Wheel robot tracking control method and system oriented to network delay and interference

Abstract

The application discloses a wheel robot tracking control method and system for network delay and interference, aiming at improving the trajectory tracking performance of the wheel robot under the influence of communication time lag and external disturbance. The method first establishes the kinematic model of the wheel robot, designs the control system architecture, constructs the tracking error model and performs linearization and discretization processing, and combines disturbance modeling to obtain the state space expression of the error system. Further, a state and disturbance joint observer is constructed, and a network predictive control method is used to multi-step predict the error state to actively compensate for the control lag caused by the communication time delay. Subsequently, a sliding mode function is constructed based on the prediction information, and a sliding mode predictive control law is designed, so that the wheel robot can stably track the reference trajectory in the network delay and interference environment. The experimental results show that the control strategy has good robustness and implementability, and is suitable for mobile robot systems in complex network control scenarios.

Description

Technical Field

[0001] This invention belongs to the field of automatic control, specifically relating to a tracking control method and system for wheeled robots accommodating network latency and interference, applicable to remote and precise tracking tasks of robots in networked control environments. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] In modern robotics, wheeled robots are widely used in intelligent manufacturing, warehousing and logistics, urban inspection, and disaster search and rescue due to their advantages such as simple structure, flexible operation, and low energy consumption. In recent years, with the continuous development of communication technology and information technology, network-based remote control has gradually replaced traditional local control, becoming an important means for wheeled robots to achieve efficient remote scheduling and target tracking.

[0004] However, introducing communication networks into control systems also brings new technical challenges. When wheeled robots operate in a networked environment, control commands and status feedback must be transmitted via wireless networks. Limited by network bandwidth, scheduling mechanisms, and data link stability, communication delays, data packet loss, and out-of-order information are highly likely to occur. These problems can lead to delayed action execution, system lag, and even deviations in tracking trajectory or system instability.

[0005] Furthermore, wheeled robots are inevitably affected by internal modeling errors and external disturbances during movement. For example, nonlinear friction of the drive system, tire slippage caused by uneven ground, speed loop control errors, and sudden environmental disturbances can all 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] Currently, researchers have proposed various control strategies to address the aforementioned problems. For network-induced delay, network predictive control (NRDC) is considered an effective active compensation method. This method, based on predictive control principles, combines the current state with the system model to predict the state until it covers the upper bound of network delay. The method consists of a model prediction unit and a time-delay compensation unit. The model prediction unit, located at the controller, predicts the state based on the current state and model information, and calculates a multi-step control input sequence by combining the upper bounds of network delay and packet loss. The time-delay compensation unit selects the control input closest to the actual execution time by comparing timestamps and applies it to the controlled object. NRDC is characterized by its simple structure and wide applicability. However, internal and external interference is prevalent in practical networked wheeled robot tracking control systems, and existing NRDC methods have not fully considered this factor. Some algorithms are difficult to apply directly in interference environments, and these related problems remain to be solved.

[0007] For system disturbance problems, traditional methods mainly include robust control, adaptive control, and sliding mode control. Among them, sliding mode control is widely used in various nonlinear systems due to its good anti-disturbance capability and robustness. Sliding mode control, by introducing a switching surface to force the system state to converge along a preset trajectory, can effectively suppress the influence of system model uncertainties and external disturbances. The disturbance observer can actively estimate the disturbance based on the system's dynamic characteristics and perform feedforward compensation, thus giving the system stronger disturbance immunity. In recent years, the composite anti-disturbance control strategy using sliding mode control and a disturbance observer has attracted widespread attention from scholars both domestically and internationally. This strategy fully leverages the robustness advantage of sliding mode control while utilizing the disturbance observer's ability to actively estimate disturbances to achieve more accurate and effective disturbance immunity control. Although sliding mode control can effectively suppress system uncertainties and external disturbances, its high-frequency switching characteristics can easily lead to significant chattering problems. By introducing a disturbance observer, the system can estimate and compensate for disturbances in real time, thereby reducing chattering and improving control stability. Summary of the Invention

[0008] To address the problems existing in the prior art, this invention provides a wheeled robot tracking control method and system oriented towards network latency and interference. By utilizing network predictive control methods, interference observers, and sliding mode control technology, the impact of time delay and interference on the tracking accuracy of the wheeled robot is effectively reduced.

