Traction-type AGV robust adaptive path tracking method considering trailer drift suppression

Abstract

The invention discloses a traction-type AGV robust adaptive path tracking method considering trailer drift suppression, and belongs to the field of intelligent transportation AGV path tracking control. First, a path tracking control system of a towed AGV is modeled, where an articulation angle and an articulation angular velocity are introduced into a control system state to suppress drifting behavior of a trailer. Then, a robust adaptive path tracking control method combining feedforward control and feedback control is developed to improve tracking performance and robustness. In feed-forward control, a feed-forward controller capable of minimizing a tracking error in advance is designed. In feedback control, an H-infinity robust feedback controller based on observation is designed to weaken the influence of random disturbance. Wherein the preview distance model and the fuzzy algorithm are introduced into the feedback controller so as to improve the tracking precision and the adaptive capability of the path tracking control system. According to the invention, the tracking precision, robustness and stability of the traction-type AGV in a path tracking scene can be effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of automated guided vehicle (AGV, Automated Guided Vehicle) control, and particularly relates to a robust adaptive control method for a towed AGV to achieve high-precision path tracking and suppress trailer fishtailing in a complex dynamic environment, which is applicable to scenarios such as warehousing logistics and industrial transportation. Background Art

[0002] A towed AGV usually consists of a tractor and a trailer, and is widely used in fields such as logistics warehousing and industrial handling due to its high transportation efficiency. However, the articulated structure of the towed AGV is complex, and it is difficult to ensure the tracking accuracy during transportation. Moreover, when turning or driving at high speed, the trailer is prone to fishtailing due to inertia or external disturbances, resulting in an increase in path tracking error or even instability. In addition, random disturbances in a complex environment (such as sensor false alarms and missed reports, sudden changes in path curvature, model uncertainties, etc.) will further exacerbate the tracking error. Therefore, traditional control methods are difficult to balance the robustness and adaptability of path tracking of the towed AGV.

[0003] The paper "Trajectory Generation and Tracking Control for Double-Steering Tractor-Trailer Mobile Robots With On-Axle Hitching" published in the 12th issue of Volume 62 of the IEEE Transactions on Industrial Electronics in 2015 proposed a backstepping controller. By constructing a Lyapunov function through hierarchical recursion, it forced the system state to converge to the desired trajectory, ultimately achieving the cooperative path tracking of the tractor and the trailer. However, this method did not consider the influence of random disturbances such as sudden changes in path curvature and modeling errors on the control system, which was prone to performance degradation. The paper "Robust Tube-Based Model Predictive Control for Lane Change Maneuver of Tractor-Trailer Vehicles Based on a Polynomial Trajectory" published in the 12th issue of Volume 50 of the IEEE Transactions on Systems, Man, and Cybernetics: Systems in 2020 proposed a robust tube-based model predictive control method. By constructing a composite control architecture of a model predictive controller oriented to the system and an auxiliary feedback control law, it effectively solved the limitations of traditional model predictive control in dealing with nonlinear constraints, parameter uncertainties, and external disturbances. However, this method did not consider the phenomenon of trailer fishtailing caused by dynamic coupling relationships or external disturbances, which was prone to potential lateral instability.

[0004] In summary, it is of great practical significance to develop a robust adaptive path tracking method for a towed AGV that takes into account the suppression of trailer fishtailing and random disturbances. Summary of the Invention

[0005] To address the above problems, the present invention proposes a robust adaptive path tracking method for a towed AGV that takes into account the suppression of trailer fishtailing. By introducing the articulated angle state, preview distance model, and fuzzy algorithm, it realizes the high-precision path tracking of the towed AGV, while suppressing trailer fishtailing and weakening the influence of random disturbances.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A robust adaptive path tracking method for a towed AGV considering trailer swing suppression aims to effectively suppress the trailer swing behavior and reduce the influence of random disturbances while adapting to changes in speed and path curvature. First, a path tracking control system model of the towed AGV is established, where the articulation angle and angular velocity between the tractor and the trailer are introduced into the control system state to suppress the trailer swing behavior. Then, a robust adaptive path tracking control method is developed, which combines feedforward control and feedback control to improve the tracking performance and robustness of the system. In the feedforward control, the feedforward controller is designed to minimize the lateral tracking error of the towed AGV. In the feedback control, an observer-based H∞ robust feedback controller is developed to limit the influence of random disturbances, and a preview distance model considering the changes in speed and path curvature is introduced to implement preview control. At the same time, a fuzzy algorithm is applied to the observer-based H∞ robust feedback controller to adapt to the changing vehicle speed. Finally, based on the H∞ theory, the design criteria of the observer-based H∞ robust feedback controller are established to achieve the rapid solution of the observer gain and control gain. The specific steps are as follows:

[0008] Step 1: Model the path tracking control system of the towed AGV. First, establish the dynamic model of the towed AGV with three degrees of freedom, and then transform the vehicle dynamic state in the Cartesian coordinate system into the path tracking error state in the Frenét coordinate system for the design of the path tracking controller. Specifically as follows:

[0009] Step 1.1: The towed AGV in the present invention includes a two-axle tractor and a single-axle trailer, which are articulated through a towing seat. This articulation form belongs to off-axis articulation, and the articulation point is behind the center line of the rear axle of the tractor. First, make the following assumptions about the dynamic model of the towed AGV: 1) The steering angle δ, tire side slip angle α, and articulation angle θ of the towed AGV are small angles; 2) Assume that the longitudinal speeds of the tractor and the trailer are equal and both equal to v x ; 3) Assume that the curvature of the desired path is a small curvature. The dynamic model of the towed AGV includes the following three degrees of freedom: 1) The lateral speed v of the tractor y1 ; 2) The yaw angular velocity ω1 of the tractor; 3) The articulation angle θ between the tractor and the trailer. Based on the above, the dynamic relationship of the towed AGV is as follows:

[0010]

[0011] Among them, v x represents the longitudinal speed of the towed AGV, m1 represents the mass of the tractor, m2 represents the mass of the trailer, I1 represents the yaw moment of inertia of the tractor, I2 represents the yaw moment of inertia of the trailer, v y1represents the lateral speed of the tractor, v y2 represents the lateral speed of the trailer, ω1 represents the yaw angular velocity of the tractor, ω2 represents the yaw angular velocity of the trailer, F yf represents the lateral tire force on the front axle of the tractor, F yr represents the lateral tire force on the rear axle of the tractor, F yt represents the lateral tire force on the axle of the trailer, F xP represents the longitudinal hinge force at the articulation point, F yP represents the lateral hinge force at the articulation point, the subscript x represents the longitudinal vector of the towed AGV, the subscript y represents the lateral vector of the towed AGV, a1 represents the distance from the front axle of the tractor to the center of mass of the tractor, a2 represents the distance from the rear axle of the tractor to the center of mass of the tractor, a3 represents the distance from the rear axle of the tractor to the articulation point, a4 represents the distance from the articulation point to the center of mass of the tractor, b1 represents the distance from the articulation point to the center of mass of the trailer, b2 represents the distance from the axle of the trailer to the center of mass of the trailer, l2 = b1 + b2 represents the distance from the axle of the trailer to the articulation point.

[0012] The kinematic constraint relationship between the tractor and the trailer is:

[0013]

[0014] where θ represents the articulation angle, represents the articulation angular velocity.

[0015] Based on Equation (2), v in Equation (1) y2 and ω2 can be replaced.

