A forklift path tracking control method based on steering time delay estimation and compensation

Abstract

The application discloses a forklift path tracking control method based on steering time delay estimation and compensation, and the path comprises the following steps according to the control method: step 1, obtaining optimal time delay in a T-1 period; step 2, obtaining forklift steering wheel turning angle parameters and wheel turning angle parameters; step 3, obtaining forklift expected wheel turning angle β and expected steering wheel turning angle θ in a path tracking period T; step 4, obtaining actual steering wheel turning angle in the path tracking period T according to step 1; step 5, the forklift steering system controls forklift steering according to the actual steering wheel turning angle obtained in step 4, and obtains optimal time delay in the path tracking period T; and step 6, T=T+1 and step 1 is executed. The application estimates steering time delay and compensates steering time delay by means of early input of the expected steering wheel turning angle in each path tracking calculation period, does not affect the path tracking process in the next period, and improves the precision of intelligent forklift path tracking.

Description

Technical Field

[0001] This invention relates to the field of path tracking control for hydraulically steering vehicles, specifically a path tracking control method for forklifts based on steering time delay estimation and compensation. Background Technology

[0002] With the advancement of technology, the application of fully hydraulic synchronous steering in engineering machinery, agricultural machinery, and military vehicles is becoming increasingly widespread, and the application environments are becoming more complex and diverse. Furthermore, the current emphasis on comprehensive intelligentization has laid the foundation for the intelligent development of various vehicles using fully hydraulic steering. Therefore, the requirements for fully hydraulic synchronous steering vehicles have shifted from functional requirements to requirements such as high efficiency, safety, and precision. The demands on steering control capabilities are also increasing accordingly.

[0003] The time delay in a fully hydraulic steering system is stochastic. This stochastic variation in time delay can be caused by the system's internal dynamics and other nonlinear characteristics, such as valve spool pressure, fluid compressibility, pump dead zone, valve flow rate, and fluid pipe friction characteristics. This stochastic time delay complicates the system identification process. In practical applications, many control algorithms and strategies may become highly inaccurate if the effects of time delay are not understood. Therefore, in path tracking control, the stochastic time delay in the steering system leads to inaccurate signal acquisition within the path tracking control acquisition cycle, resulting in a corresponding delay in wheel angle output. This causes unstable tracking performance, reduced system robustness, and sluggish response, and in severe cases, may even lead to control detuning.

[0004] With the widespread application of fully hydraulic steering systems in vehicles, the steering system accuracy during path tracking is undoubtedly one of the most pressing issues in the intelligent vehicle industry research of vehicles equipped with fully hydraulic steering systems, such as engineering vehicles, military vehicles, and agricultural machinery vehicles. The decisive factors affecting path tracking accuracy are the precision and reliability of the system's steering. Therefore, to improve the path tracking accuracy of such intelligent vehicles, research on the precision and reliability of their steering should be the primary consideration. Summary of the Invention

[0005] The purpose of this invention is to provide a forklift path tracking control method based on steering time delay estimation and compensation, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A forklift path tracking control method based on steering time delay estimation and compensation, wherein the path tracking control method includes the following steps:

[0008] Step 1: Obtain the optimal time delay within the T-1 period, where T is the path tracking calculation period and T≥1. When T=1, the optimal time delay is zero.

[0009] Step 2: Obtain the forklift steering wheel angle parameters and wheel angle parameters;

[0010] Step 3: Obtain the expected wheel angle β and expected steering wheel angle θ of the forklift within the path tracking period T;

[0011] Step 4: Calculate the actual steering wheel angle within the path tracking period T based on the optimal time delay obtained in Step 1 and the expected wheel angle β and expected steering wheel angle θ of the forklift obtained in Step 3.

[0012] Step 5: The forklift steering system controls the forklift steering based on the actual steering wheel angle obtained in Step 4, and obtains the optimal time delay within the path tracking period T.

[0013] Step 6: Set T = T + 1 and execute Step 1.

