Device and computer-implemented method for continuous-time interaction modeling of agents

Abstract

Regarding a device and a computer-implemented method for continuous-time interaction modeling of agents, the method comprises: a step (202) of providing a latent state of a first agent and a latent state of a second agent, in particular, characterizing the position or velocity of these agents; a step (204) of providing a first Gaussian process distribution for a first function for modeling the kinematic behavior of an agent independently of other agents, and a second Gaussian process distribution for a second function for modeling the interaction between agents; a step (206) of sampling the first function from the first Gaussian process distribution and the second function from the second Gaussian process distribution, wherein the first function is configured to map the latent state of one agent to the contribution to the change in the latent state of that agent, and the second function is configured to map the latent states of two agents to the contribution to the change in the latent state of one of the two agents, and the method comprises a step (208) of changing the latent state of the first agent according to a first contribution resulting from the mapping from the latent state of the first agent to the first contribution by the first function and a second contribution resulting from the mapping from the latent states of the first agent and the second agent to the second contribution by the second function.

Description

Technical Field

[0001] The present invention relates to devices and computer-implemented methods for continuous-time interaction modeling of agents, particularly objects of interest.

Background Art

[0002] Learning the behavior of unknown dynamic systems from data is a fundamental problem in machine learning.

Summary of the Invention

Problems to be Solved by the Invention

[0003] The computer-implemented method and device according to the independent claims are based on a Gaussian process (GP), operate in continuous time, and use a model that decomposes complex continuous dynamics into independent kinematic and interaction components to explain interpretable non-linear dynamics. This model treats the independent kinematics of the agents and their interactions separately. Function-level regularization via GP is the key to learning a disentangled representation. This model is based on ordinary differential equations (ODEs). This explains many complex dynamics that have a natural representation with respect to time differences. The continuous-time formulation allows for a direct integration of domain knowledge that exploits the inductive bias of the model. Thus, the kinematics of the objects and their interactions are modeled separately with two different Gaussian processes.

Means for Solving the Problems

[0004] A computer-implemented method for continuous-time interaction modeling of agents includes providing a latent state of a first agent and a latent state of a second agent, in particular, characterizing the position or velocity of these agents; providing a first Gaussian process distribution for a first function for modeling the kinematic behavior of an agent independently of other agents, and a second Gaussian process distribution for a second function for modeling the interaction between agents; sampling the first function from the first Gaussian process distribution and the second function from the second Gaussian process distribution, wherein the first function is configured to map the latent state of one agent to the degree of contribution to the change in its latent state, the second function is configured to map the latent states of two agents to the degree of contribution to the change in the latent state of one of the two agents, and the method includes changing the latent state of the first agent according to a first contribution resulting from the mapping of the latent state of the first agent to the first contribution by the first function and a second contribution resulting from the mapping of the latent state of the first agent and the latent state of the second agent to the second contribution by the second function.

[0005] This method preferably includes the step of providing an initial latent state of a plurality of agents including a first agent and a second agent, and changing the latent state of the first agent according to a second contribution degree resulting from mapping a pair of the latent states of the first agent and a different second agent among the plurality of agents by a second function, or selecting a subset of the plurality of agents and changing the latent state of the first agent according to a second contribution degree resulting from mapping a pair of the latent states of the first agent and a different second agent in the subset by a second function. Accordingly, this method considers either all agents different from the first agent or the vicinity of the agent for interaction. Agents not in the vicinity of an agent are less likely to interact with the agent. Thereby, the computational load is reduced while maintaining appropriate accuracy of the model.

[0006] This method preferably includes the step of determining an agent from the plurality of agents for a subset closer to the first agent than other agents of the plurality of agents according to a measure of distance between agents. Accordingly, this method considers the vicinity of the agent for interaction. The metric may be a measure of any kind of characteristic of the agent. For the movement of agents, the distance between each other is a preferred metric.

[0007] This method preferably includes the step of providing a data sequence, and the step of providing the initial latent state of the first agent and / or the second agent includes determining the initial latent state using an encoder configured to map the data sequence to the initial latent state.

[0008] This method preferably includes the step of determining an output according to the latent state of the first agent, particularly a trajectory sample, preferably the trajectory of the position and / or velocity of the first agent over time. The output can be related to any kind of characteristic of the agent. Regarding the movement of the agent, the trajectory sample is the preferred output.

