Moving target prediction method and system based on Gaussian mixture and Bayesian reasoning

Abstract

The invention relates to a moving target prediction method and system based on Gaussian mixture and Bayesian reasoning, and belongs to the technical field of robots. The method comprises three parts of Gaussian mixture prior model, Bayesian online reasoning and prediction step length dynamic adjustment. And estimating a Gaussian component parameter of each target point by using a Gaussian mixture model, and establishing a target-observation probability mapping relation. And calculating the posterior probability of the current data belonging to each target point based on a naive Bayes method, and outputting the target point corresponding to the maximum posterior probability. And a prediction step length dynamic adjustment method based on the motion speed is introduced, and the prediction step length is dynamically adjusted according to the real-time motion speed. And carrying out a motion target prediction experiment in man-machine cooperation. The problem that prediction accuracy is reduced due to moving target change and redundant historical data in contact type man-machine cooperation is solved, the provided prediction method shows good performance in the aspects of target change adaptability, accuracy and real-time performance, and target prediction can be effectively achieved.

Description

Technical Field

[0001] This invention relates to a moving target prediction method and system based on Gaussian mixture and Bayesian inference, belonging to the field of robotics technology. Background Technology

[0002] With the continuous development of embodied intelligence, human-machine collaboration is gradually shifting from a human-led to a robot-led approach. In robot-led proactive human-machine collaboration scenarios, for the robot to truly play a leading role, it must accurately grasp the current motion target. However, in highly customized, small-batch production environments, robots struggle to directly perceive specific collaborative goals. To address this challenge, the prior cognitive advantage of human collaborators regarding task objectives can be fully utilized. By predicting the movement target of the human arm, the robot can indirectly acquire information about the collaborative goal, thereby achieving effective proactive collaboration. Existing research indicates that human motion behavior is predictable, which lays the theoretical foundation for proactive human-machine collaboration with robots as the dominant force.

[0003] Current research primarily focuses on non-contact human-machine collaboration. However, in contact-based human-machine collaboration scenarios, moving targets may dynamically change as the task progresses. This necessitates prediction algorithms capable of capturing these changes in real time and quickly and accurately inferring new moving targets. However, existing prediction methods still have significant limitations in handling target changes: these methods typically rely on all historical motion trajectory data and employ a fixed prediction step size. When the target changes during task execution, redundant historical data that does not match the current new target's movement trend significantly reduces prediction accuracy and also affects the real-time nature of the prediction. Furthermore, if the moving target changes only after the prediction model has completed its prediction, the model will be unable to predict the new target, making it difficult to adapt to the demands of dynamic collaboration.

[0004] Therefore, an effective target prediction model not only needs to accurately identify the current target and improve prediction accuracy and timeliness, but also needs to have the ability to predict new targets after dynamic changes. This continuous dynamic prediction of moving targets is the key to achieving a smooth transition from passive to proactive collaboration. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a moving target prediction method based on Gaussian mixture modeling and Bayesian inference. First, a motion prediction framework is constructed, comprising Gaussian mixture prior modeling, real-time motion data acquisition, and Bayesian online inference. Based on this, a contact-based human-machine collaborative motion experiment was conducted, and motion data during the collaborative process was collected. Based on the collected data, a Gaussian mixture prior model was established. In the Bayesian online inference stage, relying on the trained Gaussian mixture model and combining it with real-time human-machine collaborative motion information, the prediction of moving targets is achieved. To reduce the interference of redundant historical data on the prediction and improve the accuracy and real-time performance of moving target prediction, a dynamic adjustment method for the prediction step size based on motion speed is introduced, dynamically adjusting the prediction step size according to the real-time motion speed.

[0006] The technical solution of the present invention is as follows:

[0007] A moving target prediction method based on Gaussian mixture and Bayesian inference, comprising the following steps:

[0008] Step 1: Obtain human-machine collaboration experiment data;

[0009] Step 2: Use a Gaussian mixture model to perform cluster analysis on the collected dataset, map each target point to a Gaussian component, and establish a probability mapping relationship between "motion observation - potential target" through parameter estimation to complete the prior model training.

[0010] Step 3: Combine the trained Gaussian mixture model with the Naive Bayes method to calculate the posterior probability of the current data belonging to each target online, and output the target corresponding to the maximum posterior probability as the prediction result.

[0011] Step 4: Monitor the prediction results of multiple consecutive frames in real time. When the predicted target is detected to be changing continuously, it is determined that the operator's intention has changed, and the outdated historical data is cleared and the prediction is switched to the new target.

[0012] Step 5: Establish a quantitative relationship model between speed and prediction step size, so that the historical data window length (i.e. prediction step size) h can be adjusted autonomously according to the movement speed, so as to balance prediction accuracy and real-time performance.