[0014] As a further aspect of the present invention: the desired steering wheel angle θ = β*K v , where K v This refers to the steering system gear ratio.

[0015] As a further aspect of the present invention: obtaining the optimal time delay includes the following steps:

[0016] S1. Establish a hydraulic steering input-output probability model;

[0017] S2. Establish a time-delay acquisition timeline;

[0018] S3. Combine the input-output probability model and the time delay acquisition time axis with the variational Bayes estimation algorithm to estimate the steering time delay and obtain the optimal time delay for each path tracking calculation cycle.

[0019] As a further aspect of the present invention: the hydraulic steering input-output probability model is f(X; θ);

[0020] Where X is a vector composed of steering wheel input angles, θ is a distribution parameter, and the hydraulic steering input-output probability model is established for each path tracking calculation cycle;

[0021] The error caused by time delay is regarded as process noise. Assuming that the system has normally distributed noise, the time delay probability can be expressed as:

[0022] p(Y|X,θ,σ 2 )=N(Y|T(X;θ),σ 2 )

[0023] The maximum likelihood distribution is:

[0024] p(θ|Y,X)∝p(Y|X,θ,σ2 )·p(θ)

[0025] Where Y is a vector composed of system reference outputs, with reference wheel angle, σ 2 Let V be the variance of the noise.

[0026] As a further aspect of the present invention: the time-delay acquisition time axis includes the wheel angle sensor acquisition period, the path tracking calculation period, and the lag time difference; the establishment of the time-delay acquisition time axis in S2 includes the following steps:

[0027] S2.1 Define the lag time difference k. There is a k-unit time difference between the actual corresponding angle acquisition time of each path tracking calculation cycle and the steering wheel angle input time. One unit is the time length of one wheel angle sensor acquisition cycle t.

[0028] S2.2, Define latent variable parameters A vector composed of binary 0 and 1 data under each control time domain period T corresponding to the acquisition time axis. The vector set represents the time delay error between the input steering wheel angle X at time T and the output wheel angle, and is used to represent this error.

[0029] The superscript indicates the difference in timestamps between the model input and the reference output, and the upper limit of the time delay is set to K, where K≤5t.

[0030] As a further aspect of the present invention: the wheel angle sensor acquisition cycle refers to the interval at which the angle information is acquired; the path tracking calculation cycle refers to the cycle in which the path tracking control algorithm processes the acquired signals and calculates and updates the desired wheel angle.

[0031] As a further aspect of the present invention: the steps in S3 for obtaining the optimal steering delay step using the variational Bayesian estimation algorithm are as follows:

[0032] In the variational Bayesian estimation algorithm, the estimated values ​​corresponding to different steering wheel angle inputs are assigned to the distribution parameters and the latent variables. Combining the maximum likelihood distribution formula, the approximate joint distribution is:

[0033]

[0034] Where: q() is the proposed distribution;

[0035] In the variational Bayesian estimation algorithm, the remaining proposal distributions are optimized by fixing the other proposal distributions. The optimal time-delay proposal distribution of the system is given by the Kullback-Leibler Divergence formula:

[0036]

[0037] Where: p(X) T Y T The variational Bayesian estimation algorithm remains constant during the solution process, therefore formula (4) is equivalent to:

[0038]

[0039] Where: q(θ) and q(σ) 2 Considering the distribution as a fixed value, both distributions are known. Integrating them separately yields the corresponding constant values ​​of the integral, and the known distributions can be used as conditions to obtain the expected value in the corresponding maximum likelihood estimate, i.e.

