A method and system for calculating expected speed using hidden Markov model and double-layer Bayesian in teleoperation

Abstract

The present invention belongs to the technical field related to robot teleoperation and discloses a method and system for calculating the expected speed during teleoperation using a hidden Markov model and a double-layer Bayesian approach. The method comprises: obtaining the offline motion trajectory of the master robot during offline motion, using the offline motion trajectory to train a hidden Markov model offline until convergence, thereby determining the model parameters of the hidden Markov model; inputting the current motion speed of the master robot into the trained hidden Markov model to obtain the hidden Markov model parameters; using the Bayesian formula to calculate the probability of each hidden state appearing at the current moment and the next moment; and using the probability of each hidden state appearing at the next moment to calculate the expected speed of the slave robot at the current moment. The present invention solves the problem of suppressing human hand jitter in complex trajectory teleoperation tasks.

Description

Technical Field

[0001] The present invention belongs to the technical field related to robot teleoperation, and more specifically, relates to a method and system for calculating expected speed by using a hidden Markov model and a double-layer Bayesian method in teleoperation. Background Art

[0002] Teleoperation relies on the operator's movements to control the movement of a slave robot. Typically, the slave robot strictly replicates the trajectory of the master operator's hand. However, due to physiological reasons, hand jitter is inevitable during movement. Directly sending commands containing jitter interference to the slave robot will seriously affect speed stability and trajectory smoothness. Therefore, hand jitter suppression is necessary.

[0003] Kalman filters can predict and filter hand jitter signals, but their prediction accuracy for nonlinear signals is low. Machine learning methods such as support vector machines and neural networks can also be applied to eliminate hand jitter and are suitable for nonlinear systems. However, they only filter high-frequency, small-amplitude hand jitter signals at the data level and cannot suppress low-frequency, large-amplitude signals caused by accumulated jitter from the perspective of task completion. The fundamental reason why operators still generate jitter signals even when they are aware of the required task path is the randomness of human behavior, so this randomness needs to be characterized.

[0004] Hidden Markov models have been used to characterize the randomness of human behavior. Using them to identify human intention, specifically the expected speed of hand movement, can filter out jitter signals. Currently, existing jitter reduction methods are limited to linear trajectories. In more diverse application scenarios, such as teleoperated glue coating, task trajectories vary, and using only Hidden Markov models lacks adaptability to these diverse trajectories. Therefore, a method suitable for teleoperation jitter reduction is urgently needed. Summary of the Invention

[0005] In response to the above defects or improvement needs of the existing technology, the present invention provides a method and system for calculating the expected speed in teleoperation using a hidden Markov model and a double-layer Bayesian method to solve the problem of suppressing human hand jitter in complex trajectory teleoperation tasks.

[0006] To achieve the above object, according to one aspect of the present invention, a method for calculating expected speed using a hidden Markov model and a two-layer Bayesian method in teleoperation is provided, the method comprising the following steps:

[0007] Obtaining an offline motion trajectory of the master robot during offline motion, and using the offline motion trajectory to offline train a hidden Markov model until convergence, thereby determining model parameters in the hidden Markov model, where the speed of the master robot is an observable state and the expected speed of the slave robot is a hidden state;

[0008] The current movement speed of the master robot is input into the trained hidden Markov model to obtain the hidden Markov model parameters corresponding to the movement speed at the current moment; the probability of each hidden state in the hidden Markov model appearing at the current moment is calculated using the Bayesian formula; the probability of each hidden state appearing at the next moment is calculated using the Bayesian formula again in combination with the probability of each hidden state appearing at the current moment, and the expected speed of the slave robot at the current moment is calculated using the probability of each hidden state appearing at the next moment.

[0009] Further preferably, after offline training of the hidden Markov model, the offline trained hidden Markov model is trained online, and the process of online training is as follows:

[0010] The real-time motion speed of the master robot at each moment is obtained online, and then the real-time motion speed is input into the hidden Markov model after offline training for training, thereby performing an online training process.