[0013] Step 6: Integrate the above-mentioned prior modeling, online reasoning, target change recognition and prediction step size autonomous adjustment into a complete motion target prediction framework, receive real-time motion data streams, and output the current predicted target to support the robot's active collaborative control.

[0014] Step 7: Conduct a human-machine collaborative motion target prediction experiment to verify the target prediction accuracy of the motion target prediction model.

[0015] Preferably, in step 1, the human-machine collaboration experiment refers to designing a standardized experimental scenario that requires human collaborators to collaborate with robots through force sensors to complete a motion task from a designated starting point to a target point. The human collaborator is the leader and the robot is the follower. The core purpose of this experiment is to collect the natural motion characteristics of humans in the contact-type human-machine collaboration process, including but not limited to: end-effector position, speed, acceleration and contact force (measured by force sensors).

[0016] Preferably, in step 2, the dataset is constructed as follows: K=6 motion target points were designed in the human-machine collaborative motion experiment; N data points were collected for each target point. k Sub-human-machine collaborative motion; the length of each motion data is expressed as... The text indicates that the superscript (i) represents the motion index; the dataset includes human-machine collaborative motion locations. ,speed acceleration The interaction force F; the dataset representation of the k-th person-machine cooperative motion target point is as follows:

[0017] (1)

[0018] In the formula, , , and These are the robot's end effector position, velocity, acceleration, and interaction force. , , and Let represent the data from the i-th motion, and each motion contains . One data point;

[0019] The expression for the Gaussian mixture model is:

[0020] (2)

[0021] This represents the observation data of human-machine collaborative motion at time t; It is the mixing coefficient. ,and ; For the k-th sub-model, Let be the mean vector of the k-th sub-model. Let be the covariance matrix of the k-th sub-model. It is a multivariate Gaussian distribution. , , These are the parameters to be estimated for the Gaussian mixture model;

[0022] The establishment of the probabilistic mapping relationship between "motion observation and potential target" through parameter estimation is specifically carried out as follows:

[0023] Since the endpoint (i.e., the target point) of each collaborative movement is preset and known during the data acquisition phase, the target category k to which the observed data sample (human-machine collaborative movement data) belongs at each moment is clear; based on this, the parameters of the k-th component (corresponding to the k-th target point) of the Gaussian mixture model are... , and It can be directly calculated from all sample data belonging to the target point, as follows:

[0024] (3)

[0025] This represents the data at time j during the i-th demonstration of the motion of the k-th target point;

[0026] Dataset By substituting all the observation data into equation (3), the parameters of the k-th component of the Gaussian mixture model (i.e., the k-th target point) can be estimated.

[0027] Preferably, in step 3, the Naive Bayes model is:

[0028] (4)

[0029] Given partial historical data, the probability that the currently observed data belongs to the k-th sub-model (target point) is given. This represents the historical observation data of human-machine collaborative motion from time th to time t-1; The probability that the motion observation data at time t belongs to the k-th target is represented by the output of the Gaussian mixture model. ; This represents the probability that historical data will appear when the motion observation data at time t belongs to the k-th target. The probability of historical data appearing from time th to time t-1;

[0030] because , ,therefore

[0031] (5)

[0032] Given the current data Given that it belongs to the k-th Gaussian component, the historical data sequence The joint probability is equal to the product of the probabilities of each historical observation belonging to that component at each time step;

[0033] From the law of total probability, we get:

[0034] (6)

[0035] Substituting equations (5) and (6) into equation (4), we get:

[0036] (7)

[0037] and All calculations are performed using the trained Gaussian mixture model. Substituting these values ​​into equation (7) yields:

[0038] (8)

[0039] Using equation (8), we can obtain the probability that the observed motion data at the current time t belongs to target K, given the known human-machine collaborative motion data at the previous h time points.

[0040] Therefore, the probability that the current portion of historical data belongs to the k-th target is:

[0041] (9)

[0042] In the formula, Let be the probability that the historical data from time (th) to time t belongs to the k-th target, where K is the total number of targets;

[0043] (10)

[0044] The value of k that makes equation (9) reach its maximum value can be obtained through equation (10), which is the target point that the human collaborator intends to reach in human-machine collaborative motion.

[0045] Preferably, in step 4, to distinguish whether the change in the predicted target is due to short-term interference such as operation jitter and sensor noise, or a change in the true intention, a sliding time window is set to analyze the change pattern of the predicted target in real time within the time window; when the proportion of the new target with the highest frequency of occurrence within the time window (target proportion) is greater than a preset threshold (70%), it indicates that the target has changed.

[0046] Triggering the clearing of outdated historical data involves clearing outdated data from the historical data buffer; this allows the predictive model to break free from the historical "inertia" of old targets and quickly adapt to new trends.

[0047] For further optimization, the preset threshold is 70%.