[0009] The technical solution of the present invention is as follows:

[0010] In a first aspect of the invention, a tracking control method for a wheeled robot resistant to network latency 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 disturbances to the wheeled robot, obtain the state space model of the error system.

[0013] Construct state and disturbance observers to jointly estimate error state and disturbance;

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

[0015] We design a sliding mode function based on predictive information and derive a sliding mode predictive control law accordingly to ensure the reachability of the sliding surface. This ensures that the error state remains bounded under the control law, enabling the wheeled robot to track and control the reference trajectory under network time 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, a given circular tracking trajectory (X) r ,Y r ,θ r Thus, the tracking error model is obtained:

[0020]

[0021] cosδ θ With sinδ θ Approximately 1 and δ respectively θ The equation is then discretized, and a state-space model of the error system is constructed accordingly:

[0022]

[0023] Where y(k) is the system output; A, B and C are known system matrices with dimension adaptation; ω0(k) represents the perturbation.

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

[0025]

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

[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 value, a network predictive control method is used to predict the error state until the upper bound of network delay is covered, so as to actively compensate for time delay.

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

[0029]

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

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

[0032]

[0033] wherein, (GB) -1 represents the inverse of the matrix (GB), q is a designed power exponent parameter, which generally satisfies 0<q<1 and is used to adjust the sliding mode approaching speed; Λ is a gain factor in sliding mode control, which determines the response strength of the controller to changes in the sliding surface and is often used to suppress high-frequency chattering that may occur during system switching; sgn(·) is a sign function, which represents the positivity and negativity of the input value and is used to produce a directional switching effect in sliding mode control.

[0034] In a second aspect of the present invention, there is provided a wheeled robot tracking control system facing network delay and interference, comprising:

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

[0036] a linearization and discretization module, configured to: define a tracking error between a reference trajectory and an actual output, construct a tracking error model, linearize and discretize the same, and obtain a state space model of an error system by considering interference suffered by the wheeled robot;

[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 estimated value, and actively compensate for network time delay by using network predictive control methods;

[0039] The sliding mode predictive control law module is configured to: design a sliding mode function based on the predicted information, and derive the sliding mode predictive control law accordingly, ensuring the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, and realize the tracking control of the wheeled robot on the reference trajectory under the influence of network time delay and interference.

[0040] In a third aspect of the invention, a non-transitory computer-readable storage medium is provided for storing computer instructions, which, when executed by a processor, implement the aforementioned wheeled robot tracking control method oriented towards network latency and interference.

[0041] In a fourth aspect of the 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 to cause the electronic device to execute the wheeled robot tracking control method for network latency and interference.

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

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

[0044] By utilizing state and disturbance observers, the error state and disturbance are jointly estimated. Combining the error system model and the estimated values, the error state and disturbance are further predicted through network predictive control. Based on the multi-step predicted values ​​of the error state and disturbance, a sliding mode predictive control law is applied to obtain a control input sequence with strong anti-disturbance capability. This sequence is applied to the wheeled robot, which actively compensates for network delay while enhancing the anti-disturbance capability of the tracking error system and improving tracking accuracy.

[0045] The networked wheeled robot tracking control method of this invention, oriented towards network latency and interference, actively compensates for time delays compared to traditional network time delay handling methods, offering advantages in simplicity and versatility. Compared to traditional anti-interference control methods, it utilizes the strong robustness of sliding mode control and the active anti-interference capability of the interference observer to alleviate the chattering problem of sliding mode control and enhance the system's anti-interference capability. Numerical examples and wheeled robot tracking control experiments in a real communication environment verify the effectiveness and practicality of the proposed method. Attached Figure Description

[0046] Figure 1 Explanation of kinematic symbols for a wheeled robot according to Embodiment 1 of this disclosure;

[0047] Figure 2 This is the experimental system of Embodiment 1 of this disclosure;