[0011] Further preferably, the formula for calculating the probability of each hidden state in the hidden Markov model appearing at the current moment using the Bayesian formula is as follows:

[0012]

[0013] in, The hidden state at time n is z i The probability of The observation state at time n is {o1,o2,…,o n} and the hidden state is z i The probability of , i∈{1,2,…M} is the number of the hidden state, and M is the total number of hidden states.

[0014] Further preferably, the forward factor is calculated as follows:

[0015]

[0016] in, The observed state at time 1 is o1 and the hidden state is z i The probability of π i The hidden state at time 1 is z i The probability of P(o1|s1=z i ) is the hidden state z at time 1 iUnder the condition of , the probability of the observable state is o1; The observation state at time n+1 is {o1,o2,…,o n ,o n+1} and the hidden state is z i The probability of a ij =P(s n+1 =z j |s n =z i ) is the hidden state at time n is z i Under the condition that the hidden state at time n+1 is z j The probability of P(o n+1 |s n+1 =z i ) is the hidden state z at time n+1 i Under the condition of n+1 probability; The observation state at time n is {o1,o2,…,o n} and the hidden state is z i The probability of ; i∈{1,2,…M} is the number of the hidden state at the current moment, j∈{1,2,…M} is the number of the hidden state at the next moment, and M is the total number of hidden states.

[0017] Further preferably, the Bayesian formula is used again in combination with the state transition matrix at the current moment in the hidden Markov model parameters to calculate the probability of each hidden state appearing at the next moment, according to the following formula:

[0018]

[0019] in, At time n+1, the hidden state is z i The probability of a ij =P(s n+1 =z j |s n =z i ) is the current hidden state z i Under the condition that the next hidden state is z j probability; At time n, the hidden state is z i where i∈{1,2,…M} is the number of the hidden state at the current moment, j∈{1,2,…M} is the number of the hidden state at the next moment, and M is the total number of hidden states.

[0020] Further preferably, the expected speed of the slave robot at the current moment is calculated using the probability of each hidden state appearing at the next moment, according to the following formula:

[0021]

[0022] Among them, v n,intend is the expected speed of the slave robot at the current time n; At time n+1, the hidden state is z i The probability of At time n, the hidden state is z i Under the condition that the observable state is o n The mean of the Gaussian probability distribution satisfied, i∈{1,2,…M} is the number of the hidden state at the current moment.

[0023] More preferably, the Calculate using the following formula:

[0024]

[0025] Among them, μ i The hidden state at the current moment is z i Under the condition that the observable state is o n The Gaussian probability distribution P(o n |s n =z i ), is the first-order sufficient statistic of the Gaussian probability distribution, indicating that the observable state at the current moment is {o1,o2,...,o n}under the condition of hidden state z i The mean number of occurrences at all times, is the second-order sufficient statistic of the Gaussian probability distribution, indicating that the observable state at the current moment is {o1,o2,...,o n} appears under the condition of hidden state z i is the mean of the cumulative sum of the observable states corresponding to the time, i∈{1,2,…M} is the number of the hidden state at the current moment.

[0026] Further preferably, after obtaining the expected speed of the slave robot at the current moment, the joint space position of the slave robot at the current moment is calculated using the expected speed, thereby controlling the slave robot.

[0027] Further preferably, the joint space position of the slave robot at the current moment is calculated using the expected speed according to the following steps:

[0028] Integrate the expected velocity of the robot at the current moment to obtain the expected position P of the slave robot at the current moment intend ;

[0029] The desired position of the slave robot is mapped to the base coordinate system of the slave robot using an incremental space mapping method to obtain the Cartesian space position P of the desired position of the slave robot. s ;

[0030] The Cartesian space position P is converted into s Converted into the robot joint space position q intend .

[0031] According to another aspect of the present invention, a system for calculating the expected speed using a hidden Markov model and a double-layer Bayesian in teleoperation is provided. The system includes an actuator for executing the above-mentioned method for calculating the expected speed using a hidden Markov model and a double-layer Bayesian in teleoperation.

