the original continuous physical actions of the robot. Indicates the expansion rate. Indicates the time prediction step size.

[0015] Furthermore, the expression for the hyperbolic flow matching objective function is as follows:

[0016] in, This represents the hyperbolic flow matching objective function. Indicates convection matching time t Prior noise and target hyperbolic representation features Expectation operation, Represents the hyperbolic manifold in time t The corresponding conformal factor, This represents the vector field predicted by the flow matching neural network. Indicates time t The following observations This represents the target vector field.

[0017] The beneficial effect of the above-mentioned further scheme is that the present invention proposes to use conformal factors to adaptively weight the hyperbolic flow matching loss function, thereby avoiding gradient interference caused by outliers and boundary noise during model training.

[0018] Furthermore, the expression for the robot's predicted action sequence is as follows:

[0019] in, This indicates that the robot predicts the sequence of actions. This represents the original continuous physical actions of the robot. Indicates a fixed scaling factor. This represents the logarithmic mapping at the origin. Indicates the predicted hyperbolic features, Indicates the time scaling factor. This represents the conformal factor at the origin. Represents the hyperbolic tangent mapping. This represents the curvature parameter.

[0020] The beneficial effects of the above-mentioned further scheme are as follows: by performing origin logarithmic mapping and inverse time scaling on the predicted hyperbolic features, the present invention can convert the predicted results after trajectory decoupling in hyperbolic space into a continuous physical action sequence of the robot, so that the geometric separation effect obtained by the aforementioned time geometric embedding and hyperbolic flow matching can be reflected in the actual control action of the robot; at the same time, the back projection process uses curvature parameters and time scaling factors corresponding to the aforementioned exponential mapping, which is conducive to maintaining the consistency between the action mapping and action restoration process, reducing the scale deviation caused by the transformation from manifold space to Euclidean space, and improving the executability and generation stability of the robot's predicted action sequence.

[0021] The present invention also provides a hyperbolic trajectory decoupled motion generation system, comprising: The first processing module is used to acquire multimodal observation inputs and corresponding sequences of continuous physical actions of the robot; The second processing module is used to adaptively calculate the curvature parameters of the Poincaré sphere hyperbolic manifold based on the continuous physical motion sequence of the robot, taking into account the differences in motion distribution for different robot control tasks, and to construct a hyperbolic space based on the curvature parameters. The third processing module is used to scale the robot's continuous physical action sequence according to the time prediction step size using a time geometry embedding mechanism, and project the scaled action onto the hyperbolic space through the origin exponential mapping to obtain hyperbolic representation features. The fourth processing module is used to construct the hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on the Riemann metric, and use the hyperbolic representation features as the target endpoint features to train the flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. The fifth processing module is used in the inference stage to start from the prior noise, and based on the optimal transport geodesic vector field, to use the trained flow matching neural network to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. Then, through logarithmic mapping and inverse time scaling, the predicted hyperbolic features are back-projected back into Euclidean space to obtain the final robot predicted action sequence, thus completing the generation of the decoupled action of the hyperbolic trajectory. Attached Figure Description

[0022] Figure 1 This diagram illustrates a comparison of motion trajectory generation effects in Euclidean and hyperbolic spaces. Figure 1 (a) is a schematic diagram of spatial congestion, trajectory entanglement and mode averaging of multimodal motion trajectories in a confined Euclidean space; Figure 1 (b) is a schematic diagram of the spatial isolation and decoupling of multimodal motion trajectories using a Poincaré sphere hyperbolic manifold according to the present invention in Euclidean space.

[0023] Figure 2A schematic diagram of the overall architecture and processing flow of the hyperbolic trajectory decoupling motion generation method.

[0024] Figure 3 A visual comparison of the effects of different geometric embedding methods on trajectory space isolation within a manifold. Figure 3 (a) shows the standard exponential mapping embedding effect. Figure 3 (b) shows the temporal geometry embedding effect of the present invention.

[0025] Figure 4 A comparative diagram of qualitative action sequences performed by robots in complex environments.

[0026] Figure 5 This is a flowchart of the method of the present invention.

[0027] Figure 6 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0028] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0029] Example 1 The purpose of this invention is to solve the problems of trajectory entanglement and mode averaging caused by spatial capacity bottleneck in Euclidean space in multimodal continuous control methods in the field of robotics, so as to achieve real-time, accurate and diverse robot motion control.