[0048] Figure 3 This is the structure of the network communication framework in Embodiment 1 of this disclosure;

[0049] Figure 4 This is the data flow of the network communication framework in Embodiment 1 of this disclosure;

[0050] Figure 5 The structure of the wheeled robot of Embodiment 1 of this disclosure;

[0051] Figure 6 This is a network latency statistic for Embodiment 1 of this disclosure;

[0052] Figure 7 This is the control structure of Embodiment 1 of this disclosure;

[0053] Figure 8 This is the actual tracking result of Embodiment 1 of this disclosure;

[0054] Figure 9 The tracking error in the X direction of Embodiment 1 of this disclosure;

[0055] Figure 10 This refers to the Y-direction tracking error in Embodiment 1 of this disclosure;

[0056] Figure 11 This refers to the heading angle tracking error in Embodiment 1 of this disclosure. Detailed Implementation

[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 tracking control method for a wheeled robot accommodating network latency and interference is proposed, comprising:

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

[0061] Step 2: Define the tracking error between the reference trajectory and the actual output, construct the tracking error model, and linearize and discretize it. Consider the disturbances to the wheeled robot to obtain the state space model of the error system.

[0062] Step 3: Construct state and disturbance observers to jointly estimate error state and disturbance; based on the tracking error model and estimated value, use network predictive control method to predict the error state to actively compensate for network time delay; design a sliding mode function based on the prediction information, and derive the sliding mode predictive control law accordingly to ensure the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, realizing the tracking control of the wheeled robot on the reference trajectory under the action of network time delay and disturbance.

[0063] As one embodiment, this disclosure presents a tracking control method for a wheeled robot accommodating network latency and interference. The method investigates the tracking control of a wheeled robot under network latency and system interference, and the specific implementation process is as follows:

[0064] Step 1: Establish the 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) represents the position (m) of the wheeled robot, θ (rad) is the counterclockwise angle between the robot's orientation and the x-axis, v (m / s) and w (rad / s) represent the linear velocity and angular velocity of the robot's rear wheel center, respectively; the linear velocities of the left and right drive wheels are v0 and v1, respectively. 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 control inputs, they are mapped to the linear and angular velocities of the kinematic model using the following forward kinematics formula:

[0068]

[0069] Building such Figure 2 The networked wheeled robot tracking and control system shown employs a cloud server as the controller, establishing communication with a Raspberry Pi via a wide area network. The Raspberry Pi acts as a bridge between the cloud server and the wheeled robot, running a network communication framework, the structure of which and the data flow are as follows: Figure 3 and Figure 4 As shown.

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

[0071] Figure 4 This demonstrates the information flow between the cloud server and the Raspberry Pi. In each control cycle, the Raspberry Pi first sends feedback information carrying a UNIX timestamp (the UNIX timestamp represents the current number of seconds, used in network predictive control methods for 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 predictive input from the input sequence.

[0072] Figure 5 This diagram illustrates the structure of a wheeled robot, including modules such as a DC motor, motor drive circuit, and inertial measurement unit (MPU6050). The PWM signal is used to adjust the motor input voltage to achieve speed control. In the diagram, items labeled "meas" under the variable subscript represent the measured value of the corresponding physical quantity, such as v. L,meas This represents the actual measured value of the speed of the left drive wheel.

[0073] When the sampling period T is fixed s At 0.05s, network latency was statistically analyzed, and the results are as follows: Figure 6 As shown, the maximum number of prediction steps for network predictive control is 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 disturbances experienced by the wheeled robot, obtain the state-space model of the error system:

[0075] Given a circular tracking trajectory (X) r ,Y r ,θ r The corresponding reference speeds for the left and right wheels are v, respectively. Lr =0.193m / s and v Rr = 0.207 m / s. Let as well as Thus, the tracking error model is obtained:

[0076]

[0077] cosδθ With sinδ θ Approximately 1 and δ respectively θ And discretize the equation. Define the tracking error state. In the formula, col{a,b,c} 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 error system can be constructed as follows:

[0078]

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

[0080] C = [0.6 0.5 0.1],

[0081] The output matrix C is artificially constructed to simulate real-world situations where error states cannot be directly measured, thereby enhancing the system model's adaptability to real-world application scenarios.