[0016] Step 1.2: Modeling the tire model of the towed AGV. Since the lateral tire force is proportional to the tire side slip angle when the tire side slip angle is small, the lateral tire force on each axle of the towed AGV is expressed as:

[0017]

[0018] where C f represents the tire side slip stiffness of the front axle of the tractor, C r represents the tire side slip stiffness of the rear axle of the tractor, C t represents the tire side slip stiffness of the trailer axle, α f represents the tire side slip angle of the front axle of the tractor, α r represents the tire side slip angle of the rear axle of the tractor, α t represents the tire side slip angle of the trailer axle. The tire side slip angle of each axle of the towed AGV is expressed as:

[0019]

[0020] Among them, δ represents the steering angle of the towed AGV.

[0021] Step 1.3: Based on the content described in Step 1.1 and Step 1.2, convert the vehicle dynamics state in the Cartesian coordinate system to the path tracking error state in the Frenét coordinate system for designing the path tracking controller. Specifically:

[0022] First, according to the kinematic relationship of the towed AGV in the Frenét coordinate system, the heading angle error e2, the heading angular velocity error and the heading angular acceleration error are expressed as:

[0023]

[0024] Among them, ψ1 represents the heading angle of the tractor, ψ des represents the desired heading angle of the tractor, represents the heading angular velocity of the tractor, represents the desired heading angular velocity of the tractor, ρ represents the path curvature of the desired trajectory corresponding to the tractor, represents the yaw angular acceleration of the tractor.

[0025] At the same time, the lateral distance error e1, the lateral velocity error and the lateral acceleration error are expressed as:

[0026]

[0027] Among them, y1 represents the lateral position of the center of mass of the tractor, y des represents the desired lateral position of the center of mass of the tractor, represents the lateral velocity of the center of mass of the tractor, represents the lateral acceleration of the center of mass of the tractor.

[0028] Step 1.4: Define the system state of the path tracking control system of the towed AGV as: And according to Formulas (1) - (6), the path tracking control system can be modeled as:

[0029]

[0030] Among them,

[0031]

[0032] Among them, A, B1, and B2 represent the system state matrices. Ω, a 22 、a 24 、a 25, a 26 , a 42 , a 44 , a 45 , a 46 , a 62 , a 64 , a 65 , a 66 , κ1, κ2, κ4, κ5, κ7, and κ8 represent the coefficients of the system state matrix and are expressed as:

[0033]

[0034] a 25 = κ1C t - κ2a4C t + κ3C t l2,

[0035]

[0036] a 45 = κ4C t - κ5a4C t - κ6C t l2,

[0037]

[0038] a 65 = κ7C t - κ8a4C t + κ9C t l2,

[0039]

[0040] κ1 = a4b1m2M 64 - M 44 M 66 ,

[0041] κ2 = b1m2M 64 + M 24 M 66 ,

[0042]

[0043] κ7 = (a4M 64 - b1M 44 )m2,

[0044] κ8 = b1m2M 24 + m1M 64 + m2M 64 ,

[0045] where κ3, κ6, κ9, M24 , M 44 , M 64 , M 66 , E 22 , E 24 , E 42 , E 44 and E 64 represent coefficients, and they are expressed as:

[0046] κ3 = (a4M 24 + M 44 )m2b1,

[0047] κ6 = a4b1m1m2,

[0048] κ9 = a4m2M 24 + m1M 44 + m2M 44 ,

[0049] M 24 = -m2(b1 + a4),

[0050]

[0051] E 22 = C f + C r + C t ,

[0052]

[0053] E 42 = a1C f - a2C r - a4C t ,

[0054]

[0055] It should be noted that since it is assumed in the present invention that the curvature of the desired trajectory is a small curvature, during the driving process, the articulation angle θ of the towed AGV tends to zero, so it can be known that the desired articulation angle of the towed AGV also tends to zero. In addition, under complex driving conditions, the towed AGV is likely to exhibit a fishtailing behavior due to different ground adhesion forces acting on the two wheels of the trailer axle. For this reason, θ and are introduced into the system state X of the path tracking control system of the towed AGV. This can suppress the amplitude and frequency of the trailer fishtailing, and thus can effectively improve the stability and safety of the path tracking of the towed AGV.

[0056] Step 1.5: Considering the random disturbances of the path tracking control system, such as the uncertainty disturbance w1 of the transmission ratio of the steering drive system of the towed AGV and the modeling error w2 of the path tracking control system, the path tracking control system with random disturbances can be defined as:

[0057]

[0058] Thus, the path tracking control system of the towed AGV is established.

[0059] Step 2: In this step, based on the path tracking control system with random disturbances designed in Step 1, a feedforward controller will be designed to reduce the tracking error of the path tracking control system with random disturbances in advance.

[0060] Step 2.1: First, considering the feedforward controller, the path tracking control system with random disturbances can be rewritten as:

[0061]

[0062] where δ f represents the steering wheel angle obtained by the feedforward controller, δ b represents the steering wheel angle obtained by the feedback controller, and i w represents the transmission ratio from the steering wheel angle to the steering wheel angle of the steering drive system of the towed AGV. And in Equation (9),

[0063]

[0064] Step 2.2: According to Equation (10), it can be known that it is difficult to ensure that B1(δ f / i w ) + B2ρ = 0. To minimize the lateral velocity error and improve the lateral stability, the feedforward controller needs to be used to ensure For this reason, it can be obtained that:

[0065]

[0066] For this reason, the feedforward controller can be designed as:

[0067]

[0068] Step 2.3: Based on the feedforward controller (12) designed in Step 2.2, the path tracking control system with random disturbances after feedforward control is defined as:

[0069]

[0070] where B3 is the system state matrix considering the feedforward control, and it is expressed as:

[0071]

[0072] Step 3: Introduce a preview distance model into the path tracking control system (13) with random disturbances after feedforward control obtained in Step 2, laying a foundation for the feedback controller of the towing AGV designed later to achieve preview control.

[0073] Specifically:

[0074] Step 3.1: Considering that the curvature of the desired path will change continuously due to the influence of the road environment, the present invention introduces a preview distance model. This preview distance model can simulate the driving behavior of an experienced driver, make full use of road information, adapt to the changing speed and path curvature, and thus effectively improve the accuracy of path tracking. The preview distance model is expressed as follows:

[0075]

[0076] Where L p represents the preview distance, ρ th represents the threshold for judging the path curvature of a straight or curved road, T p1 represents the preview time interval when |ρ| < ρ th and ε1 represents the constant term when |ρ| < ρ th ; T p2 represents the preview time interval when |ρ| ≥ ρ th and ε2 represents the constant term when |ρ| ≥ ρ th .

[0077] Step 3.2: Assume that the desired path is a clothoid curve. Then, the system state X of the path tracking control system of the towing AGV can be transformed into the system preview state of the path tracking control system of the towing AGV for the preview point through the second-order approximation theory. Where e 1p represents the lateral distance error at the preview point, represents the lateral velocity error at the preview point, e 2p represents the heading angle error at the preview point, represents the heading angular velocity error at the preview point. They can be expressed as a linear combination of the variables e1, e2 and in the system state X of the path tracking control system of the towing AGV as follows:

[0078]

[0079] Thus, the system state X and the system preview state X of the path tracking control system of the towing AGV psatisfy the following relationship:

[0080]

[0081] wherein, and represent the system relationship matrix, and they are expressed as:

[0082]

[0083] It should be noted that in step 3.2, by converting the system state X of the path tracking control system of the towed AGV into the system preview state X p , the path tracking control system (13) with random disturbance based on feedforward control can be made to achieve preview control. At the same time, since the preview distance model (14) can adapt to the changing speed and path curvature, the proposed preview control method will have better robustness and can achieve better tracking performance in different driving scenarios.

