Robot double-closed-loop sliding mode control method based on NIFPRRL

Abstract

The invention discloses a robot double-closed-loop sliding mode control method based on NIFPRRL, and the method comprises the steps: firstly considering the performance of a robot under the influence of sliding and sideslip, designing a linear expansion state observer LESO for real-time observation, and improving the anti-interference capability of the robot; secondly, an NIFPRRL double-closed-loop sliding mode controller is designed based on a variable exponential power term, accurate control of an inner loop over the attitude and stable tracking of an outer loop over the position are achieved, and the problem that the trajectory tracking precision is low due to the fact that the robot is prone to disturbance in a complex environment is solved. The control convergence speed and trajectory tracking precision of a robot operation control system can be improved, and it is ensured that the robot has excellent motion control performance under the dynamic condition of complex working conditions.

Description

Technical Field

[0001] The invention relates to the technical field of wheeled robot intelligent control, and in particular to a robot double closed-loop synovial control method based on NIFPRRL. Background Art

[0002] Over the years, the intelligence level and functions of wheeled mobile robots have been continuously improved, showing strong adaptability and flexibility, and are widely used in various industries. The key to its efficient execution of tasks lies in high-performance control strategies, especially the research on trajectory tracking control has received widespread attention. Due to the multivariable strong coupling and non-complete constraint characteristics of wheeled mobile robots, most studies assume that the robot maintains "pure rolling without sliding" during movement. However, as the application scenarios expand to complex outdoor environments, such as forests, wet or icy roads, side slips and skidding occur frequently, destroying the ideal non-complete constraints of the robot, resulting in a decrease in control accuracy and a significant impact on trajectory tracking performance. Therefore, the trajectory tracking control problem considering the influence of slip and side slip is of great research significance.

[0003] At present, researchers have proposed a variety of nonlinear control methods to address these challenges, such as adaptive control, intelligent control, and sliding film control. Among them, sliding film control has received widespread attention because it can effectively cope with the changes of wheeled mobile robots under conditions of side slip, skidding, and dynamic uncertainty. However, the control rate discontinuity of traditional sliding film control can easily cause chattering, affecting the trajectory tracking accuracy. In order to overcome this problem, researchers have proposed a variety of improvement methods. In the existing literature, an improved fractional power reaching law (IFPRRL) is proposed, and a new sliding film control algorithm is designed in combination with the extended state observer (ESO). The unmodeled disturbance is estimated in real time by ESO, which improves the robustness of the system. Some literatures have proposed an adaptive sliding film control method based on barrier function. The proposed control strategy can ensure that the sliding film variables converge to the predefined origin area with a predefined arrival time, providing high-precision, fast response performance and robustness for non-holonomic mobile robots. There are also literatures that propose control methods based on sliding film control and disturbance observers, which quickly compensate for system uncertainties through disturbance observers, reduce chattering and improve control accuracy.

[0004] The above methods basically suppress the chattering problem of synovial control by improving the reaching law and adaptive control. However, the existing improved reaching law is still relatively dependent on the adjustment of parameters in practical applications, lacks adaptive ability, and may lead to performance degradation in complex environments. Secondly, although some methods have improved robustness and dynamic performance, they may not be able to respond in time under rapidly changing system conditions, thus affecting the accuracy and stability of control. Therefore, it is necessary to further study more flexible and efficient synovial control methods to meet the needs of mobile robot motion control in changing environments. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a robot dual closed-loop synovial membrane control method based on NIFPRRL, which is used to solve the problem of low trajectory tracking accuracy caused by the robot being susceptible to disturbances in complex environments, and helps to improve the control convergence speed and trajectory tracking accuracy of the robot operation control system.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A robot double closed-loop synovial control method based on NIFPRRL comprises the following steps:

[0008] S1. Using the designed linear extended state observer LESO, the posture control quantity and motion trajectory output of the robot's motion state are observed in real time, and the total disturbance of the robot's motion is estimated in real time to obtain the motion posture estimation value taking into account the robot's operation disturbance;

[0009] S2. Using the designed NIFPRRL double closed-loop sliding film controller, the motion posture error between the motion posture estimation value observed by the linear extended state observer LESO and the set motion trajectory expected value is calculated in real time, and then the motion posture control quantity for error compensation adjustment of the robot motion state is calculated;

[0010] S3, according to the motion posture control quantity output by the NIFPRRL double closed-loop sliding membrane controller, the motion state of the robot is controlled;

[0011] S4. Execute steps S1 to S3 in a loop until the robot's motion control process is completed.

[0012] Specifically, the NIFPRRL dual closed-loop sliding film controller includes an outer loop position controller and an inner loop attitude controller; the control process of the NIFPRRL dual closed-loop sliding film controller is:

[0013] The motion pose estimation value obtained by the linear extended state observer LESO is output to the outer loop position controller, which calculates the motion trajectory tracking error according to the motion pose estimation value and the set motion trajectory expected value, and then calculates the linear velocity control rate v′ for error compensation adjustment of the robot motion state and the expected value θ of the posture angle of the expected trajectory tracking. d , and the expected value of the attitude angle θ d The inner loop attitude controller is transmitted to the inner loop attitude controller; the inner loop attitude controller is based on the motion posture estimation value and the attitude angle expected value θ dThe deviation between them is used to calculate the angular velocity control rate ω′ for error compensation adjustment of the robot's motion state; thus, the linear velocity control rate v′ output by the outer loop position controller and the angular velocity control rate ω′ output by the inner loop posture controller are used as the motion posture control quantity for error compensation adjustment of the robot's motion state.

