A robot social behavior control method based on comprehensive evaluation and optimal control principle

Abstract

The application discloses a robot social behavior control method based on comprehensive evaluation and optimal control principles, and the method comprises the following steps: collecting external multi-modal information, making a comprehensive decision on a social object, modeling a robot eye-head actuator, solving a motion trajectory with minimum nerve conduction noise, and performing optimal control by using an MPC controller to realize parallel interaction between the robot and multiple social objects. The optimal control is performed on the robot to generate human-like motion and gaze effects.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, and particularly relates to a robot social behavior control method based on comprehensive evaluation and optimal control principle. BACKGROUND

[0002] In recent years, service robots have grown into a vibrant field and continue to gain attention. For robots working in human-robot environments, the ability to socially interact with people is essential. To achieve effective human-robot interaction (HRI), multi-object perception driven by social attention is proposed, aiming to make robots explicitly consider human intentions in the decision-making and object selection process. A successful multi-object interaction depends on two aspects: a social attention model that specifies how a person perceives social cues and selects a target from several social objects, and a kinematic model to represent the relevant behavior. Although people are very good at using social behavior in daily life, the difficulty of exhibiting social behavior on robots is often underestimated. Due to the complex nature of social environments and protocols, some of their properties may be difficult or even impossible to formalize in an analytical way. On the other hand, to improve the success rate of HRI collaboration, it would be beneficial to understand the underlying mechanisms by which individuals react to stimuli and produce movements as a response. Artificial systems must be integrated into natural social states by mixing multi-modal, expressing human-like behavior. SUMMARY

[0003] In order to overcome the deficiencies of the prior art, the present application provides a robot social behavior control method based on comprehensive evaluation and optimal control principle, which collects external multi-modal information, makes comprehensive decisions on social objects, models robot eye-head actuators, solves the motion trajectory with the smallest neural conduction noise, uses an MPC controller for optimal control, and realizes parallel interaction between the robot and multiple social objects.

[0004] The purpose of the present application is to solve the selection mechanism and attention control problem of robots in multi-target social scenarios. For social conditions composed of multiple social objects and multi-modal social cues, a quantitative social intention evaluation method can be used to generate the priority of social objects according to the quantitative social intention strength. At the behavior level, the eye-head coordinated gaze is represented in the motor servo model, and the kinematic minimum neural noise constraint method is established through optimal control to implement optimal control on the robot, produce human-like motion and gaze effect, and establish the connection between social object selection and gaze behavior control based on physiological mechanisms in multi-target scenarios.

[0005] To achieve the above purpose, the robot social behavior control method based on comprehensive evaluation and optimal control principle provided by the present application comprises the following steps:

[0006] (1) Collect visual and acoustic multi-modal information of multiple social objects, which includes sound angle, sound size, field position, distance, expression, mouth opening, head deflection angle, hand waving action, etc.

[0007] (2) Further obtain multi-modal information weight through entropy weight calculation, obtain social intention EA of each social object through comprehensive evaluation, and select the social object with the highest EA value, i.e. the highest social intention, as the communication object for the robot to gaze;

[0008] (3) Determine the social object with the highest EA value of the robot gaze under the condition of minimum neural conduction noise, and the motion trajectory of the head and eye;

[0009] (4) Finally, through the model predictive control system based on the Gaussian process online disturbance observer, the motion trajectory of the head and eye of the robot is controlled according to the minimum neural conduction noise, and the behavior of the robot is optimally controlled.

[0010] Step (2) is specifically:

[0011] (201) For a given social scene containing n social objects, collect m social cues corresponding to each social object, construct a decision matrix Q, and organize the social cue information as

[0012]

[0013] Where each column represents the same type of social cue (modal information), each row represents the social cue corresponding to the same social object, subscript j represents different types of social cues, i represents different social objects, and q ij represents the jth social cue of the ith social object,

[0014] For the social cue q ij in the decision matrix Q, if it has a cost attribute, it is converted to a benefit attribute according to formula (2) if it has a benefit attribute, it is not processed, and then a normalized decision matrix e is obtained through linear normalization,

