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

Abstract

Apparatus and computer-implemented method for continuous time interaction modeling of agents, the method comprising: providing (202) a hidden state of a first agent and a hidden state of a second agent, in particular characterizing the position or velocity of these agents; providing (204) a first Gaussian process distribution of a first function for modeling the kinematic behavior of the agent independently of the other agents and a second Gaussian process distribution of a second function for modeling the interaction between the agents; a first function from the first Gaussian process distribution and a second function from the second Gaussian process distribution are sampled (206), where the first function is configured to map a hidden state of one agent to a contribution to a change in the hidden state thereof, wherein the second function is configured to map the hidden state of the two agents to a contribution to a change in the hidden state of one of the two agents, wherein the method comprises changing (208) the hidden state of the first agent depending on a first contribution derived from mapping the hidden state of the first agent to the first contribution using a first function and a second contribution derived from mapping the hidden state of the first agent and the hidden state of the second agent to the second contribution using a second function.

Description

Background Art

[0001] The present invention relates to an apparatus and a computer-implemented method for modeling continuous-time interactions of intelligent agents, in particular of bodies of objects.

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

[0003] The computer-implemented method and device according to the independent claim use a model based on Gaussian processes (GP) and operate in continuous time, and decompose complex continuous dynamics into independent kinematic components and interaction components to account for interpretable nonlinear dynamics. The model handles the independent kinematics of the agents and their interactions separately. Function-level regularization via GP is the key to learning disentangled representations. The model is based on ordinary differential equations (ODEs). This accounts for many complex dynamics that have natural representations in terms of time differences. The continuous-time formulation allows the direct integration of domain knowledge using the inductive bias of the model. Therefore, the kinematics of the objects and their interactions are modeled using two different Gaussian processes, respectively.

[0004] A computer-implemented method for modeling continuous-time interactions of agents comprises: providing a hidden state of a first agent and a hidden state of a second agent, in particular characterizing the positions or velocities of these agents; providing a first Gaussian process distribution of a first function for modeling the kinematic behavior of the agents independently of other agents and a second Gaussian process distribution of a second function for modeling interactions between the agents; sampling a first function from the first Gaussian process distribution and a second function from the second Gaussian process distribution, wherein the first function is configured to map the hidden state of one agent to a contribution to a change in its hidden state, wherein the second function is configured to map the hidden states of two agents to a contribution to a change in the hidden state of one of the two agents, wherein the method comprises changing the hidden state of the first agent depending on a first contribution obtained from mapping the hidden state of the first agent to the first contribution using the first function and a second contribution obtained from mapping the hidden state of the first agent and the hidden state of the second agent to the second contribution using the second function.

[0005] The method preferably includes providing an initial hidden state of a plurality of agents including a first agent and a second agent, and either changing the hidden state of the first agent depending on a second contribution obtained from mapping pairs of hidden states of the first agent and different second agents in the plurality of agents using a second function, or selecting a subset of the plurality of agents and changing the hidden state of the first agent depending on a second contribution obtained from mapping pairs of hidden states of the first agent and different second agents in the subset using a second function. Thus, the method either considers all agents different from the first agent, or considers a neighborhood of agents for interaction. Agents that are not in the neighborhood of an agent are less likely to interact with the agent. This reduces the computational load while maintaining reasonable accuracy of the model.

[0006] The method preferably includes determining an agent from the plurality of agents of the subset that is closer to a first agent than to other agents of the plurality of agents according to a measure of distance between agents. Thus, the method takes into account the neighborhood of agents for interaction. The metric may be a measure of any kind of property of the agents. For the movement of the agents, their distance from each other is a preferred metric.

[0007] The method preferably includes providing a data sequence, wherein providing an initial hidden state of the first agent and / or the second agent includes determining its initial hidden state using an encoder, which is configured to map the data sequence to its initial hidden state.

[0008] The method preferably comprises determining an output, in particular a trajectory sample, preferably a trajectory of the position and / or velocity of the first agent over time, depending on the hidden state of the first agent. The output may relate to any kind of property of the agent. For the movement of the agent, the trajectory sample is a preferred output.

