Robust control method for differential wheeled robot based on variable gain eso

Abstract

The application provides a differential wheeled robot robust control method based on variable gain ESO, and relates to the technical field of robot control. The method comprises the following steps: constructing a robot model, wherein the robot model comprises a kinematics model and a dynamics model; constructing a corresponding trajectory tracking controller according to the robot model, wherein the trajectory tracking controller comprises a feedback controller and a kinematics controller based on variable gain filter ESO; performing displacement control on the robot by using control parameters calculated by the trajectory tracking controller according to expected parameters, wherein the expected parameters comprise an expected position and an expected angular velocity, and the control parameters comprise a wheel speed control parameter and a feedforward compensation, and the feedforward compensation comprises a differential feedforward and a disturbance feedforward. In this way, the problem of insufficient robustness of the traditional robot control method in nonlinear control can be improved.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and more specifically, to a robust control method for a differential wheel robot based on a variable gain ESO. Background Technology

[0002] Wheeled mobile robots are widely used in environmental exploration, counter-terrorism and riot control, urban rescue, and extraterrestrial exploration, and their motion control is a hot topic in robotics research. The main tasks that mobile robots need to perform are trajectory tracking and cooperative formation. To achieve the desired results, the tracking accuracy, stability, and robustness of motion control have become key issues that need to be addressed.

[0003] Differential-drive wheeled mobile robots are underactuated systems because their lateral tire velocity is zero, making the design of their kinematic controllers challenging. While the underactuated characteristic offers significant advantages in system design and manufacturing, it often results in more complex internal dynamics compared to fully actuated systems. This leads to coupling between system states and nonholonomic constraints, all of which complicate control. Due to the lack of partial actuators, underactuated systems cannot achieve complete feedback linearization, and some state variables cannot be directly controlled, rendering many control strategies used in fully actuated systems inapplicable. Existing methods are mostly based on kinematic control. However, for the dynamic control portion, current mainstream underlying control algorithms such as PID control, fuzzy control, and adaptive control are insufficient for addressing underactuated control. PID control struggles to suppress nonlinear control disturbances; fuzzy control faces challenges in designing complex linear rules for nonlinear control; and adaptive control involves a large number of parameters with inherent uncertainties. Current mainstream control schemes employ partial feedback linearization, but the underactuated subsystem remains a nonlinear system. Furthermore, its coupling with the linearized actuated subsystem through new control inputs and other nonlinear terms further complicates the control design of underactuated systems. Summary of the Invention

[0004] In view of this, the purpose of this application is to provide a robust control method for differential wheeled robots based on variable gain ESO, which can improve the problem of insufficient robustness of traditional robot control methods in nonlinear control.

[0005] To achieve the above technical objectives, the technical solution adopted in this application is as follows:

[0006] In a first aspect, embodiments of this application provide a robust control method for a differential wheeled robot based on a variable gain ESO, the method comprising:

[0007] Construct a robot model, which includes a kinematic model and a dynamic model;

[0008] Based on the robot model, a corresponding trajectory tracking controller is constructed, which includes a feedback controller and a kinematic controller based on variable gain filtering ESO (Extended State Observer).

[0009] Based on the desired parameters, the robot's displacement is controlled by the control parameters calculated by the trajectory tracking controller. The desired parameters include the desired position and the desired angular velocity. The control parameters include wheel speed control parameters and feedforward compensation. The feedforward compensation includes differential feedforward and disturbance feedforward.

[0010] In conjunction with the first aspect, in some alternative implementations, the kinematic model is represented as follows:

[0011]

[0012] In the formula, φ represents the azimuth angle of the robot, v represents the linear velocity, and w represents the angular velocity;

[0013] The linear velocity v and the angular velocity w, which are the control variables, are represented as follows:

[0014]

[0015] In the formula, w L and w R Let r represent the rotational speed of the left wheel and the rotational speed of the right wheel of the robot, respectively; r represents the radius of the left and right wheels; and b represents the distance between the two wheels.

[0016] The dynamic model of the robot is represented as follows:

[0017]

[0018] in:

[0019]

[0020] In the formula, τ L and τ R These represent the driving torques of the robot's left and right wheels, respectively, where β represents the coefficient of friction, and m and I are also mentioned. Q and I o Let a represent the robot's mass, inertia matrix, and wheel-motor assembly moment of inertia, respectively, and let a represent the robot's width.