[0015]

[0016] Where, is the maximum value that this type of social cue can achieve, a c is a small amount relative to ,

[0017]

[0018] The entropy weight method is used to assign weights to social cues, and the proportion of the jth social cue of the ith sample value is calculated as

[0019]

[0020] Define the entropy and coefficient of the j-th social cue as follows:

[0021]

[0022] d j =1-η j ,j∈{1,2,...,m} (7)

[0023] The weight w of the j-th social cue j This leads to the weight matrix W = diag(w1, w2, ..., w) which includes the weights of m types of social cues. m )

[0024]

[0025] Using the weight matrix W = diag(w1, w2, ..., w m Left-multiply each normalized vector e i =(e1,e2,...,e m ), thus obtaining the weighted decision matrix E′={e′ ij Through the above calculations, each social cue is assigned a weight based on its dispersion. Then, the TOPSIS algorithm is used based on e′ ij With the ideal point set Social contacts are sorted by distance. and Let each be a set of the maximum and minimum values ​​of the same social cue among n social objects, defined as follows:

[0026]

[0027]

[0028] Among them, J + For the benefit attribute index set, This represents the maximum value of the j-th social cue. Let j represent the minimum value of the j-th social cue, j∈{1,2,...,m}, and let each normalized state vector be a vector representing the minimum value of the j-th social cue. and The distance is defined as and

[0029]

[0030] Each social object and negative ideal point The degree of closeness is

[0031]

[0032] (202)E' is used to calculate the i-th social object e i GC coefficient between the ideal point, with the positive ideal point coefficient is

[0033]

[0034] In the formula, ρ∈[0,1] represents the resolution factor, then the GC coefficient matrix between each target and the positive ideal point E +

[0035] Then, the grey correlation degree of the i-th social object to the positive ideal solution is obtained

[0036]

[0037] Similarly, the following is obtained:

[0038] Z - and

[0039]

[0040] The GC proximity Z i of the i-th social object is calculated by formula (17),

[0041]

[0042] In actual interaction, the potential social object does not necessarily have high and high Z i (203) According to the least square optimization principle, the two evaluation indexes and Z i are fused as follows

[0043]

[0044] The robot will select the social object with the highest EA value, i.e. the highest social intention, as the communication object for gaze.

[0045] Specifically, step (4) finally performs optimal control on the behavior of the robot according to the motion trajectory of the head and eye of the robot under the condition of the minimum neural conduction noise through the model predictive control system based on the Gaussian process online disturbance observer, specifically:

[0046] The state space equation of the robot eye movement and head rotation is

[0047] ​

[0048] Equation (21) is expanded by Taylor series to obtain the error state equation of the discrete-time linear system as

[0049]

[0050] where, represents the state matrix of the discrete system, represents the input matrix of the discrete system, s(k) represents the error at time k, u(k) represents the input at time k, and the subscript d represents the reference value of each variable, i.e., s d (k) represents the reference value of s(k), and u d (k) represents the reference value of u(k).

[0051] When considering the constraint condition, the MPC optimization problem is defined as follows

[0052]

[0053] where, represents the state variable at time i based on time k, Q and R are weighting matrices, N p and N c represent the prediction level and the control level, respectively, represents the state variable at time k+i, represents the input at time k+1, and represent x e and x h at the corresponding discrete time, and γ max represents the distance constraint between the head and the eye of the robot, and represent the reachable range of the actuator, and represent the intensity constraint of the control signal, and equation (30) is solved by using the quadratic programming method to obtain the optimal control sequence U k * ={u(k+1|k),i=0,1,…,N c -1} and the optimal state sequence S k * ={s(k+1|k),i=1,2,…,N p}, the robot is controlled to run according to the optimal control sequence U k * and the optimal state sequence S k * , so as to realize the effect of the human-like gaze behavior of the robot.