[0048] Preferably, in step 5, in order to establish a quantitative relationship between motion speed and predicted step length, at least two velocity nodes are selected; more preferably, eight velocity nodes are selected at intervals of 0.02 m / s; the following operations are performed for each velocity node:

[0049] 1) Data filtering: Filter data segments from the experimental data, including 180 frames before and after the velocity node;

[0050] 2) Data extraction: Starting from a prediction step size h=20 frames, the data is gradually extracted in increments of 10 frames up to 180 frames.

[0051] 3) Prediction and Evaluation: Input the extracted historical data into the prediction model (Formula 10), output the prediction results, and calculate the prediction accuracy; Prediction accuracy = (number of correctly predicted samples) / (total number of samples) * 100%;

[0052] 4) Determining the optimal prediction step size: Record the minimum prediction step size for each velocity node with a prediction accuracy greater than 80%;

[0053] To enable the historical data window length h (prediction step size) to adjust autonomously based on the movement speed, a scatter plot of movement speed and prediction step size is obtained using the above method. The relationship between movement speed and prediction step size is then obtained by fitting the plot using a nonlinear least squares method:

[0054] (11)

[0055] In the formula, v represents the speed of human-machine collaborative motion. To predict the step size.

[0056] The coefficient of determination for the fitting function is R² = 0.9941, and RSME = 4.5986, indicating a good fit. This fitting function can represent the relationship between motion speed and predicted step length.

[0057] Preferably, in step 6, the target prediction system framework includes three modules: Gaussian mixture prior model, Bayesian online inference, and real-time data acquisition.

[0058] The Gaussian mixture prior model mainly estimates the parameters of the Gaussian mixture model, thereby establishing the probability mapping relationship between "target-observation" and providing a prior model for subsequent online target prediction.

[0059] The Bayesian online inference primarily relies on partial historical motion data (predicted step length) and uses the Naive Bayes method to infer the target point that the human collaborator intends to reach. This module sets up a sliding window of historical data with a length of h frames and continuously monitors the human-machine collaborative motion data falling within this window, including position, velocity, acceleration, and interaction force. The likelihood of each candidate target is calculated using a trained Gaussian mixture model. Then, the likelihood of historical frame data is fused using Naive Bayes rules to determine which target the current frame data best matches and stores the data. If the maximum posterior target of several consecutive frames changes, and the proportion of the new target (target percentage) is greater than a preset threshold (70%), it is determined that the human operator has changed their intention. The length of historical data h (i.e., the predicted step length) is dynamically adjusted according to the real-time motion speed of the collaborative movement.

[0060] The real-time data acquisition module primarily addresses real-time interaction needs, responsible for synchronously acquiring and outputting human-robot collaborative motion data; force sensors capture the interactive forces applied by the operator in real time; based on the admittance control principle, the robot converts the real-time detected interactive force signals into smooth and natural compliant motion; simultaneously, the robot outputs its end-effector position in real time. ,speed acceleration The interaction force F data provides real-time motion data as input for online prediction;

[0061] The admittance control is used to drive the robot to conform to the movements of the human dominator, and the admittance control model adopted is as follows:

[0062] (12)

[0063] M∈R 6×6 C∈R 6×6 and K∈R 6×6 These are the virtual mass matrix, virtual damping matrix, and virtual stiffness matrix, respectively. f is the interaction force vector in Cartesian space. x f y f z These represent the values ​​of the interaction forces along the x, y, and z axes, respectively. These represent the axial torque values ​​for x, y, and z respectively; X d =[x d ,y d ,z d ,r xd ,r yd ,r zd ] T Let x be the desired pose vector. d ,y d ,z d These represent the desired positions along the x, y, and z axes, respectively, and r xd ,ryd ,r zd These are the desired attitude angles along the x, y, and z axes, respectively; X r =[x r ,y r ,z r ,r xr ,r yr ,r zr ] T x is the actual pose vector. r ,y r ,z r These are the actual positions of the x, y, and z axes, respectively, and r xr ,r yr ,r zr These are the actual attitude angles along the x, y, and z axes, respectively. For the desired speed, This refers to the actual speed; For the desired acceleration, This is the actual acceleration.

[0064] Preferably, in step 7, a motion target prediction model based on Gaussian mixture and Bayesian inference is used to predict the motion target of the human arm; the performance of the prediction model is evaluated using target prediction accuracy and target change adaptability as core indicators; the overall prediction accuracy of the model is quantified by calculating the proportion of correct predictions to total predictions; target change adaptability includes target change recognition rate (the proportion of experiments in which the model successfully detects a change in the target) and adaptation time (the difference in the number of frames required from the occurrence of a target change to the model's stable output of a new target again). The two indicators comprehensively evaluate the prediction model's response and recovery ability to dynamic intention changes.

