Wheeled robot tracking control method and system facing network delay and interference

Abstract

The invention discloses a wheeled robot tracking control method and system facing network delay and interference, and aims to improve the trajectory tracking performance of a wheeled robot under the influence of communication time lag and external disturbance. The method comprises the following steps: firstly, establishing a kinematic model of the wheeled robot, designing a control system architecture, constructing a tracking error model, carrying out linearization and discretization processing, and combining disturbance modeling to obtain a state space expression of an error system; furthermore, a state and interference combined observer is constructed, and a network prediction control method is adopted to carry out multi-step prediction on an error state so as to actively compensate control lag caused by communication time delay. And then, a sliding mode function is constructed based on the prediction information, and a sliding mode prediction control law is designed, so that stable tracking of the wheeled robot on the reference trajectory in the network delay and interference environment is realized. Experimental results show that the control strategy has good robustness and feasibility and is suitable for a mobile robot system in a complex network control scene.

Description

Technical Field

[0001] The present invention belongs to the field of automatic control, and in particular relates to a wheeled robot tracking control method and system oriented to network delay and interference, which is suitable for robot remote precision tracking tasks in a networked control environment. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] In modern robotics, wheeled robots, due to their simple structure, flexible control, and low energy consumption, are widely used in scenarios such as intelligent manufacturing, warehousing and logistics, urban inspections, and post-disaster search and rescue. In recent years, with the continuous advancement of communication technology and information technology, network-based remote control has gradually replaced traditional local control and become a key means for wheeled robots to achieve efficient remote dispatch and target tracking.

[0004] However, integrating communication networks into control systems also presents new technical challenges. When wheeled robots operate in a networked environment, control commands and status feedback must be transmitted over the wireless network. Limited by network bandwidth, scheduling mechanisms, and data link stability, communication delays, packet loss, and information disarray are highly susceptible to these issues. These issues can lead to action delays, system status lags, and even tracking trajectory deviations or system instability.

[0005] Furthermore, wheeled robots are inevitably affected by internal modeling errors and external disturbances during their motion. For example, nonlinear friction in the drive system, tire slip caused by uneven surfaces, velocity loop control errors, and sudden environmental disturbances can disrupt the robot's original trajectory. These disturbances are particularly prominent in complex working conditions and highly dynamic tasks, severely impacting the tracking accuracy and response robustness of the control system.

[0006] To address these issues, researchers have proposed a variety of control strategies. Network predictive control (NPC) is considered an effective active compensation method for network-induced delays. Based on the concept of predictive control, this method combines the current state with the system model to predict the state until the upper bound of the network delay is covered. The method consists of a model prediction unit and a time-delay compensation unit. The model prediction unit, located on the controller side, predicts the state based on the current state and model information, and calculates a multi-step control input sequence based on the upper bound of network delay and packet loss. The time-delay compensation unit compares timestamps and selects the control input closest to the actual execution time to act on the controlled object. NPC has the characteristics of a simple structure and wide applicability. However, internal and external interference is common in actual networked wheeled robot tracking control systems, and existing NPC methods have not fully considered this factor. Some algorithms are difficult to apply directly in interference environments, and related issues remain to be addressed.

[0007] Traditional approaches to addressing system disturbances include robust control, adaptive control, and sliding mode control. Sliding mode control, due to its excellent disturbance rejection and robustness, is widely used in various nonlinear systems. Sliding mode control effectively mitigates the effects of system model uncertainty and external disturbances by introducing a switching surface to force the system state to converge along a preset trajectory. A disturbance observer proactively estimates disturbances based on the system's dynamic characteristics and performs feedforward compensation, thus enhancing the system's disturbance rejection. In recent years, a hybrid disturbance rejection control strategy combining sliding mode control and a disturbance observer has attracted widespread attention from scholars both domestically and internationally. This strategy leverages the robustness of sliding mode control while leveraging the active disturbance estimation capabilities of the disturbance observer to achieve more precise and effective disturbance rejection. While sliding mode control effectively mitigates system uncertainties and external disturbances, its high-frequency switching characteristics can easily lead to significant chattering. By introducing a disturbance observer, the system can estimate and compensate for disturbances in real time, thereby reducing chattering and improving control smoothness. Summary of the Invention

[0008] In response to the problems existing in the prior art, the present invention provides a wheeled robot tracking control method and system oriented to network delay and interference. It utilizes network predictive control method, interference observer and sliding mode control technology to effectively reduce the impact of time delay and interference on the tracking accuracy of the wheeled robot.

