Fuzzy robust control method and system for mobile robot based on neurodynamics

Abstract

The application belongs to the technical field of robot trajectory tracking, and discloses a mobile robot fuzzy robust control method and system based on neural dynamics. The control method comprises the following steps: S1, a dynamic model of a mobile robot to be processed is established, the pose error of the mobile robot to be processed is calculated, and a controller corresponding to the pose error converging to zero is constructed; S2, the controller obtained in step S1 is improved by using a biological heuristic neural dynamic model to obtain an improved neural dynamic controller; S3, upper limit and lower limit output conditions are constructed; S4, the pose error is taken as input, the passive attenuation rate of the neural dynamic controller is taken as output, a control equation of the passive attenuation rate is constructed, the passive attenuation rate is adjusted by using the control equation, and the control of the mobile robot to be processed is realized. Through the application, the problem that the control amount suddenly changes and the actuator is saturated when the backstepping controller faces a larger trajectory tracking error is solved.

Description

Technical Field

[0001] This invention belongs to the field of robot trajectory tracking technology, and more specifically, relates to a fuzzy robust control method and system for mobile robots based on neurodynamics. Background Technology

[0002] Differential mobile robots employ a simple structure, consisting of two drive wheels located on the left and right sides of the vehicle body, each driven by an independent motor. By adjusting the speed of these two motors to meet specific speed requirements, the basic movements of the mobile robot, including straight-line movement and turning, are achieved. Thanks to their lower manufacturing costs and relatively simple control methods, differential mobile robots are widely used in the warehousing and logistics industry. Currently, most warehouse robots on the market use differential chassis as their motion platform, and their primary working environment is a warehouse environment filled with dense shelving. In this working environment, the robot is required to possess excellent control precision, stability, and movement flexibility.

[0003] Currently, methods for trajectory tracking control of differential mobile robots mainly include robust control methods, sliding mode control methods, intelligent control methods, backstepping control methods, and hybrid control methods that combine these methods. Among them, backstepping control is the most widely used. The design of backstepping controllers typically involves rigorous stability and convergence proofs, exhibiting good global stability. Simultaneously, backstepping is a step-by-step controller design method, allowing designers to consider the details of system dynamics in greater detail, providing high flexibility when dealing with complex nonlinear systems. Furthermore, backstepping controllers usually possess a certain degree of robustness, capable of coping with changes in system parameters and external disturbances, thus ensuring that the robot maintains a good performance level under different working conditions. Currently, backstepping controllers are widely used in various types of systems, including autonomous vehicles, unmanned aerial vehicles, underwater robots, and wheeled mobile robots, making them an ideal controller type for achieving high-precision, high-stability trajectory tracking in differential mobile robots. Despite the obvious advantages of backstepping control methods, the following issues still exist in their application:

[0004] (1) When a large trajectory tracking error occurs, the controller may trigger a sudden speed change. To achieve this sudden speed change, the actuator needs to provide acceleration beyond its normal driving force range, which is usually not feasible for the actuator. This sudden speed change may seriously affect the trajectory tracking effect and even cause the actuator to saturate, damaging the mechanical system.

[0005] (2) The calculation of the control quantity lacks consideration of constraints. In practical applications, it is usually necessary to set an upper limit for the control quantity, and the differential mobile robot itself is an underactuated system, subject to additional nonholonomic constraints. The controller fails to fully consider the constraints of the output control quantity, which may lead to the output control quantity failing to meet the requirements of hardware design and environmental conditions, thereby affecting the control accuracy.

[0006] To address the aforementioned problems, this invention proposes a fuzzy robust control method for mobile robots based on neurodynamics. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a fuzzy robust control method and system for mobile robots based on neurodynamics, which solves the problem of abrupt changes in control quantity and actuator saturation when the backstep controller faces a large trajectory tracking error.

[0008] To achieve the above objectives, according to one aspect of the present invention, a fuzzy robust control method for a mobile robot based on neurodynamics is provided, the control method comprising the following steps:

[0009] S1 establishes a dynamic model of the mobile robot to be processed, calculates the pose error of the mobile robot to be processed, and constructs a controller that makes the pose error converge to zero.

[0010] S2 uses a bio-inspired neurodynamics model to improve step S1 to obtain a controller, thus obtaining an improved neurodynamic controller.

[0011] S3 constructs the upper and lower limits of the output conditions of the neurodynamic controller based on the actual situation of the mobile robot to be processed;

[0012] S4 takes the pose error as input and the passive decay rate of the neurodynamic controller as output, constructs the control equation for the passive decay rate, and uses the control equation to adjust the passive decay rate; this passive decay rate is used to control the robot to be processed.