[0014] Specifically, the motion pose estimation value obtained by the linear extended state observer LESO taking into account the robot operation disturbance is expressed as:

[0015]

[0016] in, are the estimated values ​​of the state quantities x1 and x2, and are the disturbance estimation errors respectively; z=[v ω] T Represents the current posture control quantity of the robot's motion state, v and ω are the robot's current linear velocity and angular velocity respectively; l1=diag{2ω0,2ω0,2ω0}, are estimated compensation coefficients, ω0 is the bandwidth of the linear extended state observer LESO;

[0017] The expressions of state quantities x1 and x2 are:

[0018]

[0019] in, is the total disturbance estimator, and:

[0020]

[0021] Among them, d1, d2, and d3 are the total disturbance estimates respectively. The lateral component, longitudinal component and angular velocity component of the robot; θ is the attitude angle of the robot's current driving direction; φ represents the lateral sliding speed of the robot; ξ v and ω They are the longitudinal slip disturbance and yaw rate disturbance of the robot caused by the longitudinal slip.

[0022] Specifically, the linear velocity control rate v′ output by the outer loop position controller is expressed as:

[0023]

[0024] Where u1 and u2 are the virtual lateral velocity component and virtual longitudinal velocity component of the linear velocity control rate v′ respectively; where k 11 , k 12 ,ε1, , λ1, α1, σ1 are the reaching law parameters corresponding to the virtual velocity component u1, k21 , k 22 ,ε2, , λ2, α2, σ2 are the reaching law parameters corresponding to the virtual velocity component u2; η1, η2 are the convergence parameters corresponding to the virtual velocity components u1, u2; s1, s2 are the sliding film functions of the outer loop position controller, and satisfy:

[0025]

[0026] Among them, x d ,y d The x and y coordinates of the expected value of the set motion trajectory.

[0027] Specifically, the expression of the line speed control rate v′ is:

[0028]

[0029] in, is the expected value of the attitude angle for the desired trajectory tracking.

[0030] Specifically, the angular velocity control rate ω′ output by the inner loop attitude controller is expressed as:

[0031]

[0032] Among them, k 31 , k 32 ,ε3, , λ33, α3, σ3 are the reaching law parameters corresponding to the angular velocity control rate ω′; η3 is the convergence parameter corresponding to the angular velocity control rate ω′.

[0033] Specifically, the motion posture control quantity output by the NIFPRRL double closed-loop sliding film controller for error compensation adjustment of the robot motion state is expressed as q = [v′ ω′] T .

[0034] Compared with the prior art, the present invention has the following technical effects:

[0035] The present invention proposes a robot double closed-loop sliding film control method based on NIFPRRL. The method firstly considers the performance of the robot under the influence of slipping and sideslipping, designs a linear extended state observer LESO for real-time observation, and improves the robot's anti-interference ability; secondly, a NIFPRRL double closed-loop sliding film controller is designed based on variable exponential power terms to achieve precise control of the inner loop for posture and stable tracking of the outer loop for position, which solves the problem of low trajectory tracking accuracy caused by the robot's susceptibility to disturbance in complex environments, helps to improve the control convergence speed and trajectory tracking accuracy of the robot's operation control system, and ensures that the robot has superior motion control performance under dynamic conditions of complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0037] Figure 1 It is a flow chart of the robot double closed-loop synovial control method based on NIFPRRL of the present invention;

[0038] Figure 2 This is a schematic diagram of the kinematic structure model of a wheeled mobile robot;

[0039] Figure 3 It is a control logic block diagram of the robot double closed-loop synovial control method based on NIFPRRL of the present invention;

[0040] Figure 4 This is a comparison chart of trajectory tracking results under four schemes in the simulation experiment;

[0041] Figure 5-Figure 7 They are the comparison diagrams of the tracking errors of the X-axis, Y-axis and attitude angle θ of the mobile robot in trajectory tracking control under different control schemes in the simulation experiment example over time;

[0042] Figure 8 is the total disturbance estimate in the simulation experiment The relationship between the actual value and the observed value of the transverse component d1, longitudinal component d2 and angular velocity component d3 over time;

[0043] Fig. 9 This is an example diagram of the wheeled mobile robot experimental platform in the simulation experiment example;

[0044] Fig.10 To adopt Fig. 9 The comparison diagram of the actual running trajectory and the expected trajectory of the wheeled mobile robot experimental platform using the method of the present invention to carry out the trajectory tracking real vehicle experiment;

[0045] Fig.11 To adopt Fig. 9 The wheeled mobile robot experimental platform shown is a graph of linear velocity and angular velocity when performing a trajectory tracking real vehicle experiment using the method of the present invention;

[0046] Fig.12 To adopt Fig. 9 The trajectory tracking error curve of the wheeled mobile robot experimental platform using the method of the present invention to conduct a trajectory tracking real vehicle experiment;

[0047] Fig.13 To adopt Fig. 9 The disturbance estimation curve diagram of the wheeled mobile robot experimental platform in the trajectory tracking real vehicle experiment using the method of the present invention is shown. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but only represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0049] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0050] The reaching law parameters of the existing mobile robot synovial control method are relatively fixed, and it is difficult to adaptively adjust the exponent or gain parameters of the reaching law. The control performance of the mobile robot still needs to be further improved. In view of the above problems, the present invention provides a robot double closed-loop synovial control method based on NIFPRRL, such as Figure 1 As shown, the method comprises the following steps:

[0051] S1. Using the designed linear extended state observer LESO, the posture control quantity and motion trajectory output of the robot's motion state are observed in real time, and the total disturbance of the robot's motion is estimated in real time to obtain the motion posture estimation value taking into account the robot's operation disturbance;

[0052] S2. Using the designed NIFPRRL double closed-loop sliding film controller, the motion posture error between the motion posture estimation value observed by the linear extended state observer LESO and the set motion trajectory expected value is calculated in real time, and then the motion posture control quantity for error compensation adjustment of the robot motion state is calculated;

[0053] S3, according to the motion posture control quantity output by the NIFPRRL double closed-loop sliding membrane controller, the motion state of the robot is controlled;

[0054] S4. Execute steps S1 to S3 in a loop until the robot's motion control process is completed.