[0040]

[0041] Therefore, formula (5) can be equivalent to:

[0042]

[0043] Finally, the system time-delay proposal distribution formula can be expressed as the entropy difference between the likelihood expectation exponents of the other two fixed proposal distributions, and the optimal solution can be expressed as:

[0044]

[0045] Will The parameterized representation of the proposed distribution of υ is as follows:

[0046]

[0047] The model's likelihood distribution and prior distribution are conjugate distributions. The parameters of υ can be obtained from the probability conjugate, and are as follows:

[0048]

[0049]

[0050] Where: <.> represents the expected value of its own distribution. The parameters related to υ are expressed as follows:

[0051]

[0052]

[0053]

[0054] Ultimately, the time delay statistics under different turning angle inputs X can all obtain an effective posterior distribution, and the optimal time delay can be calculated for each cycle.

[0055] As a further aspect of the present invention: the optimal time delay is combined with the time delay acquisition time axis to obtain the input-output time equation;

[0056] The input-output time equation is:

[0057]

[0058] Where: t is any current sampling time, T is the calculation time of the path tracking control time domain period, and X T：t-k Y represents the system input for the current period, where the subscript indicates the signal input time considering time delay compensation; T：t This is the system reference output at the current moment; the subscript indicates the time of wheel angle acquisition; θ is the distributed parameter - the steering ratio of steering wheel angle to wheel angle; k represents the time delay.

[0059] Combining the input-output time equations, the time delay compensation model within the path tracking calculation cycle can be represented by the expected log-likelihood function Λ of the time delay at the current cycle T, the optimal time delay k units in the previous cycle, and the input time t at the turning angle:

[0060]

[0061] Compared with the prior art, the beneficial effects of the present invention are:

[0062] 1. This invention compensates for steering lag by estimating the steering lag and pre-inputting the expected steering wheel angle within each path tracking calculation cycle. This does not affect the path tracking process in the next cycle, thus improving the accuracy of path tracking for intelligent forklifts.

[0063] 2. This invention treats time delay as a time parameter along the time axis, establishes an input-output probability model and a time delay acquisition time axis, and combines a variational Bayesian estimation algorithm to estimate the steering time delay for each path tracking calculation cycle and steering wheel angle input.

[0064] 3. This invention establishes an input-output timing equation, which uses the optimal time delay estimate as a reference advance amount and combines it with the input-output timing equation to input the expected steering wheel angle in each cycle in advance, thereby offsetting the wheel angle response delay caused by the time delay and compensating for the steering time delay. Attached Figure Description

[0065] Figure 1 This is a diagram of the input-output probability model of the present invention;

[0066] Figure 2 This is a timeline diagram of the data acquisition process of this invention;

[0067] Figure 3 This is a schematic diagram of the time delay compensation principle of the present invention;

[0068] Figure 4 This is a schematic diagram of the pre-compensation time axis of the present invention;

[0069] Figure 5 , Figure 6 This is a comparison chart of path tracking and tracking error in this invention. Detailed Implementation

[0070] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0071] Please see Figure 1-6 In this embodiment of the invention, a forklift path tracking control method based on steering time delay estimation and compensation is provided, wherein the path tracking control method includes the following steps:

[0072] Step 1: Obtain the optimal time delay within the T-1 period, where T is the path tracking calculation period and T≥1. When T=1, the optimal time delay is zero.

[0073] Step 2: Obtain the forklift steering wheel angle parameters and wheel angle parameters. Install wheel angle sensors at the forklift steering wheels (rear wheels) to obtain wheel angle parameters; define the steering wheel angle sensor and the wheel angle sensor acquisition time t.

[0074] Step 3: Obtain the expected wheel angle β and expected steering wheel angle θ of the forklift within the path tracking period T. Expected steering wheel angle θ = β * K v , where K v The steering system gear ratio; system gear ratio K v Due to the specific characteristics of the vehicle's steering system, each model uses a different steering system gear ratio; and the path tracking algorithm outputs the desired wheel angle in different cycles, and then calculates the desired wheel angle based on the steering system gear ratio K. v The desired steering wheel angle input is converted and fed into the forklift hydraulic steering system to perform path-tracking steering operations.