[0021] In conjunction with the first aspect, in some optional implementations, a corresponding trajectory tracking controller is constructed based on the robot model, including:

[0022] Based on the kinematic model, the feedback controller is constructed to calculate the wheel speed control parameters for position tracking, which include left wheel speed commands and right wheel speed commands.

[0023] Based on a preset identification model, the kinematic controller is constructed to calculate the feedforward compensation.

[0024] In conjunction with the first aspect, in some optional implementations, based on the kinematic model, the feedback controller is constructed to calculate the wheel speed control parameters for position tracking, including:

[0025] The kinematic model is parametrically transformed to obtain a virtual kinematic model of the robot:

[0026]

[0027] In the formula, (x d y d ) represents the desired position, v d Represents the virtual linear velocity, ω d Represents the virtual angular velocity, θ d The desired angular velocity is represented by v; where the virtual linear velocity v is the control variable. d and virtual angular velocity ω d It is expressed as follows:

[0028]

[0029] In the formula, w Ld and w Rd These represent the left wheel speed command and the right wheel speed command, respectively.

[0030] Define error:

[0031]

[0032] In the formula, (x e y e ) represents the position error, θ e Indicates attitude error, (x c y c ) and θ c These represent the actual position and the actual angular velocity, respectively.

[0033] Define the longitudinal speed command and the lateral speed command as follows:

[0034]

[0035] Where, k p For the first gain, when k p When the value is greater than 0, the above variables are transformed as follows:

[0036]

[0037] When the position error (x) e y e It converges to zero, that is and When it converges to zero, the virtual linear velocity v pseudo for:

[0038] v pseudo =cos(θ) c )X+sin(θ c Y (10)

[0039] Define θ * =atan2(Y,X), where atan2(Y,X) represents a tangent in a four-quadrant vector, then the virtual linear velocity v is converted. pseudo The expression is:

[0040]

[0041] Determine the virtual angular velocity ω pseudo for:

[0042] ω pseudo =(θ * -θ c )*k w (12)

[0043] In the formula, k w This is the second gain;

[0044] The virtual linear velocity ω pseudo and the virtual angular velocity ω pseudo Substituting into formula (2), the left wheel speed command w is calculated. Ld and the right wheel speed command w Rd , to be used as the wheel speed control parameter.

[0045] In conjunction with the first aspect, in some optional implementations, the dynamic controller is constructed based on a preset identification model to calculate the feedforward compensation, including:

[0046] Based on a preset identification model, a tracking differentiator is constructed to filter the wheel speed control parameters in order to suppress the noise contained in the wheel speed control parameters, and the differential feedforward is calculated.

[0047] Based on the preset identification model, an ESO velocity tracking dynamic controller is constructed to calculate the disturbance feedforward.

[0048] In conjunction with the first aspect, in some optional embodiments, the continuous-time expression of the tracking differentiator is:

[0049]

[0050] Where G(t) is the Sigmoid variable gain function, as follows:

[0051]

[0052] In the formula, a, b, and R are adjustment parameters; nf = 1, 2, 3, ...; nd = 0, 1, 2, 3, ...; k = 0, 1, 2, 3, ...; nf + nd = k; u(t) is the wheel speed input signal; z0(t), z1(t), ..., z n w(t) is the nd-order derivative estimate of the wheel speed input signal; w1(t), w2(t), ..., w n (t) are auxiliary variables; λ0, λ1, λ2, ..., λ k >0 is a recursive sequence; the expression for the symbolic function sgn() is:

[0053]

[0054] Substituting the wheel speed control parameter into u(t) in formula (13), the differential signal is obtained. and This serves as the differential feedforward.

[0055] In conjunction with the first aspect, in some alternative implementations, the ESO velocity tracking dynamics controller is represented as:

[0056]

[0057]

[0058]

[0059] In the formula, τ i b represents the driving torque. i This represents an estimate of the friction coefficient β, a i This indicates the inertial parameter D. 11 and D 22 The estimate, e i =w id -w i For wheel speed tracking error, w id Indicates wheel speed command, w i w represents the actual wheel speed. if The filtered wheel speed. Let τ represent the wheel velocity and lumped uncertainty of the filtered ESO estimate, respectively.f κ1, κ2 and ∈ represent the filter ESO gain, k i This represents the wheel speed tracking gain, and t represents time.