[0032] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0033] 1. The present invention uses a hidden Markov model as the basic model combined with a two-layer Bayesian algorithm to identify the operator's intention to smoothly move the master robot during teleoperation, and calculates the desired trajectory that the operator subjectively intends to achieve, hidden under the trajectory of human hand jitter. This trajectory is the smooth trajectory after eliminating human hand jitter, thereby achieving human hand jitter suppression in teleoperation tasks.

[0034] 2. After using the actual motion speed to obtain the parameters of the hidden Markov model, the present invention first uses the Bayesian algorithm to calculate the probability of each hidden state appearing, and then uses the Bayesian algorithm again to calculate the probability of the hidden state appearing at the next moment. Because humans have reaction time, the jitter at the current moment is adjusted in the next time step. That is, the true expected speed at the current moment will be reflected in the next moment. Therefore, the probability of the hidden state appearing at the next moment is finally used to calculate the expected speed at the current moment, achieving more accurate expected speed calculation.

[0035] 3. After offline training of the hidden Markov model, the present invention uses the offline trained model as the initial model for online training, realizing both offline and online training of the hidden Markov model. This allows the parameters of the hidden Markov model to be updated while executing the teleoperation task, thereby identifying new operator intentions that are different from those in the offline training trajectory, and achieving hand jitter suppression for any complex trajectory not limited to the offline trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The present invention is a control framework diagram of an operator desired speed estimation method based on an online hidden Markov model and a double-layer Bayesian method, constructed according to a preferred embodiment of the present invention.

[0037] Figure 2 is a structural diagram of a hidden Markov model according to a preferred embodiment of the present invention.

[0038] Figure 3 is a flow chart of an expectation-maximization algorithm according to a preferred embodiment of the present invention.

[0039] Figure 4 is a flow chart of an online expectation-maximization algorithm according to a preferred embodiment of the present invention.

[0040] Figure 5 It is a diagram of a double-layer Bayesian module framework constructed according to a preferred embodiment of the present invention.

[0041] Figure 6 It is the estimation result of the expected speed of different human hand movement trajectories according to the preferred embodiment of the present invention, wherein, (a1), (a2) and (a3) ​​are the estimation results of the expected speed in the x, y and z directions of the straight line trajectory respectively, (b) is the displacement result obtained by integrating the speed of the straight line trajectory; (c1), (c2) and (c3) are the estimation results of the expected speed in the three directions of the circular trajectory respectively, (d) is the displacement result obtained by integrating the speed of the circular trajectory, (e1), (e2) and (e3) are the estimation results of the expected speed in the three directions of the "S"-shaped trajectory respectively, and (f) is the displacement result obtained by integrating the speed of the "S"-shaped trajectory.

[0042] Figure 7 It is a remote-controlled gluing task experimental platform according to a preferred embodiment of the present invention.

[0043] Figure 8 1 is a diagram showing the results of remote-controlled gluing according to a preferred embodiment of the present invention, wherein (a) and (b) are the results of remote-controlled gluing of a straight trajectory without and with the method of the present invention, respectively; (c) and (d) are the results of remote-controlled gluing of a circular trajectory without and with the method of the present invention, respectively; and (e) and (f) are the results of remote-controlled gluing of an "S"-shaped trajectory without and with the method of the present invention, respectively.

[0044] Figure 9 1 is a diagram showing the results of remote-controlled gluing on an engine oil pan according to a preferred embodiment of the present invention, wherein (a) shows the results of remote-controlled gluing on a straight track with and without the method of the present invention, and (b) shows the results of remote-controlled gluing on a straight track with the method of the present invention. DETAILED DESCRIPTION

[0045] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0046] like Figure 1 As shown, a method for estimating operator expected speed based on an online hidden Markov model and a two-layer Bayesian method includes the following steps:

[0047] S1 Hidden Markov Model Training

[0048] (1) Offline training

[0049] A hidden Markov model is established with the actual speed of the human hand as the observable state and the expected speed as the hidden state. The original offline trajectory data of the human hand along the random straight line direction is collected by motion tracking equipment. The offline trajectory refers to the situation where the master robot does not drive the slave robot to move. The model parameters are obtained by offline training using the classic hidden Markov model method, such as Figure 3 shown.