[0009] Preferably, the first Gaussian process distribution comprises a posterior, wherein the method comprises, in particular, learning a sparse approximation to the posterior of the first Gaussian process distribution for which variational parameters are required, and providing the approximation of the first Gaussian process distribution as the first Gaussian process distribution, and / or wherein the second Gaussian process distribution comprises a posterior, wherein the method comprises, in particular, learning a sparse approximation to the posterior of the second Gaussian process distribution for which variational parameters are required, and providing the approximation of the second Gaussian process distribution as the second Gaussian process distribution. In this way, parameters defining the Gaussian process distribution are learned for the unknown function.

[0010] The method preferably includes determining a first Gaussian process distribution or a second Gaussian process distribution having an expected likelihood term that depends on the output and is decomposed between agents and between time points. The likelihood term is an approximation of a portion of an evidence lower bound ELBO that allows determination of parameters defining the Gaussian process distribution.

[0011] The method can be applied to a second-order ordinary differential equation, wherein the hidden state of a first agent includes a first component and a second component, wherein the method includes changing the hidden state of the first component of the hidden state of the first agent depending on the second component of the hidden state of the first agent and a change in the second component of the hidden state of the first agent, wherein the second component changes depending on a first contribution to the change in the hidden state of the first agent and a second contribution to the change in the hidden state of the first agent.

[0012] To control the first agent, the method may include determining an action for the first agent dependent on the output.

[0013] The method preferably includes determining a hidden state of the first agent and a hidden state of the second agent depending on a measurement of a sequence of observable states of the agents.

[0014] The first agent may be an existing object in the physical world, wherein the hidden state of the first agent is determined depending on measurements of properties of the first agent, and / or wherein the second agent may be an existing object in the physical world, wherein the hidden state of the second agent is determined depending on measurements of properties of the second agent, in particular wherein the measurements comprise position data, in particular from a satellite navigation system, or in particular digital images (preferably video images, radar images, lidar images, ultrasound images, motion images and / or thermal images), preferably from information about the position or velocity of the agents. This allows the determination of the hidden state from the measurements, and in particular the corresponding control of the first agent.

[0015] The device for continuous time interaction modeling of intelligent agents comprises at least one processor and at least one memory configured to perform the steps in the method. The device has advantages corresponding to those of the method.

[0016] The device preferably comprises an interface suitable for observing the continuous-time interaction of the intelligent agent, in particular digital images (preferably video images, radar images, lidar images, ultrasound images, motion images and / or thermal images), or for receiving information about the continuous-time interaction of the intelligent agent.

[0017] The interface may be adapted to control an action of at least one agent depending on the output or the action.

[0018] Advantages corresponding to those of the method are provided by a computer program comprising computer readable instructions which, when executed by a computer, cause the computer to perform the method.

[0019] Further advantageous embodiments emerge from the following description and the accompanying drawings. In the drawings:

[0020] Figure 1Schematic depiction of a device for modeling continuous-time interactions of intelligent agents.

[0021] Figure 2 Describes the steps in a method for modeling continuous-time interactions of intelligent agents.

[0022] Figure 1 An apparatus 100 for continuous-time interaction modeling of an agent 102 is depicted. Figure 1 , four agents 102 are depicted. More or less than four agents 102 may be present.

[0023] The device 100 comprises at least one processor 104 and at least one memory 106. The device 100 may comprise an interface 108.

[0024] The at least one processor 104 is adapted to perform the steps of the method described below. The at least one memory 106 is adapted to store instructions, in particular computer programs, which when executed by the at least one processor 104 cause the processor 104 to perform the steps of the method.

[0025] In one example, the interface 108 is adapted to observe or receive information about the continuous temporal interactions of the agents 102. In one example, the interface 108 is adapted to control the actions of at least one agent 102.

[0026] This information is provided, for example, in digital images, such as video images, radar images, lidar images, ultrasound images, motion images and / or thermal images.

[0027] The continuous time interaction of the agents 102 includes, for example, the position or velocity of the agents 102. The position may be a relative position (such as the distance between a pair of agents 102), or an absolute position of the agents 102.

[0028] In this example, system 110 includes agent 102. System 110 may be a physical system. Agent 102 may be a physical system, in particular a technical system. Agent 102 may be a real object existing in the physical world. Agent 102 may include a vehicle, a pedestrian, or other moving object (such as a ball).