[0065] A computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the steps in the moving target prediction method based on Gaussian mixture model and Naive Bayes inference as described above.

[0066] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the moving target prediction method based on Gaussian mixture model and Naive Bayes inference as described above.

[0067] This invention is mainly aimed at target prediction scenarios with "target mutation" in human-machine collaboration. It dynamically adjusts the historical data required for prediction through a speed-based variable prediction step size mechanism, reduces the impact of redundant historical data on prediction, and thus achieves rapid re-prediction after the target changes. It has the ability to adjust the prediction step size online according to speed changes.

[0068] The beneficial effects of this invention are as follows:

[0069] 1. A dynamic adjustment mechanism for the prediction step size based on real-time motion velocity is proposed. This mechanism can autonomously optimize the length of historical data (prediction step size) according to the motion state, effectively overcoming the contradiction in fixed prediction step size methods where "insufficient features occur when the prediction step size is too short, and redundant lag occurs when the prediction step size is too long." This method can significantly reduce the interference of redundant historical data on prediction, and greatly improve the real-time response capability of the system while ensuring high prediction accuracy.

[0070] 2. By combining Gaussian mixture prior models with Bayesian online inference, a framework was developed to infer motion intentions in real time from multimodal time-series data, providing key technical support for the transformation of human-machine collaboration from passive response to active coordination. Attached Figure Description

[0071] Figure 1 A schematic diagram of an experimental scenario in a human-machine collaboration context.

[0072] Figure 2 A schematic diagram showing the locations of the starting point and the target point in a human-machine collaboration scenario.

[0073] Figure 3 A scatter plot of motion speed and predicted step length.

[0074] Figure 4 This is a schematic diagram of the framework for a moving target prediction method based on Gaussian mixture-naive Bayes. Detailed Implementation

[0075] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0076] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0077] Example 1

[0078] A method for predicting moving targets based on Gaussian mixture and Bayesian inference is proposed. This invention combines a Gaussian mixture prior model and Bayesian inference to establish a method for predicting moving targets of a human arm, which is used for predicting the moving targets of a human arm in contact-based human-robot collaboration. The method includes the following steps:

[0079] Step 1: Obtain human-machine collaboration experiment data;

[0080] Human-robot collaborative experiments refer to the design of a standardized experimental scenario where a human collaborator works with a robot via force sensors to complete a movement task from a designated starting point to a target point. The human collaborator is the leader, and the robot is the follower. The experimental scenario and the setting of the starting and target points are as follows: Figure 1 , 2 As shown. The human-machine collaborative motion experiment designed two types of human-machine collaborative motion: motion with a fixed target and motion with a changing target. Motion with a fixed target requires the operator to move directly from a designated starting point to a designated target location, such as... Figure 2 The solid black line from S5 to T6 indicates this. The movement of the target simulates a scenario in actual operation where the target's position needs to be changed midway. For example... Figure 2 The initial planned path is represented by the red dashed line S1-T2. However, the actual path is represented by the red solid line S1-M-T1, meaning that the moving target changed at point M.

[0081] The core objective of this experiment is to collect the natural motion characteristics of humans during contact-based human-machine collaboration, including but not limited to: end-effector position, velocity, acceleration, and contact force magnitude (measured by force sensors).

[0082] Step 2: Use a Gaussian mixture model to perform cluster analysis on the collected dataset, map each target point to a Gaussian component, and establish a probability mapping relationship between "motion observation - potential target" through parameter estimation to complete the prior model training.

[0083] The dataset was constructed as follows: K=6 motion target points were designed in the human-machine collaborative motion experiment. Data was collected for each target point. This is a human-machine collaborative motion. The length of each motion data is expressed in terms of... The data is represented by the superscript (i), which indicates the motion index. The dataset consists of human-machine collaborative motion locations. ,speed acceleration It consists of the interaction force F. The dataset of the k-th person-machine cooperative motion target point is represented as follows:

[0084] (1)

[0085] In the formula, , , and These are the robot's end effector position, velocity, acceleration, and interaction force. , , and Let represent the data from the i-th motion, and each motion contains . Data points.

[0086] The Gaussian mixture model expression is:

[0087] (2)

[0088] This represents the observation data of human-machine collaborative motion at time t; It is the mixing coefficient. ,and ; For the k-th sub-model, Let be the mean vector of the k-th sub-model. Let be the covariance matrix of the k-th sub-model. It is a multivariate Gaussian distribution. , , These are the parameters to be estimated for the Gaussian mixture model.

[0089] Since the category to which each sample belongs is known, , and The calculation process is as follows:

[0090] (3)

[0091] This represents the data at time j of the i-th demonstration motion of the k-th target point.

[0092] Dataset By substituting all the observation data into equation (3), the parameters of the k-th component of the Gaussian mixture model (i.e., the k-th target point) can be estimated.