[0050] The actual movement speed of the hand o={v x ,v y ,v z} is regarded as the observable state of the hidden Markov model, and a two-dimensional matrix of observable sequence O = {o1,o2,...,o n} (n represents the time), each column of the two-dimensional matrix is ​​the actual movement speed of the human hand o = {v x ,v y ,v z}.

[0051] The human intention is defined as the desired speed of the operator's hand movement, which should be smooth. As the hidden state of the hidden Markov model, a two-dimensional matrix S = {s1, s2, ...s n}, each column of the two-dimensional matrix is ​​the expected movement speed of the human hand Hidden state s n It must be from a fixed set Z = {z1,z2,…z M}, where M is the number of hidden states.

[0052] The parameters of the hidden Markov model are λ={π,A,B}, where π={π1,π2,…π M} is the initial state matrix, π i=P(s1=z i ) represents the initial hidden state z i The probability of (i∈{1,2,…M}); A M×M is the state transition matrix, where each element a ij It is called the state transition probability, which represents the probability a from the current hidden state to the next hidden state ij =P(s n+1 =z j |s n =z i )(i,j∈{1,2,…M});B M×1 is the emission matrix, where each row represents an emission probability, and the probability distribution P(o) of observing the observable state under the current hidden state n |s n =z i )(i∈{1,2,…M}). The emission probability is considered to satisfy the multivariate Gaussian distribution as follows:

[0053]

[0054] μ,Σ represent the mean and standard deviation matrices of the multivariate Gaussian distribution, respectively, so the emission matrix The relationship diagram of each parameter is as follows Figure 2 As shown.

[0055] The master robot collects the original offline trajectory data of the human hand along the random straight line direction as the observable sequence O = {o1,o2,...,o n}.

[0056] First, initialize the parameters of the hidden Markov model to λ with arbitrary values init ={π init ,A init ,B init}, and then calculate the forward factor and backward factor according to the properties of the hidden Markov model and the forward-backward algorithm:

[0057]

[0058]

[0059] The forward factor Represents the hidden state at time n is z i And the observable sequence is (o1,o2,...,o n ), the backward factor Represents the hidden state at time n is z i And the observable sequence is (o n+1 ,o n+2 ,...,o N ) probability.

[0060] Calculate the intermediate variable γ n (i),ξ n (i,j):

[0061]

[0062]

[0063] The parameters λ = {π, A, B} that need to be trained are expressed by the following iterative formula:

[0064]

[0065] Where D is the number of observation sequence samples used to train the parameters. The above calculation is performed iteratively until the parameters λ = {π, A, B} converge.

[0066] The final converged parameter λ con Sent to the online hidden Markov model module as the initial value for parameter update.

[0067] (2) Online training

[0068] An online hidden Markov model module is added to the teleoperation framework, and real-time training is performed using the online trajectory data collected by the master robot.

[0069] During teleoperation, the observable state of the human hand movement speed is o n ={v x ,v y ,v z} are sent to the online hidden Markov model module in sequence. And the initial parameters of the online hidden Markov model module are set to λ calculated by the offline hidden Markov model con .

[0070] Further preferably, in step S3, each time an observable state o is received n ={v x ,v y ,v z}, then the online expectation maximization algorithm is used to update the initial parameters calculated by the offline hidden Markov model to λ new ={A n ,μ n ,Σ n According to the established hidden Markov model, the emission probability B is Gaussian distributed, and four sufficient statistics of Gaussian distribution are selected:

[0071]

[0072] in Represents the indicator function, which takes 1 if the value in the brackets is true and 0 if the value in the brackets is false; i,j,k∈{1,2,3,4,5} is the index of the hidden state.

[0073] Then calculate the intermediate variable q n ,φ n :

[0074]

[0075]

[0076] For sufficient statistics To update:

[0077]

[0078] where {χ1,χ2…χ n} is a sequence of decreasing step lengths, satisfying the random approximation requirements: ∑ n≥1 χ n =∞,∑ n≥1 χ n 2 <∞. The above expression uses only one sample point for iterative update each time.