[0055] The robot double closed-loop sliding film control method based on NIFPRRL proposed in the present invention is a control strategy based on double closed-loop sliding film control of Linearly Expanded State Observer (LESO) and Novel Improved Fractional Power Reaching Law (NIFPRRL). Firstly, based on the kinematic model of the mobile robot under the conditions of slipping and sideslipping, the linear extended state observer LESO is designed, and the robot is observed in real time under the influence of slipping and sideslipping disturbances during operation, so as to improve the anti-interference ability of the robot operation control system; then, the NIFPRRL double closed-loop sliding film controller is designed, and the precise tracking of the wheeled mobile robot is realized by combining the outer loop control position and the inner loop control posture, and a variable exponential power term is designed in its reaching law, and the exponential parameter in the reaching law is adaptively changed, which is helpful to improve the control convergence speed and trajectory tracking accuracy of the robot operation control system, and improve the robustness of the robot operation control system.

[0056] The robot double closed-loop synovial membrane control method based on NIFPRRL of the present invention is described in more detail below.

[0057] 1 Kinematic model construction

[0058] In order to accurately design the trajectory tracking controller of the mobile robot, it is necessary to construct a kinematic model of the mobile robot. This paper takes a four-wheel differential wheeled mobile robot as the research object. It is assumed that the global coordinate system XOY is established with the ground as the reference system, and the robot coordinate system X1O1Y1 is established with the mobile robot as the reference system. The model of the wheeled mobile robot is as follows: Figure 2 shown.

[0059] Figure 2 In the figure, 2l is the distance between the left and right wheels in the Y1-axis direction of the robot coordinate system, 2r is the diameter of the driving wheel, d is the vertical distance from the robot's mass center o to the line connecting the driving wheel axle, that is, the distance between the mobile robot's mass center o and the line connecting the driving wheel axle in the X1-axis direction of the robot coordinate system, and θ is the angle between the robot's driving direction and the horizontal direction. Suppose the reference trajectory pose coordinates given in the XOY coordinate system are q d =[x d y d θ d ] T , the linear velocity and angular velocity of the reference trajectory are [v d ω d ]. The actual position coordinates of the mobile robot are q = [xy θ] T , the velocity and angular velocity are [v ω].

[0060] Ideally, the kinematic constraints of the mobile robot are:

[0061]

[0062] In actual operation, due to slippery roads or fast turns, the mobile robot may slip and skid, and the ideal non-holonomic constraints will be destroyed. At this time, the new constraint equation is:

[0063]

[0064] Where φ represents the lateral sliding speed of the robot, which is caused by the centrifugal force when the robot slips; ξ l and r are the angular velocity disturbances caused by the slippage of the left and right wheels of the robot; θ l and θ r are the rotation angles of the left and right wheels of the robot respectively. Assuming that the mass center of the mobile robot coincides with the geometric center d = 0, the new constraint matrix expression is:

[0065]

[0066] Where p = [xy θ θ r θ l ] T , p represents the current position information of the robot and the rotation angles of the left and right wheels, A(q) represents the control input change matrix, Λ=[φ -rξ r -rξ l ] T , Λ is the external disturbance input.

[0067] Define the disturbance influence matrix S(q), and satisfy A(q)S(q)=0, expressed as follows:

[0068]

[0069] Define the current posture control quantity of the robot's motion state as z and introduce it into the kinematic model. Then the kinematic model of the mobile robot under side slip and skidding is:

[0070]

[0071] In the formula,

[0072] z=[vω] T ,

[0073] ξ=[ξ v ξ w ] T =[r(ξ r +ξl ) / 2 r(ξ r -ξ l ) / 2l] T ,

[0074]

[0075] Where v and ω are the linear velocity and angular velocity of the robot, ξ v and ω They represent the longitudinal slip disturbance and yaw rate disturbance of the robot caused by the longitudinal slip, Represents the disturbance vector caused by lateral sliding of the robot wheel.

[0076] The total disturbance estimator is defined as Thus, the kinematic model (5) is simplified to:

[0077]

[0078] In the formula,

[0079] q=[xy θ] T ;

[0080]

[0081] Among them, d1, d2, and d3 are the total disturbance estimates respectively. The lateral component, longitudinal component and angular velocity component of . Expanding equation (6), we can obtain the kinematic model of the mobile robot under sideslip and skidding:

[0082]

[0083] 2 Trajectory tracking controller design

[0084] In order to achieve accurate tracking of a mobile robot under side slip and skidding conditions, the present invention designs a novel improved fractional power reaching law (NIFPRRL) double closed-loop sliding film control method based on a linearly expanded state observer (LESO). In this method, on the one hand, a linear extended state observer LESO is designed to observe the posture control quantity and motion trajectory output of the robot's motion state in real time, and to estimate the total disturbance to the robot's motion in real time, so as to obtain the motion posture estimation value taking into account the robot's running disturbance; on the other hand, a NIFPRRL double closed-loop sliding film controller is designed to calculate the motion posture error between the motion posture estimation value observed by the linear extended state observer LESO and the set motion trajectory expected value in real time, and then calculate the motion posture control quantity for error compensation adjustment of the robot's motion state.

[0085] Among them, the NIFPRRL dual closed-loop sliding film controller adopts a two-layer control structure, including outer loop position control and inner loop attitude control. Each loop uses the NIFPRRL sliding film control strategy based on LESO to enhance the robustness of the system to uncertainty and external interference. By combining the NIFPRRL dual closed-loop sliding film controller with the LESO observer, the robot system can dynamically adjust the control inputs v and ω to ensure efficient and accurate trajectory tracking. Its control logic block diagram is shown in the figure below. Figure 3 shown.