[0009] The technical solutions of the present invention are as follows:

[0010] In a first aspect of the present invention, a wheeled robot tracking control method oriented to network delay and interference is provided, comprising:

[0011] Establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot;

[0012] Define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it. Considering the interference to the wheeled robot, the state space model of the error system is obtained.

[0013] Construct a state and disturbance observer to jointly estimate the error state and disturbance;

[0014] Based on the tracking error model and estimated value, the network predictive control method is used to predict the error state to actively compensate for network delay;

[0015] A sliding mode function based on prediction information is designed, and the sliding mode predictive control law is derived accordingly to ensure the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the influence of network delay and interference.

[0016] In some embodiments of the present invention, the kinematic model of the wheeled robot is described as follows:

[0017]

[0018] Where (X, Y) is the position of the wheeled robot, θ is the counterclockwise angle between the robot's orientation and the x-axis, and v and w represent the linear velocity and angular velocity of the center of the robot's rear wheel, respectively.

[0019] In some embodiments of the present invention, given a circular tracking trajectory (X r ,Y r ,θ r ), we get the tracking error model:

[0020]

[0021] cosδ θ and sinδ θ are approximately 1 and δ respectively θ , and discretize the equation to construct the following state space model of the error system:

[0022]

[0023] Where y(k) is the system output; A, B and C are dimensionally adapted known system matrices; and ω0(k) represents the disturbance.

[0024] In some embodiments of the present invention, the disturbance ω0(k) is modeled as follows:

[0025]

[0026] Among them, ξ(k) is the interference state, A ω 、B ω and Cω is a known coefficient matrix, and ω(k) represents the additional unmodeled disturbance.

[0027] In some embodiments of the present invention, a state and disturbance observer is constructed to jointly estimate the error state and the disturbance state; based on the error model and the estimated values, the network predictive control method is used to predict the error state until the upper bound of the network delay is covered, so as to actively compensate for the time delay.

[0028] In some embodiments of the present invention, the sliding mode function is designed as follows:

[0029]

[0030] where s is the sliding mode function, and K x is the control gain to be designed, G is the gain matrix introduced in the system feedback link, and to ensure that the control law can be accurately solved, it is necessary to ensure that (GB) is a non-singular matrix.

[0031] In some embodiments of the present invention, the constructed composite disturbance rejection predictive control law is as follows:

[0032]

[0033] where (GB) -1 represents the inverse of the matrix (GB), q is the designed power exponent parameter, usually satisfying 0 < q < 1, which is used to adjust the sliding mode approaching speed; Λ is the gain factor in the sliding mode control, which determines the response intensity of the controller to the change of the sliding mode surface, and is often used to suppress the high-frequency chattering phenomenon that may occur during the system switching process; sgn(·) is the sign function, which represents the positive and negative of the input value and is used to generate a directional switching effect in the sliding mode control.

[0034] In the second aspect of the present invention, a wheeled robot tracking control system for network delay and disturbance is provided, including:

[0035] A system construction module, configured to: establish the kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot;

[0036] A linearization and discretization module, configured to: define the tracking error between the reference trajectory and the actual output, construct the tracking error model, and linearize and discretize it, considering the disturbance received by the wheeled robot, to obtain the state space model of the error system;

[0037] An observer construction module, configured to: construct a state and disturbance observer for jointly estimating the error state and the disturbance;

[0038] The interference estimation and time delay compensation module is configured to: predict the error state based on the tracking error model and the estimated value using a network predictive control method to actively compensate for the network time delay;

[0039] The sliding mode predictive control law module is configured to design a sliding mode function based on the prediction information and derive the sliding mode predictive control law accordingly to ensure the accessibility of the sliding surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the influence of network delay and interference.