[0029] System 110 includes environment 112. Environment 112 may include road infrastructure or building infrastructure. Agent 102 in the example moves in environment 112 and may be affected by environment 112. Agent 102 may include objects of environment 112, such as fixed infrastructure systems that are part of environment 112. System 110 in the example follows certain physical rules. One physical rule is, for example, that the integral of velocity is position.

[0030] Continuous-time interactions are not limited to these physical quantities. Continuous-time interactions can include other physical, technical, or chemical quantities. Continuous-time interactions may also involve global latent variables, for example, agent-specific properties such as mass or radius.

[0031] Figure 2 Depicted are steps in a method for modeling continuous-time interactions of intelligent agents.

[0032] The method depends on the model:

[0033]

[0034] f s (·)~GP(0,k s (·,·))

[0035] f b (·)~GP(0,k b (·,·))

[0036]

[0037] where f s (·) is the first Gaussian process distribution (i.e., Gaussian process), and f b (·) is the second Gaussian process distribution (i.e., Gaussian process), and in the initial hidden state has a standard Gaussian distribution N(0, I) over the data, and assumes that the data likelihood is decomposed across time and agents. The hidden state of agent a at any time t is In this example, it is a D-dimensional vector. The hidden state May or may not be associated with measurements of the physical properties of agent a In the same space.

[0038] In one example,

[0039]

[0040] in is fixed B = [I, 0], where and maps from the interpretable latent space to the observation space, and is the noise variance.

[0041] The model depends on the estimation of two independent additive functions: the kinematic function and interaction functions

[0042] The kinematic function f in the example sLearn how the agent would move over time if no other agents were present, and therefore independent of other agents. The interaction function f in the example b Learn how agents interact with each other.

[0043] The method is described for a plurality of a=1, ..., A agents a.

[0044] In one example, the method comprises determining for each agent a its dynamics depending on a sum consisting of A terms, namely: a term depending on the kinematic function f s independent kinematic terms; and in this example A-1 interaction terms, each of which is represented by an interaction function f b Model the interaction of agent a with one of the remaining A-1 agents a'. The method is not limited to determining the dynamics of each agent a. The method may also include determining the dynamics of a single agent a from a subset of a plurality of a=1,..., A agents or a plurality of a=1,..., A agents. The method is not limited to determining the dynamics of agent a depending on the interaction of agent a with the remaining A-1 agents a'. The method may include determining the dynamics of a single agent a from a subset of a plurality of a=1,..., A agents or a plurality of a=1,..., A agents. a Or the dynamics of agent a is determined by one agent a′ among multiple a=1,...,A agents. In one example, the subset N a is the neighborhood of agent a.

[0045] In this example, the method performs The data set is operated on, where Including at N time points Measurement of A agents.

[0046] The method comprises step 200 .

[0047] In step 200, a data sequence is provided

[0048] According to the exemplary method, the agent 102 of the system 110 is observed for a fixed amount of time. In this example, a plurality of a=1, ..., A agent a represents the agent 102, and the data sequence Indicates that in the time interval [t1, t N ] within a=1,...,A observations of agent a. In one example, the data sequence Included are the position and velocity of agent 102 measured at a particular time.

[0049] Data Series It may be a sequence of observable states of the agent 102. The observable states may be determined depending on measurements. The observable states may in particular be determined from digital images (preferably video images, radar images, lidar images, ultrasound images, motion images and / or thermal images) of the system 110. In this example, these include information about the position and velocity of the agent 102.

[0050] The method includes step 202 .

[0051] In step 202, the initial latent state of at least one agent a at the start time t1 is provided.

[0052] Provide at least one initial hidden state of agent a Can include encoder Determine the initial hidden state of at least one agent a The encoder is configured to convert the data sequence Mapped to the initial hidden state In this example, multiple a=1,..., the initial hidden state of A agent a It is an encoder Sure.

[0053] In the exemplary method, the initial values ​​of agent a required for the integration of the ordinary differential equation are determined. These initial values ​​can generally represent a variety of things. In this example, the initial values ​​correspond to the initial position and velocity of the corresponding agent a. In this example, the initial values ​​represent the initial hidden state of the system 110 at the starting time t1

[0054] The encoder q in this example Θ is a combination of a recurrent neural network and a multi-layer perceptron. Another exemplary encoder would contain a graph neural network layer in order to capture interactions. Encoder q Θ It can also be another neural network architecture. Encoder q Θ is configured to output a distribution, rather than a single value.