[0009] Preferably, the first Gaussian process distribution includes a posterior distribution, and this method includes the step of learning a particularly sparse approximation to the posterior distribution for the first Gaussian process distribution with variational parameters, and the step of providing an approximation for the first Gaussian process distribution as the first Gaussian process distribution, and / or the second Gaussian process distribution includes a posterior distribution, and this method includes the step of learning a particularly sparse approximation to the posterior distribution for the second Gaussian process distribution with variational parameters, and the step of providing an approximation for the second Gaussian process distribution as the second Gaussian process distribution. In this way, the parameters defining the Gaussian process distribution are learned for the unknown function.

[0010] This method preferably includes the step of determining a first Gaussian process distribution or a second Gaussian process distribution that depends on the output and has an expected likelihood term decomposed between agents and over time points. The likelihood term is an approximation of part of the evidence lower bound (ELBO) that enables the determination of the parameters defining the Gaussian process distribution.

[0011] This method may be applied to a second-order ordinary differential equation. The latent state of the first agent includes a first component and a second component. This method includes the step of changing the latent state of the first component of the latent state of the first agent according to the change in the second component of the latent state of the first agent and the change in the second component of the latent state of the first agent. The second component changes according to the first contribution to the change in the latent state of the first agent and the second contribution to the change in the latent state of the first agent.

[0012] To control the first agent, the method may include the step of determining the action of the first agent according to the output.

[0013] The method preferably includes the step of determining the potential state of the first agent and the potential state of the second agent according to the measured values of a series of observable states of the agents.

[0014] The first agent may be an existing object in the physical world. The potential state of the first agent is determined according to the measured values of the characteristics of the first agent, and / or the second agent may be an existing object in the physical world. The potential state of the second agent is determined according to the measured values of the characteristics of the second agent. In particular, the measured values include position data, especially position data from a satellite navigation system, or in particular digital images, preferably video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images, preferably position data from information regarding the position or velocity of the agent. Thereby, it becomes possible to determine the potential state from the measured values, especially from the appropriate control of the first agent.

[0015] The device for continuous-time interaction modeling of agents includes at least one processor and at least one memory configured to execute the steps of the method. This device has advantages corresponding to the advantages of the method.

[0016] The device preferably includes an interface configured to observe the continuous-time interaction of the agents, especially digital images, preferably video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images, or to receive information regarding the continuous-time interaction of the agents.

[0017] The interface may be configured to control the action of at least one of the agents according to the output or action.

[0018] A computer program including computer-readable instructions that, when executed by a computer, cause the computer to execute a method provides advantages corresponding to the advantages of the present method.

[0019] Further advantageous embodiments are derived from the following description and the drawings.

Brief Description of the Drawings

[0020]

Figure 1

Figure 2

Embodiments for Carrying Out the Invention

[0021] FIG. 1 shows a device 100 for continuous-time interaction modeling of an agent 102. Four agents 102 are shown in FIG. 1. The number of agents 102 may be more or less than four.

[0022] The device 100 includes at least one processor 104 and at least one memory 106. The device 100 may include an interface 108.

[0023] At least one processor 104 is configured to execute the steps of the method described below. At least one memory 106 is configured to store instructions that, when executed by at least one processor 104, cause the processor 104 to execute the steps of the method, particularly a computer program.

[0024] In one example, interface 108 is configured to observe the continuous-time interaction of agent 102 or to receive information regarding the continuous-time interaction of agent 102. In one example, interface 108 is configured to control at least one action of agent 102.

[0025] The information is provided, for example, by digital images, such as video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images.

[0026] The continuous-time interaction of agent 102 includes, for example, the position or velocity of agent 102. The position may be a relative position, such as the distance between pairs of agent 102, or an absolute position of agent 102.

[0027] In this example, system 110 includes agent 102. System 110 may be a physical system. Agent 102 may be a physical system, particularly a technical system. Agent 102 may be an existing physical object in the physical world. Agent 102 may include other moving objects such as vehicles, pedestrians, or balls.

[0028] System 110 includes environment 112. Environment 112 may include road infrastructure or building infrastructure. Agent 102 in this example moves within environment 112 and may be affected by environment 112. Agent 102 may include objects of environment 112, such as a fixed infrastructure system that is part of environment 112. System 110 in this example follows specific physical rules. The physical rules are, for example, that the integral of velocity is position.

[0029] The continuous-time interaction is not limited to these physical quantities. The continuous-time interaction may include other physical quantities, technical quantities, or chemical quantities. The continuous-time interaction may also include global latent variables, for example, agent-specific characteristics such as mass or radius.