[0086] like Figure 3 As shown, x d ,y d is the value of the desired trajectory position in the x and y directions, which is used as the input of the NIFPRRL double closed-loop sliding film controller. d is the desired angle output by the outer loop position controller. e ,y e ,θ e is the error between the actual value and the expected value of the trajectory position in the x, y direction and azimuth. The control quantities v and ω of the system are obtained through the inner and outer loop position controllers, and the output is the robot's posture information q. In the NIFPRRL double closed-loop sliding membrane controller, the cascade control of the mobile robot can be realized, and the specific control process is:

[0087] The motion pose estimation value obtained by the linear extended state observer LESO is output to the outer loop position controller, which calculates the motion trajectory tracking error according to the motion pose estimation value and the set motion trajectory expected value, and then calculates the linear velocity control rate v′ for error compensation adjustment of the robot motion state and the expected value θ of the posture angle of the expected trajectory tracking.d , and the expected value of the attitude angle θ d The inner loop attitude controller is transmitted to the inner loop attitude controller; the inner loop attitude controller is based on the motion posture estimation value and the attitude angle expected value θ d The deviation between them is used to calculate the angular velocity control rate ω′ for error compensation adjustment of the robot's motion state; thus, the linear velocity control rate v′ output by the outer loop position controller and the angular velocity control rate ω′ output by the inner loop attitude controller are used as the motion posture control quantity for error compensation adjustment of the robot's motion state. Through this control process, the inner loop attitude controller controls the attitude tracking so that the robot's attitude error θ e Convergence, the outer loop position controller finally performs outer loop control to make the robot position error x e and e Convergence, achieving efficient and accurate trajectory tracking.

[0088] 2.1 Linear Extended State Observer LESO

[0089] In the kinematic trajectory tracking control of mobile robots, skidding and sliding phenomena are nonlinear disturbance factors that cannot be ignored, which seriously affect the control accuracy and stability of the system. In order to effectively deal with these complex external disturbances and internal model errors, LESO is widely used in control systems as an important observation method. The linear extended state observer LESO can timely estimate and compensate for the nonlinear disturbances caused by skidding and sliding through real-time observation of the system state and external disturbances, thereby greatly improving the anti-disturbance ability of the control system. Therefore, the trajectory tracking control method based on LESO provides an effective solution for improving the control performance of mobile robots under complex working conditions.

[0090] Rewrite the mobile robot kinematic equation (6), let x1 = q, and define the extended state vector x2 = d, then the system can be expressed as:

[0091]

[0092] The estimated motion pose of the robot taking into account the disturbance of the robot operation is obtained by the linear extended state observer LESO as follows:

[0093]

[0094] in, are the estimated values ​​of the state quantities x1 and x2, and are the disturbance estimation errors, l1=diag{2ω0,2ω0,2ω0}, are estimated compensation coefficients, ω0 is the bandwidth of the linear extended state observer LESO.

[0095] is the total disturbance estimator:

[0096]

[0097] Among them, d1, d2, and d3 are the total disturbance estimates respectively. The lateral component, longitudinal component and angular velocity component of the robot; θ is the attitude angle of the robot's current driving direction; φ represents the lateral sliding speed of the robot; ξ v and ω They are the longitudinal slip disturbance and yaw rate disturbance of the robot caused by the longitudinal slip.

[0098] 2.2 NIFPRRL double closed-loop sliding membrane controller

[0099] From the kinematic model of the wheeled mobile robot, it can be seen that the mobile robot motion control system is a classic underactuated system that can only actively control two input variables, and the three variables output by the model are in a following or stable state. In practical applications, robots are often easily disturbed by external factors, causing the robot to slip and skid. These factors will affect the stability and control accuracy of the system. Therefore, for this model, the core of the trajectory tracking of the wheeled mobile robot under side slip and skidding lies in designing the control rate q=[v′ ω′] of the NIFPRRL double closed-loop sliding film controller. T , v′ and ω′ are the linear velocity control rate and angular velocity control rate output by the NIFPRRL dual closed-loop sliding film controller, respectively, which are used to achieve accurate tracking of the robot position (x, y), while also ensuring stable tracking of the posture angle θ and enhancing the system's anti-interference ability.

[0100] First, set the desired trajectory to x d =f(t),y d =g(t), where f(t) and g(t) are smooth functions related to time. Then the trajectory tracking error differential equation is:

[0101]

[0102] Among them, x e =x′-x d ,y e =y′-y d ,θ e =θ-θ d .

[0103] Define the virtual velocity components:

[0104]

[0105] That is, u1 and u2 are respectively the virtual lateral velocity component and the virtual longitudinal velocity component of the linear velocity control rate v′.

[0106] Select the synovial function of the outer loop control system:

[0107]

[0108] By taking the derivative of the synovial function (12), we can obtain:

[0109]

[0110] The present invention designs a NIFPRRL:

[0111]

[0112] In the formula, k1, k2, ε, , λ, α, σ are all reaching law parameters, and k1, k2>0, 0<ε<1, , 0<α<1, 0<α≤1.

[0113] In the new reaching law, a new coefficient term is introduced It is strictly positive according to the choice of parameters, so it has no effect on the stability of the system. Compared with IFPRRL, because , so the larger the value of |s|, The smaller, On the contrary, the smaller the value of |s|, When |s| is large, the coefficient term and the variable exponential term λ will increase with |s|, and the synovial function can move toward the sliding surface at a greater rate. When |s| is small, the coefficient term As |s| decreases, the approach speed is slowed down to ensure that it approaches the sliding surface more smoothly. Therefore, using NIFPRRL, the system can adaptively select the parameters of the variable exponential power approach law according to |s| in different situations to shorten the convergence time and alleviate the chattering phenomenon. Selecting appropriate parameters, the above approach law formula (14) can be written as follows:

[0114]

[0115] Using the approach rate of formula (15), the control rate of the outer loop control system can be obtained:

[0116]

[0117] From the definition of virtual velocity component (11), we can get Since in the actual operation process, the θ obtained by the virtual velocity component is different from the expected attitude angle θ d It is impossible to be exactly the same, especially in the initial stage of control, which may cause the entire closed-loop control system to be in an unstable state. The obtained attitude angle θ is considered to be the ideal value, and the expected attitude angle θ for the desired trajectory tracking can be obtained. d for:

[0118]

[0119] Select the synovial function of the inner loop control system:

[0120] s3=θ e =θ-θ d ; (18)

[0121] The inner loop attitude controller reaching law also adopts NIFPRRL, and the angular velocity control rate ω′ can be obtained as the output:

[0122]

[0123] It is worth mentioning that in order to achieve stable inner loop sliding mode control, the inner loop convergence speed is made greater than the outer loop convergence speed to achieve θ′ fast tracking θ d , thus ensuring the stability of the closed-loop system. In this system, the control gain coefficients of the inner and outer loops are adjusted to achieve this, which ensures that the convergence speed of the inner loop is greater than that of the outer loop.