[0060] The solution yields τ i , to serve as the perturbation feedforward.

[0061] In conjunction with the first aspect, in some optional implementations, before constructing the corresponding trajectory tracking controller based on the robot model, the method further includes:

[0062] Based on the aforementioned dynamic model, a recognition model for the robot is constructed as the preset recognition model, wherein the state-space expression of the channel used in the recognition model is:

[0063]

[0064] In the formula, a i For the inertial parameter D 11 and D 22 The estimate, w i τ represents the actual wheel speed. i b represents the driving torque. i For the estimation of the friction coefficient β, τ di This represents the lumped disturbance torque.

[0065] Secondly, embodiments of this application also provide a robot, the robot including a processor and a memory coupled to each other, the memory storing a computer program, and when the computer program is executed by the processor, the robot performs the above-described method.

[0066] Thirdly, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when run on a computer, causes the computer to perform the above-described method.

[0067] The invention employing the above technical solution has the following advantages:

[0068] The technical solution provided in this application first constructs a kinematic and dynamic model of the robot, and then constructs a corresponding trajectory tracking controller based on the robot model. The trajectory tracking controller includes a feedback controller and a kinematic controller based on a variable gain filter ESO. Then, using the desired position and desired angular velocity as inputs, the robot's displacement is controlled by the wheel speed control parameters calculated by the trajectory tracking controller and feedforward compensation. In this way, the lumped uncertainty of the robot is estimated and compensated for by the variable gain filter ESO, improving the problem of insufficient robustness of traditional robot control methods in nonlinear control. Attached Figure Description

[0069] This application can be further illustrated by the non-limiting embodiments given in the accompanying drawings. It should be understood that the following drawings only illustrate some embodiments of this application and should not be considered as limiting the scope. For those skilled in the art, other related drawings can be obtained from these drawings without any inventive effort.

[0070] Figure 1 This is a flowchart illustrating the robust control method for a differential wheeled robot based on variable gain ESO provided in an embodiment of this application.

[0071] Figure 2 This is a schematic diagram of a wheeled mobile robot model provided in an embodiment of this application.

[0072] Figure 3 This is one of the simulation trajectory tracking results of a reconfigurable robot provided in the embodiments of this application.

[0073] Figure 4 The second figure shows the simulation trajectory tracking result of the reconfigurable robot provided in the embodiments of this application.

[0074] Figure 5 This is a schematic diagram of the reconfigurable robot perturbation estimation results provided in an embodiment of this application.

[0075] Figure 6 This is a schematic diagram of the reconfigurable robot wheel speed tracking results provided in an embodiment of this application.

[0076] Figure 7 This is a schematic diagram of the reconfigurable robot trajectory tracking error provided in an embodiment of this application. Detailed Implementation

[0077] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that similar or identical parts are referred to by the same reference numerals in the drawings or description. Implementations not shown or described in the drawings are forms known to those skilled in the art. In the description of this application, terms such as "first" and "second" are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0078] This application provides a robot that may include a processing module and a storage module. The storage module stores a computer program, which, when executed by the processing module, enables the server to perform corresponding steps in the following robust control method for a differential wheeled robot based on variable gain ESO.

[0079] In this embodiment, the robot can be a wheeled mobile robot.

[0080] Please refer to Figure 1This application also provides a robust control method for a differential wheeled robot based on a variable gain ESO. The robust control method for a differential wheeled robot based on a variable gain ESO may include the following steps:

[0081] Step 110: Construct a robot model, which includes a kinematic model and a dynamic model;

[0082] Step 120: Based on the robot model, construct a corresponding trajectory tracking controller, which includes a feedback controller and a kinematic controller based on variable gain filter ESO (Extended State Observer).

[0083] Step 130: Based on the desired parameters, the robot is subjected to displacement control using the control parameters calculated by the trajectory tracking controller. The desired parameters include the desired position and the desired angular velocity. The control parameters include wheel speed control parameters and feedforward compensation. The feedforward compensation includes differential feedforward and disturbance feedforward.