[0030] Figure 2 shows the steps in a method for continuous-time interaction modeling of agents.

[0031] The method depends on the model:

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[0032] The model depends on the estimation of two additive functions that are independent of each other, namely, the kinematic function [Number] and the interaction function [Number] .

[0033] The kinematic function f of this example s learns how an agent moves over time when there are no other agents and thus is independent of other agents. The interaction function f in this example b learns how agents interact with each other.

[0034] This method is described for a plurality of agents a (a = 1,..., A).

[0035] In one example, the method has, for each agent a, A terms, namely, the kinematic function f sincluding a step of determining its dynamics according to the sum of one independent kinematic term that depends on b and, in this example, A - 1 interaction terms, each of the interaction terms modeling the interaction of agent a with one of the remaining A - 1 agents a' by means of one interaction function f a The method is not limited to determining the dynamics of each agent a. The method may also include a step of determining the dynamics for a subset of a plurality of agents (a = 1, …, A) or for a single agent a among a plurality of agents (a = 1, …, A). The method is not limited to determining the dynamics of agent a according to its interaction with the remaining A - 1 agents a'. The method may include a step of determining the dynamics of agent a according to a subset N a of a plurality of agents (a = 1, …, A), or according to one agent a' among a plurality of agents (a = 1, …, A). The subset N

[0036] The method operates on an example for a dataset of P sequences

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[0037] The method includes step 200.

[0038] In step 200, the data sequence

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[0039] According to an exemplary method, agent 102 of system 110 is observed over a certain period of time. In this example, a plurality of agents a (a = 1, …, A) represent agent 102, and the data sequence

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[0040] The data sequence

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[0041] The observable states may in particular be determined from digital images of system 110, preferably video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images. These include information regarding the position and velocity of agent 102 in this example.

[0042] This method includes step 202.

[0043] In step 202, the initial potential state of at least one agent a at the start time t 1 is provided.

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[0044] At least one initial latent state of agent a

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[0045] In an exemplary method, the initial values of agent a required for ordinary differential equation integration are determined. These initial values can generally represent various things. In this example, the initial values correspond to the initial position and velocity of each agent a. The initial values, in this example, are the initial latent state of system 110 at the start time t 1 represent the initial latent state of system 110 at

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[0046] Θ ​is a combination of a recurrent neural network and a multi-layer perceptron. Another exemplary encoder includes a graph neural network layer to capture interactions. Encoder q Θ can also be another neural network architecture. Encoder q Θ is configured to output a distribution rather than a single value.

[0047] If the model includes global latent variables, such as object-specific properties like mass or radius, another encoder may be used to extract these variables. Both encoders may have the same architecture. Both encoders output a distribution rather than a single value.

[0048] The method includes step 204.

[0049] In step 204, a first function f for modeling the kinematic behavior of agent a independently of other agent a' s is provided with a first Gaussian process distribution

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[0050] In step 204, a second function f for modeling the interaction between agents a, a' b is provided with a second Gaussian process distribution

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[0051] The kinematic function f s and the interaction function f b are unknown in one example. The first Gaussian process distribution

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[0052] The method includes step 206.

[0053] In step 206, the first function f s is sampled from the first Gaussian process distribution

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[0054] from the second Gaussian process distributionb is sampled from the second Gaussian process distribution

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[0055] The first function f s maps the latent state h a (τ) of one agent a to the contribution to the change in its latent state h a (τ), f s (h a (τ)) and is configured to map to

[0056] The second function f b maps the latent states

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[0057] The kinematic function f s and the interaction function f b are defined in continuous time using ordinary differential equations. The kinematic function f s and the interaction function f b correspond to the time derivative.

[0058] This method includes step 208.

[0059] In step 208, the latent state h n of at least one agent a at time point t a (t n ) is determined.

[0060] Time point tn The latent state h of at least one agent a at a (t n ) is determined by integrating the change from the initial latent state [Number] from the start time t 1 to the time point t n and changing it according to the result of the integral of the change. In one example, the change is determined for a plurality of agents (a = 1, …, A). [Number] The latent state h of one agent a resulting from this change

[0061] (t a (t n ) is determined, for example, as follows. [Number]

[0062] In one example, the latent state h is determined for a plurality of agents (a = 1, …, A). a (t n ) is determined.