[0054] Compared with the prior art, the present application has the following beneficial effects: the present application takes robot control in a multi-target social scene as the research object, proposes a quantitative social intention evaluation method and a gaze behavior control strategy. Through the proposed question, the robot can fuse multi-modal social cues from multiple objects, obtain their social attention values, and finally generate a social priority. For the selected target group, a kinematic model of eye-head coordinated gaze behavior is established, and a control strategy based on the optimal neural noise criterion is proposed. In addition, the control criterion proposed by the present application can be migrated to the participation mechanism of the robot body, and a complete control strategy of the "eye-head-body" coordination model is constructed. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 It is a schematic diagram of a robot social behavior system.

[0056] Figure 2 It is a schematic diagram of the dynamic gaze behavior principle of a robot.

[0057] Figure 3 It is a schematic diagram of a model predictive control (MPC) system based on a Gaussian process (GP) online disturbance observer.

[0058] Figure 4 It is a multi-social object human-computer interaction scene.

[0059] Figure 5 It is a social attention curve in the interaction experiment.

[0060] Figure 6 It is an eye-head coordination curve in the interaction experiment. DETAILED DESCRIPTION

[0061] In order to more clearly illustrate the content of the present application, the present application will be further described below in combination with the drawings and specific examples:

[0062] Example 1

[0063] In order to meet the requirements of efficient decision-making and natural and rapid reaction, the present embodiment adopts a small fat robot as a carrier for social behavior display, and a depth camera and a microphone array are used to collect external information in real time. Visual and acoustic multi-modal information exhibited by multiple social objects within a predetermined spatial range can be collected, which includes sound angle, sound size, field position, distance, expression, mouth opening and closing, head deflection angle, waving action, etc. Then, multi-modal information weights are obtained through entropy weight calculation, social intentions of each social object are obtained through comprehensive evaluation, and finally the behavior of the robot is optimally controlled by a controller.

[0064] 1.1 Overall structure diagram

[0065] The robot social behavior control method proposed in this embodiment is as shown in the figure. Figure 1 The social behavior is defined as the selection of social objects and the occurrence of eye-head coordination gaze behavior. The selection of social objects relies on the data support of multi-modal information outside the robot. In this model, a depth camera is used to perceive image information, and a microphone array is used to perceive sound information. After the social attention calculation of the evaluation module, the social intention of each social object is obtained. In order to keep the neural conduction noise minimum, the invention proposes to use the Pontryagin minimum principle to minimize the noise processing, and obtain a series of eye-head distribution angles (i.e. the robot motion trajectory under the condition of minimum neural conduction noise). When the robot eye-head system focuses on a given interactive object, the MPC controller with disturbance observer is used to control the robot.

[0066] 1.2 Social attention evaluation strategy

[0067] For a robot in a multi-target social scene, it is necessary to establish the relationship between target selection and gaze behavior control. The invention proposes a multi-modal information fusion method combining TOPSIS method and grey correlation analysis method. In order to reproduce this process, the invention mixes multi-modal social cues from multiple social objects and quantifies their social intentions. For this purpose, the entropy weight method (EWM) is mainly used to construct the normalization criterion. Specifically, for a given social scene containing n social objects, m kinds of social cues corresponding to each social object are collected, a decision matrix Q is constructed, and the social cue information is organized as

[0068]

[0069] Where each column represents the same kind of social cue (modal information), each row represents the social cue corresponding to the same social object, subscript j represents different kinds of social cues, i represents different social objects, and q ij represents the jth social cue of the ith social object. For the social cue q ij in the decision matrix Q, if it has a cost attribute (the lower the better), it is converted into a benefit attribute (the higher the better) according to formula (2) if it has a benefit attribute, it is not processed, which can also be understood as q′ ij =q ij .

[0070]

[0071] Where, is the maximum value that this kind of social cue can achieve, and a c is a small amount relative to .

[0072] Then, the normalized decision matrix E can be obtained through linear normalization.

[0073]

[0074] This invention proposes using the entropy weight method to assign weights to social cues. It calculates the proportion of the i-th sample value of the j-th social cue as (i.e., the proportion of the j-th social cue in the i-th social object to the total number of social cues in the n social objects).