[0030] like Figure 5 As shown, this invention provides a method for generating decoupled hyperbolic trajectories, the implementation of which is as follows: S1. During the training phase, acquire multimodal observation input and the robot's continuous physical action sequence corresponding to the multimodal observation input, wherein the robot's continuous physical action sequence is located in Euclidean space, and Euclidean space is used to characterize the continuous control actions that the robot actuator can directly execute. S2. To address the differences in motion distribution for different robot control tasks, based on the robot's continuous physical motion sequence, the curvature parameters of the Poincaré sphere hyperbolic manifold are adaptively calculated, and a hyperbolic space is constructed based on the curvature parameters. This hyperbolic space serves as the intermediate motion representation space after the robot's continuous physical motion sequence is geometrically embedded. The implementation method is as follows: To address the differences in motion distribution for different robot control tasks, expert teaching motion sequences are extracted from continuous physical motion sequences of the robot to construct an expert motion dataset. For zero-mean physical actions in the expert action dataset, calculate the empirical cumulative distribution function of their Euclidean norm. :

[0031] in, This represents the total number of data samples. This represents the expert's actions after zero-mean normalization. Describing the Euclidean norm, Indicates the radius threshold. Indicates an indicator function, i Indicates the first i One data sample.

[0032] Extract the boundary radius of the empirical cumulative distribution function that reaches the preset percentile (such as the 90th percentile). ; Based on boundary radius Calculate the curvature parameters of the Poincaré spherical hyperbolic manifold. .

[0033] In this embodiment, when a typical action generation network handles highly divergent tasks, such as a robot navigating around a central obstacle to grasp a target, the future action distribution naturally exhibits a tree-like or divergent topology. This invention first analyzes the limitation that the volume of Euclidean space only grows polynomially with radius, and proposes modeling the robot's action space as... Viponcaré Sphere Hyperbolic Manifold ,in, And has a constant negative curvature. , The dimension is d The curvature is c The Poincaré sphere model express The elements in the manifold, the Riemannian metric Equivalent to Euclidean conformal measurement, its conformal factor is defined as When an action indicates a tendency toward the manifold boundary, the conformal factor... It tends to infinity, thus providing an exponentially growing spatial capacity and a natural geometric decoupling space for trajectories of different modes.

[0034] In this embodiment, data-driven adaptive curvature estimation is employed. To address the differences in motion distribution across various robot control tasks, this invention designs an adaptive curvature estimation method instead of using fixed preset values. Specific steps include: extracting expert-taught motion sequences from the robot's continuous physical motion sequence to construct an expert motion dataset. The expert action dataset was preprocessed with zero-mean preprocessing. ,in, The first in the expert action dataset represents the... i A sample of continuous physical actions of a robot. i Indicates the sequence number of the robot's continuous physical action sample. N This represents the total number of continuous physical action samples of the robot in the expert action dataset. This represents the expert's actions after zero-mean normalization. Represent the expectation of a series of physical motion samples of the robot; calculate the Euclidean norm of expert actions. Empirical cumulative distribution function Extract the boundary radius corresponding to the 90th percentile. ,in, Represents the infimum operation. This represents the radius threshold used to calculate the empirical cumulative distribution function. Represent the set of real numbers; determine the optimal negative curvature based on this boundary radius. This ensures that the vast majority of motion data can be robustly mapped to the high-capacity region of the manifold, avoiding numerical overflow or spatial degradation.

[0035] S3. Using a temporal geometric embedding mechanism, the continuous physical motion sequence of the robot is scaled temporally based on the predicted time step size. The scaled motion is then projected onto hyperbolic space through an origin exponential mapping to obtain hyperbolic representation features. These hyperbolic representation features serve as the target endpoint features and supervision signals for hyperbolic flow matching training in S4. The implementation method is as follows: Predicting a scalar function with a monotonically increasing step size over time. Calculate the time scaling factor :

[0036] in, This represents the expansion rate, used to simulate the range of potential decision uncertainty that expands exponentially over time. Continuous physical actions of the robot Apply time scaling factor Get the scaling action Among them, the robot's continuous characteristic actions are Euclidean physical actions; Calculate the origin exponential mapping using scaling actions; Based on the origin exponential mapping, the scaling action is projected into hyperbolic space to obtain hyperbolic representation features. Specifically, by increasing the time prediction step size, the magnified time scalar causes the hyperbolic representation features to approximate the manifold boundary of a Poincaré sphere. The exponential expansion property of the manifold boundary is used to spatially isolate and decouple the uncertainty of the robot's actions in the long term. The expression for the hyperbolic representation features is as follows:

[0037] in, Hyperbolic representation is a characteristic. This represents the exponential mapping at the origin. Indicates scaling action, Indicates a fixed scaling factor. Represents the hyperbolic tangent mapping. This represents the curvature parameter.