[0082] The disturbance ω0(k) model is generated by the following system:

[0083]

[0084] Where ξ(k) is the disturbance state, A ω B ω and C ω It is a known coefficient matrix, and ω(k) represents the unmodeled additional bounded perturbation.

[0085] Step 3: Construct state and disturbance observers to jointly estimate error state and disturbance; based on the tracking error model and estimated value, use network predictive control method to predict the error state to actively compensate for network time delay; design a sliding mode function based on the prediction information, and derive the sliding mode predictive control law accordingly to ensure the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, realizing the tracking control of the wheeled robot on the reference trajectory under the action of network time delay and disturbance.

[0086] In this invention, the sliding mode function is the core variable in the sliding mode control method. It is typically constructed from the system state and its combinations, 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 controller's switching behavior, and its set of zeros defines the system's sliding surface. The sliding surface defines the system's target trajectory, and its reachability indicates whether the system can enter the surface within a finite time under control. The controller design must ensure that the sliding surface has good reachability and retention.

[0087] Specifically, to achieve networked wheeled robot tracking control, network delay compensation, and interference suppression, a composite network predictive control scheme based on state and disturbance observers and sliding mode control is designed. The control structure is as follows: Figure 7 As shown.

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

[0089]

[0090] in, and For the estimation of error state and disturbance, The output of the state observer, L represents an estimate of the state of the disturbed system. x With L ω These are the gain matrices for the state and disturbance observers, respectively.

[0091] Define estimation error and And construct the estimation error augmentation vector Combining the tracking error system model (1), the disturbance model (2), and the observer model (3), the following estimation error augmentation system can be obtained:

[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 introduces a τ-step delay. Therefore, based on the output feedback y(k), after estimating the error state and disturbance through the observer equation (3), the controller further predicts the state and disturbance until the upper bound of the coverage delay is reached. The prediction process is as follows:

[0096]

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

[0098]

[0099] in,

[0100] Considering the observer in Formula (3), for any network delay design the following sliding mode function:

[0101]

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

[0103] In Formula (7), the symbol "|" is used to represent a prediction structure, which means "predicting or estimating the variable at the left moment based on the information at the right moment". For example, represents predicting the state at moment k based on the available information at moment k-τ; s(k|k-τ) represents a sliding mode function constructed based on the error state and other information predicted at moment k from the earliest moment k-τ. This symbol is used in the state prediction, control input calculation and sliding mode function design of the present invention, and represents a common temporal prediction relationship in networked control systems.

[0104] In particular, when the time delay τ=0, the predictive sliding mode function of Formula (7) is further organized into the form of multi-step prediction vector S(k):

[0105]

[0106] wherein, (·) T represents matrix transposition operation. Subsequently, the following composite disturbance rejection predictive control law is proposed:

[0107]

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

[0109] The controller end constructs an input sequence at moment k and sends it to the controlled plant end. At the controlled plant end, the round-trip delay τ of data transmission in the current control cycle is calculated according to the time stamp in the received data packet, and the corresponding u(k+τ) is selected from the input sequence and applied to the controlled plant, thereby compensating for the network delay.

[0110] Next, based on the sliding mode function of formula (7) and the predictive control law of 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 of formula (1) of the networked wheeled robot tracking control system, the observer of formula (2), and the composite active disturbance rejection predictive control law of formula (9), if the control law parameters satisfy 0<q<1 and Λ>Λ1, and (‖·‖ denotes the 2-norm, ∈ denotes the tolerance parameter for the convergence of the sliding mode surface, which is used to set the allowable minimum fluctuation range of the system error to ensure that the system can still approach the zero neighborhood under actual disturbances), then the sliding mode function of formula (7) converges to a bounded neighborhood centered at zero.

[0112] Proof: Based on the predictive sliding mode vector of formula (8) and the predictive control law of formula (9), for 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 of formula (2) and the prediction process of 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}, diag{...} in the formula denotes 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-wise.