[0093] Step 3: Combine the trained Gaussian mixture model with the Naive Bayes method to calculate the posterior probability of the current data belonging to each target online, and output the target corresponding to the maximum posterior probability as the prediction result.

[0094] To improve prediction accuracy and the ability to predict new targets after changes in the moving target, partial historical observation data of human-machine collaborative motion is used in online target point prediction. This reduces the impact of redundant historical data on motion prediction. Before predicting the moving target, it is necessary to calculate the probability that the observed data at each moment belongs to each target given the historical data. That is, to solve for the probability that the current observed data belongs to the k-th sub-model (target point) given partial historical observation data. To this end, the Naive Bayes method is used, combined with the prior probability obtained from the Gaussian mixture model, to calculate the posterior probability that the current observed data belongs to each target. Naive Bayes is a method for calculating posterior probabilities given prior probabilities and conditions. The Naive Bayes model is as follows:

[0095] (4)

[0096] Given partial historical data, the probability that the currently observed data belongs to the k-th sub-model (target point) is given. This represents the historical observation data of human-machine collaborative motion from time th to time t-1; The probability that the motion observation data at time t belongs to the k-th target is represented by the output of the Gaussian mixture model. ; This represents the probability that historical data will appear when the motion observation data at time t belongs to the k-th target. Let t be the probability of historical data appearing from time t to time t-1.

[0097] because , ,therefore

[0098] (5)

[0099] Given the current data Given that it belongs to the k-th Gaussian component, the historical data sequence The joint probability is equal to the product of the probabilities of each historical observation belonging to that component at each time step;

[0100] From the law of total probability, we get:

[0101] (6)

[0102] Substituting equations (5) and (6) into equation (4), we get:

[0103] (7)

[0104] and All calculations are performed using the trained Gaussian mixture model. Substituting these values ​​into equation (7) yields:

[0105] (8)

[0106] Using equation (8), we can obtain the probability that the observed motion data at the current time t belongs to target K, given the known human-machine collaborative motion data at the previous h time.

[0107] Therefore, the probability that the current portion of historical data belongs to the k-th target is:

[0108] (9)

[0109] In the formula, Let be the probability that the historical data from time (th) to time t belongs to the k-th target, where K is the total number of targets.

[0110] (10)

[0111] The value of k that makes equation (9) reach its maximum value can be obtained through equation (10), which is the target point that the human collaborator intends to reach in human-machine collaborative motion.

[0112] Step 4: Monitor the prediction results of multiple consecutive frames in real time. When the predicted target is detected to be changing continuously, it is determined that the operator's intention has changed, and the outdated historical data is cleared and the prediction is switched to the new target.

[0113] To distinguish whether changes in the predicted target stem from short-term interference such as operational jitter and sensor noise, or from a change in the true intent, a sliding time window is set up to analyze changes in the predicted target in real time within the time window. When the proportion of the most frequently occurring new target within the time window (target percentage) exceeds a preset threshold (70%), it indicates that the target has changed. Simultaneously, outdated data in the historical data buffer is cleared. This allows the prediction model to break free from the historical "inertia" of old targets and quickly adapt to new movement trends.

[0114] Step 5: Establish a quantitative relationship model between speed and prediction step length, so that the historical data window length h can be adjusted autonomously according to the movement speed, in order to balance prediction accuracy and real-time performance.

[0115] To establish a quantitative relationship between motion velocity and predicted step size, eight velocity nodes were selected: 0.02 m / s, 0.04 m / s, 0.06 m / s, 0.08 m / s, 0.10 m / s, 0.12 m / s, 0.14 m / s, and 0.16 m / s. The following operations were performed for each velocity node:

[0116] 1. Data filtering. Data segments of 180 frames before and after the velocity node were filtered from the experimental data.

[0117] 2. Data extraction. Starting from a prediction step size h=20 frames, the data is extracted sequentially in increments of 10 frames up to 180 frames.

[0118] 3. Prediction and Evaluation. Input the extracted historical data into the prediction model (Formula 10) to output the prediction results and calculate the prediction accuracy; Prediction accuracy = (number of correctly predicted samples) / (total number of samples) * 100%.

[0119] 4. Determine the optimal prediction step size. Record the minimum prediction step size at which the prediction accuracy of each velocity node is greater than 80%.

[0120] The scatter plot of motion velocity and predicted step length obtained by the above method is as follows: Figure 3 As shown. The relationship between motion velocity and predicted step size obtained by fitting using the nonlinear least squares method is as follows:

[0121] (11)

[0122] In the formula, v represents the speed of human-machine collaborative motion. To predict the step size.

[0123] The coefficient of determination for the fitting function is R² = 0.9941, and RSME = 4.5986, indicating a good fit. This fitting function can represent the relationship between motion speed and predicted step length.