[0063] In one example, the method includes the step of selecting a subset N of a plurality of agents (a = 1, …, A) including agent a, and the step of determining the change of this agent a according to other agents a' within the subset N. Thus, only the agents in the vicinity of this agent a are used. The agents a' within the subset N are selected, for example, according to a measure of the distance between agents. a and the step of determining the change of this agent a according to other agents a' within the subset N. Thus, only the agents in the vicinity of this agent a are used. The agents a' within the subset N are selected, for example, according to a measure of the distance between agents. a The agents a' within the subset N are selected, for example, according to a measure of the distance between agents. a In one example, the method includes the step of selecting a subset N of a plurality of agents (a = 1, …, A) including agent a, and the step of determining the change of this agent a according to other agents a' within the subset N. Thus, only the agents in the vicinity of this agent a are used. The agents a' within the subset N are selected, for example, according to a measure of the distance between agents.

[0064] In one example, the method includes the step of selecting a subset N of a plurality of agents (a = 1, …, A) including agent a, and the step of determining the change of this agent a according to other agents a' within the subset N. Thus, only the agents in the vicinity of this agent a are used. The agents a' within the subset N are selected, for example, according to a measure of the distance between agents. a within the subset N, and within the subset N aAt time t, according to at least one agent a' that is independent of at least one of a plurality of agents (a = 1, …, A) outside n the latent state h of at least one agent a in a (t n ) is changed. The latent state h of one agent a resulting from this change a (t n ) is determined as follows, for example.

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[0065] This method includes step 210.

[0066] In step 210, this method includes the step of determining the output of the model.

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[0067] The output in this example is the trajectory sample of each agent a

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[0068] For inference, this method may end, or another output may be repeated, for example, for another data sequence

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[0069] The output may be used to determine an action for at least one agent 102. The path taken by agent 102 is determined according to the positions of other agents, for example, to avoid collisions. For example, the action is to send an instruction to agent 102 to move to a target position. The instruction may be sent to agent 102 or may be executed by agent 102 as its own action. In one example, the action of agent 102 is determined according to the output.

[0070] For training, the method may include step 212.

[0071] Step 212 includes determining a first Gaussian process distribution

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[0072] In one example, during training, a sparse approximation to the posterior distribution with respect to the first Gaussian process distribution

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[0073] In one example, during training, the second Gaussian process distribution

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[0074] Training may be used as an optimization objective to maximize the evidence lower bound (ELBO) logp(Y 1:N )≧E q [logp(Y 1:N │H 1 ,f,U)]-KL[q(H 1 )||p(H 1 )]-KL[q(U)||p(U)] wherein H 1 ~q Φ (H 1 |Y 1:N ) and Φ are the parameters of a neural network encoder that outputs a Gaussian distribution with diagonal covariance, p(H 1 )=N(0,I) is a prior standard Gaussian distribution with dimensions suitable for the initial latent state,

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[0075] Training may also include learning the parameters Φ of the neural network encoder and other parameters such as the variance of the kernel or the noise variance.

[0076] Since this ELBO does not have a closed-form expression, the trajectory sample [Number] is the expected likelihood term [Number] It is used to approximate, where the log-likelihood term is decomposed between agents and over time points, enabling double variational inference.

[0077] The term KL[·] corresponds to the Kullback-Leibler regularizer. The prior distribution over the induced variables is a Gaussian process p(U)=p(U s )p(U b ), where

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[0078] In one example, the model includes a second-order ordinary differential equation. h a (t)≡[s a (t),v a (t)]

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[0079] This means that the latent state h a (t) of agent a includes a first component s a (t) and a second component v a (t). The method includes the step of changing the latent state h a (t) of agent a according to the change a in the second component v

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[0080] This removes other indistinguishable problems and improves the interpretation of the latent states s a (t), v a (t), thus relaxing the inference. In this example, s a (t) is the latent state corresponding to the position, and v a (t) is the latent state corresponding to the speed of agent a. Therefore, embodiments of the present method are as follows.

[0081] Second-order ordinary differential equations provide significantly better performance than first-order ordinary differential equations in the presence of missing data.