[0038] In this embodiment, a time scaling factor that monotonically increases with the time prediction step size is applied to amplify the sequence of robot physical actions in Euclidean space; the scaled physical actions are used to calculate an exponential mapping, projecting the Euclidean physical actions into hyperbolic representation features; as the prediction step size increases, the amplified time scalar will cause the hyperbolic representation features to gradually approach the manifold boundary of the Poincaré sphere, and the exponential expansion characteristic of the manifold boundary is used to spatially isolate and decouple the uncertainty of robot actions in the long term.

[0039] In this embodiment, temporal geometric embedding is used to address the temporal prediction step size in long-view tasks. To address the exponentially accumulating prediction uncertainty, this invention designs a temporal geometric embedding within the training and inference processes, for the first... A robot's continuous physical actions with a time-predicted step size First, apply a monotonically increasing time scaling factor. (Expansion rate in the examples) (Set to 2.0), to obtain the scaling action. The scaling motion is then projected onto hyperbolic space via an origin exponential mapping: ; in, This represents a fixed scaling factor (set to 1.0). This mechanism achieves strong isolation of different branching paths at the geometric level by forcing actions from more distant times toward the boundary of an exponentially expanding manifold.

[0040] S4. Construct a hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on Riemann metric, and use hyperbolic representation features as target endpoint features. Train the flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. The optimal transport geodesic vector field is used to solve the single-step geodesic integral of the ordinary differential equation in S5. In this embodiment, the expression for the hyperbolic flow matching objective function is as follows:

[0041] in, This represents the hyperbolic flow matching objective function. Indicates convection matching time t Prior noise and target hyperbolic representation features Expectation operation, Represents the hyperbolic manifold in time t The corresponding conformal factor, This represents the vector field predicted by the flow matching neural network. Indicates time t The following observations This represents the target vector field.

[0042] In this embodiment, the first-order Riemann-Euler method is used for single-step manifold integral update:

[0043] in, Indicates time, Indicates time t The predicted representation features are as follows. Indicates time t The following observations Indicates time t The difference, Indicates time The predicted representation features are as follows. This represents the velocity field predicted by the flow matching neural network. Indicates in The index mapping at that location.

[0044] Because the optimal transport geodesic stream vector field has zero covariant acceleration characteristics, it eliminates the local truncation error of the trajectory and supports large step-length single-step inference without iterative noise reduction.

[0045] In this embodiment, hyperbolic flow matching training: This invention constructs a hyperbolic flow matching objective function to regress the optimal transport geodesic vector field in hyperbolic space. Flow matching neural network. Receive current prediction status ,time and multimodal observation Fit the geodesic field connecting the noise and the target. To enhance the model's suppression of anomalous trajectories and ensure spatial separation, the hyperbolic flow matching objective function is defined in the manifold tangent space and dynamically weighted using a conformal factor: Conform factor Applying a higher geometric penalty to samples near the boundary acts as a natural geometric soft clipping mechanism, ensuring that the generated motion trajectories do not physically intersect.

[0046] S5. In the inference stage, starting from the prior noise, based on the optimal transmission geodesic vector field, the trained flow matching neural network is used to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. The predicted hyperbolic features are then back-projected back into Euclidean space through logarithmic mapping and inverse time scaling to obtain the final robot predicted action sequence, thus completing the generation of the decoupled hyperbolic trajectory action.

[0047] In this embodiment, the first-order Riemann-Euler method is used to perform a single-step update to obtain the predicted hyperbolic features. Then, the physical motion is restored through logarithmic inverse mapping and inverse scaling. The formula is: , in, This indicates that the robot predicts the sequence of actions. This represents the original continuous physical actions of the robot. Indicates a fixed scaling factor. This represents the logarithmic mapping at the origin. Indicates the predicted hyperbolic features, Indicates the time scaling factor. This represents the conformal factor at the origin. Represents the inverse hyperbolic tangent function. This represents the curvature parameter.

[0048] In this embodiment, the extremely fast single-step inference driven by zero covariant acceleration: This invention mathematically proves that the constructed hyperbolic flow is the optimal transport geodesic vector field, which has strict zero covariant acceleration characteristics. , (This represents the covariant derivative of the geodesic). Benefiting from this property, the trajectory exhibits extremely high local linearity on the manifold, causing the local truncation error of the first Riemann-Euler integral to be reduced from that in Euclidean space. Reduced to , and All of these represent local truncation errors. During inference deployment, the system directly starts from the sampled prior noise and performs single-step geodesic integral updates: ,in, , express The predicted features at each time step are then used to represent the physical actions. Finally, the generated predicted hyperbolic features are converted back to physical actions via a logarithmic inverse mapping.