[0084] In the above implementation, a kinematic and dynamic model of the robot is first constructed. Then, based on the robot model, a corresponding trajectory tracking controller is constructed. The trajectory tracking controller includes a feedback controller and a kinematic controller based on a variable gain filter ESO. Finally, using the desired position and desired angular velocity as inputs, the robot's displacement is controlled by the wheel speed control parameters calculated by the trajectory tracking controller and feedforward compensation. Thus, by estimating and compensating for the robot's lumped uncertainty through a variable gain filter ESO, the robustness of traditional robot control methods in nonlinear control is improved.

[0085] The following section will elaborate on each step of the robust control method for differential wheeled robots based on variable gain ESO:

[0086] In step 110, refer to Figure 2 The robot can be a wheeled mobile robot, where O w -xyz is the inertial coordinate system, O v -xyz represents the body coordinate system. The pose of the mobile robot in the inertial coordinate system is represented as q = [xy φ], where x and y are the position coordinates of the point of contact with the ground in the fixed coordinate system and their azimuth angle φ relative to the x-axis, respectively, and the linear velocity and angular velocity are v and w, respectively. Based on the above definitions and geometric and nonholonomic constraint analysis, the kinematic model is as follows:

[0087]

[0088] The linear velocity v and the angular velocity w, which are the control variables, are represented as follows:

[0089]

[0090] In the formula, w L and w R Let r represent the rotational speed of the left wheel and the rotational speed of the right wheel of the robot, respectively; r represents the radius of the left and right wheels; and b represents the distance between the two wheels.

[0091] The matrix form of the underlying dynamics model of a wheeled mobile robot is as follows:

[0092]

[0093] in:

[0094]

[0095] In the formula, τ L and τ R These represent the driving torques of the robot's left and right wheels, respectively, where β represents the coefficient of friction, and m and I are also mentioned. Q and I o Let a represent the robot's mass, inertia matrix, and wheel-motor assembly moment of inertia, respectively, and let a represent the robot's width.

[0096] In step 120, based on the robot model, a corresponding trajectory tracking controller is constructed, including:

[0097] Based on the kinematic model, the feedback controller is constructed to calculate the wheel speed control parameters for position tracking, which include left wheel speed commands and right wheel speed commands.

[0098] Based on a preset identification model, the kinematic controller is constructed to calculate the feedforward compensation.

[0099] In this embodiment, based on the kinematic model, a feedback controller is constructed to calculate the wheel speed control parameters for position tracking, including:

[0100] The kinematic model is parametrically transformed to obtain a virtual kinematic model of the robot:

[0101]

[0102] In the formula, (x d y d ) represents the desired position, v d Represents the virtual linear velocity, ω d Represents the virtual angular velocity, θ d The desired angular velocity is represented by v; where the virtual linear velocity v is the control variable. d and virtual angular velocity ωd It is expressed as follows:

[0103]

[0104] In the formula, w Ld and w Rd These represent the left wheel speed command and the right wheel speed command, respectively.

[0105] Define error:

[0106]

[0107] In the formula, (x e y e ) represents the position error, θ e Indicates attitude error, (x c y c ) and θ c These represent the actual position and the actual angular velocity, respectively.

[0108] Define the longitudinal speed command and the lateral speed command as follows:

[0109]

[0110] Where, k p For the first gain, when k p When the value is greater than 0, the above variables are transformed as follows:

[0111]

[0112] When the position error (x) e y e It converges to zero, that is and When it converges to zero, the virtual linear velocity v pseudo for:

[0113] v pseudo =cos(θ) c )X+sin(θ c Y (10)

[0114] Define θ * =atan2(Y,X), where atan2(Y,X) represents a tangent in a four-quadrant vector, then the virtual linear velocity v is converted. pseudo The expression is:

[0115]

[0116] Determine the virtual angular velocity ω pseudo for:

[0117] ω pseudo =(θ* -θ c )*k w (12)

[0118] In the formula, k w This is the second gain;

[0119] The virtual linear velocity v pseudo and the virtual angular velocity ω pseudo Substituting into formula (2), the left wheel speed command w is calculated. Ld and the right wheel speed command w Rd , to be used as the wheel speed control parameter.