[0040] In a third aspect of the present invention, a non-transitory computer-readable storage medium is provided, wherein the non-transitory computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the wheeled robot tracking control method oriented to network delay and interference is implemented.

[0041] In a fourth aspect of the present invention, an electronic device is provided, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the wheeled robot tracking control method for network delay and interference.

[0042] One or more technical solutions of the present invention have the following beneficial effects:

[0043] The present invention proposes a networked wheeled robot tracking control method and system for network delay and interference, provides a kinematic model of the wheeled robot, and establishes a state-space expression of the tracking error, thereby transforming the original tracking control problem into a stabilization control problem of the error system.

[0044] The error state and disturbance are jointly estimated using the state and disturbance observer. The error system model and the estimated value are combined to further predict the error state and disturbance through the network predictive control method. Based on the multi-step prediction values of the error state and disturbance, the sliding mode predictive control law is applied to obtain a control input sequence with strong anti-disturbance capability. When applied to the wheeled robot, it actively compensates for the network delay while enhancing the anti-disturbance capability of the tracking error system and improving the tracking accuracy.

[0045] Compared with traditional network time-delay processing methods, this proposed method for tracking and controlling a networked wheeled robot, which is designed for network delay and interference, actively compensates for time delay, offering the advantages of simplicity and versatility. Furthermore, compared with traditional anti-interference control methods, this method leverages the robustness of sliding mode control and the active anti-interference capability of a disturbance observer, alleviating the chattering problem inherent in sliding mode control and enhancing the system's anti-interference capability. Numerical examples and experiments with wheeled robot tracking and control in a real-world communication environment demonstrate the effectiveness and practicality of the proposed method. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 This is a kinematic symbol description of the wheeled robot according to Example 1 of the present disclosure;

[0047] Figure 2 This is the experimental system of Example 1 of the present disclosure;

[0048] Figure 3 This is the structure of the network communication framework of embodiment 1 of the present disclosure;

[0049] Figure 4 The data flow of the network communication framework of embodiment 1 of the present disclosure;

[0050] Figure 5 The structure of the wheeled robot according to embodiment 1 of the present disclosure;

[0051] Figure 6 The network delay statistics of Example 1 of the present disclosure;

[0052] Figure 7 This is the control structure of Example 1 of the present disclosure;

[0053] Figure 8 This is the actual tracking result of Example 1 of the present disclosure;

[0054] Figure 9 is the X-direction tracking error of Example 1 of the present disclosure;

[0055] Figure 10 is the Y-direction tracking error of Example 1 of the present disclosure;

[0056] Figure 11 is the heading angle tracking error of Example 1 of the present disclosure. DETAILED DESCRIPTION

[0057] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0058] Example 1

[0059] In a typical embodiment of the present invention, a wheeled robot tracking control method oriented to network delay and interference is proposed, comprising:

[0060] Step 1: Establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot;

[0061] Step 2: Define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it. Considering the interference to the wheeled robot, the state space model of the error system is obtained.

[0062] Step 3. Construct a state and disturbance observer to jointly estimate the error state and disturbance. Based on the tracking error model and the estimated value, use the network predictive control method to predict the error state to actively compensate for the network time delay. Design a sliding mode function based on the predicted information and derive the sliding mode predictive control law based on it to ensure the accessibility of the sliding mode surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the action of network time delay and disturbance.

[0063] As an embodiment, the present disclosure discloses a tracking control method for a wheeled robot facing network delay and interference, which studies the tracking control of a wheeled robot in the presence of network delay and system interference. The specific implementation process is as follows:

[0064] Step 1: Establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot:

[0065] Kinematic modeling reference for wheeled robots Figure 1 In the world coordinate system xOy, (X, Y) is the position of the wheeled robot (m), θ (rad) is the counterclockwise angle between the robot's orientation and the x-axis, v (m / s) and w (rad / s) are the linear velocity and angular velocity of the robot's rear wheel center respectively; the linear velocities of the left and right driving wheels are v and L (m / s) and v R (m / s); wheelbase L = 0.144m. The wheeled robot has the following differential kinematic model:

[0066]

[0067] In addition, select v L With v R As the control input, it is mapped into the linear velocity and angular velocity of the kinematic model through the following kinematic forward solution formula:

[0068]

[0069] Build as Figure 2 The networked wheeled robot tracking control system shown in FIG uses a cloud server as a controller and establishes communication with the Raspberry Pi through a wide area network. The Raspberry Pi serves as a bridge between the cloud server and the wheeled robot and runs a network communication framework. Its structure and data flow are shown in FIG. Figure 3 and Figure 4 shown.