[0075] Obtaining the optimal time delay includes the following steps:

[0076] S1. Establish a hydraulic steering input-output probability model;

[0077] The specific input-output probability model is determined as follows: For each path tracking calculation cycle, a hydraulic steering input-output probability model f(X; θ) is established, where X is a vector composed of steering wheel input angles, and θ is a distribution parameter that characterizes the relationship distribution between the model's input and output.

[0078] The input-output probability model diagram is as follows: Figure 1 As shown. In the probabilistic model estimation process, the error caused by time delay is regarded as process noise. Considering the time delay noise error, the estimation of the latent distribution parameters is transformed into probabilistic inference. Assuming that the system has normally distributed noise, the time delay probability can be expressed as:

[0079] p(Y|X,θ,σ 2 )=N(Y|f(X;θ),σ 2 (1)

[0080] Where Y is a vector composed of the system reference output (reference wheel rotation angle), σ 2 Let V be the variance of the noise.

[0081] The maximum likelihood distribution is:

[0082] p(θ|Y,X)∝p(Y|X,θ,σ 2 )·p(θ) (2)

[0083] S2. Establish a time-delay acquisition timeline;

[0084] The specific time delay acquisition time axis is established as follows: The time delay is represented as a parameter in the time dimension along the path tracking control period T, and the time delay acquisition time axis is established as follows: Figure 2 As shown, this includes the wheel angle sensor acquisition cycle, the path tracking calculation cycle, and the lag time difference. The wheel angle sensor acquisition cycle refers to the interval at which angle information is acquired; the path tracking calculation cycle refers to the cycle in which the path tracking control algorithm processes the acquired signals and calculates and updates the desired wheel angle, which is also the cycle of the desired steering wheel angle input signal. In one path tracking control calculation cycle T, wheel angle outputs are acquired at five different times. The steering wheel angle input time also marks the beginning of a new control time domain calculation cycle; in the absence of time lag, the wheel angle acquired during the path tracking calculation is consistent with the steering wheel angle input cycle. However, due to the existence of time lag, there is a lag time difference (K units) between the actual corresponding angle acquisition time and the steering wheel angle input time within each control time domain cycle (K = 0, 1, 2, 3, 4), where one unit is the length of one wheel angle sensor acquisition cycle t.

[0085] During normal steering, the steering system gear ratio is K. vFor the same desired steering wheel angle input, there is a unique reference wheel angle output. Latent variable parameters are introduced. The measurement error caused by the time delay of the reference wheel steering angle output is quantified by using a vector composed of binary 0 and 1 data for each control time domain period T corresponding to the acquisition time axis. The vector set represents the time delay error between the input steering wheel angle X at time T and the output wheel angle. In addition, the constrained vector The modulus is 1, ensuring that each steering wheel angle has a unique hysteresis correspondence at each sampling instant.

[0086] The superscript indicates the difference in timestamps between the model input and the reference output, such as: The probability that the difference between the current input steering wheel angle X and the simultaneous wheel angle output acquisition delay is 0 is 1. This means that the probability of the difference between the current input steering wheel angle X and the time delay of the wheel angle output acquisition at the same moment being 1 is 0, and so on. The upper limit of the time delay is set to K, K≤5t, that is, the path tracking control calculation cycle should be greater than or equal to the maximum time delay, to ensure that a reasonable wheel angle value considering the time delay can be acquired in all calculation cycles.

[0087] S3. Combine the input-output probability model and the time delay acquisition time axis with the variational Bayes estimation algorithm to estimate the steering time delay and obtain the optimal time delay for each path tracking calculation cycle.

[0088] The specific process of estimating the steering time delay using the variational Bayesian estimation algorithm is as follows.

[0089] In the variational Bayesian estimation algorithm, the estimated values ​​(suggested distributions) corresponding to different steering wheel angle inputs are assigned to the distribution parameters and the latent variables, and the approximate joint distribution is:

[0090]

[0091] Where q() is the proposal distribution. The smaller the difference between the decomposed proposal distribution and the posterior distribution, the greater the similarity between the distributions, and the better the parameter estimation can be obtained.