[0120] In this embodiment, the dynamic controller is constructed based on a preset identification model to calculate the feedforward compensation, including:

[0121] Based on a preset identification model, a tracking differentiator is constructed to filter the wheel speed control parameters in order to suppress the noise contained in the wheel speed control parameters, and the differential feedforward is calculated.

[0122] Based on the preset identification model, an ESO velocity tracking dynamic controller is constructed to calculate the disturbance feedforward.

[0123] Understandably, through the aforementioned feedback controller, the input virtual linear velocity v pseudo and virtual angular velocity ω pseudo The left wheel speed command w is calculated. Ld And right wheel speed command w Rd Subsequently, to construct a stable speed tracking closed-loop system, feedback control based on a preset identification model is employed, using a tracking differentiator to apply the wheel speed command w. Ld and w Rd Filtering is performed to obtain a smooth differential signal, and the problem of inaccurate identification caused by filtering lag is taken into account. At the same time, the excitation and wheel speed commands are filtered.

[0124] The continuous-time expression of the tracking differentiator is as follows:

[0125]

[0126] Where G(t) is the Sigmoid variable gain function, as follows:

[0127]

[0128] In the formula, a, b, and R are adjustment parameters; nf = 1, 2, 3, ...; nd = 0, 1, 2, 3, ...; k = 0, 1, 2, 3, ...; nf + nd = k; u(t) is the wheel speed input signal; z0(t), z1(t), ..., zn w(t) is the nd-order derivative estimate of the wheel speed input signal; w1(t), w2(t), ..., w n (t) are auxiliary variables; λ0, λ1, λ2, ..., λ k >0 is a recursive sequence; the expression for the symbolic function sgn() is:

[0129]

[0130] Substituting the wheel speed control parameter into u(t) in formula (13), the differential signal is obtained. and This serves as the differential feedforward.

[0131] Thus, the aforementioned tracking differentiator can change the slope of the Sigmoid variable gain function by adjusting parameter a, and can change the lower limit of the Sigmoid variable gain function by adjusting parameter b. The tracking differentiator proposed in this embodiment, as a variable gain high-order sliding mode tracking differentiator, in the absence of a noise-free step input signal, when the tracking error is large, the system is in the response phase. At this time, the value of function G(t) approaches the upper limit infinitely, thereby accelerating the system's state convergence. When the aforementioned velocity tracking closed-loop system approaches steady state and the tracking error is small, the value of function G(t) approaches the lower limit, thereby improving the filtering effect.

[0132] Meanwhile, to address the lumped uncertainty of wheeled mobile robots, an ESO speed tracking dynamic controller is constructed based on the identified parameters in the preset identification model to estimate the lumped uncertainty. The collected signals are filtered and denoised to improve the stability and accuracy of the disturbance signals. The estimated disturbance signals are then used as disturbance feedforwards for feedforward compensation.

[0133] The ESO velocity tracking dynamics controller is represented as follows:

[0134]

[0135]

[0136]

[0137] In the formula, τ i b represents the driving torque. i This represents an estimate of the friction coefficient β, a i This indicates the inertial parameter D. 11 and D 22 The estimate, e i =w id -w i For wheel speed tracking error, w id Indicates wheel speed command, w iw represents the actual wheel speed. if The filtered wheel speed. Let τ represent the wheel velocity and lumped uncertainty of the filtered ESO estimate, respectively. f κ1, κ2 and ∈ represent the filter ESO gain, k i t represents wheel speed tracking gain, and t represents time.

[0138] The solution yields τ i , to serve as the perturbation feedforward.

[0139] Thus, by adjusting k L and k R To adjust the speed tracking error, τ f The accuracy and smoothness of the compromise adjustment set uncertainty estimation of κ1, κ2 and ∈.

[0140] In step 130, after the construction of the above trajectory tracking controller is completed and the wheel speed control parameters and feedforward compensation are calculated, the desired parameters are used as inputs and the trajectory tracking controller is used as the execution algorithm to control the robot to perform displacement and achieve accurate trajectory tracking.