[0070] Figure 3 The four cores of the Raspberry Pi shown run independent processes, achieving parallelism and scheduling through an operating system that supports real-time patching, and using inter-process communication mechanisms to interact, accelerating local data processing, thereby highlighting the impact of network latency on control performance.

[0071] Figure 4 This figure illustrates the information flow between the cloud server and the Raspberry Pi. During each control cycle, the Raspberry Pi first sends feedback information with a UNIX timestamp (a UNIX timestamp represents the current second and is used in network predictive control methods to facilitate cross-system time alignment). The cloud server retains this timestamp when returning the input sequence. The Raspberry Pi calculates the round-trip time (RTT) by comparing the received timestamps and extracts the corresponding prediction input from the input sequence.

[0072] Figure 5 The diagram shows the structure of a wheeled robot, which includes a DC motor, a motor drive circuit, and an inertial measurement unit (MPU6050). The PWM signal is used to adjust the motor input voltage to achieve speed control. The items marked with "meas" in the subscript of each variable in the figure represent the measured value of the corresponding physical quantity, such as v L,meas Indicates the actual measurement of the left drive wheel speed.

[0073] When the fixed sampling period T s = 0.05s, the network delay is counted, and the results are as follows Figure 6 As shown, the maximum prediction steps of network predictive control are set accordingly

[0074] Step 2: Define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it. Considering the interference to the wheeled robot, the state space model of the error system is obtained:

[0075] Given a circular tracking trajectory (X r ,Y r ,θ r ), the corresponding left and right wheel reference speeds are v Lr =0.193m / s and v Rr =0.207m / s. as well as Thus we get the tracking error model:

[0076]

[0077] cosδθ and sinδ θ are approximately 1 and δ respectively θ , and discretize the equation. Define the tracking error state Where col{a,b,c} in the formula represents the column vector composed of a, b and c; the control input is Based on this, the state space model and related parameters of the following error system can be constructed:

[0078]

[0079] Where y(k) is the system output; A, B, and C are known system matrices with dimension adaptation; ω0(k) represents the disturbance, and the related parameters are:

[0080] C=[0.60.50.1],

[0081] Among them, the output matrix C is artificially constructed to simulate the actual situation where the error state cannot be directly measured, thereby enhancing the adaptability of the system model to real application scenarios.

[0082] The disturbance ω0(k) is modeled as follows:

[0083]

[0084] Among them, ξ(k) is the interference state, A ω 、B ω and C ω is a known coefficient matrix, ω(k) which represents the unmodeled additional bounded perturbation.

[0085] Step 3. Construct a state and disturbance observer to jointly estimate the error state and disturbance. Based on the tracking error model and the estimated value, use the network predictive control method to predict the error state to actively compensate for the network time delay. Design a sliding mode function based on the predicted information and derive the sliding mode predictive control law based on it to ensure the accessibility of the sliding mode surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the action of network time delay and disturbance.

[0086] In the present invention, the sliding mode function is the core variable in the sliding mode control method, which is usually constructed by the system state and its combination, and is used to characterize the distance and direction of the system state relative to the sliding surface. In the sliding mode controller, the sign of the sliding mode function determines the switching behavior of the controller, and its zero point set defines the sliding surface of the system. The sliding surface is used to define the target motion trajectory of the system, and its accessibility indicates whether the system can enter the surface within a finite time under the control action. The design of the controller must ensure that the sliding surface has good accessibility and retention.

[0087] Specifically, in order to realize the tracking control, network delay compensation and interference suppression of networked wheeled robots, a composite network predictive control scheme based on state and disturbance observer and sliding mode control is designed. The control structure is as follows: Figure 7 shown.