[0092] Therefore, the goal of variational Bayes estimation is to minimize the relative entropy, or statistical distance dispersion, of the distributions on both sides of the above equation.

[0093] In the variational Bayesian estimation algorithm, the remaining proposal distributions are optimized by fixing the other proposal distributions. The fixed proposal distributions are the parameter proposal distribution q(θ) and the system time delay error proposal distribution q(σ). 2 The optimal time-delay proposal distribution of the system can be obtained using the Kullback-Leibler Divergence formula:

[0094]

[0095] Where: p(X) T Y T The expression remains constant during the solution process of the variational Bayesian estimation algorithm, therefore, equation (4) is equivalent to:

[0096]

[0097] Where: q(θ) and q(σ) 2 Considering the distribution as a fixed value, both distributions are known. Integrating them separately yields the corresponding constant values ​​of the integral, and the known distributions can be used as conditions to obtain the expected value in the corresponding maximum likelihood estimate, i.e.

[0098]

[0099] Therefore, formula (5) can be equivalent to:

[0100]

[0101] Finally, the system time-delay proposal distribution formula can be expressed as the entropy difference between the likelihood expectation exponents of the other two fixed proposal distributions, and the optimal solution can be expressed as:

[0102]

[0103] The optimal solution update equations for the other two terms can also be derived in a similar way. To find... A detailed explanation will be provided. The parameterized representation of the proposed distribution of υ is as follows:

[0104]

[0105] The model's likelihood distribution and prior distribution are conjugate distributions; therefore, the posterior distribution and prior distribution are uniform. Using the variational Bayesian estimation algorithm... The parameters of υ can be obtained from the probability conjugate, and are as follows:

[0106]

[0107]

[0108] Where: <.> represents the expected value of its own distribution, and the relevant expressions of formulas (10) and (11) are as follows:

[0109]

[0110]

[0111]

[0112] Ultimately, the time delay statistics under different turning angle inputs X can all obtain an effective posterior distribution, and the optimal time delay can be calculated for each cycle.

[0113] Step 4: Calculate the actual steering wheel angle within the path tracking period T based on the optimal time delay obtained in Step 1 and the expected wheel angle β and expected steering wheel angle θ of the forklift obtained in Step 3.

[0114] By using the optimal time delay as a reference lead and combining it with the input-output timing equation, the desired steering wheel angle within the path tracking cycle is input to the forklift hydraulic steering system in advance, thereby compensating for the steering time delay. The time delay compensation principle diagram and the advance compensation time axis diagram are shown below. Figure 3 , 4 As shown. The specific steps for establishing the input-output time equations and implementing the time delay compensation scheme are as follows:

[0115] The optimal time delay value for each calculation cycle of path tracking can be obtained, but the estimated value for the current cycle depends on the steering angle response result of the current cycle. Therefore, it will be later than the steering wheel angle input time of the current cycle. That is, the optimal time delay value of the current cycle cannot be used as the reference control quantity for the early input of the steering wheel angle in the current cycle. However, since the steering angle is continuous during the steering process and the change in time delay value between adjacent cycles is not large, we consider using the optimal time delay value obtained in the previous cycle (T-1) as the reference advance amount to input the steering wheel angle in advance, and compensate for and eliminate the time delay that may occur in the current cycle T. The signal value collected at the normal wheel acquisition time of the current cycle is the reasonable signal value after eliminating the influence of time delay. Combining the time delay advance compensation scheme with the acquisition time axis, we can obtain the input-output time equation as follows:

[0116]

[0117] Where: t is any current sampling time, T is the calculation time of the path tracking control time domain period, and X T：t-k Y represents the system input for the current period, where the subscript indicates the signal input time considering time delay compensation; T：t This is the system reference output at the current moment, with the subscript indicating the time of wheel angle acquisition; θ is the distributed parameter - the steering ratio of the steering wheel angle to the wheel angle; k represents the time delay.