[0124] Step 6: Integrate the above-mentioned prior modeling, online reasoning, target change recognition and prediction step size autonomous adjustment into a complete motion target prediction framework, receive real-time motion data streams, and output the current predicted target to support the robot's active collaborative control.

[0125] The moving target prediction method based on Gaussian mixture-Naive Bayes mainly consists of three modules: a Gaussian mixture prior model, Bayesian online inference, and real-time data acquisition. Figure 4 As shown, the Gaussian mixture prior model is mainly used for estimating the parameters of the Gaussian mixture model. First, a collaborative motion experiment is designed for a human-machine collaborative task to collect multi-dimensional time series data on human-machine collaborative motion position, velocity, acceleration, and interaction force, constructing a collaborative motion dataset. Then, the Gaussian mixture model is used to perform cluster analysis on this dataset, mapping each potential target point to an independent Gaussian component. The mean vector, covariance matrix, and mixing weights of the Gaussian mixture model are estimated. This establishes a probabilistic mapping relationship between "target-observation," providing a prior model for subsequent online target prediction.

[0126] The Bayesian online inference primarily relies on historical motion data, using the Naive Bayes method to infer the target point that the human collaborator intends to reach. This module continuously monitors the human-machine motion data (position, velocity, acceleration, and interaction force) for the most recent h timeframes (frames). A trained Gaussian mixture model is used to calculate the likelihood for each candidate target. Then, the likelihoods of historical frame data are fused using Naive Bayes rules to determine which target best matches the current frame data and store this data. If the maximum a posteriori target changes across several consecutive frames, it is determined that the human operator has changed their intention. The length h of the historical data (i.e., the prediction step size) is dynamically adjusted based on the real-time motion speed of the collaborative movement: at higher speeds, the displacement characteristics per unit time are more pronounced, and h can be appropriately shortened to capture rapidly changing intention signals, thereby improving the real-time nature of the prediction and the sensitivity to rapid motion changes; at lower speeds, h can be appropriately lengthened to improve the accuracy of motion prediction.

[0127] The real-time data acquisition module primarily addresses real-time interaction needs, responsible for synchronously acquiring and outputting human-robot collaborative motion data. Force sensors capture the interactive forces applied by the operator in real time. Based on the admittance control principle, the robot converts the real-time detected interactive force signals into smooth and natural compliant motion. Simultaneously, the robot outputs its end-effector position in real time. ,speed acceleration The interaction force F data provides real-time motion data as input for online prediction.

[0128] The admittance control model adopted is as follows:

[0129] (12)

[0130] M∈R 6×6 C∈R 6×6 and K∈R 6×6 These are the virtual mass matrix, virtual damping matrix, and virtual stiffness matrix, respectively. f is the interaction force vector in Cartesian space. x f y f z These represent the values ​​of the interaction forces along the x, y, and z axes, respectively. These represent the axial torque values ​​for x, y, and z respectively; X d =[x d ,y d ,z d ,r xd ,r yd ,r zd ] T Let x be the desired pose vector. d ,y d ,z d These represent the desired positions along the x, y, and z axes, respectively, and r xd,r yd ,r zd These are the desired attitude angles along the x, y, and z axes, respectively; X r =[x r ,y r ,z r ,r xr ,r yr ,r zr ] T x is the actual pose vector. r ,y r ,z r These are the actual positions of the x, y, and z axes, respectively, and r xr ,r yr ,r zr These are the actual attitude angles along the x, y, and z axes, respectively. For the desired speed, This refers to the actual speed; For the desired acceleration, This is the actual acceleration.

[0131] To facilitate application in robot control, the admittance control model can be transformed into a discrete form to solve for the desired robot trajectory:

[0132] (13)

[0133] (14)

[0134] (15)

[0135] In the formula, X d (t), and Let X be the desired position, desired velocity, and desired acceleration at time t, respectively; r (t), and Let be the actual position, actual velocity, and actual acceleration at time t, respectively; for the sake of formula simplicity, let . , T is the sampling period.

[0136] Step 7: Conduct a human-machine collaborative motion target prediction experiment to verify the target prediction accuracy of the motion target prediction model.

[0137] Motion prediction accuracy and target change adaptability are used as performance evaluation metrics for the prediction model. These represent the prediction accuracy and response performance to target changes, respectively. Target change adaptability refers to the prediction model's ability to recognize target changes and quickly and stably predict new targets. In short, target change adaptability is the prediction model's ability to quickly adjust and recover accurate predictions when faced with target changes. Target change adaptability can be measured by the motion target change recognition rate and the time required for the prediction model to stably and accurately predict new targets again after a target change. To verify the target change adaptability of the prediction model, experiments were designed involving target changes in human-machine collaborative motion, such as... Figure 1 As shown, the statistical prediction model demonstrates its accuracy in predicting the new objective and its adaptability to objective changes.