[0075]

[0076] Define the entropy and coefficient of the j-th social cue as follows:

[0077]

[0078] d j =1-η j ,j∈{1,2,...,m} (7)

[0079] In this way, we can obtain the weight w of the j-th social cue. j This leads to the weight matrix W = diag(w1, w2, ..., w) which includes the weights of m types of social cues. m )

[0080]

[0081] Using the weight matrix W = diag(w1, w2, ..., w m Left-multiply each normalized vector e i =(e1,e2,...,e m ), thus obtaining the weighted decision matrix E′={e′ ij}. Through the above calculations, each social cue is assigned a weight based on its dispersion. Then, the TOPSIS algorithm is used based on e′ ij With the ideal point set The distance between social objects is used to sort them. and Let each be a set of the maximum and minimum values ​​of the same social cue among n social objects, defined as follows:

[0082]

[0083] Among them, J + For the benefit attribute index set, This represents the maximum value of the j-th social cue. Let represent the minimum value of the j-th social cue, where j∈{1,2,...,m}. Each normalized state vector is then... and The distance between two points is defined as and

[0084]

[0085] Here, the closeness of each social object to the negative ideal point can represent his social intention

[0086]

[0087] Through the above calculation, the general social intention of each social object can be preliminarily evaluated. However, it cannot distinguish potential social objects with the same . To this end, the gray correlation method (GC) is introduced to deal with this problem. The gray correlation degree is a measure of the correlation between elements. E' is used to calculate the GC coefficient between the ith social object e i and the ideal point. Take the calculation of the coefficient with the positive ideal point E as an example

[0088]

[0089] where ρ ∈ [0, 1] represents the resolution factor. Then, the GC coefficient matrix between each target and the positive ideal point E + can be established as follows

[0090]

[0091] Then, the gray correlation degree of the positive ideal solution of the ith social object is obtained

[0092]

[0093] Similarly, we can get: Z - and are defined as follows, respectively:

[0094]

[0095] The GC closeness Z i of the ith social object can be calculated by formula (17), which is equal to the contribution of in the evaluation process.

[0096]

[0097] In actual interaction, potential social objects do not necessarily have high and high Z i at the same time. Therefore, according to the least square optimization principle, the two evaluation indexes are fused as follows

[0098]

[0099] Through the above evaluation, the robot will select the social object with the highest EA value (i.e., the highest social intention) as the communication object for the gaze. Then, the gaze behavior of the robot is controlled.

[0100] 1.3 Robot gaze behavior control strategy

[0101] The robot gaze behavior control strategy in this embodiment is to control the robot to move along the robot motion trajectory under the condition of the minimum neural conduction noise described in the CN114872036A patent (a robot eye-head coordinated gaze behavior control method based on bionic principle).

[0102] 1.3.1 Robot actuator (eye-head) model construction

[0103] The dynamic gaze behavior of the robot is as shown in Figure 2 , which includes eye movement (line of sight (LOS) rotation ω) and head twist (rotation ω ) causing focal line movement. h

[0104] In this invention, the mechanical differential equations of eye movement and head rotation can be constructed as

[0105]

[0106]

[0107] The overall state space equation is written as

[0108]

[0109] where

[0110] 1.3.2 Solve the robot motion trajectory sequence under the condition of the minimum neural conduction noise

[0111] For coordinated gaze behavior, the control signal [u e ,u h ] T may be affected by neural noise. The neural noise increases with the increase of the amplitude of the control signal, resulting in a trade-off between the speed and accuracy of the gaze behavior. To ensure accuracy, the minimum standard error J of neural noise is constructed, and the deviation caused by neural noise is represented as formula (22). In the formula, C1, C2 are the amplitude coefficients between the control signal and the noise, H e ,H h ​​Impulse response function of the eye, head system.

[0112]

[0113] According to the above assumptions, the coordinated gaze behavior model can be reconstructed as Hamilton equation

[0114]

[0115] In solving x e and x h , J can be used as a loss function for processing Hamilton equation.

[0116] By setting and giving the current focal line angle δ, the final state of the line of sight rotation and head twist can be obtained In order to establish the relationship between and δ, the under the given δ is fitted in the form of exponential function as The form provides the basis for the behavior expression of the robot.