[0049] In this embodiment, the present invention aims to address the trajectory entanglement and mode averaging problems encountered by existing Euclidean space-based generative motion methods when handling highly divergent multimodal continuous control tasks. In complex interactions in the real world, robot motion distribution often exhibits a tree-like topological structure, while the volume of Euclidean space only increases polynomially with radius. This limitation of flat geometry forces different modes of motion to overlap within a limited space, resulting in erroneous compromise predictions during model training. To fundamentally expand the geometric capacity of robot motion representation, the present invention elevates the multimodal motion generation process from the constrained Euclidean space to a Poincaré sphere hyperbolic manifold with constant negative curvature.

[0050] This manifold exhibits a volumetric property of exponential expansion with radius through its metric tensor, and its conformal factor is defined as... ,in, This represents the negative curvature of the manifold. To enable the manifold to accurately match the motion distribution of a robot for a specific task, this invention abandons the traditional method of manually setting the curvature and instead employs a data-driven adaptive estimation method. By zero-mean normalizing the expert motion dataset and calculating its Euclidean norm empirical cumulative distribution function, the boundary radius corresponding to the preset percentile is extracted. Thus, the curvature parameters are determined. This ensures that most motion samples can be distributed in the high-capacity region of the manifold.

[0051] To address the uncertainty of long-term forecasting, this invention introduces a temporal geometric embedding mechanism, which uses a forecasting step size over time. Monotonically increasing time scaling factor The robot's continuous physical actions are dynamically amplified. The scaled actions are then projected onto a hyperbolic manifold through an exponential mapping from the origin. Under this mechanism, robot continuous physical actions with later prediction times are pushed toward the exponentially expanding manifold boundary. The huge spatial span at the boundary forces the separation of potentially conflicting action paths, achieving geometric trajectory decoupling.

[0052] During the model training phase, this invention constructs a hyperbolic flow matching objective function, and uses a flow matching neural network to regress the optimal transport geodesic vector field connecting prior noise and the target state. This objective function specifically introduces a conformal factor weighting mechanism. Since the conformal factor tends to infinity near the boundary, this weight can impose a very high geometric penalty on samples near the boundary, significantly enhancing the spatial isolation effect and improving the model's robustness to outlier noise.

[0053] To address the stringent low-latency requirements of real-time control, this invention utilizes the mathematical property that geodesic flows generated by hyperbolic flow matching possess zero covariant acceleration. This implies that the evolution path on the manifold exhibits extremely high local linearity, reducing the truncation error of the first-order Riemann-Euler integral from the conventional local truncation error. Reduce to local truncation error Therefore, during the inference phase, this invention only requires a single-step integral update to obtain high-precision motion prediction, greatly reducing computational overhead. Finally, through origin logarithmic mapping and inverse time scaling, the predicted hyperbolic features are losslessly restored back to physical Euclidean space for robot execution.

[0054] In this embodiment, as Figure 1 As shown, Figure 1 (a) shows that highly divergent multimodal trajectories become crowded and entangled in a flat space, leading to catastrophic mode averaging and execution failure. Figure 1 (b) demonstrates that the present invention utilizes the exponential volume growth of hyperbolic space to clearly decouple conflicting paths and perfectly preserve the tree-like topology of complex actions.

[0055] In this embodiment, as Figure 2 As shown, the overall architecture of the hyperbolic trajectory decoupling action generation method comprises two core stages: the tangent space section in the lower left illustrates the temporal geometry embedding mechanism, where the robot's physical action sequence is dynamically scaled and projected onto the Poincaré sphere boundary to achieve spatial isolation; the right side section demonstrates the hyperbolic trajectory decoupling flow dynamics, where the optimal transport geodesic vector field in hyperbolic space is learned through neural networks (such as ResNet-18 and U-Net) combined with multimodal conditions (such as text features extracted by CLIP). The generated predicted hyperbolic features are finally losslessly mapped back to Euclidean space via backprojection for robot execution. Figure 2 middle, Indicates the robot's continuous physical actions. This indicates a hyperbolic characteristic.

[0056] In this embodiment, as Figure 3 As shown, Figure 3 (a) shows the standard exponential mapping embedding effect. Figure 3 (b) shows the temporal geometric embedding effect of the present invention. It should be noted that the temporal geometric embedding mechanism explicitly pushes actions that are far away in time and have high uncertainty to the high-capacity manifold boundary, thereby achieving effective isolation of long-field uncertainty at the geometric level.

[0057] In this embodiment, as Figure 4 As shown, Figure 4 (Above) shows the process by which the Euclidean baseline method encounters a bifurcation path, resulting in physical collisions or mission failures (red crosses) due to trajectory entanglement and pattern averaging. Figure 4 The results of this invention (green checkmark) are shown below, demonstrating that the Hyperbolic Trajectory Decoupling Method (HTDP) can clearly distinguish different action modes and ensure highly stable and accurate execution in long-field-of-view operations and multi-target navigation.