[0118] The optimal time delay calculated in the previous cycle is used as a signal to input the time delay compensation for the expected steering wheel angle in the current cycle in advance, thereby eliminating the impact of response delay caused by time delay.

[0119] Combining the input-output time formula, the time delay compensation within the final path tracking calculation cycle can be expressed by the expected log-likelihood function Λ of the time delay at the current cycle T, the optimal time delay k units in the previous cycle, and the turning input time t:

[0120]

[0121] Step 5: The forklift steering system controls the forklift steering based on the actual steering wheel angle obtained in Step 4, and obtains the optimal time delay within the path tracking period T.

[0122] Step 6: Let T = T + 1 and execute Step 1. After hydraulic steering time delay estimation and compensation, the time delay of the forklift hydraulic steering system in the path tracking cycle is eliminated. The kinematics, position parameters and other information of the forklift after the path tracking steering operation is performed by the forklift hydraulic steering system will be used as input into the calculation of the next cycle of the path tracking algorithm to form a closed loop and complete the entire path tracking process.

[0123] Example

[0124] The time delay estimation and compensation process during path tracking in a certain type of 3-ton intelligent forklift is as follows:

[0125] Step 1: Obtain the optimal time delay value of 2 under the previous tracking calculation cycle (T-1);

[0126] Step 2: The path tracking algorithm calculates the theoretical wheel turning angle as β = 22° under a certain path tracking cycle T, and the steering system transmission ratio K. v =11, which translates to a theoretical steering wheel angle parameter θ = 242°;

[0127] Step 3: Combine the input-output time alignment equation to obtain the theoretical steering wheel angle input time X under the current cycle. T：t-2 ;

[0128] Step 4: Input the theoretical steering wheel angle into the hydraulic steering system in advance under the current period T;

[0129] Step 5: Control the forklift's steering based on the obtained theoretical steering wheel angle and obtain the optimal time delay within the current period T;

[0130] Step 6: Bring the optimal time delay within period T to step 1, and repeat the above steps to perform closed-loop path tracking control.

[0131] The final comparison charts are as follows: path tracking considering time delay estimation and compensation versus path tracking without time delay estimation and compensation, and tracking error comparison charts. Figure 5 , Figure 6 As shown.

[0132] In summary, the forklift path tracking control method based on hydraulic steering time delay estimation and compensation of the present invention can effectively estimate and compensate for the time delay of the hydraulic steering system during intelligent forklift path tracking, thereby improving the path tracking accuracy of intelligent forklifts.

[0133] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0134] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A forklift path tracking control method based on steering time delay estimation and compensation, characterized in that, The path, according to the control method, includes the following steps: Step 1, Obtain The optimal time delay within the period is: The path tracking calculation cycle, and ,when The optimal time delay is zero. Obtaining the optimal time delay includes the following steps: S1. Establish a hydraulic steering input-output probability model; S2. Establish a time-delay acquisition timeline; S3. Combine the input-output probability model and the time delay acquisition time axis with the variational Bayesian estimation algorithm to estimate the steering time delay, and obtain the optimal time delay for each path tracking calculation cycle. Step 2: Obtain the forklift steering wheel angle parameters and wheel angle parameters; Step 3: Obtain the path tracking cycle Forklift Expected Wheel Angle Expected steering wheel angle ; Step 4, based on the information obtained in Step 1 The optimal time delay within the cycle and the expected wheel angle of the forklift in step 3 Expected steering wheel angle Calculate path tracking cycle The actual steering wheel angle inside; Step 5: The forklift steering system controls the forklift steering based on the actual steering wheel angle obtained in Step 4, and obtains the path tracking cycle. The optimal time delay within; Step 6, let Then proceed with step 1.

2. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 1, characterized in that, The desired steering wheel angle ,in, This refers to the steering system gear ratio.

3. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 1, characterized in that, The hydraulic steering input-output probability model is as follows: ; in Input a vector consisting of the steering wheel angles. The hydraulic steering input-output probability model is established for each path tracking calculation cycle, using distributed parameters. The error caused by time delay is regarded as process noise. Assuming that the system has normally distributed noise, the time delay probability can be expressed as: The maximum likelihood distribution is: in, This is a vector composed of system reference outputs, with the reference wheel angle as the reference. Let V be the variance of the noise.

4. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 1, characterized in that, The time-delay acquisition time axis includes the wheel angle sensor acquisition period, the path tracking calculation period, and the lag time difference; the establishment of the time-delay acquisition time axis in S2 includes the following steps: S2.1, Define the time lag. Each path tracking calculation cycle corresponds to a different turning angle acquisition time relative to the steering wheel turning angle input time. A unit of time difference, one unit being one acquisition cycle of the wheel angle sensor. The length of time; S2.2, Define latent variable parameters In each control time domain period corresponding to the acquisition time axis Below is a vector composed of binary 0s and 1s. Indicates the steering wheel angle input to the model. And the input time is The time delay error between the time and the output wheel rotation angle is denoted by the vector set. ; The superscript indicates the difference in timestamps between the model input and the reference output, and the upper limit of the time delay is set to... , ; in, This is the data acquisition cycle for the wheel angle sensor.

5. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 4, characterized in that, The wheel angle sensor acquisition cycle refers to the interval at which angle information is acquired; the path tracking calculation cycle refers to the cycle during which the path tracking control algorithm processes the acquired signals and calculates and updates the desired wheel angle.

6. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 4, characterized in that, The steps in S3 for obtaining the optimal steering delay step using the variational Bayesian estimation algorithm are as follows: In the variational Bayesian estimation algorithm, the estimated values ​​corresponding to different steering wheel angle inputs are assigned to the distribution parameters and the latent variables. Combining the maximum likelihood distribution formula, the approximate joint distribution is: in: This is the suggested distribution, which is the estimated value corresponding to different working conditions; In the variational Bayesian estimation algorithm, the remaining proposal distributions are optimized by fixing the other proposal distributions. The optimal time-delay proposal distribution of the system is given by the Kullback-Leibler Divergence formula: in: Since the variational Bayesian estimation algorithm remains constant during the solution process, formula (4) is equivalent to: in: as well as Assuming the values ​​are fixed, both distributions are known. Integrating each distribution yields the corresponding constant values ​​for the integral, and the known distributions can be used as conditions to obtain the expected value in the corresponding maximum likelihood estimate, i.e. Therefore, formula (5) can be equivalent to: = Finally, the system time-delay proposal distribution formula can be expressed as the entropy difference between the likelihood expectation exponents of the other two fixed proposal distributions, and the optimal solution can be expressed as: Will and The proposed distribution can be parameterized as follows: The model's likelihood distribution and prior distribution are conjugate distributions. and The parameters can be obtained from the probability conjugate, and are as follows: Where: <.> represents the expected value of its own distribution. and The relevant parameters are expressed as follows: Final different corner inputs The time delay statistics can all obtain an effective posterior distribution, and the optimal time delay can be made for each period.

7. The forklift path tracking control method based on steering time delay estimation and compensation according to claim 1, characterized in that, The optimal time delay is combined with the time delay acquisition time axis to obtain the input-output time equation; The input-output time equation is: in: For any current sampling time, The calculation time for the time domain period of path tracking control. This represents the system input for the current period, with the subscript indicating the signal input time considering time delay compensation. This is the system reference output at the current moment, with the subscript indicating the time when the wheel rotation angle was collected; The distributed parameter is the steering ratio between the steering wheel angle and the wheel angle. Represents time lag; Combining the input-output time equations, the time delay compensation model within the path tracking calculation cycle can be used in the current cycle. The optimal time delay in the previous cycle Units and angle input time The expected log-likelihood function under time delay To indicate: 。

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