[0088] First, to estimate the states and disturbances in the error system that cannot be directly measured, the following joint state and disturbance observer is designed:

[0089]

[0090] in, and is the estimate of the error state and disturbance, is the output of the state observer, represents the estimation of the interference system state; L x With L ω are the gain matrices of the state and disturbance observers, respectively.

[0091] Defining the estimation error and And construct the estimated error augmented vector Combining the tracking error system model (1), the interference model (2) and the observer (3), we can obtain the following estimation error augmentation system:

[0092] e χ (k+1)=A e e χ (k)+B e ω(k),(4)

[0093] in,

[0094]

[0095] Due to the introduction of the network, data transmission generates a τ-step delay. Therefore, based on the output feedback y(k), after estimating the error state and disturbance through the observer (3), the controller further predicts the state and disturbance until the upper bound of the delay is covered. The prediction process is as follows:

[0096]

[0097] According to the recursive structure of the prediction process (5), the system state and interference prediction value when the network delay τ ≥ 2 can be expressed by the estimated value at time k + 1 as follows:

[0098]

[0099] in,

[0100] Consider the observer in Equation (3). For any network delay Design the following sliding mode function:

[0101]

[0102] where s is the sliding mode function, and K x is the control gain to be designed, G is the gain matrix introduced in the system feedback link. To ensure that the control law can be solved accurately, it is necessary to ensure that (GB) is a non-singular matrix.

[0103] In Equation (7), the symbol "|" is used to represent the prediction structure, and its meaning is "predict or estimate the variable at the left moment based on the information at the right moment". For example,[[]] represents predicting the state at time k based on the information available at time k - τ; s(k|k - τ) represents the sliding mode function constructed based on the error state and other information predicted from time k - τ to time k. This symbol is used in the state prediction, control input calculation, and sliding mode function design of this invention, representing the common temporal prediction relationship in network control systems.

[0104] Specifically, when the time delay τ = 0, Further organize the predictive sliding mode function in Equation (7) into the form of a multi-step prediction vector S(k):

[0105]

[0106] where (·) T represents the matrix transpose operation. Subsequently, propose the following composite disturbance rejection predictive control law:[[ID=二十九]]

[0107]

[0108] where (GB) -1 represents the inverse of the matrix (GB), q is the designed power exponent parameter, usually satisfying 0 < q < 1, which is used to adjust the sliding mode approaching speed; Λ is the gain factor in sliding mode control, which determines the response intensity of the controller to the change of the sliding mode surface and is often used to suppress the high-frequency chattering phenomenon that may occur during the system switching process; sgn(·) is the sign function, which represents the positive and negative of the input value and is used to generate a directional switching effect in sliding mode control.

[0109] The controller constructs the input sequence at time k and sends it to the controlled object side. At the controlled object side, according to the timestamp in the received data packet, calculate the round-trip delay τ of data transmission within the current control period, and select the corresponding u(k + τ) from the input sequence and apply it to the controlled object, so as to compensate for the network delay.

[0110] Next, based on the sliding mode function formula (7) and the predictive control law formula (9), the reachability of the sliding mode surface is analyzed by means of the Lyapunov method.

[0111] Theorem 1: Given the tracking error model formula (1) and the observer formula (2) of the networked wheeled robot tracking control system, and the composite disturbance rejection predictive control law formula (9), if the control law parameters satisfy 0 < q < 1 and Λ > Λ1, and (‖·‖ represents the 2-norm, ∈ represents the tolerance parameter for the convergence of the sliding mode surface, whose role is to set the allowable minimum fluctuation range of the system error to ensure that the system can still approach the neighborhood of zero under actual disturbances), then the sliding mode function formula (7) converges to a bounded neighborhood centered at zero.

[0112] Proof: From the predictive sliding mode vector formula (8) and the predictive control law formula (9), for the two cases where the delay is less than one sampling period and the delay is greater than or equal to one sampling period, combined with the observer formula (2) and the prediction process formula (5), the evolution law of the sliding mode function in the prediction domain can be obtained as follows:

[0113] S(k + 1) = QS(k) - Γsgn(S(k)) + D(k), (10)

[0114] where, Q = diag{1 - q, 1 - q,..., 1 - q}, and diag{...} in the formula represents a diagonal matrix with 1 - q as the diagonal elements; and

[0115]

[0116] Here, sgn(·) takes the sign of each component of the vector S(k) element by element.