[0124] From the control rate of the inner loop attitude controller above, it can be seen that it is necessary to achieve This requires θ d is a continuous value, so when designing the virtual velocity components u1 and u2, the switching function cannot be included. Therefore, the present invention uses the hyperbolic tangent function instead of the sign function. In addition, a convergence parameter for adjusting the convergence speed is introduced, and equation (16) is changed to:

[0125]

[0126] Finally, the linear velocity control rate v′ output by the outer loop position controller and the angular velocity control rate ω′ output by the inner loop attitude controller are obtained from equations (11), (19) and (20):

[0127]

[0128] In the formula, k 11 , k 12 ,ε1, , λ1, α1, σ1 are the reaching law parameters corresponding to the virtual velocity component u1, k 21 , k 22 ,ε2, , λ2, α2, σ2 are the reaching law parameters corresponding to the virtual velocity component u2, k 31 , k 32, ε3, ω3, λ3, α3, σ3 are the reaching law parameters corresponding to the angular velocity control rate ω′; η1, η2, η3 are adjustable convergence parameters.

[0129] The smaller the values ​​of convergence parameters η1, η2, and η3, the greater the boundary thickness, the slower the convergence speed of the entire system, and the smaller the jitter, but the robustness of the system is poor; when the values ​​of convergence parameters η1, η2, and η3 are infinite, the hyperbolic tangent function is equivalent to the sign function, and the jitter of the system is large.

[0130] Finally, the NIFPRRL double closed-loop sliding film controller outputs the motion posture control quantity for error compensation adjustment of the robot motion state as q = [v′ ω′] T , used to control the robot's motion state, the motion posture control quantity q = [v′ ω′] T At the next moment, the current posture control value z=[vω] becomes the new robot motion state T The passive extended state observer LESO continues to observe, and then continues to estimate the disturbance and transmits it to the NIFPRRL dual closed-loop sliding membrane controller to make compensation adjustments for the motion posture error at the next moment; thus, the loop control is executed until the robot's motion control process is completed.

[0131] 2.3 Controller stability analysis

[0132] First, define the disturbance observer observation error i=1,2, and Available,

[0133]

[0134] Theorem 1 In the above formula, if all elements in the perturbation d are bounded and differentiable, for any bandwidth ω0>0 there exists a constant vector b=[δ1 δ2 δ3] T ,δ i > 0, so that within a limited time Each element in satisfy Where i = 1, 2, j = 1, 2, 3

[0135] Certificate: Order ε=[ε1 ε2] T have to,

[0136]

[0137] in,

[0138]

[0139] I2 represents the second-order identity matrix, and 02 represents the second-order zero matrix.

[0140] Assuming the observer initial error is zero, we can get from the above formula:

[0141]

[0142] Since every element in d(t) is bounded, there exists a normal vector d m , satisfying d(t)≤d m , therefore,

[0143]

[0144] If A0 is a Hurwitz matrix, then there exists a finite time T1 such that for all t≥T1,

[0145]

[0146] Let's assume m -d(0)=[γ1 γ2] T , γ1 and γ2 are constants, then B0×[d m -d(0)]=[0 0 γ1 γ2] T , can be obtained,

[0147]

[0148] Let ε(t)=[ε 11 ε 12 ε 211 ε 22 ] T , the above formula is changed to,

[0149]

[0150] Depend on have to,

[0151]

[0152] It can be concluded that the linear extended state observer is stable and the observation error is inversely proportional to the selected bandwidth ω0.

[0153] Theorem 2 In the kinematic system of the wheeled mobile robot, using the linear extended state observer and the double closed-loop sliding film controller, if d(t) is bounded and differentiable, by selecting appropriate observer parameters and controller parameters, the entire inner and outer loop trajectory tracking error will converge to zero within a finite time.

[0154] Proof: Consider the Lyapunov function Taking the inner loop control rate formula (19) as an example, the following can be derived:

[0155]

[0156] Obviously, -s3sign(s3)≤0, therefore If and only if s3=0, there exists This shows that the system is stable under this control rate. Similarly, the outer loop control rate can be verified.

[0157] According to the continuity of the system, the existence theorem of the synovial reaching law and the definition of reachability, if If the designed reaching law satisfies the reachable condition of sliding mode, then the reaching law exists and can reach the equilibrium point s=0.

[0158] 3 Simulation results and experimental analysis

[0159] 3.1 Analysis of Simulink simulation results

[0160] In order to verify the feasibility and effectiveness of the method of the present invention, the system was simulated using Matlab / Simulink software, and four groups of experiments were compared with the mobile robot trajectory tracking double closed-loop controller of ERL, IFPRRL and NIFPRRL without LESO. The reaching law and parameters used in the comparative experiments are shown in Tables 1 and 2.

[0161] Table 1 Reaching law settings

[0162]

[0163] Table 2 Setting of reaching law parameters

[0164]

[0165] The model parameters of the mobile robot are: r = 0.03, 2l = 0.11. In order to ensure the fairness of the comparative experiment, except for the unique parameters of the present invention, the other basic parameters are selected to be consistent. The simulation time is set to 30s and the simulation step is 0.01s. Assuming that 15≤t≤30, the robot is affected by external interference, and its side slip and skidding disturbance parameters are shown in Table 3.