[0058] In this embodiment, the typical generative network uses an architecture based on Euclidean flat space, attempting to accommodate multimodal action distribution within a constrained space. Real-world continuous actions typically exhibit a highly branched tree-like topology, such as... Figure 1 As shown in (a), due to the polynomial volume growth, multimodal actions inevitably become entangled in Euclidean space. When the network minimizes the regression error, it often outputs a compromise value of multiple effective paths, leading to "modal averaging" and task failure. This invention considers whether the generated manifold can be elevated to a Poincaré sphere hyperbolic manifold with exponential volume growth. Spatial decoupling and physical isolation are achieved by pushing highly divergent trajectories into a high-capacity geometric space. This invention first calculates the empirical cumulative distribution function (CDF) of the expert dataset on the zero-mean Euclidean norm, and then extracts the boundary radius corresponding to the 90th percentile of the calculated distribution. And calculate the final optimal negative curvature. This design avoids the numerical overflow or spatial degradation problems caused by a fixed preset curvature. This invention finds that when using adaptive curvature, the vast majority of effective motion samples can be robustly distributed within the exponentially expanding region of the manifold, significantly reducing error accumulation caused by insufficient spatial capacity. This indirectly enables the invention to more easily separate bifurcation paths in complex long-view tasks.

[0059] Based on previous multimodal uncertainty analysis, isolating trajectory deviations at future steps is an ideal method for long-field-of-view tasks. The core idea of ​​this invention's hyperbolic trajectory decoupling action generation method is to establish a temporal geometric embedding mechanism (TGE) and reshape uncertainties using manifold boundaries. Since accumulated errors and action divergences amplify exponentially during the backward extrapolation of action sequences, this invention considers directly using a time scaling factor to amplify long-term actions, projecting them as input to the origin exponential mapping onto the hyperbolic manifold. This utilizes the large conformal factor (spatial span) near the boundary of the hyperbolic manifold to forcibly separate action paths with longer time horizons and higher conflict probabilities into spatially distinct paths. Detailed procedures can be found in [reference needed]. Figure 2 and Figure 3 .

[0060] Previous studies have typically focused on generative tasks within Euclidean space (such as image generation or diffusion methods in flat spaces) or sought better fitting paths through time-consuming multi-step iterative denoising. However, these methods often perform poorly or require significant inference latency when encountering highly bifurcated multimodal data. This invention proposes a dynamic flow matching mechanism based on hyperbolic conformal factor weighting to adaptively guide the network to learn a decoupled geodesic vector field. Traditional diffusion methods typically use unweighted Euclidean distance for model fitting. The goal of this invention is to dynamically penalize boundary trajectories based on the manifold's inherent metric properties. The final loss of the flow matching neural network is determined by the predicted vector field. With the target vector field The difference determines the value. Higher penalties should be applied to boundary regions with larger deviations to reduce trajectory crossings. Although the model predicts action sequences, the conformal factor of the Poincaré sphere metric is used. It can naturally reflect the spatial expansion rate at that point. Therefore, the metric weighting method in Riemannian geometry is also applicable here. This invention combines hyperbolic metrics to construct a weighted hyperbolic flow matching objective function. The conformal factor tends to infinity as the feature approaches the boundary, acting as a "soft pruning" mechanism to effectively suppress outlier noise.

[0061] Complex generative dynamics can lead to lengthy inference steps, affecting the real-time performance of the final trajectory on a real robot. To address this issue, this invention theoretically derives and proves that the hyperbolic flow constructed in this invention is an optimal transport geodesic vector field with strictly zero covariant acceleration characteristics. This implies that the trajectory evolution on the manifold has extremely high local linearity. Then, the integral truncation error is determined by the local truncation error in conventional Euclidean space. Significantly reduced to local truncation error To avoid the time-consuming iterative denoising during the inference process, this invention directly adopts a step size of... The first-order Riemann-Euler method is used for extremely rapid single-step updates. It is important to note that the method of this invention aims to eliminate modal averaging and significantly reduce inference time while maintaining a high success rate of the task, without requiring re-distillation or retraining of student models. However, important baseline methods of this invention (such as the diffusion method DP and the consistency method CP) are based on multi-step denoising and flat spatial architectures, respectively. Therefore, for a fair performance comparison, this invention employs the exact same perceptual backbone module configuration as the baseline methods (such as a ResNet-18-based image encoder extractor). Furthermore, this invention also uses the same multimodal observation data (including wrist camera images, third-person view camera images, and CLIP-encoded language instructions) as input and outputs a continuous sequence of end-effector actions. This demonstrates to some extent the effectiveness and superiority of this invention through its purely geometric architecture enhancement.