[0117] 1.3.3 MPC implementation with disturbance observer and optimal control of robot

[0118] In order to realize accurate and rapid tracking of these trajectories through the eye and head mechanism of the robot, while minimizing the impact of external disturbances on the control signal and internal model disturbance, this embodiment designs a model predictive control (MPC) system based on Gaussian process (GP) online disturbance observer. The control system schematic diagram is shown as Figure 3

[0119] According to the optimal control method based on neural noise minimum standard error, under the condition of given focal line rotation, the line of sight rotation and head twist can be guaranteed to reach the specified position. Considering the influence of external disturbance τ and system disturbance, formula (21) can be reorganized as

[0120]

[0121] Where (A, B) represents the nominal term of state matrix and input matrix, (A P ,B P ) represents the disturbance term of state matrix and input matrix. C T represents the output matrix. represents the lumped external environmental disturbance in the process of neural transmission. In order to realize the control of x e and x h ​To achieve the precise control of the focal line, a control framework consisting of online perturbation learning and model predictive controller is proposed. It realizes the continuous state of the robot focal line to the target, which meets the following requirements: 1) to meet the speed, acceleration saturation and other constraint conditions. 2) to suppress the uncertainty of disturbance in neural signal transmission. In addition to the control signal u, the remaining state variables and external disturbances are defined as the lumped disturbance of the system as follows:

[0122] d(ξ)=τ+Ax,ξ=[x e T x h T ] T (25)

[0123] Assume that the lumped disturbance of each dimension can be considered as a one-dimensional Gaussian process where m j (ξ) is the mean function, and k j (ξ,ξ′) is the kernel function. The kernel function is selected as the RBF kernel. The training data of the GP observer is selected as The output data can be represented as

[0124]

[0125] First, the GP observer is trained, that is, a set of training data z i is input to the GP observer, and a set of data y i is output. After training, the explicit prediction of the future output of the new input z * can be generated by the training data set. The prior distribution d(z * ) and the observation value Y obviously satisfy the joint Gaussian distribution, which meets the properties of GP:

[0126]

[0127] where Z={z i}, m(Z)={m(z i )},K={K ij}=k(z i ,z j ),k * =k(z * ,z * ),K ij denotes the covariance matrix of Y, z i ,z j

[0128] Both denote the traversal of the training set data. Based on the Bayes theorem, the posterior distribution of d(z * ) is determined by using the marginalization theorem and the conditional distribution theorem

[0129]

[0130] where d(z * |Y,Z) represents the prior distribution of d(z * ), in the online GP disturbance prediction module, the application proposes a dynamic control framework composed of a GP observer and a model predictive controller (MPC). T For the MPC controller, define s e T , x h T as the state vector, and u e , u h ) T represent the control output. The disturbance term is represented as Equation (21) uses Taylor series expansion to obtain the error state equation of the discrete-time linear system as

[0131]

[0132] wherein represents the state matrix of the discrete system, represents the input matrix of the discrete system, s(k) represents the error at time k, u(k) represents the input at time k, and the subscript d represents the reference value of each variable, i.e. d (k) represents the reference value of s(k), and u d (k) represents the reference value of u(k).

[0133] When considering the constraint condition, the MPC optimization problem is defined as follows

[0134]

[0135] wherein represents the state variable at the i-th time based on the k-th time. Q and R are weighting matrices. Adjusting Q and R can respectively adjust the utility of the controller to make the error converge faster or achieve energy saving. p N c represent the prediction level and the control level, respectively. represents the state variable at the k+i-th time, represents the input at the k+1-th time. and represent x e and x h at the corresponding discrete time. γ max represents the distance limit between the head and the eye of the robot. and represent the reachable range of the actuator, and denotes the intensity constraint of the control signal. The optimal control sequence U k * = {u(k+1|k), i = 0, 1,..., N c -1} and the optimal state sequence S k * = {s(k+1|k), i = 1, 2,..., N p} can be obtained by solving equation (30) using the quadratic programming method. k * and the optimal state sequence S k * By controlling the robot to run according to the optimal control sequence U ij and the optimal state sequence S 5×3 , the effect of the human-like gaze behavior of the robot can be achieved.