[0079] When n≥n min Then, the model parameters and sufficient statistics of the hidden Markov model are updated according to:

[0080]

[0081] Among them, n min The role of is to ensure that there is enough data for parameter update, because when the sample points are very small, the estimation of the expectation maximization algorithm is inaccurate. By looping the above steps, you can achieve the goal of receiving an observable variable o online. n ={v x ,v y ,v z}Update the hidden Markov model parameters once.

[0082] The updated parameter λ new ={A n ,μ n ,Σ n}Sent to the two-layer Bayesian module.

[0083] S2 adds a double-layer Bayesian module to the teleoperation framework, and uses the online trained hidden Markov model and double-layer Bayesian method to calculate the operator's expected speed; the identified expected speed is used for the motion control of the slave robot.

[0084] Calculate the known observable sequence O = {o1,o2,...,o n}, each hidden state z i The probability of occurring at the current moment This probability represents the likelihood that multiple possible desired speeds of hand movements actually exist at the current moment:

[0085]

[0086]

[0087] Using the Bayesian formula and the total probability formula, ζ n i It can be expressed by the forward factor as:

[0088]

[0089] Using the current state transfer matrix A and the total probability formula to calculate the known observable sequence O={o1,o2,...,o n}, each hidden state z i The probability of appearing at the next moment ε i =P(s n+1 =z i |o1,o2,...,o n ), which represents the possibility that the expected speed of multiple possible hand movements actually exists at the next moment:

[0090]

[0091] For each hidden state z i , the mean μ of the Gaussian distribution it satisfies i The actual expected speed is represented by the weighted average of the basic expected speed factors. However, due to human reaction time, it takes a certain amount of time to adjust in the right direction after realizing the deviation caused by jitter. In other words, the actual expected speed at the current moment will be reflected in the next moment, so the final expected speed at the current moment v intend Calculated by the following formula

[0092]

[0093] in, Represents the expected speed at the next moment.

[0094] Finally, the desired position P of the end of the slave robot is obtained by integrating the desired velocity. intend={x,y,z,r,p,y}, where x,y,z represent the desired displacement, and r,p,y=0 means keeping the hand posture unchanged.

[0095] The desired pose of the human hand is mapped to the base coordinate system of the slave robot through the incremental space mapping method to obtain P s , the Cartesian space position P is converted to s Transformed joint space position q intend ={q1,q2,...,q n}, where n is the number of slave robot joints.

[0096] q intend It is sent as the actual control signal to the slave robot to control its movement.

[0097] The present invention will be further described below with reference to specific embodiments.

[0098] S1 Hidden Markov Model Training

[0099] (1) Offline training

[0100] In this embodiment, a total of eight offline training data are collected. Taking one of them, O, as an example, the matrix with 3 rows and 782 columns is as follows, with the unit being mm / s:

[0101]

[0102] The expectation maximization algorithm is used to train the collected data. First, the parameters of the hidden Markov model are initialized to λ with arbitrary values. init ={π init ,A init ,B init},in:

[0103] π init =[0.2 0.2 0.2 0.2 0.2]

[0104]

[0105]

[0106]

[0107] Then, the forward factor and backward factor are calculated according to the properties of the hidden Markov model and the forward-backward algorithm:

[0108]

[0109]

[0110] The forward factor Represents the hidden state at time n is z i And the observable sequence is (o1,o2,...,o n ), the backward factor Represents the hidden state at time n is z i And the observable sequence is (o n+1 ,o n+2 ,...,o N ) probability.

[0111] Calculate the intermediate variable γ n (i),ξ n (i,j):

[0112]

[0113] The parameters λ = {π, A, B} that need to be trained are expressed by the following iterative formula:

[0114]

[0115] Where D is the number of observation sequence samples used to train the parameters. In this embodiment, D = 8. The above calculation is repeated until the parameters λ = {π, A, B} converge. In this embodiment, the offline parameters λ finally converged are con ={π,A,B} is as follows:

[0116] π=[0.433 0.148 0.313 0.106 0.000]

[0117]

[0118]

[0119]

[0120]

[0121] The final converged model parameter λ con Sent to the online hidden Markov model module as the initial value for parameter update.