Claims

1. A computer-implemented method for continuous-time interaction modeling of agents, comprising: providing a latent state of a first agent and a latent state of a second agent, in particular, characterizing the position or velocity of these agents (102) (step 202); providing a first Gaussian process distribution for a first function for modeling the kinematic behavior of an agent independently of other agents, and a second Gaussian process distribution for a second function for modeling the interaction between agents (step 204); sampling the first function from the first Gaussian process distribution and the second function from the second Gaussian process distribution (step 206); characterized by the first function is configured to map the latent state of one agent to its contribution to the change in the latent state; the second function is configured to map the latent states of two agents to the contribution of one of the two agents to the change in the latent state; the method further comprises changing the latent state of the first agent according to a first contribution resulting from mapping the latent state of the first agent to the first contribution by the first function and a second contribution resulting from mapping the latent state of the first agent and the latent state of the second agent to the second contribution by the second function (step 208). A method as described above.

2. providing an initial latent state of a plurality of agents including the first agent and the second agent (step 202); changing the latent state of the first agent according to the second contribution resulting from mapping a pair of the latent states of the first agent and a different second agent among the plurality of agents by the second function (208), or selecting a subset of the plurality of agents (208), and changing the latent state of the first agent according to the second contribution resulting from mapping a pair of the latent states of the first agent and a different second agent in the subset by the second function (208); A method according to claim 1, characterized by the above.

3. Determining an agent from the plurality of agents for the subset that is closer to the first agent than other agents of the plurality of agents according to a measure of distance between agents (208) The method according to claim 2, characterized by (the step of claim 0). **Claim 4** Providing a data sequence ( 【Number 1】 ) (200) Characterized by The step of providing the initial latent state of the first agent and / or the second agent (202) includes determining the initial latent state using an encoder configured to map the data sequence to its initial latent state. The method according to any one of claims 1 to 3. **Claim 5** Characterized by a step (210) of determining an output according to the latent state of the first agent, in particular a trajectory sample, preferably the trajectory of the position and / or velocity of the first agent over time The method according to any one of claims 1 to 4. **Claim 6** The first Gaussian process distribution includes a posterior distribution The method For the first Gaussian process distribution with variational parameters, learning a particularly sparse approximation to the posterior distribution (212); Providing the approximation for the first Gaussian process distribution as the first Gaussian process distribution (204); Including And / or The second Gaussian process distribution includes a posterior distribution The method includes learning a particularly sparse approximation to the posterior distribution for the second Gaussian process distribution with variational parameters (212); Providing the approximation for the second Gaussian process distribution as the second Gaussian process distribution (204); Including The method according to claim 5, characterized in that. **Claim 7** Determining the first Gaussian process distribution or the second Gaussian process distribution having an expected likelihood term that depends on the output and is decomposed between agents and between time points (212) Characterized by The method according to claim 5 or 6. **Claim 8** The latent state of the first agent includes a first component and a second component The method changing the latent state of the first component of the latent state of the first agent in response to the second component of the latent state of the first agent and a change to the second component of the latent state of the first agent comprising wherein the second component of the latent state of the first agent changes according to the first contribution degree to the change of the latent state of the first agent and the second contribution degree to the change of the latent state of the first agent A method according to any one of claims 1 to 7, characterized in that

9. determining an action of the first agent according to the output characterized by A method according to any one of claims 1 to 8

10. determining the latent state of the first agent and the latent state of the second agent according to the measured values of a series of observable states of the agent (102) (200, 202) characterized by A method according to any one of claims 1 to 9

11. the first agent is an existing object in the physical world the latent state of the first agent is determined according to the measured values of the characteristics of the first agent (200) and / or the second agent is an existing object in the physical world the latent state of the second agent is determined according to the measured values of the characteristics of the second agent (202) In particular, the measured values include position data, in particular position data from a satellite navigation system, or, in particular, digital images, preferably video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images, preferably position data from information regarding the position or velocity of the agent (102) A method according to claim 10, characterized in that

12. a device (100) for continuous-time interaction modeling of agents, characterized by comprising at least one processor (104) and at least one memory (106) configured to perform the steps of the method according to any one of claims 1 to 11

13. The device (100) according to claim 12, characterized in that it comprises an interface (108) configured to observe the continuous-time interaction of the agent (102), in particular to capture a series of measured values of observable states, in particular digital images, preferably video images, radar images, LiDAR images, ultrasonic images, moving images, and / or thermal images, or to receive information regarding the continuous-time interaction of the agent (102).

14. The device (100) according to claim 13, characterized in that the interface (108) is configured to control at least one action of the agent (102) according to the output according to claim 5 or the action according to claim 9.

15. A computer program comprising computer-readable instructions for causing a computer to perform the method according to any one of claims 1 to 11 when executed by the computer.

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