[0062] Experimental Results: It should be noted that all simulation task evaluations in the embodiments of this invention were calculated using the same settings on a single NVIDIA L40 GPU graphics card; all real physical environment tasks were deployed and evaluated on a single NVIDIA RTX 4090 GPU and Franka Panda robotic arm hardware platform.

[0063] Table 1 presents a comprehensive comparison of the Hyperbolic Trajectory Decoupling Method (HTDP) of this invention with traditional Euclidean space-based generation methods (such as diffusion method DP, genetic denoising diffusion strategy GDP, flow matching strategy Flow Policy, Euclidean corrected flow matching, and conventional Riemann flow matching method (RFMP)) in multimodal control performance. In Table 1, TGE represents the temporal geometry embedding mechanism. It can be seen that this invention achieves superior accuracy in both single-arm tasks (Square, Can) and tasks requiring complex dual-arm collaboration (Transport). Particularly in multi-human (MH) collaborative datasets containing highly divergent data, Euclidean space methods suffer from severe trajectory congestion and pattern averaging, leading to a sharp drop in success rate; while this invention naturally decouples conflicting trajectories using the exponential spatial capacity of the Poincaré sphere, maintaining an extremely high success rate across all sub-tasks.

[0064] Table 1 illustrates the average task success rate of each generative model on the Robomimic (Robot Imitation Learning Benchmark) simulation benchmark. All models were trained with the same hyperparameter configuration, and the evaluation results are the average of 500 independent executions on a single L40 GPU (Graphics Processing Unit).

[0065] Table 1

[0066] Table 2 presents a comprehensive comparison of the Hyperbolic Trajectory Decoupling Method (HTDP) of this invention with existing Euclidean space-based accelerated motion generation methods (such as Consistency Policy CP, One-step Diffusion Policy OneDP, Implicit Maximum Likelihood Estimation Method IMLE, FreqPolicy (an efficient visual motion policy based on frequency consistency), and Average Velocity Policy MVP) and conventional Riemann Flow Matching Method (RFMP) under single-step inference conditions in terms of robot motion generation performance. In Table 2, TGE represents the temporal geometry embedding mechanism. Thanks to the theoretically zero covariant acceleration characteristic of the geodesic flow constructed in this invention, the local truncation error of single-step integration is greatly reduced. On a single L40 GPU (Graphics Processing Unit), this invention achieves an average success rate of up to 0.94 on the Robomimic (Robot Imitation Learning Benchmark) (PH) dataset with only one inference step, without requiring time-consuming distillation training. This not only significantly outperforms the basic conventional Riemann Flow Matching Method (RFMP) but also surpasses or matches the accuracy of complex Euclidean accelerated networks, achieving a balance between inference speed and control accuracy.

[0067] Table 2

[0068] Table 3 illustrates the system-level performance of the Hyperbolic Trajectory Decoupling Method (HTDP) provided by this invention in the real physical world. In the Lift and PaP tasks performed on the Franka Panda robotic arm, this invention achieved a success rate exceeding that of the diffusion method (DP) which performs 100 denoising steps. More importantly, based on the computing power of a single RTX 4090 GPU, the system-level end-to-end inference latency of this invention is only 0.064 seconds, achieving nearly ten times the physics response speedup compared to the traditional method's 0.608 seconds, significantly improving the real-time deployment capability of this invention on resource-constrained real-world devices.

[0069] Table 3

[0070] In summary, addressing the spatial congestion, trajectory entanglement, and pattern averaging problems inherent in existing Euclidean space generation models when handling highly branched motion distributions, this invention elevates the robot motion generation process to a Poincaré sphere hyperbolic manifold. Specifically: a data-driven method based on expert physical motion sequences adaptively estimates the curvature parameters of the hyperbolic manifold; a temporal geometry embedding module scales the continuous physical motion sequence of the robot over time and projects it onto hyperbolic space, utilizing the exponential expansion of the boundary to isolate long-term prediction uncertainties; the optimal transport geodesic stream vector field is learned in hyperbolic space, and the flow matching neural network is optimized using a hyperbolic flow matching loss function weighted by conformal factors; during inference, a first-order Riemann-Euler single-step integral is performed based on the geodesic stream with zero covariant acceleration characteristics, and finally, the model is inversely scaled and back-projected back into Euclidean space. This invention leverages the exponentially growing volume advantage of hyperbolic space to naturally decouple conflicting trajectories, avoids the pattern averaging problem, and achieves high-precision single-step motion generation with extremely low latency.