[0117] Define the Lyapunov function as follows:

[0118] V(k) = S T (k)WS(k), (11)

[0119] where the weight matrix W = diag{w1, w2,..., w τ} > 0, that is, W is a positive definite matrix. The increment of V(k) is:

[0120] ΔV(k + 1) = V(k + 1) - V(k)

[0121] = [QS(k) - Γsgn(S(k)) + D(k)] T W[QS(k) - Γsgn(S(k)) + D(k)] - S T (k)WS(k)

[0122] = S T (k)Q TWQS(k)-2S T (k)Q T WΓsgn(S(k))+sgn T (S(k))Γ T WΓsgn(S(k))+2D T (k)W[QS(k)-Γsgn(S(k))]+D T (k)WD(k)-S T (k)WS(k).

[0123] Note that Q T WQ=(1-q) 2 W, the above formula can be transformed into:

[0124] ΔV(k+1)=-q(2-q)S T (k)WS(k)-2S T (k)Q T WΓsgn(S(k))+Δ d (k),

[0125] The disturbance term is:

[0126] Δ d (k)=sgn T (S(k))Γ T WΓsgn(S(k))+2D T (k)W[QS(k)-Γsgn(S(k))]+D T (k)WD(k).

[0127] Since only the first term of D(k) is non-zero, and ‖D(k)‖≤‖GL x Ce x (k)‖, combined with the construction method of Γ, it can be seen that if the gain Λ satisfies:

[0128] Λ>max k {‖GL x Ce x (k)‖}+∈1,

[0129] Then the control item -2S T (k)Q T The strength of WΓsgn(S(k)) can effectively suppress the disturbance term Δ d (k), thus ensuring that the Lyapunov function decreases, that is, the sliding mode vector S(k) converges to a bounded neighborhood centered at zero. Proof completed.

[0130] When the reachability condition is met, the error state will approach and remain within the neighborhood of the sliding surface. The equivalent control law can be obtained from the sliding function (7) and Theorem 1. That is, after sliding to the surface, in order to ensure that the state continues to evolve within the sliding surface, according to the condition that the sliding surface change rate is zero, the control input form obtained by reverse deduction is:

[0131]

[0132] It is worth noting that when τ = 0, the sliding mode function includes the estimated value of the system state at the previous moment; however, when τ > 0, the sliding mode function is based on the predicted value of the state, and the equivalent control law degenerates into a standard state feedback form. This shows that when τ = 0, an additional compensation term appears in the equivalent control law, reflecting the system's anti-disturbance design.

[0133] Due to the delay τ in network transmission, the control input sequence arrives at one end of the wheeled robot at time k+τ. Combining the error system formula (1) and the sliding mode function formula (7), the closed-loop structure of the system can be derived:

[0134]

[0135] in

[0136]

[0137] In order to analyze the stability of the tracking error closed-loop system (Equation (13)) in the sliding mode phase, this paper adopts the concept of “ultimately uniform boundedness” widely used in control theory as the criterion for judging the robustness and stability of the closed-loop system, which is defined as follows:

[0138] Definition: If the closed-loop system consisting of the wheeled robot tracking error system (1) and the control law (9) with the cloud server as the controller exists a convex compact set containing the origin For any initial state x(0) = x0, there exists a finite time T(x0) such that:

[0139]

[0140] Among them, T(x0)∈{0,1,...}, then the closed-loop system has the property of eventually uniformly bounded.

[0141] Theorem: Given the wheeled robot tracking error system (1), the sliding mode predictive control law (9) is adopted, and the conditions in the sliding mode reachability theorem 1 are satisfied so that the sliding mode function converges to a bounded neighborhood of zero. If there exists an observation gain L x With L ω And the control gain K x , so that the matrix A of the estimation error augmented system (4) e and (A-BK in the closed-loop system (13)x ) are all Schur stable, then the closed-loop system (13) satisfies the eventual uniform boundedness.