[0013] More preferably, in step S1, the dynamic model is based on the following relationship:

[0014]

[0015] Where (x,y,θ) is the robot's current posture, (x,y) is the position of robot G in the local coordinate system, the angle between the X-axis and the XC-axis is θ, d is the distance between the robot's center and the midpoint of the two drive rear wheels, and v and w are the robot's linear velocity and angular velocity, respectively.

[0016] More preferably, in step S1, the controller performs the following:

[0017]

[0018] Where e1 is the longitudinal error, e2 is the lateral error, e3 is the heading angle error, and v r and w r These are the desired linear velocity and angular velocity, respectively, k a ,k b ,k c These are the parameters of the controller, all of which are positive real numbers. v1 and w1 are the linear velocity and angular velocity calculated by the controller.

[0019] More preferably, in step S2, the bio-inspired neurodynamic model is performed as follows:

[0020]

[0021] in, Let ψ be the first derivative of the neuron's neural activity with respect to time t, and let ψ be the neuron's neural activity with parameters δ, ε, and ε. These are the passive decay rate of neurons, the upper limit of neural activity, and the lower limit of neural activity. and The input signal is converted into either an excitation or a suppression input, where x is the value of the input signal and sign(x) is the sign function. If x is positive, the output value is 1; if x is negative, the output value is -1; and if x is 0, the output value is 0.

[0022] More preferably, in step S2, the neurodynamic controller performs the following:

[0023]

[0024] Where e1 is the longitudinal error, e2 is the lateral error, e3 is the heading angle error, ψ1 and ψ3 are intermediate variables calculated by the bio-inspired neurodynamics model based on the input, and v r and w r These are the desired linear velocity and angular velocity, respectively. k1, k2, and k3 are the parameters of the neurodynamic controller, and v2 and w2 are the linear velocity and angular velocity calculated by the neurodynamic controller.

[0025] More preferably, in step S3, the upper and lower limits of the output of the neurodynamic controller are determined according to the following conditions:

[0026]

[0027] Where k1, k2, and k3 are controller parameters, v max wmax These are the maximum linear velocity and angular velocity, v r w r These are the expected linear velocity and angular velocity, e 1max It is the upper bound of the longitudinal error, e 2max It is the upper bound of the lateral error, e 3max δ1 and δ3 are the upper bounds of the heading angle error, respectively. δ1 and δ3 are the passive decay rates of the neurodynamic model, respectively. e1 and e3 are the real-time longitudinal error and heading angle error values ​​during robot operation.

[0028] More preferably, in step S4, the control equation for constructing the passive attenuation rate is constructed using a fuzzy algorithm.

[0029] More preferably, in step S4, the passive attenuation rate is determined according to the following formula:

[0030]

[0031] Where, δ i This is the passive decay rate in the neurodynamic model, i = 1, 3, δ ij It is δ i In the j-th region corresponding to the universe of discourse U, u(δ) i ) is δ ij Membership degree of a location.

[0032] According to another aspect of the invention, a system for fuzzy robust control of a mobile robot based on neurodynamics is provided, including a processor for executing the control method described above.

[0033] According to another aspect of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the control method described above.

[0034] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0035] 1. The method provided by this invention utilizes the characteristics of a bio-inspired neurodynamic model to smooth the control signal, designs the upper and lower limit parameters of the bio-inspired neurodynamic model, and uses a fuzzy method to adaptively determine the value of the passive decay rate of the bio-inspired neurodynamic model, thus providing a solution for robust and high-precision control of differential mobile robots.

[0036] 2. To prevent abrupt changes in control quantity when the tracking error is large during the trajectory tracking process of the mobile robot, this invention uses a bio-inspired neurodynamic model to smooth the error value, constructs a new intermediate variable ψ, and uses the intermediate variable ψ to calculate the control quantity, making the change of the control quantity smoother. At the same time, fuzzy rules are used to adaptively adjust the parameter in the bio-inspired neurodynamic model: the passive decay rate, so that the controller maintains good control effect for tracking errors of different sizes, further improving the robustness of the system.

[0037] 3. To prevent the output control quantity from failing to meet the requirements of hardware design and environmental conditions, its upper and lower limit parameters are designed to ensure that the control quantity always remains within the upper limit and satisfies the nonholonomic constraints of the differential mobile robot. This control strategy avoids additional processing of the control quantity and effectively improves the stability of the system. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of a differential mobile robot model constructed according to a preferred embodiment of the present invention;

[0039] Figure 2 This is a control block diagram of a fuzzy robust control method for differential mobile robots based on bio-inspired neurodynamics, constructed according to a preferred embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0041] This invention is implemented as follows: a fuzzy robust control method for differential motion robots based on a bio-inspired neurodynamics model, comprising the following steps:

[0042] Step 1: Establish the kinematic model of the differential mobile robot system;

[0043] A kinematic model of the differential motion robot is established. In this embodiment, the object to be processed is a three-wheeled differential motion robot, whose chassis consists of two drive wheels mounted on the rear axle and a front wheel that can steer freely. All wheel radii are represented by r, the distance between the two rear drive wheels is 2b, and the attitude of the DWMR is represented by three generalized coordinates q = (x, y, θ). T Let (x, y) be the position of the center of the DWMR in the local coordinate system, and let θ be the angle between the central axis of the DWMR and the X-axis.