[0166] Table 3 Sideslip and skidding disturbance parameters

[0167]

[0168] In order to demonstrate the superiority of the control method of the present invention, a nonlinear trajectory that matches the actual running trajectory of the mobile robot is used for simulation experiments, and four groups of comparative experiments are performed. The expected trajectory is set as: d =t,y d = sin(0.5xd )+0.5x d +1, the initial position of the mobile robot q = [0 0 0] T .

[0169] Figure 4 The figure shows the comparison of trajectory tracking results under four schemes. It can be seen from the figure that compared with other control methods, the proposed method can track the ideal trajectory more closely throughout the process, and its tracking error in multiple curved sections is small, especially in the local enlarged figure, the red dotted trajectory almost coincides with the black ideal trajectory, indicating that it has strong anti-interference ability and robustness. ERL, on the other hand, shows a large trajectory deviation, especially in the area where the trajectory changes sharply, the blue solid line deviates significantly from the ideal trajectory, showing its limited ability to handle nonlinear interference. Although NIFPRRL and IFPRRL have improved tracking accuracy compared to ERL, due to the lack of dynamic error estimation of LESO, their errors in local areas are still large.

[0170] Figure 5-Figure 7 The following is a comparison of the tracking errors of the X-axis, Y-axis and attitude angle θ of the mobile robot in trajectory tracking control under different control schemes. There are significant differences in the error performance of different control methods in mobile robot trajectory tracking. It can be seen from the figure that the error of the tracking trajectory continues to converge over time. In the scheme of the present invention, x is e ,y e ,θ e They are kept in the range of 0.01m, 0.01m, and 0.01rad respectively, and the time is 7.70s, 8.05s, and 1.10s respectively, which is the shortest time compared with other schemes. Therefore, the control strategy proposed in the present invention shows the best tracking performance in the control of three directions. Specifically, this method can quickly converge the error to zero in a short time and maintain high stability, and there is almost no overshoot and residual in the whole control process, which proves its robustness and accuracy in dealing with complex working conditions such as nonlinear disturbances, sideslips and skidding. In contrast, the ERL strategy converges significantly slower than the method of the present invention under the same initial error. Even when it tends to be stable in the later stage, there are still significant fluctuations and residuals, indicating that the performance of this method is insufficient when dealing with nonlinear interference. In addition, although the IFPRRL and NIFPRRL methods have some improvements in the error convergence speed, they still fail to achieve control accuracy comparable to the method of the present invention, especially in terms of error convergence and stability.

[0171] Figure 8 The total perturbation estimator is shown The relationship between the actual value and the observed value of the lateral component d1, longitudinal component d2 and angular velocity component d3 over time. In the initial stage, the interference term is almost zero, and the observed value is consistent with the actual value. In the mutation stage, the actual interference term undergoes a mutation, and the observed value changes immediately afterwards. Therefore, the use of LESO can accurately track the actual interference, indicating that the observer has good adaptability when dealing with interferences of different frequencies and amplitudes.

[0172] In summary, the proposed control strategy shows the most superior control effect in mobile robot trajectory tracking, can effectively cope with external disturbances, and maintain high trajectory tracking accuracy and stability. This shows that LESO+NIFPRRL is a more reliable and superior choice in mobile robot control tasks involving complex motion conditions.

[0173] In order to quantitatively analyze the control accuracy of different methods, three indicators, namely, integral absolute error (IAE), integral square error (ISE) and standard error (STD), were used to quantitatively evaluate the position tracking error and attitude tracking error of the four methods. The results are shown in Table 4, Table 5 and Table 6. In Tables 4-6, IAE represents the sum of the absolute values ​​of the errors, reflecting the overall tracking error of the system; ISE represents the sum of the squares of the errors, reflecting the sensitivity to larger errors; STD is the volatility or discreteness of the error, reflecting the stability of the system tracking error.

[0174] Table 4 Evaluation index of X-axis trajectory tracking error

[0175]

[0176] Table 5 Y-axis trajectory tracking error evaluation index

[0177]

[0178] Table 6 Evaluation index of attitude angle trajectory tracking error

[0179]

[0180] It can be seen from Tables 4-6 that the proposed method has the highest tracking accuracy under the same conditions. The IAE of the X-axis, Y-axis and attitude angle tracking errors of the scheme of the present invention are 0.5253, 0.7644 and 0.1156 respectively, which are the smallest compared with other schemes, indicating that the scheme has the best overall error performance in trajectory tracking. However, the IAE of ERL is 3.0055, 7.5706 and 0.3096 in position error and attitude angle error respectively, indicating that its overall tracking error is the worst. Among them, the IAE of IFPRRL and NIFPEEL is relatively large, but better than ERL, indicating that the overall error control of these two methods has been improved to a certain extent. The ISE of the method of the present invention is the smallest (0.0590, 0.2281, 0.0437), indicating that this method performs best in reducing large errors. The ISE of ERL is still the largest (0.4880, 3.6363, 0.1473), indicating that it is less effective in controlling large errors. IFPRRL and NIFPRRL also performed well on ISE, but were still inferior to the method of the present invention. The STD of the method of the present invention was the smallest (0.0411, 0.0845, 0.0420), which means that the error fluctuation was the smallest and the system tracking performance was the most stable. The STD of ERL was the largest (0.1204, 0.3460, 0.0705), indicating that the error fluctuation was the largest and the stability was the worst. IFPRRL and NIFPRRL improved in STD, but were still inferior to the method of the present invention.

[0181] It can be seen from Tables 4-6 that the proposed method performs well in terms of convergence time and three evaluation indicators (IAE, ISE and STD). However, the improvement is not achieved by adjusting the parameter size. The superiority of the proposed method in trajectory tracking of mobile robots subject to side slipping and sliding can be attributed to multiple factors. First. LESO can effectively estimate the external disturbances in the system and feed back to the inner and outer loop position controllers in real time, thereby improving the control accuracy and system stability. Secondly, NIFPRRL combines a dynamic adjustment strategy. When the initial error is large in the early stage of control, the system can converge to the sliding membrane surface at a faster convergence speed. In the middle stage of control, the convergence speed is slowed down to ensure that the system approaches the sliding membrane surface more smoothly and weaken the jitter of the system.