[0084] Step 4: This step will design an observer-based H∞ robust feedback controller according to the path tracking control system (13) with random disturbance based on feedforward control obtained in step 2 and the system preview state X p of the path tracking control system of the towed AGV obtained in step 3. Specifically as follows:

[0085] Step 4.1: First, for the system preview state X p of the path tracking control system of the towed AGV obtained in step 3, the observer-based H∞ robust feedback controller is defined as:

[0086] δ b =i w KX p (17)

[0087] wherein, δ b represents the steering wheel angle obtained by the observer-based H∞ robust feedback controller, and K represents the control gain of the observer-based H∞ robust feedback controller.

[0088] Then, based on formula (16) and formula (17), the path tracking control system with random disturbance based on feedforward and feedback control is defined as:

[0089]

[0090] Here, it is assumed that the path curvature ρ of the expected trajectory corresponding to the tractor is the environmental disturbance, and by constructing the disturbance variable w = [ρ, w1, w2] T , w ∈ L2[0, ∞), and let the control law of the observer-based H∞ robust feedback controller be Then, the path tracking control system (18) with random disturbances after feedforward and feedback control is transformed into:

[0091]

[0092] where B0 and represent the system matrices, which are expressed as: B0 = [B3, B1, 1] and Here, 0 and 1 represent the column vectors of all 0s and all 1s respectively.

[0093] Meanwhile, considering that in the system state X of the path tracking control system of the towing AGV, only the lateral distance error e1, the heading angle error e2, and the articulation angle θ can be directly measured by sensors. Therefore, the measurement vector is defined as: Y = [e1, e2, θ] T , which is expressed as follows:

[0094] Y = CX (20)

[0095] where C represents the measurement matrix of the path tracking control system of the towing AGV, which is expressed as:

[0096]

[0097] Step 4.2: Considering the random disturbances caused by sensor failures (such as data packet loss, false data reports, and missed data reports), a Luenberger observer will be designed to avoid the influence of the random disturbances caused by sensor failures on the control performance of the observation-based H∞ robust feedback controller. The Luenberger observer is designed as follows:

[0098]

[0099] where, and represent the observed values of X and Y respectively; L represents the observation gain of the observer.

[0100] Step 4.3: Based on the Luenberger observer (21) designed in Step 4.2, the control law of the observation-based H∞ robust feedback controller is redefined as Therefore, the path tracking closed-loop control system is expressed as follows:

[0101]

[0102] Define the observation error of the Luenberger observer as Then the path tracking closed-loop control system (22) is equivalent to:

[0103]

[0104] Then, by constructing the augmented vector The path-tracking closed-loop augmented control system is expressed as:

[0105]

[0106] where and represent the system augmented matrices, which are expressed as:

[0107]

[0108] where I represents the identity matrix of appropriate dimension.

[0109] It should be noted that the control law of the observer-based H∞ robust feedback controller designed in step 4.3 fully considers the uncertainties of the path-tracking control system of the towed AGV and the influence of random disturbances caused by sensor failures. Therefore, the observer-based H∞ robust feedback controller designed in the present invention can theoretically exhibit excellent robustness.

[0110] Step 4.4: Next, based on the H∞ theory, design the design criterion of the observer-based H∞ robust feedback controller to solve the control gain K and the observer gain L. First, introduce the following two lemmas to provide a theoretical basis for the subsequent design criterion. The lemmas are as follows:

[0111] Lemma 1: Given two real matrices G and Z, then there exists a positive number ε > 0 satisfying the following inequality:

[0112]

[0113] where G and Z represent real matrices, and ε represents a positive number.

[0114] Lemma 2 (Schur complement lemma): Given positive definite symmetric matrices H and R, then the following two linear matrix inequalities are equivalent.

[0115]

[0116] H - SR -1 S T < 0 (27)

[0117] where H and S represent positive definite symmetric matrices.

[0118] Step 4.5: The design criterion for the observer-based H∞ robust feedback controller to satisfy the H∞ performance is given below, which is presented by Theorem 1 as follows:

[0119] Theorem 1: If there exist positive definite symmetric matrices \(P_1\) and \(P_2\), matrix \(Q\), positive numbers \(\varepsilon>0\) and \(\alpha>0\) satisfying the linear matrix inequality (28):

[0120]

[0121] Then the path - tracking closed - loop augmented control system (24) satisfies the \(H_{\infty}\) performance with a given attenuation factor \(\gamma>0\), that is:

[0122]

[0123] where \(\Sigma\) represents a linear matrix, \(\lambda\) max \((P)\) represents the maximum eigenvalue of the positive definite symmetric matrix \(P\), where \(P = \text{diag}\{P_1\) -1 , \(P_2\}\).

[0124] Step 4.6: By solving the linear matrix inequality (28), the positive definite symmetric matrices \(P_1\) and \(P_2\), matrix \(Q\) and the control gain \(K\) can be obtained, and then the observer gain \(L\) can also be obtained, that is: For this reason, an observer - based \(H_{\infty}\) robust feedback controller is designed and completed.

[0125] Step 5: During the process of solving the linear matrix inequality (28) proposed in Step 4, the speed \(v\) of the towed AGV x is assumed to be constant. However, during the path - tracking process of the towed AGV, the speed is variable. To ensure better tracking performance, it is necessary to solve the linear matrix inequality (28) for different speeds. However, if the linear matrix inequality for each different speed is solved, the required computing power is relatively large. For this reason, in order to reduce the computational pressure, a fuzzy algorithm is introduced in the observer - based \(H_{\infty}\) robust feedback controller to online determine the control gain \(K\) and the observer gain \(L\) at different speeds, so as to enhance the adaptive ability of the observer - based \(H_{\infty}\) robust feedback controller. The specific process is as follows:

[0126] Step 5.1: First, assume that the speed range is between \([0, 20]\) (m / s) and it is divided into 10 sub - intervals, that is, \([0, 2), [2, 4),\cdots, [18, 20]\) (m / s). Then, solve the control gain \(K\) and the observer \(L\) corresponding to the end - point speeds of each sub - interval. Next, use the fuzzy algorithm to find the control gain \(K\) and the observer gain \(L\) corresponding to different speeds within each sub - interval.

[0127] Here, assume that the speed within each speed sub - interval satisfies: \(v\) x \(\in[v\) xmin , \(v\) xmax , where \(v\) xmin and \(v\) xmaxrespectively represent the minimum speed and the maximum speed of each sub-interval. Then define and Then, the speed v x can be expressed as:

[0128]

[0129] where, ζ1 = v x , M1(ζ1) and M2(ζ1) represent membership functions, which satisfy: M1(ζ1) + M2(ζ1) = 1, and are expressed as:

[0130]

[0131] Step 5.2: According to the content of Step 5.1, the control gains K and the observer gains L corresponding to different speeds can be expressed as:

[0132]

[0133] where, K1 represents the control gain corresponding to the maximum speed of the sub-interval, K2 represents the control gain corresponding to the minimum speed of the sub-interval, L1 represents the observer gain corresponding to the maximum speed of the sub-interval, L2 represents the observer gain corresponding to the minimum speed of the sub-interval, h i (ζ1(t)) represents the fuzzy weighting function, which is expressed as:

[0134]

[0135] and it satisfies Through the above fuzzy algorithm, the gain matrices K and L for different speeds can be solved online, so that the observer-based H∞ robust feedback controller realizes adaptive control, and at the same time reduces the computing power requirement of the controller.