[0122] (2) Online training

[0123] An online hidden Markov model module is added to the teleoperation framework, and the online movement trajectory data of the human hand collected by the master robot is used as an observable sequence for real-time training. The training process is as follows: Figure 4 shown.

[0124] During teleoperation, the hand movement speed o is used as the observable state. n ={v x,v y ,v z} are sent to the online hidden Markov model module in sequence, and the initial parameters of the online hidden Markov model module are set to λ calculated by the offline hidden Markov model con .

[0125] Each time an observable state o is received n ={v x ,v y ,v z}, then the online expectation maximization algorithm is used to update the initial value of the offline hidden Markov model to λ new ={π,A n ,B n}.

[0126] First, the emission probability B in the established hidden Markov model is determined to be a Gaussian distribution, which meets the prerequisites of the online expectation maximization algorithm, and the four sufficient statistics of the Gaussian distribution are selected as follows:

[0127]

[0128] in Represents the indicator function, which takes 1 if the value in the brackets is true and 0 if the value in the brackets is false; i,j,k∈{1,2,3,4,5} is the index of the hidden state.

[0129] Then calculate the intermediate variable q n ,φ n :

[0130]

[0131]

[0132] For sufficient statistics To update:

[0133]

[0134] where {χ1,χ2…χ n} is a sequence of decreasing step lengths, satisfying the random approximation requirements: ∑ n≥1 χ n =∞,∑ n≥1 χ n 2 <∞. The above expression uses only one sample point for iterative update each time.

[0135] When n≥n min Then, the model parameters and sufficient statistics of the hidden Markov model are updated according to:

[0136]

[0137] Among them, n min The role of is to ensure that there is enough data for parameter update, because when the sample points are very small, the estimation of the expectation maximization algorithm is inaccurate. By looping the above steps, you can achieve the goal of receiving an observable variable o online. n ={v x ,v y ,v z}Update the hidden Markov model parameters once.

[0138] In this embodiment, x n =n -0.7 , n min = 10. When n = 1, the received observable state o1 = {-0.349 1.053 0.197}, which is calculated as follows:

[0139] First calculate the initial parameter λ con The emission probability of each hidden state under P(o1|s1=z i ):

[0140]

[0141] Then calculate the intermediate variable φ1:

[0142]

[0143] Then calculate the sufficient statistic S A (i,j),S B (i), taking i=1 as an example, the calculation is:

[0144]

[0145] Loop through the above steps to calculate q at each step n ,φ n , Until n=10, the received observable state o 10 =[-0.498 0.717 0.948], and use the above intermediate variables to update the model parameters. The specific calculation is as follows:

[0146] First calculate the initial parameter λ con The emission probability of each hidden state under P(o1|s1=z i ):

[0147]

[0148] Then calculate the intermediate variable q 10 (i, j) (taking i=j=1 as an example):

[0149]

[0150] Calculate the intermediate variable φ 10 (i) (taking i = 1 as an example, φ9(i) is known) is calculated as follows:

[0151]

[0152] Then calculate the sufficient statistic S 10 A (i,j),S 10 B (i) (Take i=j=1 as an example, S9 A (i,j),S9 B (i) Known):

[0153] Finally calculate the parameter a 11 (i,j),μ 10 (i),Σ 10 (i) and update (taking i=j=1 as an example):

[0154]

[0155] The final parameter update is:

[0156] λ new ={π,A n ,B n}:

[0157] π=[0.433 0.148 0.313 0.106 0.000]

[0158]

[0159]

[0160]

[0161]

[0162] The updated parameter λ new ={A n ,μ n ,Σ n}Sent to the two-layer Bayesian module.