[0182] In summary, the method designed by the present invention performs best in all aspects, whether it is convergence time, overall error, control of large errors, or error stability, it is better than other methods. ERL performed the worst, and was significantly behind other methods in every indicator. The performance of IFPRRL and NIFPRRL is between LESO+NIFPRRL and ERL, showing some improvement, but is not as good as the method of the present invention in error control and stability. In summary, the method of the present invention shows obvious advantages in all indicators of trajectory tracking error, and is particularly suitable for trajectory tracking applications that require high precision and stability.

[0183] 4.2 Experimental Results Analysis

[0184] In order to further verify the effectiveness of the proposed method, Fig. 9 The wheeled mobile robot experimental platform shown in the figure was experimentally verified. The wheeled mobile robot consists of four drive wheels, which are directly connected by four DC reduction motors, and the different motion requirements of the mobile robot are met through the inter-wheel differential. The relevant parameters used in the experiment are: the radius of the drive wheel is 0.03m, the distance between the center of mass and the center of the axis is 0.05m, and the distance between the two drive wheels is 0.15m. The robot is equipped with a Jetson Xavier Nx ROS master control, an STM32F405 microprocessor, 4 500-line photoelectric rotary encoders, a battery, and a 3-axis inertial measurement unit IMU.

[0185] In the open source robot operating system ROS, the STM32 processor can fuse the IMU inertial measurement unit and motor encoder data through serial communication, and use the EKF extended Kalman filter algorithm to obtain the position and posture of the mobile robot. The algorithm is deployed in the Jetson Xavier Nx master through C++ language, and the execution cycle of the motion controller is 0.05s. The control process is as follows: First, the ROS master sends a request to the underlying STM32 controller through serial communication to receive the robot's true posture information. Then, the control commands such as the expected linear velocity and angular velocity calculated by the upper master are sent to the underlying controller through serial communication. Finally, the motor speed controller in the underlying controller uses the PI control algorithm to complete the speed tracking of the four DC reduction motors. During the experiment, the parameters of the controller are consistent with the simulation, and the reference trajectory tracked by the robot is: x d =0.2t,y d =sin(0.2t)+0.2t+0.2. The actual starting position is: q(0)=[0,0,0] T , after running for 20 seconds, a wooden stick was used to apply force to the side of the mobile robot to simulate the phenomenon that the mobile robot was suddenly disturbed by the outside world in an unknown environment, resulting in side slipping and sliding.

[0186] Figure 10-13 This is a diagram showing the experimental results of a real vehicle trajectory tracking of a wheeled mobile robot using the method proposed in the present invention. Fig.10 The figure shows the comparison between the actual trajectory of the robot and the expected trajectory. It can be seen from the figure that in the early stage of control, the mobile robot, which is not affected by side slip and skidding, gradually approaches the expected trajectory until the tracking error converges to a very small range. When the robot is disturbed by human interference, it will side slip and deviate from the expected trajectory, but it can also quickly track the expected trajectory. Fig.11The figure shows the linear velocity and angular velocity curve of the wheeled mobile robot. At 20 seconds, the disturbance estimate fed back by LESO in real time is fed forward to the controller, causing a change in the linear velocity and angular velocity, so that the mobile robot can return to the desired trajectory faster. Fig.12 The figure below is the robot's trajectory tracking error result. When there is no external disturbance, the error can quickly converge to near zero. However, after side slipping and sliding, the error remains within 0.1 and can quickly return to the desired trajectory, indicating that the control accuracy is very high and the stability is good. The real-time estimation of the linear extended state observer LESO for external disturbances is shown in Figure 1. Fig.13 As shown, it can be seen that at 20s, the disturbance estimates in the three directions undergo a sudden change and the system is compensated.

[0187] In summary, the experiment verifies that the dual closed-loop sliding mode control strategy combining LESO and NIFPRRL in the present invention can ensure that the wheeled mobile robot can quickly and effectively track the desired trajectory under the influence of the external environment, such as side slipping and skidding, and improve the overall performance and reliability of the system. The experimental results also show that compared with the existing methods, the NIFPRRL dual closed-loop sliding film control scheme based on LESO proposed in the present invention has higher tracking accuracy and better anti-interference performance. The scheme of the present invention can improve the control accuracy and tracking robustness of the wheeled mobile robot under skidding conditions.

[0188] 5 Conclusion

[0189] In order to improve the anti-interference ability and trajectory tracking accuracy of wheeled mobile robots under complex working conditions, this paper proposes a dual-loop sliding mode control scheme based on a linear extended state observer. Based on the kinematic model of the wheeled mobile robot under side slip and skidding interference, a linear extended state observer LESO is designed to estimate the total disturbance to the robot's motion, and the estimation result is transmitted to the NIFPRRL dual closed-loop sliding film controller to perform error compensation adjustment on the robot's motion state, thereby improving the control accuracy of the robot's trajectory tracking. The main technical contributions of this invention are as follows:

[0190] 1. A new improved fractional power reaching law is proposed, which has faster arrival time and stronger robustness than the traditional sliding film algorithm. Based on this reaching law, the NIFPRRL dual closed-loop sliding film controller is designed. The outer loop position controller is used to achieve smooth and finite-time convergence of the position, and the inner loop attitude controller is used to ensure rapid convergence of the attitude, which meets the collaborative control requirements of the NIFPRRL dual closed-loop sliding film controller. The stability of the system is proved based on the Lyapunov stability theory.

[0191] 2. Through simulation and experimental verification, it is proved that the method proposed in the present invention is superior to traditional control methods in terms of control accuracy, anti-interference and convergence speed of robot trajectory tracking, has stronger robustness and stability, and is suitable for mobile robot control under complex working conditions.