[0055] In cases where the model involves global latent variables (e.g., object-specific properties such as mass or radius), another encoder can be used to extract these variables. The two encoders can have the same architecture. Both encoders output distributions instead of single values.

[0056] The method includes step 204 .

[0057] In step 204, the first function f s Provide the first Gaussian process distribution GP(0, k s(·,·)), which is used to model the kinematic behavior of agent a independently from other agents a′.

[0058] In step 204, the second function f b Provides the second Gaussian process distribution GP(0,k b (·,·)), which is used to model the interaction between agents a and a′.

[0059] In one example, the kinematic function f s and the interaction function f b is unknown. In one example, the first Gaussian process distribution GP(0,k s (·,·)) is placed in the kinematic function f s In one example, the second Gaussian process distribution GP(0,k b (·,·)) is placed in the interaction function f b The method is not limited to having zero mean and kernel k s The first Gaussian process distribution GP(0, k s (·,·)). This method is not limited to having zero mean and kernel k b The second Gaussian process distribution GP(0, k b The method can also be used with non-zero means. The first Gaussian process distribution GP(0, k s (·,·)) can be approximated by a sparse Gaussian process, and the second Gaussian process distribution GP(0,k b b(·,·)) can be approximated by a sparse Gaussian process for efficient training and prediction.

[0060] The method includes step 206 .

[0061] In step 206, from the first Gaussian process distribution GP(0, k s (·,·)) in which the first function f is sampled s .

[0062] In step 206, a second Gaussian process distribution GP(0, k b (·,·)) in which the second function f is sampled b .

[0063] The first function f s is configured to transform the hidden state h of an agent a a (τ) is mapped to its hidden state h a Contribution to the change of (T)

[0064] f s (h a (τ)).

[0065] The second function f b is configured to transform the hidden states h of at least two agents a and a′ a (τ), h a′ (τ) is mapped to the hidden state h of one of the at least two agents a and a′ a The contribution of the change in (τ)

[0066] f b (h a (τ), h a′ (τ)).

[0067] Kinematic function f s and the interaction function f b The kinematic function f is defined in continuous time using ordinary differential equations. s and the interaction function f b corresponds to the time derivative.

[0068] The method includes step 208 .

[0069] In step 208, it is determined that at least one agent a is at time point t n The hidden state h a (t n ).

[0070] Determine at least one agent a at time point t n The hidden state h a (t n ) includes the time from the start time t1 to the time point t n The result of the change in the integral

[0071]

[0072] Change the initial hidden state h 1：A (t1). In one example, a change is determined for a plurality of a=1, ..., A agents.

[0073] The hidden state h of an agent a obtained from this change a (t n ) is determined, for example, as

[0074]

[0075] In one example, a hidden state h is determined for multiple a=1,...,A agents. a (t n ).

[0076] In one example, the method includes selecting a subset N of a plurality of a=1, ..., A agents including agent a a, and depends on the subset N a The other agents a′ in the agent a determine the change of the agent a. Therefore, only agents in the neighborhood of the agent a are used. For example, the subset N is selected depending on a measure of the distance between agents. a The agent a′ in .

[0077] In one example, the method includes changing at least one agent a at time point t n The hidden state h a (t n ), which depends on the subset N a At least one agent a′ in the subset N a At least one of the multiple agents a=1,...,A other than A. The hidden state h of an agent a obtained from the change a (t n ) is determined, for example, as

[0078]

[0079] The method includes step 210 .

[0080] In step 210, the method includes determining an output of the model.

[0081] y a (t n )~p(y a (t n )|h a (t n ))

[0082] The output in this example is a sample trajectory y for each agent a a (t n ), which in this example describes how the position and velocity of agent 102 will change over time.

[0083] To infer, the method can end or can be repeated to determine another output, such as for another data sequence

[0084] The output can be used to determine an action for at least one agent 102. The route taken by agent 102 is determined, for example, depending on the locations of other agents in order to avoid collisions. For example, the action is to send an instruction to instruct agent 102 to move to a target location. The instruction can be sent to agent 102 or executed by agent 102 as its action. In one example, the action of agent 102 is determined depending on the output.