[0138] Example 2

[0139] A computer-readable storage medium having a program stored thereon that, when executed by a processor, implements the steps in the moving target prediction method based on Gaussian mixture and Bayesian inference as described in Example 1.

[0140] Example 3

[0141] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the moving target prediction method based on Gaussian mixture and Bayesian inference as described in Example 1.

Claims

1. A moving target prediction method based on Gaussian mixture and Bayesian inference, characterized in that, The steps are as follows: Step 1: Obtain human-machine collaboration experiment data; Step 2: Use a Gaussian mixture model to perform cluster analysis on the collected dataset, map each target point to a Gaussian component, and establish a probability mapping relationship between "moving observation and potential target" through parameter estimation to complete the prior model training. Step 3: Combine the trained Gaussian mixture model with the Naive Bayes method to calculate the posterior probability of the current data belonging to each target online, and output the target corresponding to the maximum posterior probability as the prediction result. Step 4: Monitor the prediction results of multiple consecutive frames in real time. When the predicted target is detected to be continuously changing, it is determined that the operator's intention has changed, and the outdated historical data is cleared and the prediction is switched to the new target. Step 5: Establish a quantitative relationship model between speed and predicted step length, so that the historical data window length h can be adjusted autonomously according to the movement speed; Step 6: Integrate the above-mentioned prior modeling, online reasoning, target change recognition and prediction step size autonomous adjustment into a complete motion target prediction framework, receive real-time motion data streams, and output the current predicted target to support the robot's active collaborative control. Step 7: Conduct a human-machine collaborative motion target prediction experiment to verify the target prediction accuracy of the motion target prediction model.

2. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 1, the human-robot collaborative experiment refers to a standardized experimental scenario that requires human collaborators to work with robots through force sensors to complete a motion task from a designated starting point to a target point. The human collaborator is the leader and the robot is the follower. Collect natural motion characteristics of humans in contact-based human-machine collaboration processes, including: end-effector position, velocity, acceleration, and contact force magnitude.

3. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 2, the dataset was constructed as follows: K=6 motion target points were designed for the human-machine collaborative motion experiment; data were collected for each target point. Sub-human-machine collaborative motion; the length of each motion data is expressed as... The text indicates that the superscript (i) represents the motion index; the dataset includes human-machine collaborative motion locations. ,speed acceleration The interaction force F; the dataset representation of the k-th person-machine cooperative motion target point is as follows: （1） In the formula, , , and These are the robot's end effector position, velocity, acceleration, and interaction force. , , and Let represent the data from the i-th motion, and each motion contains . One data point; The Gaussian mixture model expression is: （2） This represents the observation data of human-machine collaborative motion at time t; It is the mixing coefficient. ,and ; For the k-th sub-model, Let be the mean vector of the k-th sub-model. Let be the covariance matrix of the k-th sub-model. It is a multivariate Gaussian distribution. , , These are the parameters to be estimated for the Gaussian mixture model; The probabilistic mapping relationship between "moving observations and potential targets" is established through parameter estimation. The specific operation is as follows: , and The calculation process is as follows: （3） This represents the data at time j during the i-th demonstration of the motion of the k-th target point; Dataset Substituting all the observation data into equation (3), we can calculate the parameters of the k-th component of the Gaussian mixture model, which corresponds to the k-th target point.

4. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 3, the Naive Bayes model is: （4） Given historical data, the probability that the currently observed data belongs to the k-th target point, where, This represents the historical observation data of human-machine collaborative motion from time th to time t-1; The probability that the motion observation data at time t belongs to the k-th target is represented by the output of the Gaussian mixture model. ; This represents the probability that historical data will appear when the motion observation data at time t belongs to the k-th target. The probability of historical data appearing from time th to time t-1; because , ,therefore （5） From the law of total probability, we get: （6） Substituting equations (5) and (6) into equation (4), we get: （7） and All calculations are performed using the trained Gaussian mixture model. Substituting these values ​​into equation (7) yields: （8） Using equation (8), we can obtain the probability that the observed motion data at the current time t belongs to target K, given the known human-machine collaborative motion data at the previous h time points. Therefore, the probability that the current historical data belongs to the k-th target is: （9） In the formula, Let be the probability that the historical data from time (th) to time t belongs to the k-th target, where K is the total number of targets; （10） The value of k that makes equation (9) reach its maximum value is obtained through equation (10), which is the target point that the human collaborator intends to reach in human-machine collaborative motion.

5. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 4, a sliding time window is set to analyze the changing patterns of the predicted target in real time within the time window; when the proportion of the most frequently occurring new target within the time window exceeds a preset threshold, it indicates that the target has changed; preferably, the preset threshold is 70%; Triggering the clearing of outdated historical data involves clearing outdated data from the historical data buffer.

6. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 5, to establish a quantitative relationship between motion velocity and predicted step length, at least two velocity nodes are selected, and more preferably, eight velocity nodes are selected at intervals of 0.02 m / s; the following operations are performed for each velocity node: 1) Data filtering: Filter data segments from the experimental data, including 180 frames before and after the velocity node; 2) Data extraction: Starting from a prediction step size h=20 frames, the data is gradually extracted in increments of 10 frames up to 180 frames. 3) Prediction and Evaluation: Input the extracted historical data into the prediction model, output the prediction results, and calculate the prediction accuracy; Prediction accuracy = (number of correctly predicted samples) / (total number of samples) * 100%; 4) Determining the optimal prediction step size: Record the minimum prediction step size for each velocity node with a prediction accuracy greater than 80%; The scatter plot of motion speed and predicted step size obtained using the above method is then fitted using the nonlinear least squares method to obtain the relationship between motion speed and predicted step size as follows: (11) In the formula, v represents the speed of human-machine collaborative motion. To predict the step size.

7. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 6, the target prediction system framework includes three modules: Gaussian mixture prior model, Bayesian online inference, and real-time data acquisition. The Gaussian mixture prior model is used to estimate the parameters of the Gaussian mixture model; the probability mapping relationship between the target and the observation is established to provide a prior model for subsequent online target prediction. The Bayesian online inference module uses Naive Bayes to infer the target point that the human collaborator intends to reach, based on partial historical motion data. This module sets up a sliding window of historical data with a length of h frames and continuously monitors the human-machine collaborative motion data falling within this window, including position, velocity, acceleration, and interaction force. A trained Gaussian mixture model is used to calculate the likelihood for each candidate target. Then, Naive Bayes rules are used to fuse the likelihoods of the historical frame data to determine which target best matches the current frame data and store this data. If the maximum posterior target changes in several consecutive frames, and the proportion of the new target exceeds a preset threshold, it is determined that the human operator has changed their intention. The length h of the historical data is dynamically adjusted according to the real-time motion speed of the collaborative movement. The real-time data acquisition module is designed for real-time interaction, responsible for synchronously acquiring and outputting human-robot collaborative motion data; the force sensor captures the interactive forces applied by the operator in real time; based on the admittance control principle, the robot converts the real-time detected interactive force signals into smooth and natural compliant motion; simultaneously, the robot outputs the end-effector position in real time. ,speed acceleration The interaction force F data provides real-time motion data as input for online prediction; The admittance control is used to drive the robot to conform to the movements of the human dominator, and the admittance control model adopted is as follows: （12） M∈R 6×6 C∈R 6×6 and K∈R 6×6 These are the virtual mass matrix, virtual damping matrix, and virtual stiffness matrix, respectively. f is the interaction force vector in Cartesian space. x f y f z These represent the values ​​of the interaction forces along the x, y, and z axes, respectively. These represent the axial torque values ​​for x, y, and z respectively; X d =[x d ,y d ,z d ,r xd ,r yd ,r zd ] T Let x be the desired pose vector. d ,y d ,z d These represent the desired positions along the x, y, and z axes, respectively, and r xd ,r yd ,r zd These are the desired attitude angles along the x, y, and z axes, respectively; X r =[x r ,y r ,z r ,r xr ,r yr ,r zr ] T x is the actual pose vector. r ,y r ,z r These are the actual positions of the x, y, and z axes, respectively, and r xr ,r yr ,r zr These are the actual attitude angles along the x, y, and z axes, respectively. For the desired speed, This refers to the actual speed; For the desired acceleration, This is the actual acceleration.

8. The moving target prediction method based on Gaussian mixture and Bayesian inference according to claim 1, characterized in that, In step 7, a motion target prediction model based on Gaussian mixture and Bayesian inference is used to predict the motion target of the human arm; The performance of the prediction model is evaluated using target prediction accuracy and target change adaptability as core indicators. The overall prediction accuracy of the model is quantified by the proportion of correct predictions out of the total number of predictions. Target change adaptability includes target change recognition rate and adaptation time. Target change recognition rate is the proportion of experiments in which the model successfully detects a change in the target. Adaptability time is the difference in the number of frames required from the occurrence of a target change to the model's stable output of a new target. The two indicators are used to comprehensively evaluate the prediction model's response and recovery ability to dynamic intention changes.

9. A computer-readable storage medium, characterized in that, It stores a program that, when executed by a processor, implements the steps in the moving target prediction method based on Gaussian mixture and Bayesian inference as described in any one of claims 1-8.

10. An electronic device, characterized in that, It includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the moving target prediction method based on Gaussian mixture and Bayesian inference as described in any one of claims 1-8.

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