[0192] In summary, the present invention proposes a robot double closed-loop sliding film control method based on NIFPRRL. The method first considers the performance of the robot under the influence of slipping and sideslipping, designs a linear extended state observer LESO for real-time observation, and improves the robot's anti-interference ability; secondly, based on the variable exponential power term, the NIFPRRL double closed-loop sliding film controller is designed to achieve precise control of the inner loop for the posture and stable tracking of the outer loop for the position, which solves the problem of low trajectory tracking accuracy caused by the robot's susceptibility to disturbance in complex environments, helps to improve the control convergence speed and trajectory tracking accuracy of the robot's operation control system, and ensures that the robot has superior motion control performance under dynamic conditions of complex working conditions. Through Matlab / Simulink simulation experiment verification, the performance of four convergence laws in robot trajectory tracking is compared. The simulation results show that the method proposed in the present invention can effectively cope with external disturbances and maintain high trajectory tracking accuracy and stability. At the same time, in order to further verify the effectiveness of the proposed method, experimental verification was carried out on a four-wheel differential mobile robot, and the experimental results proved the feasibility and stability of the proposed method.

[0193] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described with reference to the preferred embodiments of the present invention, it should be understood by those skilled in the art that various changes may be made in form and details without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A robot double closed-loop synovial control method based on NIFPRRL, characterized in that: The steps include: S1. Using the designed linear extended state observer LESO, the posture control quantity and motion trajectory output of the robot's motion state are observed in real time, and the total disturbance of the robot's motion is estimated in real time to obtain the motion posture estimation value taking into account the robot's operation disturbance; S2. Using the designed NIFPRRL double closed-loop sliding film controller, the motion posture error between the motion posture estimation value observed by the linear extended state observer LESO and the set motion trajectory expected value is calculated in real time, and then the motion posture control quantity for error compensation adjustment of the robot motion state is calculated; S3, according to the motion posture control quantity output by the NIFPRRL double closed-loop sliding membrane controller, the motion state of the robot is controlled; S4. Execute steps S1 to S3 in a loop until the robot's motion control process is completed.

2. The robot double closed-loop synovial control method based on NIFPRRL according to claim 1 is characterized in that: The NIFPRRL dual closed-loop sliding film controller includes an outer loop position controller and an inner loop attitude controller; the control process of the NIFPRRL dual closed-loop sliding film controller is: The motion pose estimation value obtained by the linear extended state observer LESO is output to the outer loop position controller, which calculates the motion trajectory tracking error according to the motion pose estimation value and the set motion trajectory expected value, and then calculates the linear velocity control rate v′ for error compensation adjustment of the robot motion state and the expected value θ of the posture angle of the expected trajectory tracking. d , and the expected value of the attitude angle θ d The inner loop attitude controller is transmitted to the inner loop attitude controller; the inner loop attitude controller is based on the motion posture estimation value and the attitude angle expected value θ d The deviation between them is used to calculate the angular velocity control rate ω′ for error compensation adjustment of the robot's motion state; thus, the linear velocity control rate v′ output by the outer loop position controller and the angular velocity control rate ω′ output by the inner loop posture controller are used as the motion posture control quantity for error compensation adjustment of the robot's motion state.

3. The robot double closed-loop synovial control method based on NIFPRRL according to claim 2 is characterized in that: The motion pose estimation value obtained by the linear extended state observer LESO taking into account the robot operation disturbance is expressed as: in, are the estimated values ​​of the state quantities x1 and x2, and are the disturbance estimation errors respectively; z=[v ω] T Represents the current posture control quantity of the robot's motion state, v and ω are the robot's current linear velocity and angular velocity respectively; l1=diag{2ω0,2ω0,2ω0}, are estimated compensation coefficients, ω0 is the bandwidth of the linear extended state observer LESO; The expressions of state quantities x1 and x2 are: in, is the total disturbance estimator, and: Among them, d1, d2, and d3 are the total disturbance estimates respectively. The lateral component, longitudinal component and angular velocity component of the robot; θ is the attitude angle of the robot's current driving direction; φ represents the lateral sliding speed of the robot; ξ v and ω They are the longitudinal slip disturbance and yaw rate disturbance of the robot caused by the longitudinal slip.

4. The robot double closed-loop synovial control method based on NIFPRRL according to claim 3 is characterized in that: The linear velocity control rate v′ output by the outer loop position controller is expressed as: Where u1 and u2 are the virtual lateral velocity component and virtual longitudinal velocity component of the linear velocity control rate v′ respectively; where k 11 , k 12 ,ε1, λ1, α1, σ1 are the reaching law parameters corresponding to the virtual velocity component u1, k 21 , k 22 ,ε2, λ2, α2, σ2 are the reaching law parameters corresponding to the virtual velocity component u2; η1, η2 are the convergence parameters corresponding to the virtual velocity components u1, u2; s1, s2 are the sliding film functions of the outer loop position controller, and they satisfy: Among them, x d ,y d The x and y coordinates of the expected value of the set motion trajectory.

5. The robot double closed-loop synovial control method based on NIFPRRL according to claim 4 is characterized in that: The expression of the line speed control rate v' is: in, is the expected value of the attitude angle for the desired trajectory tracking.

6. The robot double closed-loop synovial control method based on NIFPRRL according to claim 5 is characterized in that: The angular velocity control rate ω′ output by the inner loop attitude controller is expressed as: Among them, k 31 , k 32 ,ε3, λ3, α3, σ3 are the reaching law parameters corresponding to the angular velocity control rate ω′; η3 is the convergence parameter corresponding to the angular velocity control rate ω′.

7. The robot double closed-loop synovial control method based on NIFPRRL according to claim 6 is characterized in that: The motion posture control quantity output by the NIFPRRL double closed-loop sliding film controller for error compensation adjustment of the robot motion state is expressed as q = [v′ ω′] T .

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