[0163] S2 adds a double-layer Bayesian module to the teleoperation framework, and uses the online trained hidden Markov model parameters and the double-layer Bayesian method to calculate the operator's expected speed from the original online human hand movement trajectory. The framework of the double-layer Bayesian method is as follows: Figure 5shown.

[0164] In this embodiment, when n=10, the received observable state o 10 =[-0.498 0.717 0.948], forward factor Therefore 11 i The calculation is as follows (taking i=1 as an example):

[0165]

[0166] ξ 10 =[0.011,0.027,0.000,0.00,0.961]

[0167] Using the state transfer matrix A and the total probability formula to calculate the known observable sequence O={o1,o2,...,o n}, each hidden state z i The probability of appearing at the next moment ε i =P(s n+1 =z i |o1,o2,...,o n ), which represents the possibility that the expected speed of multiple possible hand movements actually exists at the next moment:

[0168]

[0169] In this embodiment, when n=10, The calculation is as follows (taking i=1 as an example):

[0170]

[0171] ε 10 =[0.068,0.159,0.002,0.009,0.761]

[0172] In this embodiment, when n=10, v intend The calculation is as follows:

[0173]

[0174] The expected speed estimation results for different trajectories using the above method are as follows: Figure 6As shown in the figure, (a1), (a2), (a3), and (b) are the expected velocity estimates for the x, y, and z directions of a linear trajectory, respectively, and (b) is the displacement obtained by integrating the velocity; (c1), (c2), (c3), and (d) are the estimated results for a circular trajectory, respectively, and (e1), (e2), (e3), and (f) are the estimated results for an S-shaped trajectory, respectively. As can be seen from the figure, whether for a linear, circular, or S-shaped trajectory, the expected velocity estimates are significantly smoother than the original velocity, and the displacement obtained by integrating the expected velocity estimates is also smoother than the original displacement, indicating that hand shake has been effectively suppressed. …

[0175] The identified desired velocity is used for motion control of the slave robot.

[0176] Integrate the desired velocity to get the desired position P of the end of the slave robot intend ={x,y,z,r,p,y}, where r,p,y=0 means keeping the posture of the slave robot unchanged

[0177] The Cartesian space position P is converted to intend = {x, y, z, r, p, y} converted joint space position q intend ={q1,q2,…,q n}, where n is the number of slave robot joints.

[0178] q intend It is sent to the slave robot as the actual control signal.

[0179] In order to verify the effectiveness of the online matching method proposed in the present invention, the accuracy is verified using an example. In this example, a remote-operated glue-spreading task platform is built for experimental verification. Figure 7 As shown, it includes the master robot Virtuose 6D TAO, the slave robot Franka, the controller and the gluing equipment. The control frequency of the robots is 20HZ. Figure 8 The results of teleoperated gluing tasks on straight line, circular and S-shaped trajectories are shown with and without the method proposed in the present invention. Figure 9 The results of remotely applying sealant to an engine oil pan using and not using the proposed method are shown. The sealant applied using the proposed method is smoother than that applied using conventional remote control, demonstrating the effectiveness of the proposed method in suppressing hand shake.

[0180] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation, characterized in that: The method comprises the following steps: Obtaining an offline motion trajectory of the master robot during offline motion, and using the offline motion trajectory to offline train a hidden Markov model until convergence, thereby determining model parameters in the hidden Markov model, where the speed of the master robot is an observable state and the expected speed of the slave robot is a hidden state; Input the current motion speed of the master robot into the trained hidden Markov model to obtain the hidden Markov model parameters corresponding to the current motion speed; Calculate the probability of each hidden state in the hidden Markov model appearing at the current moment using the Bayesian formula; The Bayesian formula is used again and combined with the probability of each hidden state appearing at the current moment to calculate the probability of each hidden state appearing at the next moment. The probability of each hidden state appearing at the next moment is used to calculate the expected speed of the slave robot at the current moment.

2. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 1, wherein: After offline training of the hidden Markov model, the offline trained hidden Markov model is trained online. The process of online training is as follows: The real-time motion speed of the master robot at each moment is obtained online, and then the real-time motion speed is input into the hidden Markov model after offline training for training, thereby performing an online training process.

3. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 1 or 2, wherein: The formula for calculating the probability of each hidden state in the hidden Markov model appearing at the current moment using the Bayesian formula is as follows: in, The hidden state at time n is z i The probability of The observation state at time n is {o1,o2,...,o n } and the hidden state is z i The probability of , i∈{1,2,…M} is the number of the hidden state, and M is the total number of hidden states.

4. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 3, wherein: The forward factor is calculated as follows: in, The observed state at time 1 is o1 and the hidden state is z i The probability of π i The hidden state at time 1 is z i The probability of P(o1|s1=z i ) is the hidden state z at time 1 i Under the condition of , the probability of the observable state is o1; The observation state at time n+1 is {o1,o2,...,o n ,o n+1 } and the hidden state is z i The probability of a ij =P(s n+1 =z j |s n =z i ) is the hidden state at time n is z i Under the condition that the hidden state at time n+1 is z j The probability of P(o n+1 |s n+1 =z i ) is the hidden state z at time n+1 i Under the condition of n+1 probability; The observation state at time n is {o1,o2,...,o n } and the hidden state is z i The probability of ; i∈{1,2,…M} is the number of the hidden state at the current moment, j∈{1,2,…M} is the number of the hidden state at the next moment, and M is the total number of hidden states.

5. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 3 or 4, wherein: The Bayesian formula is used again in combination with the state transition matrix at the current moment in the hidden Markov model parameters to calculate the probability of each hidden state appearing at the next moment, according to the following formula: in, At time n+1, the hidden state is z i The probability of a ij =P(s n+1 =z j |s n =z i ) is the current hidden state z i Under the condition that the next hidden state is z j probability; At time n, the hidden state is z i where i∈{1,2,…M} is the number of the hidden state at the current moment, j∈{1,2,…M} is the number of the hidden state at the next moment, and M is the total number of hidden states.

6. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 5, wherein: The expected speed of the slave robot at the current moment is calculated using the probability of each hidden state appearing at the next moment, according to the following formula: Among them, v n,intend is the expected speed of the slave robot at the current time n; At time n+1, the hidden state is z i The probability of At time n, the hidden state is z i Under the condition that the observable state is o n The mean of the Gaussian probability distribution satisfied, i∈{1,2,…M} is the number of the hidden state at the current moment.

7. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 6, wherein: described Calculate using the following formula: Among them, μ i The hidden state at the current moment is z i Under the condition that the observable state is o n The Gaussian probability distribution P(o n |s n =z i ), is the first-order sufficient statistic of the Gaussian probability distribution, indicating that the observable state at the current moment is {o1,o2,...,o n }under the condition of hidden state z i The mean number of occurrences at all times, is the second-order sufficient statistic of the Gaussian probability distribution, indicating that the observable state at the current moment is {o1,o2,...,o n } appears under the condition of hidden state z i is the mean of the cumulative sum of the observable states corresponding to the time, i∈{1,2,…M} is the number of the hidden state at the current moment.

8. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 1 or 2, wherein: After obtaining the expected speed of the slave robot at the current moment, the joint space position of the slave robot at the current moment is calculated using the expected speed, thereby controlling the slave robot.

9. The method for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation according to claim 8, wherein: The expected velocity is used to calculate the joint space position of the slave robot at the current moment in the following steps: Integrate the expected velocity of the robot at the current moment to obtain the expected position P of the slave robot at the current moment intend ; The desired position of the slave robot is mapped to the base coordinate system of the slave robot using an incremental space mapping method to obtain the Cartesian space position P of the desired position of the slave robot. s ; The Cartesian space position P is converted into s Converted into the robot joint space position q intend .

10. A system for calculating expected speed using a hidden Markov model and a two-layer Bayesian approach in teleoperation, characterized in that: The system comprises an actuator, which is used to execute the method for calculating the expected speed by using a hidden Markov model and a double-layer Bayesian in a teleoperation as described in any one of claims 1 to 9.

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