[0136] Step 6: Finally, based on the feedforward controller designed in Step 2 and the observer-based H∞ robust feedback controller designed in Step 4, the steering wheel input angle of the towed AGV that can be obtained is expressed as follows:

[0137] δ = (δ f + δ b ) / i w (34)

[0138] where, δ represents the steering wheel input angle of the towed AGV. For this reason, the towed AGV can achieve stable path tracking control.

[0139] Furthermore, in the above-mentioned Step 1, when modeling the path tracking control system of the towed AGV, in order to effectively suppress the fishtailing behavior of the trailer, the articulation angle and angular velocity between the tractor and the trailer are introduced into the control system state, and this method can effectively improve the stability of the towed AGV during path tracking.

[0140] Furthermore, in the above-mentioned Step 1, when modeling the path tracking control system of the towed AGV, the uncertainty interference of the transmission ratio of the steering transmission system and the modeling error of the path tracking control system are considered, and this method improves the authenticity of the path tracking control system modeling.

[0141] Furthermore, in the above-mentioned Step 2, the design of the feedforward controller can effectively minimize the lateral tracking error of the towed AGV.

[0142] Furthermore, in the above-mentioned Step 3, the preview distance model is introduced into the path tracking control system, and this method can effectively imitate the preview driving behavior of the driver, make full use of the road environment information, and thus effectively improve the accuracy of path tracking.

[0143] Furthermore, in the above-mentioned Step 4, an observation-based H∞ robust feedback controller is proposed. Since this feedback controller also includes a Luenberger observer, it can effectively suppress the influence caused by sensor failures such as data packet loss, false alarms, and missed reports, and thus can effectively improve the robustness of the feedback controller.

[0144] Furthermore, in the above-mentioned Step 4, when designing the observation-based H∞ robust feedback controller, the influence of random disturbances such as sensor failures, environmental disturbances, the uncertainty interference of the transmission ratio of the steering transmission system, and modeling errors is fully considered, so that the controller can still maintain good H∞ performance even in the face of the above random disturbance effects, and thus effectively improves the robustness of the controller.

[0145] Furthermore, in the above-mentioned Step 4, based on Lemma 1 and Lemma 2, the bilinear matrix inequality Π < 0 is successfully transformed into the linear matrix inequality Σ < 0, and thus the control gain K and observation gain L of the observation-based H∞ robust feedback controller are quickly solved.

[0146] Furthermore, in the above-mentioned Step 5, the fuzzy algorithm is applied to the observation-based H∞ robust feedback controller to solve the control gain K and observation gain L online at different speeds, so that the observation-based H∞ robust feedback controller realizes adaptive control and also reduces the computing power requirement of this feedback controller.

[0147] The beneficial effects of the present invention are:

[0148] (1) In order to effectively suppress the trailer swing behavior, when modeling the path tracking control system, the articulation angle and the articulation angular velocity are introduced into the system state of the path tracking control system, thereby effectively improving the stability of the path tracking control system of the towed AGV in the path tracking scenario.

[0149] (2) In order to improve the path tracking accuracy and robustness, a robust adaptive path tracking control method combining feedforward control and feedback control is developed. Among them, the feedforward controller is designed to minimize the lateral tracking error of the towed AGV. Then, in order to limit the influence of random disturbances, an observation-based H∞ robust feedback controller is designed, and a preview distance model considering the changes in speed and path curvature is introduced to achieve preview control.

[0150] (3) Based on the H∞ theory, the design criteria for the observation-based H∞ robust feedback controller are established to achieve the rapid solution of the observation gain and the control gain. At the same time, the fuzzy algorithm is applied to the observation-based H∞ robust feedback controller to adapt to the changing vehicle speed. Description of the Drawings

[0151] Figure 1 is a schematic diagram of the dynamic model of the towed AGV;

[0152] Figure 2 is a schematic diagram of the path tracking error of the towed AGV;

[0153] Figure 3 is a schematic diagram of the membership function of the fuzzy algorithm;

[0154] Figure 4 is a framework flowchart of a robust adaptive path tracking method for a towed AGV considering trailer swing suppression;

[0155] Figure 5 is the control effect diagram of the robust adaptive path tracking method for the towed AGV proposed by the present invention; Figure 5 (a) is the result of the lateral distance error during the path tracking process; Figure 5 (b) is the result of the heading angle error during the path tracking process; Figure 5 (c) is the result of the articulation angle during the path tracking process. Specific Implementation Method

[0157] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail below with reference to the drawings and embodiments.

[0158] As Figures 1-5 shown, the present invention includes the following steps:

[0159] Step 1: Model the path tracking control system of the towed AGV. First, establish the dynamic model of the towed AGV with three degrees of freedom. Then, transform the vehicle dynamic state in the Cartesian coordinate system into the path tracking error state in the Frenét coordinate system for the design of the path tracking controller. Specifically as follows:

[0160] Step 1.1: The towed AGV in the present invention includes a two-axle tractor and a single-axle trailer, which are articulated through a towing seat. This articulation form belongs to off-axis articulation, and the articulation point is behind the center line of the rear axle of the tractor. The schematic diagram of the dynamic model of the towed AGV is as Figure 1 shown. First, make the following assumptions about the dynamic model of the towed AGV: 1) The steering angle δ, the tire side slip angle α, and the articulation angle θ of the towed AGV are small angles; 2) Assume that the longitudinal speeds of the tractor and the trailer are equal and both equal to v x ; 3) Assume that the curvature of the desired path is a small curvature. The dynamic model of the towed AGV includes the following three degrees of freedom: 1) The lateral speed v of the tractor y1 ; 2) The yaw angular velocity ω1 of the tractor; 3) The articulation angle θ between the tractor and the trailer. Based on the above, the dynamic relationship of the towed AGV is shown as follows:

[0161]

[0162] The kinematic constraint relationship between the tractor and the trailer is:

[0163]

[0164] where θ represents the articulation angle, represents the articulation angular velocity.

[0165] Based on formula (2), v in formula (1) y2 and ω2 can be replaced.