[0142] Note: Among them, Shure stability refers to the system matrix (A-BK x ) The modulus of all eigenvalues is less than 1, which is one of the commonly used criteria for judging the stability of a closed-loop system.

[0143] Proof: First, to analyze the error term e in the closed-loop system (13), χ To improve the stability of (k+τ|k), we introduce the following difference variable to describe the difference in prediction results for the same augmented state based on the estimated information at different times:

[0144]

[0145] Therefore, the error term e χ (k+τ|k) can be rewritten as:

[0146]

[0147] According to the prediction process (5), the state and disturbance prediction value based on the estimated information at time k+1 can be derived by analogy. When τ≥3, we have:

[0148]

[0149] Substitute equation (6) and equation (16) into get:

[0150]

[0151] Combining equation (17) with the observer equation (2), we can get The explicit expression for is as follows:

[0152]

[0153] Similarly, any forecast difference Can be expressed as the error vector e χ (k+i) is a linear function. From formula (15), we can know that e χ (k+τ|k) can also be expressed as e χ (k+i),i∈{1,2,...,τ}. Therefore, the closed-loop system error term e χ The stability analysis of (k+τ|k) can be summarized as the error augmentation vector e χ Analysis of (k+i).

[0154] To further analyze the stability of the closed-loop system, we first consider the case where ω(k) = 0. From the estimation error augmented system formula (4), we can see that if there is an observation gain matrix Lx With L ω , so that the system matrix A of the estimation error e For Schur stability, the estimated error augmentation vector e χ (k) converges asymptotically to zero (i.e. tends to zero over time). According to the above analysis results, e χ (k+τ|k) can be expressed as e χ The linear combination of (k+i), so e χ (k+τ|k) also converges asymptotically. On this basis, if there exists a control gain matrix K x So that (A-BK x ) is Schur stable, then the closed-loop system (13) is asymptotically stable (i.e., it tends to zero over time).

[0155] When ω(k)≠0, if there is an observation gain L x With L ω Let the estimated error system matrix A e For Schur stability, according to the bounded input-bounded state characteristics of the linear system, the error augmentation vector e χ (k) Ultimately uniformly bounded. According to the above structural relationship, e χ (k+τ|k) is also ultimately uniformly bounded. Furthermore, if there exists a control gain K x Make the closed-loop system matrix (A-BK x ) is Schur stable, then the closed-loop system (13) is ultimately uniformly bounded under the condition of disturbance. The proof is complete.

[0156] During the experiment, in order to verify the robustness of the proposed control method under disturbance, ω0(k) was artificially injected by the embedded processor to simulate the actual disturbance caused by environmental changes such as velocity inner loop tracking error or ground unevenness. The tracking results, X-direction tracking error, Y-direction tracking error and heading angle tracking error are shown as follows: Figures 8 to 11 As shown in the figure, it shows that under the influence of network delay and disturbance, the wheeled robot can track the given circular trajectory using the proposed anti-interference network predictive control method, and the tracking error converges, which verifies the effectiveness of this method.

[0157] Example 2

[0158] In a typical embodiment of the present invention, a wheeled robot tracking and control system resistant to network delay and interference is provided, comprising:

[0159] The system building module is configured to: establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot;

[0160] The linearization and discretization module is configured to: define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it, considering the interference to the wheeled robot, and obtain a state space model of the error system;

[0161] The observer building module is configured to: construct a state and disturbance observer for jointly estimating the error state and disturbance;

[0162] The interference estimation and time delay compensation module is configured to: predict the error state based on the tracking error model and the estimated value using a network predictive control method to actively compensate for the network time delay;

[0163] The sliding mode predictive control law module is configured to design a sliding mode function based on the prediction information and derive the sliding mode predictive control law accordingly to ensure the accessibility of the sliding surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the influence of network delay and interference.

[0164] Example 3

[0165] In a typical embodiment of the present invention, a non-transitory computer-readable storage medium is provided, which is used to store computer instructions. When the computer instructions are executed by a processor, the networked wheeled robot tracking control method oriented towards network delay and interference is implemented.

[0166] Example 4

[0167] In a typical embodiment of the present invention, an electronic device is provided, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the networked wheeled robot tracking control method oriented to network delay and interference.