[0136] Embodiment 2

[0137] In this embodiment, the proposed method is tested on a robot platform (a commercial product named Xiaopang). The interactive experiment is carried out in a multi-user scenario, as shown in Figure 4 . The experiment is equipped with an RGB-D camera, a microphone array and a screen displaying animated eye movements. An ultra-wideband (UWB) system is deployed on site to help the robot determine the accurate position of the person. In the experiment, the robot measures five social cues of three people {q ij} 5×3 , including head orientation angle, distance between robot and person, line of sight angle, mouth movement (open or close, 0-1) and emotional state (from sad to happy, 0-4). The three people will express a specific combination of social cues. During the experiment, the robot calculates their social attention (f = ~ 15 Hz) and turns its attention to the person with the highest social attention (EA) value. Before the experiment starts, the three people are far away from the robot.

[0138] In the above interactive experiment, the EA values of the three people are shown in Figure 5 . The intersection of the two high curves represents the change in social attention, thereby triggering the saccadic behavior of the robot. From Figure 5It can be seen that the experiment can be divided into three stages. In the first stage t∈[0, 22.16s], the third social object shows a smiling expression to the robot and slowly walks towards the robot. At this time, the EA of social object 3 is higher than the other two objects, so the robot's attention is generally attracted to social object 3. Subsequently, t∈[22.16s, 38.42s], social object 2 and social object 1 also approach the robot, and social object 2 and social object 3 both turn their heads and do not look at the fat boy, and the interest of the robot decreases. Therefore, the object standing in the center of the robot's field of view and looking directly at him has a higher EA, so the robot's attention is redirected to social object 1. After t = 38.48s, the second person also starts to look at the fat boy and begins to talk to him, showing a stronger social intention. It makes social object 2 get the highest EA, and the robot's attention is attracted again.

[0139] Figure 6 The trajectory of the robot's gaze movement is shown. The green line in the figure represents the target trajectory of the focal line by tracking the social object with the highest EA in real time. In the eye-head coordination, the trajectories of the gaze rotation and the head twist are generated by α e (δ) and α h (δ), respectively. In each control interval, the control framework calculates the angular assignment of the eye-head coordination system once, and then the MPC controller controls the eyeball and the head, respectively. When t∈[0, 22.16s], the focal line of the robot follows social object 3. In this process, since the position change of the object is smooth, that is, the position change between the adjacent two control periods is small, which leads to that almost all responses during this period are exerted by the eye. This is also consistent with the actual situation when people observe slowly moving and less moving objects in the field of view, in which the head does not move, but the eye moves. At t = 22.16s, social object 1 becomes the target, so the robot focal line has a step change. From Figure 6 It can be seen from the left illustration of Fig. 13 that the proposed controller has no distance error overshoot in the tracking process, and also has no oscillation in the stabilization process. This overshoot-free stabilization proves the effectiveness and robustness of the proposed control method.