[0117] The Lyapunov function is defined 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 Q T WQ=(1-q) 2 W, the above equation can be simplified to:

[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 nonzero, and ||D(k)|| ≤ ||GL x Ce x (k)‖, combined with the construction method of Γ, we know that if the gain Λ satisfies:

[0128] Λ>max k {‖GL x Ce x (k)‖}+∈1,

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

[0130] When the reachability condition is met, the error state will approach and remain within the neighborhood of the sliding surface. From the sliding function (7) and Theorem 1, the equivalent control law can be obtained. That is, after sliding to the surface, to ensure the state continues to evolve within that sliding surface, based on the condition that the rate of change of the sliding surface is zero, the control input form is derived inversely:

[0131]

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

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

[0134]

[0135] in

[0136]

[0137] To analyze the stability of the tracking error closed-loop system (13) during the sliding mode phase, this paper adopts the concept of "finally uniform boundedness" widely used in control theory as the criterion for judging the robustness and stability of the closed-loop system. Its definition is as follows:

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

[0139]

[0140] If T(x0)∈{0,1,...}, then the closed-loop system has eventually uniform boundedness.

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

[0142] Note: Here, Shure stability refers to the system matrix (A-BK). x The fact that all eigenvalues ​​have a magnitude of less than 1 is one of the commonly used standards for judging the stability of a closed-loop system.

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

[0144]

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

[0146]

[0147] Based on the prediction process (5), the predicted values ​​of the state and disturbances based on the estimated information at time k+1 can be derived by analogy. When τ≥3, we have:

[0148]

[0149] Substituting equations (6) and (16) into get:

[0150]

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

[0152]

[0153] Similarly, arbitrary prediction difference Both can be represented as error vector e χ The linear function of (k+i) can be obtained from equation (15) e χ (k+τ|k) can also be expressed as e χ A linear combination of (k+i), i∈{1,2,...,τ}. Therefore, for the closed-loop system error term e χ The stability analysis of (k+τ|k) can be uniformly reduced to the analysis of 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 equation (4) of the estimation error augmented system, it can be seen that if there exists an observation gain matrix L...x With L ω The system matrix A of the estimation error is such that e For Schuler stability, the estimated error augmentation vector e is... χ (k) asymptotically converges to zero (i.e., tends to zero with time). Based on the aforementioned analysis, e χ (k+τ|k) can be expressed as e χ A linear combination of (k+i), therefore e χ (k+τ|k) also converges asymptotically. Based on this, if there exists a control gain matrix K... x Make (A-BK) x If the system is Schulz stable, then the closed-loop system (13) is asymptotically stable (i.e., tends to zero over time).

[0155] When ω(k)≠0, if there exists an observation gain L x With L ω Make the estimation error system matrix A e For Schul stability, based on the bounded input-bounded state property of linear systems, the error augmentation vector e χ (k) Eventually uniformly bounded. From the aforementioned structural relations, e χ (k+τ|k) is also eventually uniformly bounded. Furthermore, if there exists a control gain K... x Make the closed-loop system matrix (A-BK) x If the system is Schul stable, then the closed-loop system equation (13) is eventually uniformly bounded under the condition of disturbance. Q.E.D.

[0156] During the experiment, to facilitate verification of the robustness of the proposed control method under disturbances, ω0(k) was manually injected by an embedded processor to simulate actual disturbances caused by environmental changes such as velocity inner-loop tracking error or uneven ground. The tracking results, X-direction tracking error, Y-direction tracking error, and heading angle tracking error are shown below. Figures 8 to 11 As shown, under the influence of network latency and disturbances, the proposed anti-interference network predictive control method enables the wheeled robot to track a given circular trajectory, and the tracking error converges, verifying the effectiveness of the method.

[0157] Example 2

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

[0159] The system construction module is configured to: establish the 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 the tracking error model, linearize and discretize it, consider the disturbances experienced by the wheeled robot, and obtain the state space model of the error system;

[0161] The observer building module is configured to construct state and disturbance observers for jointly estimating error states and disturbances.