[0168] The present disclosure is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present disclosure. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0169] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0170] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Those skilled in the art should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A wheeled robot tracking control method oriented to network delay and interference, characterized in that: include: Establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot; Define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it. Considering the interference to the wheeled robot, the state space model of the error system is obtained. Construct a state and disturbance observer to jointly estimate the error state and disturbance; Based on the tracking error model and estimated value, the network predictive control method is used to predict the error state to actively compensate for network delay; A sliding mode function based on prediction information is designed, and the sliding mode predictive control law is derived accordingly to ensure the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the influence of network delay and interference.

2. The wheeled robot tracking control method facing network delay and interference according to claim 1, characterized in that: The kinematic model of the wheeled robot is described as follows: Where (X, Y) is the position of the wheeled robot, θ is the counterclockwise angle between the robot's orientation and the x-axis, and v and w represent the linear velocity and angular velocity of the center of the robot's rear wheel, respectively.

3. The wheeled robot tracking control method facing network delay and interference according to claim 2, characterized in that: Given a circular tracking trajectory (X r ,Y r ,θ r ), we get the tracking error model: cosδ θ and sinδ θ are approximately 1 and δ respectively θ , and discretize the equation to construct the following state space model of the error system: Where y(k) is the system output; A, B and C are dimensionally adapted known system matrices; and ω0(k) represents the disturbance.

4. The wheeled robot tracking control method facing network delay and interference according to claim 1, characterized in that: The disturbance ω0(k) is modeled as follows: Among them, ξ(k) is the interference state, A ω 、B ω and C ω is a known coefficient matrix, ω(k) which represents the unmodeled additional disturbance.

5. The wheeled robot tracking control method facing network delay and interference according to claim 1, characterized in that: A state and disturbance observer is constructed to jointly estimate the error state and disturbance state. Based on the error model and the estimated value, the network predictive control method is used to predict the error state until it covers the upper bound of the network delay, thereby actively compensating for the time delay.

6. The wheeled robot tracking control method facing network delay and interference according to claim 1, characterized in that: The sliding mode function is designed as follows: Among them, s is the sliding mode function, K x is the control gain to be designed, G is the gain matrix introduced in the system feedback link, and to ensure that the control law can be solved accurately, it is necessary to ensure that (GB) is a non-singular matrix.

7. The wheeled robot tracking control method facing network delay and interference according to claim 6, characterized in that: The constructed composite disturbance rejection predictive control law is as follows: where, (GB) -1 represents the inverse of the matrix (GB), q is the designed power exponent parameter, usually satisfying 0 < q < 1, which is used to adjust the sliding mode approaching speed; Λ is the gain factor in the sliding mode control, which determines the response intensity of the controller to the change of the sliding mode surface and is often used to suppress the high-frequency chattering phenomenon that may occur during the system switching process; sgn(·) is the sign function, which represents the positive and negative of the input value and is used to generate the directional switching effect in the sliding mode control.

8. A wheeled robot tracking control system oriented to network delay and interference, characterized in that: include: The system building module is configured to: establish a kinematic model of the wheeled robot and design the tracking control system architecture of the wheeled robot; The linearization and discretization module is configured to: define the tracking error between the reference trajectory and the actual output, construct a tracking error model, and linearize and discretize it, considering the interference to the wheeled robot, and obtain a state space model of the error system; The observer building module is configured to: construct a state and disturbance observer for jointly estimating the error state and disturbance; The interference estimation and time delay compensation module is configured to: predict the error state based on the tracking error model and the estimated value using a network predictive control method to actively compensate for the network time delay; The sliding mode predictive control law module is configured to design a sliding mode function based on the prediction information and derive the sliding mode predictive control law accordingly to ensure the accessibility of the sliding surface, so that the error state remains bounded under the action of the control law, and the wheeled robot can track the reference trajectory under the influence of network delay and interference.

9. A non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium is used to store computer instructions, and when the computer instructions are executed by a processor, the wheeled robot tracking control method oriented to network delay and interference is implemented.

10. An electronic device comprising: A processor, a memory and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to enable the electronic device to implement the wheeled robot tracking control method for network delay and interference.

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