[0166] Step 1.2: Model the tire model of the towed AGV. Since the lateral tire force is proportional to the tire side slip angle when the tire side slip angle is small, the lateral tire force on each axle of the towed AGV is shown in formula (3). Then, the tire side slip angle of each axle of the towed AGV is shown in formula (4):

[0167] Step 1.3: Based on the content described in Step 1.1 and Step 1.2, transform the vehicle dynamic state in the Cartesian coordinate system into the path tracking error state in the Frenét coordinate system for the design of the path tracking controller. Specifically:

[0168] First, according to the kinematic relationship of the towed AGV in the Frenét coordinate system (the schematic diagram of the path tracking error of the towed AGV is as shown in Figure 2 ), the heading angle error e2, the heading angular velocity error and the heading angular acceleration error are expressed as:

[0169]

[0170] Meanwhile, the lateral distance error e1, the lateral velocity error and the lateral acceleration error are expressed as:

[0171]

[0172] Step 1.4: Define the system state of the path tracking control system of the towed AGV as: And according to formulas (1)-(6), the path tracking control system can be modeled as:

[0173]

[0174] Where,

[0175]

[0176] Where, A, B1, and B2 represent the system state matrices. Ω, a 22 , a 24 , a 25 , a 26 , a 42 , a 44 , a 45 , a 46 , a 62 , a 64 , a 65 , a 66 , κ1, κ2, κ4, κ5, κ7, and κ8 represent the coefficients of the system state matrices, expressed as:

[0177] a 25 = κ1C t - κ2a4C t + κ3C t l2,

[0178]

[0179] a 45 = κ4C t - κ5a4C t - κ6C t l2,

[0180]

[0181] a 65 = κ7C t - κ8a4C t + κ9C t l2,

[0182]

[0183] κ1 = a4b1m2M 64 -M 44 M 66 ,

[0184] κ2 = b1m2M 64 +M 24 M 66 ,

[0185]

[0186] κ7 = (a4M 64 -b1M 44 )m2,

[0187] κ8 = b1m2M 24 +m1M 64 +m2M 64 ,

[0188] where κ3, κ6, κ9, M 24 、M 44 、M 64 、M 66 、E 22 、E 24 、E 42 、E 44 and E 64 represent coefficients, and they are expressed as:

[0189] κ3 = (a4M 24 +M 44 )m2b1,

[0190] κ6 = a4b1m1m2,

[0191] κ9 = a4m2M 24 +m1M 44 +m2M 44 ,

[0192] M 24 = -m2(b1 + a4),

[0193]

[0194] E 22 = C f + C r + C t ,

[0195]

[0196] E 42 = a1C f - a2C r - a4C t ,

[0197]

[0198] Step 1.5: Considering the random disturbances of the path tracking control system, such as the uncertainty disturbance w1 of the transmission ratio of the steering drive system of the towed AGV and the modeling error w2 of the path tracking control system, the path tracking control system with random disturbances can be defined as:

[0199]

[0200] Thus, the path tracking control system of the towed AGV is established.

[0201] Step 2: In this step, based on the path tracking control system with random disturbances designed in Step 1, a feedforward controller is designed to reduce the tracking error of the path tracking control system with random disturbances in advance.

[0202] Step 2.1: First, considering the feedforward controller, the path tracking control system with random disturbances can be rewritten as:

[0203]

[0204] where δ f represents the steering wheel angle obtained by the feedforward controller, δ b represents the steering wheel angle obtained by the feedback controller, and i w represents the transmission ratio from the steering wheel angle to the steering wheel angle of the steering drive system of the towed AGV. And, in Equation (9),

[0205]

[0206] Step 2.2: According to Equation (10), it can be known that it is difficult to ensure that B1(δ f / i w ) + B2ρ = 0. To minimize the lateral velocity error and improve the lateral stability, the feedforward controller needs to be used to ensure For this, it can be obtained that:

[0207]

[0208] Therefore, the feedforward controller can be designed as follows:

[0209]

[0210] Step 2.3: Based on the feedforward controller (12) designed in Step 2.2, the path tracking control system with random disturbances after feedforward control is defined as:

[0211]

[0212] where B3 is the system state matrix considering the feedforward control, and it is expressed as:

[0213]

[0214] Step 3: Introduce a preview distance model to the path tracking control system (13) with random disturbances after feedforward control obtained in Step 2, laying a foundation for the feedback controller of the towed AGV designed later to achieve preview control.

[0215] Specifically:

[0216] Step 3.1: Considering that the curvature of the desired path changes continuously due to the influence of the road environment, the present invention introduces a preview distance model. This preview distance model can simulate the driving behavior of an experienced driver, make full use of road information, adapt to the changing speed and path curvature, and thus effectively improve the accuracy of path tracking. The preview distance model is expressed as follows:

[0217]

[0218] where L p represents the preview distance, ρ th represents the threshold of the path curvature for judging a straight road or a curved road, T p1 represents the preview time when |ρ| < ρ th ε1 represents the constant term when |ρ| < ρ th T p2 represents the preview time when |ρ| ≥ ρ th ε2 represents the constant term when |ρ| ≥ ρ th at this time.

[0219] Step 3.2: Assume that the desired path is a clothoid curve. Then, the system state X of the path tracking control system of the towed AGV can be transformed into the system preview state of the path tracking control system of the towed AGV for the preview point through the second-order approximation theory where e 1p represents the lateral distance error at the preview point. represents the lateral velocity error at the preview point, e 2p represents the heading angle error at the preview point, represents the heading angular velocity error at the preview point, and they can utilize the variables e1 in the system state X of the path tracking control system of the towing AGV, e2 and are represented by the following linear combination:

[0220]

[0221] Thus, the system state X of the path tracking control system of the towing AGV and the system preview state X p satisfy the following relationship:

[0222]

[0223] wherein, and represent the system relationship matrices, and they are represented as:

[0224]

[0225] Step 4: This step will design an observer-based H∞ robust feedback controller according to the path tracking control system (13) with random disturbances after feedforward control obtained in Step 2 and the system preview state X of the path tracking control system of the towing AGV obtained in Step 3. Specifically as follows: p , and the details are as follows:

[0226] Step 4.1: First, for the system preview state X of the path tracking control system of the towing AGV obtained in Step 3 p , the observer-based H∞ robust feedback controller is defined as:

[0227] δ b = i w KX p (17)

[0228] wherein, δ b represents the steering wheel angle obtained by the observer-based H∞ robust feedback controller, and K represents the control gain of the observer-based H∞ robust feedback controller.

[0229] Then, based on formulas (16) and (17), the path tracking control system with random disturbances after feedforward and feedback control is defined as:

[0230]

[0231] Here, it is assumed that the path curvature ρ of the desired trajectory corresponding to the tractor is an environmental disturbance, and the disturbance variable w = [ρ, w1, w2] is constructed T , w ∈ L2[0, ∞), and the control law of the H∞ robust feedback controller based on observation is defined as Then, the path tracking control system (18) with random disturbances after feedforward and feedback control is transformed into:

[0232]

[0233] where, B0 and represent the system matrices, and they are expressed as: B0 = [B3, B1, 1] and Here, 0 and 1 represent the column vectors of all 0s and all 1s respectively.

[0234] Meanwhile, considering that among the system states X of the path tracking control system of the towed AGV, only the lateral distance error e1, the heading angle error e2, and the articulation angle θ can be directly measured by sensors. Therefore, the measurement vector is defined as: Y = [e1, e2, θ] T , and it is expressed as follows:

[0235] Y = CX (20)

[0236] where, C represents the measurement matrix of the path tracking control system of the towed AGV, and it is expressed as:

[0237]

[0238] Step 4.2: Considering the random disturbances caused by sensor failures (such as packet loss, false data reporting, and data omission), a Luenberger observer will be designed to avoid the influence of the random disturbances caused by sensor failures on the control performance of the H∞ robust feedback controller based on observation. The Luenberger observer is designed as follows:

[0239]

[0240] where, and represent the observed values of X and Y respectively; L represents the observation gain of the observer.