[0085] For training, the method may include step 212 .

[0086] Step 212 includes determining a first Gaussian process distribution GP(0, k s (·,·)) and / or the second Gaussian process distribution GP(0,k b (·,·)).

[0087] In one example, during training, the learning process for the first Gaussian process distribution GP(0, k s The first sparse Gaussian process distribution GP(0,k s (·,·)) has multiple variational parameters that are iteratively learned during training, such as the mean and variance of q(U). The posterior is provided, for example, in step 204 as a first Gaussian process distribution GP(0, k s (·,·)).

[0088] In one example, during training, the learning process for the second Gaussian process distribution GP(0, k b The second sparse Gaussian process distribution GP(0, k b (·,·)) has multiple variational parameters that are iteratively learned during training, such as the mean and variance of q(U). The posterior is, for example, in step 204 in the next iteration of training as a second Gaussian process distribution GP(0,k b (·,·))supply.

[0089] Training can be used as an optimization objective to maximize the evidence lower bound ELBO

[0090] log p(Y 1：N )≥E q [log p(Y 1：N |H1, f, U)]-KL[q(H1)||p(H1)]-KL[q(U)||p(U)]

[0091] Among them, H1~q Φ (H1|Y 1：N ) and Φ are the parameters of the neural network encoder that outputs a Gaussian distribution with diagonal covariance, where p(H1)=N(0,I) is a standard Gaussian prior with a suitable dimension for the initial hidden state, where U (l) ~q(U),f (l) (·)~p(f|U), where q(H1) is the approximate posterior of the initial hidden state, where denotes the sample index, where q(U) is the variational posterior at its induced point, and where each output dimension d∈[1,D] has its own independent set of induced values and the kernel output variance In f={f s , f b}, f(l) (·) denotes the function f drawn from the corresponding Gaussian process distribution of the corresponding sample s 、f b In this context, the conditional distribution of f(X) on the input X, conditioned on the induced output U, is a Gaussian process

[0092]

[0093] Where K ZZ is the covariance between all induced points Z, and K XZ is the covariance between the induced point X and the induced point Z. Kernel k b and k s is a function where x d denotes the dth entry of the input x, σ is the corresponding variance, and l d is the length scale parameter in terms of dimension. The use of this function k(x, x′) is optional. Different kernel functions can also be chosen.

[0094] 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.

[0095] Since there is no closed-form expression for this ELBO, the trajectory sample is used for the approximation with the expected likelihood term

[0096]

[0097] The log-likelihood term is decomposed between agents and between time points, thus achieving doubly stochastic variational inference.

[0098] The KL[·] term corresponds to the Kullback-Leibler regularization term. The prior distribution of the induced variable follows a Gaussian process p(U)=p(U s )p(U b ),in and In this example, the Kullback-Leibler regularizer is determined in closed form.

[0099] In one example, the model includes a second-order ordinary differential equation:

[0100] h a (t)≡[s a (t), v a (t)]

[0101]

[0102] This means that the hidden state h of agent aa (t) includes the first component s a (t) and the second component v a (t). The method includes a second component v that depends on the hidden state of the agent a a (t) and the second component v of the hidden state of agent a a (t) Changes To change the hidden state h of agent a a (t). Depends on the contribution f to the hidden state change of agent a s (h a (t)) and the contribution f to the hidden state change of agent a b (h a (t), h a′ (t)) to change the second component v a (t).

[0103] This eases inference because it removes the problem of otherwise unidentifiable states and allows for the hidden state s a (t), v a (t). In this example, s a (t) is the hidden state corresponding to the position, and v a (t) is the hidden state corresponding to the velocity of agent a. The implementation of this method is corresponding.

[0104] When missing data are present, second-order ODEs produce significantly better performance than first-order ODEs.

Claims

1. A computer-implemented method for modeling continuous-time interactions of intelligent agents, characterized in that: Providing (202) a hidden state of a first agent and a hidden state of a second agent, in particular characterizing the positions or velocities of these agents (102); providing (204) a first Gaussian process distribution of a first function for modeling the kinematic behavior of the agents independently of other agents and a second Gaussian process distribution of a second function for modeling the interaction between the agents; sampling (206) 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 hidden state of one agent to a contribution to a change in its hidden state, wherein the second function is configured to map the hidden states of two agents to a contribution to a change in the hidden state of one of the two agents, wherein the method includes changing (208) the hidden state of the first agent depending on a first contribution obtained from mapping the hidden state of the first agent to the first contribution using the first function and a second contribution obtained from mapping the hidden state of the first agent and the hidden state of the second agent to the second contribution using the second function.