[0141] As an optional implementation, prior to step 120, the method further includes:

[0142] Based on the aforementioned dynamic model, a recognition model for the robot is constructed as the preset recognition model, wherein the state-space expression of the channel used in the recognition model is:

[0143]

[0144] In the formula, a i For the inertial parameter D 11 and D 22 The estimate, w i τ represents the actual wheel speed. i b represents the driving torque. i For the estimation of the friction coefficient β, τ di This represents the lumped disturbance moment, which represents external disturbances and modeling uncertainties, making it impossible to accurately estimate the model parameters. In uncertainty control, it can be understood as the lumped uncertainty excluding the identified portion.

[0145] Summarizing the robust control methods for differential wheeled robots based on variable-gain ESOs, a cascaded framework is proposed to address the problem of precise trajectory control for mobile robots in unknown and uncertain environments. This framework integrates kinematic and dynamic characteristics into a control structure. At the kinematic level, virtual linear and angular velocities are input and converted into desired wheel speed commands through wheel speed transformation, which are then used for dynamic tracking of the underlying wheel speeds. At the dynamic level, a feedback controller based on an identification model tracks the wheel speeds in real time, and a variable-gain ESO compensates for feedforward disturbances.

[0146] Specifically, the feedforward compensation term typically includes state and state derivative. If these are obtained directly using differential calculations, noise will be generated. Therefore, a tracking differentiator is introduced to filter out noise in the wheel speed signal and accurately estimate the true acceleration signal. Compared with commonly used tracking differentiators, the tracking differentiator proposed in this embodiment improves the structure of the traditional tracking differentiator to reduce overshoot in the response phase. By introducing a Sigmoid variable gain function, the gain can be automatically changed according to the magnitude of the tracking error, thereby balancing the response speed and the filtering effect.

[0147] Furthermore, by introducing a variable gain filtered ESO, disturbances can be estimated online in real time, and the impact of disturbances on the system can be suppressed through feedforward compensation. Due to the high gain characteristics of the ESO, there is a large initial error between the observed values ​​of the state variables and the actual values ​​of the system state variables at the initial moment of ESO operation, and the expected estimation effect cannot be obtained due to sudden disturbances. Based on the operating principle of the ESO, this embodiment proposes a variable gain ESO. By adding a continuous function, the gain is reduced in the initial stage and then increased to avoid peak values, enabling rapid tracking of disturbances in steady state. While possessing advantages such as high robustness and high accuracy, improvements have been made to address the large overshoot that may occur during the response stage.

[0148] To facilitate understanding, the following simulation experiments were conducted using a reconfigurable micro-sized differential mobile robot and the MATLAB simulation platform:

[0149] A reconfigurable modular robot kinematic model was constructed using MATLAB, and a trajectory tracking controller cascaded with kinematics and dynamics was deployed. The wheeled mobile robot model parameters a were used. i =2.6386 and b i = -0.5277, based on the identified parameters substituted into the designed controller and filter ESO.

[0150] To verify the robustness of the controller algorithm, an external disturbance τ is introduced. di =2sin(int) + 0.2sin(0.6t), i = L, R and high-frequency output noise 0.08sin(200t). The trajectory tracking controller design parameters are k. x =ky =0.5, k R =k L =5, κ1=κ2=5, ∈=0.1 and τ f =0.1, variable gain parameter k p =10,k w =2. A wheeled mobile robot model was built based on the MATLAB platform. The simulation step size was set to 0.001s, and the simulation duration was set to 30s. The position tracking results and trajectory tracking errors are as follows: Figure 3 and Figure 4 As shown, the disturbance estimation results are as follows: Figure 5 Wheel speed tracking results are as follows Figure 6 and Figure 7 As shown.

[0151] The simulation results above show that the kinematic-dynamic cascaded trajectory tracking controller proposed in this embodiment can effectively suppress the influence of lumped uncertainties such as external disturbances and model uncertainties, and achieve high-precision trajectory tracking for reconfigurable robots.

[0152] In this embodiment, the processing module can be an integrated circuit chip with signal processing capabilities. The processing module can be a general-purpose processor. For example, the processor can be a Central Processing Unit (CPU), a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components, capable of implementing or executing the methods, steps, and logic block diagrams disclosed in the embodiments of this application.