Claims

1. A method for controlling the social behavior of robots based on the principles of comprehensive evaluation and optimal control, characterized in that, Includes the following steps: (1) Collect visual and acoustic multimodal information from multiple social objects; (2) Then, the multimodal information weight is obtained by entropy weight calculation, and the social intention EA of each social object is obtained by comprehensive evaluation. The robot will select the social object with the highest EA value, that is, the social intention with the highest social intention, as the communication object for gazing. (3) Determine the movement trajectory of the head and eyes of the robot when it gazes at the social object with the highest EA value under the condition of minimum neural conduction noise; (4) Finally, the robot’s behavior is optimally controlled by a model predictive control system based on an online Gaussian process disturbance observer, according to the movement trajectory of the robot’s head and eyes under the condition of minimum neural conduction noise. Step (2) specifically involves: (201) For a given social scenario containing n social objects, collect m social cues corresponding to each social object, construct a decision matrix Q, and organize the social cue information as follows: （1） In this structure, each column represents the same type of social cue, each row represents the social cue corresponding to the same social object, the subscript j indicates different types of social cues, and i indicates different social objects. This represents the j-th social cue of the i-th social object. For social cues in decision matrix Q If it has a cost attribute, it is converted into a benefit attribute according to formula (2). If it has a benefit attribute, it is not processed. Then, the normalized decision matrix is ​​obtained by linear normalization. , （2） in, This represents the maximum value that can be obtained from this type of social clue. For relative to A small amount, （3） （4） The entropy weight method is used to assign weights to social cues, and the proportion of the j-th social cue in the i-th social object to the total number of social cues in the n social objects is calculated as follows: （5） Define the entropy and coefficient of the j-th social cue as follows: （6） （7） The weight of the j-th social cue This leads to a weight matrix that includes the weights of m types of social cues. （8） weight matrix Left-multiply normalized decision matrix , obtain the weight decision matrix Each social cue is assigned a weight based on its dispersion, and then the TOPSIS algorithm is used to... Respectively with the set of positive ideal points Negative ideal point set The distance is used to rank social objects. and Let each be a set of the maximum and minimum values ​​of the same social cues among n social objects, defined as follows: （9） （10） in, For the benefit attribute index set, This represents the maximum value of the j-th social cue. This represents the minimum value of the j-th social cue. Each normalized state vector to and The distance is defined as and , （11） （12） The degree of proximity of each social object to the negative ideal point for （13） (202) This is used to calculate the GC coefficient between the i-th social object and the ideal point set, where the GC coefficient with the positive ideal point set is... for （14） In the formula The resolution factor is represented by the following GC coefficient matrix between each social object and the positive ideal point set: （15-1） Then, the gray-level correlation degree of the positive ideal solution for the i-th social object is obtained. （16-1） Among them, the GC coefficients of the negative ideal point set for Then, the GC coefficient matrix between each social object and the negative ideal point set is as follows: (15-2) Then, the gray-level correlation of the negative ideal solution for the i-th social object is obtained. (16-2) GC proximity of the i-th social object Calculate using equation (17), (17) (203) Based on the least squares optimization principle, and The two evaluation indicators are combined as follows: (18) The robot will select the social object with the highest EA value, that is, the social intention with the highest value, as the object of communication for staring.

2. The robot social behavior control method based on comprehensive evaluation and optimal control principle according to claim 1, characterized in that, Step (4) Finally, the robot's behavior is optimally controlled by a model predictive control system based on an online Gaussian process disturbance observer, according to the motion trajectory of the robot's head and eyes under the condition of minimum neural conduction noise. Specifically: The state-space equations for the robot's eye movements and head rotations are as follows: (21) in , , This represents the state matrix of the eye subsystem. This represents the input matrix of the eye subsystem. This represents the state matrix of the head subsystem. This represents the input matrix of the head subsystem. This represents the state matrix of the overall system consisting of the head subsystem and the eye subsystem. This represents the input matrix of the overall system. This represents the output of the overall system. This indicates the output of the eye subsystem. This indicates the output of the head subsystem. This represents the output matrix of the eye subsystem. The output matrix of the head subsystem is represented by equation (21). Using Taylor series expansion, the error state equation of the discrete-time linear system is obtained as follows: (29) In the formula, Represents the state matrix of a discrete system. Represents the input matrix of the discrete system. , , This represents the error at time k. This represents the input at time k, and the subscript d indicates the reference value of each variable, i.e. express Reference value, express Reference value, When considering constraints, the MPC optimization problem is defined as follows: （30） in, Representative of the first Based on the time, the first The state variables at time t, Q and R are weighted matrices. and These represent the prediction level and the control level, respectively. Representing the The state variable at time t, Representing the Input at any time and Represent and The value at the corresponding discrete time. This indicates the distance limit between the robot's head and eyes. and Indicates the reachability of the implementing agency. and The strength constraint of the control signal is represented by equation (30) and the optimal control sequence is obtained by solving equation (30) using the quadratic programming method. and optimal state sequence By following the optimal control sequence and optimal state sequence Control the robot's operation to achieve the effect of human-like gaze behavior.

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