2. The method according to claim 1, characterized in that Providing (202) initial hidden states of a plurality of agents including a first agent and a second agent, and either changing (208) the hidden state of the first agent depending on a second contribution obtained from mapping pairs of hidden states of a first agent and a different second agent in the plurality of agents using a second function, or selecting (208) a subset of the plurality of agents, and changing (208) the hidden state of the first agent depending on a second contribution obtained from mapping pairs of hidden states of a first agent and a different second agent in the subset using a second function.

3. The method according to claim 2, characterized in that An agent is determined (208) from the plurality of agents in the subset that is closer to the first agent than other agents in the plurality of agents based on a measure of distance between agents.

4. The method according to one of the preceding claims, characterized in that Provide (200) data sequence Wherein providing (202) the initial hidden state of the first agent and / or the second agent includes determining its initial hidden state using an encoder, wherein the encoder is configured to map the data sequence to its initial hidden state.

5. The method according to one of the preceding claims, characterized in that An output, in particular a trajectory sample, preferably a trajectory of the position and / or velocity of the first agent over time, is determined (210) depending on the hidden state of the first agent.

6. The method according to claim 5, characterized in that The first Gaussian process distribution comprises a posterior, wherein the method comprises, in particular, learning (212) a sparse approximation to the posterior of the first Gaussian process distribution requiring variational parameters, and providing (204) the approximation to the first Gaussian process distribution as the first Gaussian process distribution, and / or is characterized in that The second Gaussian process distribution comprises a posterior, wherein the method comprises, in particular, learning (212) a sparse approximation to the posterior of the second Gaussian process distribution requiring variational parameters, and providing (204) the approximation to the second Gaussian process distribution as the second Gaussian process distribution.

7. The method according to claim 5, characterized in that A first Gaussian process distribution or a second Gaussian process distribution having an expected likelihood term that depends on the output and is decomposed between agents and between time points is determined (212).

8. The method according to one of the preceding claims, characterized in that The hidden state of the first agent includes a first component and a second component, wherein the method includes changing the hidden state of the first component of the hidden state of the first agent depending on the second component of the hidden state of the first agent and a change in the second component of the hidden state of the first agent, wherein the second component of the hidden state of the first agent changes depending on a first contribution to the change of the hidden state of the first agent and a second contribution to the change of the hidden state of the first agent.

9. The method according to one of the preceding claims, characterized in that The action of the first agent is determined depending on the output.

10. The method according to one of the preceding claims, characterized in that A hidden state of a first agent and a hidden state of a second agent are determined (200, 202) depending on measurements of a sequence of observable states of the agent (102).

11. The method according to claim 10, characterized in that The first agent is an existing object in the physical world, wherein the hidden state of the first agent is determined depending on measurements of properties of the first agent (200), and / or is characterized in that the second agent is an existing object in the physical world, wherein the hidden state of the second agent is determined depending on measurements of properties of the second agent (202), in particular, wherein the measurements include position data, in particular position data from a satellite navigation system, or in particular digital images, preferably video images, radar images, lidar images, ultrasound images, motion images and / or thermal images, preferably from information about the position or speed of the agent (102).

12. A device (100) for continuous-time interaction modeling of an intelligent agent, characterized in that: The device (100) comprises at least one processor (104) and at least one memory (106) configured to perform the steps of the method according to one of claims 1 to 11.

13. The device (100) according to claim 12, characterized in that The device (100) comprises an interface (108) adapted to observe the continuous-time interaction of the agent (102), in particular adapted to capture measurements of a sequence of observable states, in particular digital images, preferably video images, radar images, lidar images, ultrasound images, motion images and / or thermal images, or adapted to receive information about the continuous-time interaction of the agent (102).

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

15. A computer program, characterized in that The computer program comprises computer readable instructions which, when executed by a computer, cause the computer to perform the method according to one of claims 1 to 11.

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