[0241] Step 4.3: Based on the Luenberger observer (21) designed in Step 4.2, the control law of the H∞ robust feedback controller based on observation is redefined as Therefore, the path tracking closed-loop control system is expressed as follows:

[0242]

[0243] Define the observation error of the Luenberger observer as Then the path tracking closed-loop control system (22) is equivalent to:

[0244]

[0245] Then, by constructing the augmented vector The path tracking closed-loop augmented control system is expressed as:

[0246]

[0247] Where, and represent the system augmented matrices, and they are expressed as:

[0248]

[0249] Where, I represents the identity matrix of appropriate dimension.

[0250] It should be noted that the control law of the observation-based H∞ robust feedback controller designed in step 4.3 fully considers the uncertainties of the path tracking control system of the towed AGV and the influence of the random disturbances caused by sensor failures. Therefore, the observation-based H∞ robust feedback controller designed in the present invention can theoretically exhibit excellent robustness.

[0251] Step 4.4: Next, based on the H∞ theory, the design criteria of the observation-based H∞ robust feedback controller will be designed to solve the control gain K and the observation gain L. First, the following two lemmas are introduced to provide a theoretical basis for the subsequent design criteria. The lemmas are as follows:

[0252] Lemma 1: Given the following two real matrices G and Z, then there exists a positive number ε > 0 that satisfies the following inequality:

[0253]

[0254] Where, G and Z represent real matrices, and ε represents a positive number.

[0255] Lemma 2 (Schur complement lemma): Given positive definite symmetric matrices H and R, then the following two linear matrix inequalities are equivalent.

[0256]

[0257] H - SR -1 S T <0 (27)

[0258] Where, H and S represent positive definite symmetric matrices.

[0259] Step 4.5: The following presents the design criterion for the H∞ robust feedback controller to satisfy the H∞ performance based on observations, which is demonstrated by Theorem 1 as follows:

[0260] Theorem 1: If there exist positive definite symmetric matrices P1 and P2, matrix Q, positive numbers ε > 0 and α > 0 that satisfy the linear matrix inequality (28):

[0261]

[0262] Then the path-tracking closed-loop augmented control system (24) satisfies the H∞ performance with a given attenuation factor γ > 0, that is:

[0263]

[0264] where Σ represents a linear matrix, λ max (P) represents the maximum eigenvalue of the positive definite symmetric matrix P, where P = diag{P1 -1 , P2}.

[0265] Step 4.6: The following will prove Theorem 1 proposed in Step 4.5.

[0266] First, design the Lyapunov function as:

[0267]

[0268] The derivative of the Lyapunov function is:

[0269]

[0270] To ensure the H∞ performance, the following performance index is introduced:

[0271]

[0272] Based on Equation (24) and Equation (36), Equation (37) is equivalent to:

[0273]

[0274] where Π represents a matrix. Then, define P = diag{P1 -1 , P2} and Q = P2L, the matrix Π can be rewritten as:

[0275]

[0276] where, Π 11 and Π 22 represent matrix coefficients, here, Π 22 = P2A - QC + A T P2 - CT Q T 。

[0277] Then, by multiplying the matrix Π on the left and right by diag{P1, I, I}, the following can be equivalently obtained:

[0278]

[0279] where, denotes the matrix, and denote the matrix coefficients. Here,

[0280]

[0281] Based on Lemma 1, there exists α > 0 such that the following inequality holds:

[0282]

[0283] where α 2 The introduction of I is to eliminate the equality relationship in inequality (25) in Lemma 1.

[0284] Based on inequality (41), the following can be obtained:

[0285]

[0286] where, denotes the matrix, denotes the matrix coefficient, here,

[0287] Then, by using Lemma 2, the non - linear matrix can be transformed into the linear matrix Σ. For this purpose, from the linear matrix inequality (28), Π < 0 can be obtained, and then J < 0 can be obtained. Thus, the following can be obtained:

[0288]

[0289] where, Furthermore, inequality (43) is equivalent to:

[0290]

[0291] For this purpose, the path - tracking closed - loop augmented control system (24) has H∞ performance. Here, the proof of Theorem 1 is completed.

[0292] Step 4.7: By solving the linear matrix inequality (28), the positive definite symmetric matrices P1 and P2, the matrix Q, and the control gain K can be obtained, and then the observer gain L can also be obtained, that is: For this reason, an observation-based H∞ robust feedback controller is designed. From the above derivation, it can be seen that based on Lemma 1 and Lemma 2, the bilinear matrix inequality Π < 0 is successfully transformed into the linear matrix inequality Σ < 0, thus realizing the rapid solution of the control gain K and the observation gain L.

[0293] Step 5: During the process of solving the linear matrix inequality (28) proposed in Step 4, the speed v of the towed AGV x is assumed to be constant. However, during the path tracking of the towed AGV, the speed changes. To ensure better tracking performance, it is necessary to solve the linear matrix inequality (28) at different speeds. However, if the linear matrix inequality at each different speed is solved, the required computing power is relatively large. For this reason, in order to reduce the computational pressure, the present invention introduces a fuzzy algorithm in the observation-based H∞ robust feedback controller to online determine the control gain K and the observation gain L at different speeds, thereby enhancing the adaptive ability of the observation-based H∞ robust feedback controller. The specific process is as follows:

[0294] Step 5.1: First, assume that the speed range is between [0, 20] (m / s) and decompose it into 10 subintervals, namely [0, 2), [2, 4),..., [18, 20] (m / s). Then, solve the control gain K and the observation L corresponding to the end-point speeds of each subinterval. For the control gain K and the observation gain L corresponding to different speeds within each subinterval, use the fuzzy algorithm to find them.

[0295] Here, assume that the speed within each speed subinterval satisfies: v x ∈[v xmin , v xmax , where v xmin and v xmax respectively represent the minimum speed and the maximum speed of each subinterval. Then define and The speed v x is expressed as:

[0296]

[0297] where ζ1 = v x , M1(ζ1) and M2(ζ1) represent membership functions (the schematic diagram of the membership function of the fuzzy algorithm is as shown in Figure 3 ), they satisfy: M1(ζ1) + M2(ζ1) = 1, and are expressed as:

[0298]

[0299] Step 5.2: The obtained control gain K and observation gain L corresponding to different speeds are expressed as:

[0300]

[0301] Among them, K1 represents the control gain corresponding to the maximum speed of the sub-interval, K2 represents the control gain corresponding to the minimum speed of the sub-interval, L1 represents the observation gain corresponding to the maximum speed of the sub-interval, L2 represents the observation gain corresponding to the minimum speed of the sub-interval, and h i (ζ1(t)) represents the fuzzy weighting function, which is expressed as:

[0302]

[0303] And it satisfies Through the above fuzzy algorithm, the gain matrices K and L at different speeds can be solved online, so that the observation-based H∞ robust feedback controller realizes adaptive control, and at the same time reduces the computing power requirement of the controller.