[0153] The storage module can be, but is not limited to, random access memory, read-only memory, programmable read-only memory, erasable programmable read-only memory, electrically erasable programmable read-only memory, etc. In this embodiment, the storage module can be used to store robot models, trajectory tracking controllers, desired parameters, control parameters, etc. Of course, the storage module can also be used to store programs, which the processing module executes after receiving execution instructions.

[0154] It should be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the robot described above can be referred to the corresponding steps in the aforementioned method, and will not be elaborated further here.

[0155] This application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program that, when run on a computer, causes the computer to execute the robust control method for a differential wheeled robot based on a variable-gain ESO as described in the above embodiments.

[0156] Based on the above description of the embodiments, those skilled in the art can clearly understand that this application can be implemented by hardware or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of this application can be embodied in the form of a software product. This software product can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various implementation scenarios of this application.

[0157] In summary, this application provides a robust control method for a differential wheeled robot based on a variable-gain ESO. This scheme employs a kinematic-dynamic cascaded robust control framework for the mobile robot. At the kinematic level, virtual linear and angular velocities are converted into wheel speed commands and then encapsulated at the bottom layer. A state feedback method is used to generate speed commands and address position errors. At the dynamic level, a feedback controller is constructed based on the identified dynamics. Simultaneously, a tracking differentiator is used to acquire the differential signals of wheel speed and wheel speed commands for feedforward compensation of the model's inertial components. A variable-gain filtered ESO is created to estimate and feedforward compensate for the lumped uncertainty of the wheeled mobile robot. A front-end tracking differentiator filters the output signal, smoothing the uncertainty estimation signal. This method utilizes a modular design approach to increase control flexibility, and combined with the advantages of ESO, makes the trajectory tracking controller more robust and accurate.

[0158] In the embodiments provided in this application, it should be understood that the disclosed apparatus, systems, and methods can also be implemented in other ways. The apparatus, systems, and methods embodiments described above are merely illustrative. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code, which includes one or more executable instructions for implementing a specified logical function. It should also be noted that each block in a block diagram and / or flowchart, and combinations of blocks in block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions. Furthermore, the functional modules in the various embodiments of this application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0159] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A robust control method for a differential wheeled robot based on variable gain ESO, characterized in that, The method includes: Construct a robot model, which includes a kinematic model and a dynamic model; Based on the robot model, a corresponding trajectory tracking controller is constructed, which includes a feedback controller and a dynamic controller based on a variable gain filter (ESO). Based on the desired parameters, the robot is subjected to displacement control by the control parameters calculated by the trajectory tracking controller. The desired parameters include desired position and desired angular velocity. The control parameters include wheel speed control parameters and feedforward compensation. The feedforward compensation includes differential feedforward and disturbance feedforward. Based on the robot model, a corresponding trajectory tracking controller is constructed, including: Based on the kinematic model, the feedback controller is constructed to calculate the wheel speed control parameters for position tracking, which include left wheel speed commands and right wheel speed commands. Based on a preset identification model, the dynamic controller is constructed to calculate the feedforward compensation; Based on a preset identification model, the dynamic controller is constructed to calculate the feedforward compensation, including: Based on a preset identification model, a tracking differentiator is constructed to filter the wheel speed control parameters in order to suppress the noise contained in the wheel speed control parameters, and the differential feedforward is calculated. Based on the preset identification model, an ESO velocity tracking dynamic controller is constructed to calculate the disturbance feedforward.

2. The method according to claim 1, characterized in that, The kinematic model is represented as follows: In the formula, φ represents the azimuth angle of the robot, v represents the linear velocity, w represents the angular velocity; x and y are the position coordinates of the point of contact with the ground in the fixed coordinate system; The linear velocity v and the angular velocity w, which are the control variables, are represented as follows: In the formula, w L and w R Let r represent the rotational speed of the left wheel and the rotational speed of the right wheel of the robot, respectively; r represents the radius of the left and right wheels; and b represents the distance between the two wheels. The dynamic model of the robot is represented as follows: in: In the formula, τ L and τ R These represent the driving torques of the robot's left and right wheels, respectively, where β represents the coefficient of friction, and m and I are also mentioned. Q and I o Let represent the robot's mass, inertia matrix, and wheel-motor assembly moment of inertia, respectively; and let 'a' represent the robot's width. D 11 D 12 D 21 D 22 All are inertial parameters.