[0071] Example 2 like Figure 6 As shown, the present invention also provides a hyperbolic trajectory decoupling action generation system for executing the hyperbolic trajectory decoupling action generation method described in Embodiment 1, comprising: The first processing module is used to acquire multimodal observation inputs and corresponding sequences of continuous physical actions of the robot; The second processing module is used to adaptively calculate the curvature parameters of the Poincaré sphere hyperbolic manifold based on the continuous physical motion sequence of the robot, taking into account the differences in motion distribution for different robot control tasks, and to construct a hyperbolic space based on the curvature parameters. The third processing module is used to scale the robot's continuous physical action sequence according to the time prediction step size using a time geometry embedding mechanism, and project the scaled action onto the hyperbolic space through the origin exponential mapping to obtain hyperbolic representation features. The fourth processing module is used to construct the hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on the Riemann metric, and use the hyperbolic representation features as the target endpoint features to train the flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. The fifth processing module is used in the inference stage to start from the prior noise, and based on the optimal transport geodesic vector field, to use the trained flow matching neural network to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. Then, through logarithmic mapping and inverse time scaling, the predicted hyperbolic features are back-projected back into Euclidean space to obtain the final robot predicted action sequence, thus completing the generation of the decoupled action of the hyperbolic trajectory.

[0072] In this embodiment, the functional units can be divided according to the hyperbolic trajectory decoupling action generation method. For example, each function can be divided into its own functional units, or two or more functions can be integrated into one processing unit. The integrated unit can be implemented in hardware or as a software functional unit. It should be noted that the unit division in this invention is illustrative and represents only a logical division; other division methods may be used in actual implementation.

[0073] In this embodiment, the hyperbolic trajectory decoupling action generation system, in order to realize the principle and beneficial effects of the hyperbolic trajectory decoupling action generation method, includes hardware structures and / or software modules corresponding to the execution of various functions. Those skilled in the art should readily recognize that, in conjunction with the illustrative units and algorithm steps described in the embodiments disclosed in this invention, the present invention can be implemented in hardware and / or a combination of hardware and computer software. Whether a function is executed by hardware or computer software depends on the specific application and design constraints of the technical solution. Different methods can be used to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0074] Example 3 This embodiment also provides an electronic device, which can vary considerably due to differences in configuration or performance. It may include one or more central processing units (CPUs) (e.g., one or more processors) and memory, and one or more storage media (e.g., one or more mass storage devices) for storing applications or data. The processor executes the program to implement some or all of the steps of the hyperbolic trajectory decoupling action generation method as described in any of Embodiment 1. The memory and storage media may be temporary or persistent storage. The program stored in the storage media may include one or more modules, each module including a series of instruction operations on the electronic device. Furthermore, the processor may be configured to communicate with the storage media and execute the series of instruction operations stored in the storage media on the electronic device.

[0075] The electronic device may also include one or more power supplies, one or more wired or wireless network interfaces, one or more input / output interfaces, and / or one or more operating systems, such as Windows Server, Mac OS X, Unix, Linux, FreeBSD, etc. Those skilled in the art will understand that the structure of the electronic device does not constitute a limitation on the electronic device itself, and may include more or fewer components than described above, or combine certain components, or have different component arrangements.

[0076] Example 4 The present invention also provides a computer-readable storage medium, which may be a non-volatile computer-readable storage medium or a volatile computer-readable storage medium, wherein the computer-readable storage medium stores instructions that, when executed on a computer, cause the computer to perform some or all of the steps of the method described in Embodiment 1.

[0077] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the system, device, or unit described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0078] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0079] 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.

Claims

1. A method for generating decoupled hyperbolic trajectory actions, characterized in that, Includes the following steps: S1. During the training phase, acquire multimodal observation inputs and the robot's continuous physical action sequence corresponding to the multimodal observation inputs; S2. To address the differences in motion distribution for different robot control tasks, based on the continuous physical motion sequence of the robot, the curvature parameters of the Poincaré sphere hyperbolic manifold are adaptively calculated, and a hyperbolic space is constructed based on the curvature parameters. S3. Using a time-geometric embedding mechanism, the robot's continuous physical action sequence is scaled according to the time prediction step size, and the scaled action is projected onto the hyperbolic space through the origin exponential mapping to obtain the hyperbolic representation features. S4. Construct a hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on Riemann metric, and use hyperbolic representation features as target endpoint features to train a flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. S5. In the inference stage, starting from the prior noise, based on the optimal transmission geodesic vector field, the trained flow matching neural network is used to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. The predicted hyperbolic features are then back-projected back into Euclidean space through logarithmic mapping and inverse time scaling to obtain the final robot predicted action sequence, thus completing the generation of the decoupled hyperbolic trajectory action.