[0304] Step 6: Finally, the steering wheel input angle of the towed AGV that can be obtained by combining the feedforward controller designed in Step 2 and the observation-based H∞ robust feedback controller designed in Step 4 is expressed as follows:

[0305] δ = (δ f + δ b ) / i w (34)

[0306] Among them, δ represents the steering wheel input angle of the towed AGV. Therefore, the towed AGV can achieve stable path tracking control. The framework flowchart of a robust adaptive path tracking method for a towed AGV considering trailer swing suppression proposed by the present invention is as Figure 4 shown. And, the control effect diagram of a robust adaptive path tracking method for a towed AGV considering trailer swing suppression proposed by the present invention is as Figure 5 shown. From Figure 5 (a), it can be seen that the lateral distance error during the path tracking process is between [-0.05, 0.05] m. It can be seen from this that based on the robust adaptive path tracking method proposed by the present invention, the towed AGV can track the desired path well; from Figure 5 (b), it can be seen that the heading angle error during the path tracking process is between [-0.02, 0.02] rad. It can be seen from this that based on the robust adaptive path tracking method proposed by the present invention, the towed AGV can track the desired heading angle well; from Figure 5(c) It can be seen that during the path tracking process, the articulation angle is between [-0.02, 0.02] rad. From this, it can be known that based on the robust adaptive path tracking method proposed in the present invention, the articulation angle of the towed AGV is very small, and the behavior of the trailer fishtailing will not occur. In summary, the proposed robust adaptive path tracking method for towed AGV considering trailer fishtailing suppression in the present invention can effectively improve the tracking accuracy, robustness and stability of the towed AGV in the path tracking scenario.

[0307] The specific embodiments of the present invention disclosed above are only for illustration, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes, shall be covered by the protection scope of the present invention.

Claims

1. A robust adaptive path tracking method for a towed AGV considering trailer fishtail suppression, characterized in that, The robust adaptive path tracking method for the towed AGV includes the following steps: Step 1: Model the path tracking control system of the towed AGV. First, establish the dynamic model of the towed AGV with three degrees of freedom, and then transform the vehicle dynamic state in the Cartesian coordinate system into the path tracking error state in the Frenét coordinate system for the design of the path tracking controller. During the modeling process, the hinge angle and hinge angular velocity between the tractor and the trailer are introduced into the control system state. Step 2: Design the feedforward controller for the path tracking control system with random disturbances designed in Step 1 to obtain the path tracking control system with random disturbances after feedforward control. Step 3: Introduce the preview distance model into the path tracking control system obtained in Step 2. Step 4: Design an observer-based H∞ robust feedback controller for the system preview state X of the path tracking control system obtained in Step 2 and the path tracking control system of the towed AGV obtained in Step 3; p , Step 5: Introduce the fuzzy algorithm into the observer-based H∞ robust feedback controller to determine the control gain K and observer gain L at different speeds online, enhancing the adaptive ability of the observer-based H∞ robust feedback controller. Step 6: Use the steering wheel input angle of the towed AGV obtained by the feedforward controller designed in Step 2 and the observer-based H∞ robust feedback controller designed in Step 4 to achieve stable path tracking control. The formula is as follows: δ=(δ f +δ b ) / i w (34) where δ represents the steering wheel input angle of the towed AGV.

2. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 1, wherein, The specific steps of the robust adaptive path tracking method for the towed AGV are as follows: The specific content of Step 1 is as follows: Step 1.1: The towed AGV includes a two-axis tractor and a single-axis trailer, and its dynamic model includes the lateral velocity v of the tractor y1 , the yaw angular velocity ω1 of the tractor, and the articulation angle θ between the tractor and the trailer; obtaining the dynamic relationship of the towed AGV; and further obtaining the kinematic constraint relationship between the tractor and the trailer as: where θ represents the hinge angle, and represents the hinge angular velocity; Step 1.2: Model the tire model of the towed AGV. The lateral tire force acting on each axle of the towed AGV is expressed as: Among them, C f represents the cornering stiffness of the front axle tires of the tractor, C r represents the cornering stiffness of the rear axle tires of the tractor, C t represents the cornering stiffness of the trailer axle tires, α f represents the cornering angle of the front axle tires of the tractor, α r represents the cornering angle of the rear axle tires of the tractor, α t represents the cornering angle of the trailer axle tires; Step 1.3: Transform the vehicle dynamic state in the Cartesian coordinate system into the path tracking error state in the Frenét coordinate system for the design of the path tracking controller. Step 1.4: Define the system state of the path tracking control system of the towing AGV as: And according to Formulas (1)-(6), the path tracking control system is modeled as: where A, B1, and B2 represent the system state matrices; δ represents the steering angle of the towed AGV; ρ represents the path curvature of the expected trajectory corresponding to the tractor. Introduce θ into the system state X of the path tracking control system of the towed AGV and improve the stability and safety of the path tracking of the towed AGV; Step 1.5: Considering the random disturbance of the path tracking control system, the path tracking control system with random disturbances is defined as: So far, the path tracking control system of the towed AGV has been established. The specific content of Step 2 is as follows: Step 2.1: Considering the feedforward controller, rewrite the path tracking control system with random disturbances as: Among them, δ f represents the steering wheel angle obtained by the feedforward controller, and δ b represents the steering wheel angle obtained by the feedback controller, and i w represents the transmission ratio from the steering wheel angle of the steering transmission system of the towed AGV to the steering wheel angle of the steering wheel; Step 2.2: The feedforward controller is required to ensure that Obtain: Therefore, the feedforward controller is designed as: Step 2.3: Based on the feedforward controller (12) designed in Step 2.2, the path tracking control system with random disturbances after feedforward control is defined as: where B3 is the system state matrix considering feedforward control. The specific content of Step 3 is as follows: Step 3.1: Introduce the preview distance model to adapt to the changing speed and path curvature. The preview distance model is expressed as follows: Among them, L p represents the preview distance, ρ th represents the threshold of the path curvature for judging a straight road or a curved road, T p1 represents the preview time interval when |ρ| < ρ th and ε1 represents the constant term when |ρ| < ρ th ; T p2 represents the preview time interval when |ρ| ≥ ρ th and ε2 represents the constant term when |ρ| ≥ ρ th ; Step 3.2: Assume that the desired path is a clothoid curve, then the system state X of the path tracking control system of the towed AGV can be transformed into the system preview state of the path tracking control system of the towed AGV for the preview point through the second-order approximation theory. where e 1p represents the lateral distance error at the preview point, represents the lateral velocity error at the preview point, e 2p represents the heading angle error at the preview point, represents the heading angular velocity error at the preview point; The system state X and the system preview state X of the path tracking control system of the towed AGV p satisfy the following relationship: Among them, and represent the system relationship matrix; The specific content of Step 4 is as follows: Step 4.1: First, for the system preview state X of the path tracking control system of the towed AGV obtained in Step 3 p , define the H∞ robust feedback controller based on observation as follows: δ b = i w KX p (17) where δ b represents the steering wheel angle obtained by the observation-based H∞ robust feedback controller, and K represents the control gain of the observation-based H∞ robust feedback controller; Then, based on Formula (16) and Formula (17), the path tracking control system with random disturbances after feedforward and feedback control is defined as: The path tracking control system with random disturbances (18) after feedforward and feedback control is transformed into: Among them, B0 and represent the system matrix; Meanwhile, define the measurement vector as: Y = [e1, e2, θ] T , which is expressed as follows: Y = CX (20) Among them, \(C\) represents the measurement matrix of the path tracking control system of the towed AGV; Step 4.2: Design a Luenberger observer to avoid the influence of random disturbances caused by sensor failures on the control performance of the observer-based \(H_{\infty}\) robust feedback controller; the Luenberger observer is designed as follows: Among them, and respectively represent the observed values of X and Y; L represents the observation gain of the observer; Step 4.3: Based on the Luenberger observer designed in Step 4.2, the control law of the observer-based H∞ robust feedback controller is redefined as For this purpose, the path-tracking closed-loop control system is expressed as follows: Define the observation error of the Luenberger observer as Then the path tracking closed-loop control system (22) is equivalent to: Then, by constructing an augmented vector The path-tracking closed-loop augmented control system is expressed as: Among them, and represent the system augmented matrix; Step 4.4: Design the design criterion of the observer-based \(H_{\infty}\) robust feedback controller based on the \(H_{\infty}\) theory to solve the control gain \(K\) and the observer gain \(L\). The design criterion is represented by Theorem 1 as follows: Theorem 1: If there exist positive definite symmetric matrices \(P_1\) and \(P_2\), matrix \(Q\), positive numbers \(\varepsilon>0\) and \(\alpha>0\) that satisfy the linear matrix inequality (28): Then the path tracking closed-loop augmented control system shown in formula (24) satisfies the \(H_{\infty}\) performance with a given attenuation factor \(\gamma>0\), that is: where, Σ represents a linear matrix, λ max (P) represents the maximum eigenvalue of the positive definite symmetric matrix P, where P = diag{P1 -1 , P2}; Step 4.5: By solving the linear matrix inequality (28), obtain the positive definite symmetric matrices P1 and P2, the matrix Q, and the control gain K, and further obtain the observation gain L, that is: For this reason, the observer-based \(H_{\infty}\) robust feedback controller is designed and completed; The specific steps of step 5 are as follows: Step 5.1: First, assume a certain speed range and decompose it into multiple speed sub-intervals; then, solve the control gain \(K\) and the observer \(L\) corresponding to the end-point speeds of each speed sub-interval; then, use the fuzzy algorithm to find the control gain \(K\) and the observer gain \(L\) corresponding to different speeds within each sub-interval; Step 5.2: Based on the control gain \(K\) and the observer gain \(L\) corresponding to different speeds obtained in step 5.1, which are expressed as: Among them, K1 represents the control gain corresponding to the maximum speed of the sub-interval, K2 represents the control gain corresponding to the minimum speed of the sub-interval, L1 represents the observation gain corresponding to the maximum speed of the sub-interval, L2 represents the observation gain corresponding to the minimum speed of the sub-interval, and h i (ζ1(t)) represents the fuzzy weighting function; Through the above fuzzy algorithm, solve the gain matrices \(K\) and \(L\) at different speeds, so that the observer-based \(H_{\infty}\) robust feedback controller realizes adaptive control.

3. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that The specific steps of step 1 are as follows: In step 1.1, the dynamic relationship of the towed AGV is as follows: Among them, v x represents the longitudinal speed of the towed AGV, m1 represents the mass of the tractor, m2 represents the mass of the trailer, I1 represents the yaw moment of inertia of the tractor, I2 represents the yaw moment of inertia of the trailer, v y1 represents the lateral speed of the tractor, v y2 represents the lateral speed of the trailer, ω1 represents the yaw angular velocity of the tractor, ω2 represents the yaw angular velocity of the trailer, F yf represents the lateral tire force on the front axle of the tractor, F yr represents the lateral tire force on the rear axle of the tractor, F yt represents the lateral tire force on the axle of the trailer, F xP represents the longitudinal hinge force at the articulation point, F yP represents the lateral hinge force at the articulation point. The subscript x represents the longitudinal vector of the towed AGV, the subscript y represents the lateral vector of the towed AGV, a1 represents the distance from the front axle of the tractor to the center of mass of the tractor, a2 represents the distance from the rear axle of the tractor to the center of mass of the tractor, a3 represents the distance from the rear axle of the tractor to the articulation point, a4 represents the distance from the articulation point to the center of mass of the tractor, b1 represents the distance from the articulation point to the center of mass of the trailer, b2 represents the distance from the axle of the trailer to the center of mass of the trailer, and l2 = b1 + b2 represents the distance from the axle of the trailer to the articulation point; In step 1.2, the tire side slip angle of each axis of the towed AGV is expressed as: Among them, \(\delta\) represents the steering angle of the towed AGV; The specific content of step 1.3: First, according to the kinematic relationship of the towing AGV in the Frenét coordinate system, the heading angle error \(e_{2}\), the heading angular velocity error and the heading angular acceleration error are expressed as: where, ψ1 represents the heading angle of the tractor, ψ des represents the desired heading angle of the tractor, represents the heading angular velocity of the tractor, represents the desired heading angular velocity of the tractor, ρ represents the path curvature of the desired trajectory corresponding to the tractor, represents the yaw angular acceleration of the tractor; Meanwhile, the lateral distance error e1, the lateral velocity error and the lateral acceleration error are expressed as: Among them, y1 represents the lateral position of the center of mass of the tractor, and y des represents the desired lateral position of the center of mass of the tractor, represents the lateral velocity of the center of mass of the tractor, represents the lateral acceleration of the center of mass of the tractor; In step 1.4: Among them, Ω, a 22 、a 24 、a 25 、a 26 、a 42 、a 44 、a 45 、a 46 、a 62 、a 64 、a 65 、a 66 , κ1, κ2, κ4, κ5, κ7 and κ8 represent the coefficients of the system state matrix.

4. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that, The specific steps of step 2 are as follows: In formula (9) of step 2.1: In step 2.3, B3 is represented as:

5. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that The specific steps of step 3 are as follows: In step 3.2, the variables e1, e2 and in the system state X of the path tracking control system of the towed AGV are represented by a linear combination as follows: In the said step 3.2, and are expressed as:

6. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that The specific steps of step 4 are as follows: In the said step 4.1, B0 and is expressed as: B0 = [B3, B1, 1] and where 0 and 1 respectively represent column vectors of all 0s and all 1s; the measurement matrix C is expressed as: In the said step 4.3, and are expressed as: Among them, \(I\) represents the identity matrix of appropriate dimension.

7. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that In step 4, based on Lemma 1 and Lemma 2, the bilinear matrix inequality \(\Pi < 0\) is transformed into the linear matrix inequality \(\Sigma < 0\) to realize the fast solution of the control gain \(K\) and the observer gain \(L\) of the observer-based \(H_{\infty}\) robust feedback controller; Lemma 1: Given the following two real matrices \(G\) and \(Z\), then there exists a positive number \(\varepsilon>0\) that satisfies the following inequality: Among them, \(G\) and \(Z\) represent real matrices, and \(\varepsilon\) represents a positive number; Lemma 2: Given positive definite symmetric matrices \(H\) and \(R\), then the following two linear matrix inequalities are equivalent; H-SR -1 S T <0 (27) Among them, \(H\) and \(S\) represent positive definite symmetric matrices.

8. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that In step 5.1, assume that the speed range is between \([0, 20]\) (m / s) and decompose it into 10 speed sub-intervals, that is, \([0, 2), [2, 4),..., [18, 20]\) (m / s).

9. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that, In step 5.1, it is assumed that the speeds within each speed sub - interval satisfy: v x ∈[v xmin ,v xmax , where v xmin and v xmax represent the minimum speed and the maximum speed of each sub - interval respectively; then define and Then, the speed v x is expressed as: where ζ1 = v x , M1(ζ1) and M2(ζ1) represent membership functions, satisfying: M1(ζ1) + M2(ζ1) = 1, and are expressed as:

10. A robust adaptive path tracking method for a towed AGV considering trailer swing suppression according to claim 2, characterized in that In the said step 5.2, the fuzzy weighting function satisfies h i (ζ1(t))≥0,

Images