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

[0163] The sliding mode predictive control law module is configured to: design a sliding mode function based on the predicted information, and derive the sliding mode predictive control law accordingly, ensuring the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, and realize the tracking control of the wheeled robot on the reference trajectory under the influence of network time delay and interference.

[0164] Example 3

[0165] In a typical embodiment of the present invention, a non-transitory computer-readable storage medium is provided for storing computer instructions. When the computer instructions are executed by a processor, the networked wheeled robot tracking control method oriented towards network latency 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, 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 perform the networked wheeled robot tracking control method for addressing network latency and interference.

[0168] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0169] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0170] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A tracking control method for a wheeled robot accommodating network latency 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 disturbances to the wheeled robot, obtain the state space model of the error system. Construct state and disturbance observers to jointly estimate error state and disturbance; Based on the tracking error model and estimate, network predictive control method is used to predict the error state in order to actively compensate for network time delay; We design a sliding mode function based on predictive information and derive a sliding mode predictive control law accordingly to ensure the reachability of the sliding surface. This ensures that the error state remains bounded under the control law, enabling the wheeled robot to track and control the reference trajectory under network time delay and interference.

2. The wheeled robot tracking control method for network latency and interference as described in claim 1, characterized in that, The kinematic model of the wheeled robot is described as follows: in, The position of the wheeled robot, For the robot's orientation and The counterclockwise angle between the axes, and These represent the linear velocity and angular velocity of the center of the robot's rear wheel, respectively.

3. The wheeled robot tracking control method for network latency and interference as described in claim 2, characterized in that, Given a circular tracking trajectory ,make , as well as The tracking error model is obtained as follows: Will and They are approximated as and The equation is then discretized, and a state-space model of the error system is constructed accordingly: in, For system output; , and Known system matrices adapted to dimension; This indicates interference.

4. The wheeled robot tracking control method for network latency and interference as described in claim 1, characterized in that, interference The model is as follows: in, In a state of interference, , and It is a known coefficient matrix. It represents additional perturbations that are not modeled.

5. The wheeled robot tracking control method for network latency and interference as described in claim 1, characterized in that, Construct state and disturbance observers to jointly estimate the error state and disturbance state; based on the error model and the estimated value, use network predictive control method to predict the error state until it covers the upper limit of network delay, thereby actively compensating for time delay.

6. The wheeled robot tracking control method for network latency and interference as described in claim 1, characterized in that, The sliding mode function is designed as follows: in, For sliding mode function, For the control gain to be designed, The gain matrix introduced in the system feedback loop must be guaranteed to ensure accurate solution of the control law. It is a non-singular matrix.

7. The wheeled robot tracking control method for network latency and interference as described in claim 6, characterized in that, The constructed composite disturbance rejection predictive control law is as follows: in, Representation matrix The reverse, The designed power exponent parameters satisfy... , used to adjust the sliding mode approach speed; It is the gain factor in sliding mode control, which determines the controller's response strength to changes in the sliding surface and is used to suppress high-frequency chattering that may occur during system switching. It is a sign function that represents the positive or negative sign of the input value and is used to generate directional switching in sliding mode control.

8. A tracking and control system for a wheeled robot resistant to network latency and interference, characterized in that, include: The system construction module is configured to: establish the 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 the tracking error model, linearize and discretize it, consider the disturbances experienced by the wheeled robot, and obtain the state space model of the error system; The observer building module is configured to construct state and disturbance observers for jointly estimating error states and disturbances. The interference estimation and time delay compensation module is configured to: predict the error state based on the tracking error model and estimated value, and actively compensate for network time delay by using network predictive control methods; The sliding mode predictive control law module is configured to: design a sliding mode function based on the predicted information, and derive the sliding mode predictive control law accordingly, ensuring the reachability of the sliding surface, so that the error state remains bounded under the action of the control law, and realize the tracking control of the wheeled robot on the reference trajectory under the influence of network time delay and interference.

9. A non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the wheeled robot tracking control method for network latency and interference as described in any one of claims 1-7.

10. An electronic device comprising: The device includes 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 perform the wheeled robot tracking control method for network latency and interference as described in any one of claims 1-7.

Images