2. The hyperbolic trajectory decoupling motion generation method according to claim 1, characterized in that, S2 includes: To address the differences in motion distribution for different robot control tasks, expert teaching motion sequences are extracted from continuous physical motion sequences of the robot to construct an expert motion dataset. For zero-mean physical actions in the expert action dataset, calculate the empirical cumulative distribution function of their Euclidean norm; Extract the boundary radius of the empirical cumulative distribution function that reaches the preset percentile. ; Based on boundary radius Calculate the curvature parameters of the Poincaré spherical hyperbolic manifold. And based on the curvature parameters, a hyperbolic space matching the robot's motion distribution is constructed.

3. The hyperbolic trajectory decoupling motion generation method according to claim 2, characterized in that, The curvature parameter The expression is as follows: 。 4. The hyperbolic trajectory decoupling motion generation method according to claim 1, characterized in that, S3 includes: The time scaling factor is calculated using a scalar function whose prediction step size increases monotonically with time. Apply a time scaling factor to the robot's continuous physical movements to obtain scaled movements; Calculate the origin exponential mapping using scaling actions; Based on the origin exponential mapping, the scaling action is projected into the hyperbolic space to obtain hyperbolic representation features. Among them, based on the increase of the time prediction step, the magnified time scalar causes the hyperbolic representation features to approach the manifold boundary of the Poincaré sphere. The exponential expansion property of the manifold boundary is used to spatially isolate and decouple the uncertainty of robot actions in the long term.

5. The hyperbolic trajectory decoupling action generation method according to claim 4, characterized in that, The hyperbolic representation feature is expressed as follows: in, Indicates the first h Hyperbolic representation features corresponding to each time prediction step size This represents the exponential mapping at the origin. Indicates scaling action, Indicates a fixed scaling factor. Represents the hyperbolic tangent mapping. Represents the curvature parameter. Indicates the time scaling factor. This represents the original continuous physical actions of the robot. Indicates the expansion rate. Indicates the time prediction step size.

6. The hyperbolic trajectory decoupling action generation method according to claim 1, characterized in that, The expression for the hyperbolic flow matching objective function is as follows: in, This represents the hyperbolic flow matching objective function. Indicates convection matching time t Prior noise and target hyperbolic representation features Expectation operation, Indicates the hyperbolic manifold in time t The corresponding conformal factor, This represents the vector field predicted by the flow matching neural network. Indicates time t The following observations This represents the target vector field.

7. The hyperbolic trajectory decoupling motion generation method according to claim 1, characterized in that, The expression for the robot's predicted action sequence is as follows: in, This indicates that the robot predicts the sequence of actions. This represents the original continuous physical actions of the robot. Indicates a fixed scaling factor. This represents the logarithmic mapping at the origin. Indicates the predicted hyperbolic features, Indicates the time scaling factor. This represents the conformal factor at the origin. Represents the hyperbolic tangent mapping. This represents the curvature parameter.

8. A hyperbolic trajectory decoupling action generation system, used to execute the hyperbolic trajectory decoupling action generation method according to any one of claims 1-7, characterized in that, include: The first processing module is used to acquire multimodal observation inputs and corresponding sequences of continuous physical actions of the robot; The second processing module is used to adaptively calculate the curvature parameters of the Poincaré sphere hyperbolic manifold based on the continuous physical motion sequence of the robot, taking into account the differences in motion distribution for different robot control tasks, and to construct a hyperbolic space based on the curvature parameters. The third processing module is used to scale the robot's continuous physical action sequence according to the time prediction step size using a time geometry embedding mechanism, and project the scaled action onto the hyperbolic space through the origin exponential mapping to obtain hyperbolic representation features. The fourth processing module is used to construct the hyperbolic flow matching objective function, weight the hyperbolic flow matching loss function based on the Riemann metric, and use the hyperbolic representation features as the target endpoint features to train the flow matching neural network to fit the optimal transport geodesic vector field from prior noise to hyperbolic representation features under multimodal observation input conditions. The fifth processing module is used in the inference stage to start from the prior noise, and based on the optimal transport geodesic vector field, to use the trained flow matching neural network to solve the ordinary differential equation in hyperbolic space by single-step geodesic integration to obtain the predicted hyperbolic features. Then, through logarithmic mapping and inverse time scaling, the predicted hyperbolic features are back-projected back into Euclidean space to obtain the final robot predicted action sequence, thus completing the generation of the decoupled action of the hyperbolic trajectory.

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