3. The method according to claim 2, characterized in that, Based on the kinematic model, the feedback controller is constructed to calculate the wheel speed control parameters for position tracking, including: The kinematic model is parametrically transformed to obtain a virtual kinematic model of the robot: In the formula, (x d ,y d ) represents the desired position, v d Represents the virtual linear velocity, ω d Represents the virtual angular velocity, θ d The desired angular velocity is represented by v; where the virtual linear velocity v is the control variable. d and virtual angular velocity ω d It is expressed as follows: In the formula, w Ld and w Rd These represent the left wheel speed command and the right wheel speed command, respectively. r represents the radius of the left and right wheels, and b represents the distance between the two wheels. Define error: In the formula, (x e ,y e ) represents the position error, θ e Indicates attitude error, (x c ,y c ) and θ c These represent the actual position and the actual angular velocity, respectively. Define the longitudinal speed command and the lateral speed command as follows: Where, k p For the first gain, when k p When the value is greater than 0, the above variables are transformed as follows: When the position error (x) e ,y e It converges to zero, that is and When convergence to zero, the virtual linear velocity v pseudo for: v pseudo =cos(θ c )X+sin(θ c )Y (10) Define θ * =atan2(Y,X), where atan2(Y,X) represents a tangent in a four-quadrant vector, then the virtual linear velocity v is converted. pseudo The expression is: Determine the virtual angular velocity ω pseudo for: oh pseudo =(θ * -θ c )*k w (12) In the formula, k w This is the second gain; The virtual linear velocity v pseudo and the virtual angular velocity ω pseudo Substituting into formula (2), the left wheel speed command w is calculated. Ld and the right wheel speed command w Rd , to be used as the wheel speed control parameter.

4. The method according to claim 2, characterized in that, The continuous-time expression of the tracking differentiator is: Where G(t) is the Sigmoid variable gain function, as follows: In the formula, a, b, R are adjustment parameters; nf = 1, 2, 3, ...; nd = 0, 1, 2, 3, ...; k = 0, 1, 2, 3, ...; nf + nd = k; u(t) is the wheel speed input signal; z0(t), z1(t), ..., z n w(t) is the nd-order derivative estimate of the wheel speed input signal; w1(t), w2(t), ..., w n (t) are auxiliary variables; λ0, λ1, λ2, ..., λ k >0 is a recursive sequence, β represents the friction coefficient; the expression for the symbolic function sgn() is: Substituting the wheel speed control parameter into u(t) in formula (13), the differential signal is obtained. and This serves as the differential feedforward.

5. The method according to claim 2, characterized in that, The ESO velocity tracking dynamics controller is represented as follows: In the formula, τ i b represents the driving torque. i This represents an estimate of the friction coefficient β, a i This indicates the inertial parameter D. 11 and D 22 The estimate; a, b are adjustment parameters; e i =w id -w i For wheel speed tracking error, w id Indicates wheel speed command, w i w represents the actual wheel speed. if The filtered wheel speed. Let τ represent the wheel velocity and lumped uncertainty of the filtered ESO estimate, respectively. f κ1, κ2 and ∈ represent the filter ESO gain, k i This represents the wheel speed tracking gain, and t represents time. The solution yields τ i , to serve as the perturbation feedforward.

6. The method according to claim 2, characterized in that, Before constructing the corresponding trajectory tracking controller based on the robot model, the method further includes: Based on the aforementioned dynamic model, a recognition model for the robot is constructed as the preset recognition model, wherein the state-space expression of the channel used in the recognition model is: In the formula, a i For the inertial parameter D 11 and D 22 The estimate, w i τ represents the actual wheel speed. i Indicates driving torque, b i For the estimation of the friction coefficient β, τ di This represents the lumped disturbance torque.

7. A robot, characterized in that, The robot includes a processor and a memory coupled together, the memory storing a computer program that, when executed by the processor, causes the robot to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when run on a computer, causes the computer to perform the method as described in any one of claims 1-6.

Images