[0044] To simplify the analysis, the following assumptions are made: the mobile robot must move along the main axis, and the wheels are purely rolling, neglecting slippage. The nonholonomic constraints of the mobile robot can be expressed by the following formula:

[0045]

[0046] Where A(q)=(-sinθ,cosθ,d), q=(x,y,θ) T To describe the robot's posture.

[0047] The kinematic model of DWMR (Differential Mobile Robot) is represented as follows:

[0048]

[0049] The linear velocity and angular velocity of DWMR at the center are v and w, respectively. Furthermore, J(q) is a Jacobian matrix and satisfies:

[0050] J T (q)A T (q)=0 (3)

[0051] The control quantity η is expressed as:

[0052]

[0053] Where the linear velocity and angular velocity of DWMR at its center are v and w, respectively. r is the wheel radius, 2b is the distance between the two drive wheels, and w... L and w R These represent the angular velocities of the left and right drive wheels, respectively.

[0054] Establish a new coordinate system X with the center of DWMR as the point of exchange, the direction of travel as the X-axis, and the axial direction as the Y-axis. e -Y e The coordinates of DWMR in the new coordinate system are: q e =(e1,e2,e3) T Where e1 represents the longitudinal error, e2 represents the lateral error, and e3 represents the heading angle error. Through coordinate transformation, the DWMR pose error equation can be described as:

[0055]

[0056] Where the expected position and the actual position are q r =(x r ,y r ,θ r ) T and q=(x,y,θ) TBy differentiating equation (5), we get:

[0057]

[0058] Where v r and w r Let represent the desired linear velocity and angular velocity, respectively. Based on Lyapunov theory, in order to achieve the pose error q... e Converging to zero, the backstepping (CBC) control method is as follows:

[0059]

[0060] Where e1 is the longitudinal error, e2 is the lateral error, e3 is the heading angle error, and v r and w r These are the desired linear velocity and angular velocity, respectively, k a ,k b ,k c These are the parameters of the controller, all of which are positive real numbers. v1 and w1 are the linear velocity and angular velocity calculated by the controller.

[0061] S2 combines a bio-inspired neurodynamics model and a backstepping control method to derive a trajectory tracking controller for a differential mobile robot.

[0062] The bio-inspired neurodynamic model used in this invention is a biomembrane voltage model. This model describes the biomembrane voltage V using the following state equation. m :

[0063]

[0064] Among them, C m It is the membrane potential, parameter E k E Na E p These represent the energies of potassium ions, sodium ions, and negative drain current in the cell membrane, respectively, and the time-varying signal input function k. p k Na k m These are the admittances of potassium, sodium, and the negative electrode, respectively, making

[0065]

[0066] The bio-inspired equation is as follows:

[0067]

[0068] Where ψ represents the neural activity of the neuron, and the parameters δ, ε, and These are the passive decay rate of neurons, the upper limit of neural activity, and the lower limit of neural activity, respectively. and The input signal is converted into either an excitation input or a suppression input.

[0069] In this method, a bio-inspired neurodynamic model is used to construct the intermediate error of the backstepping controller. Due to the bounded and smooth characteristics of the neurodynamic model, even if the desired trajectory changes significantly (such as at directional inflection points), the entire system can still produce a smooth output. This characteristic ensures the trajectory tracking performance of the system.

[0070] Next, by combining a bio-inspired neurodynamic model with a classical backstepping controller, a neurodynamic model-based backstepping controller is derived such that:

[0071]

[0072] Where e1 is the longitudinal error, e2 is the lateral error, e3 is the heading angle error, ψ1 and ψ3 are intermediate variables calculated from the input of the bio-inspired neurodynamics model, and v r and w r These are the desired linear velocity and angular velocity, respectively. k1, k2, and k3 are the parameters of the neurodynamic controller, and v2 and w2 are the linear velocity and angular velocity calculated by the neurodynamic controller.

[0073] definition:

[0074]

[0075] Where, ψ i Represents the robot's posture error e i The intermediate variable corresponding to (i = 1, 3), parameter δ i ε i and These represent the passive decay rate of neurons, the upper limit of neural activity, and the lower limit of neural activity, respectively. and as well as and The input signals e1 and e3 are converted into excitation or inhibition inputs, respectively.

[0076] S3 performs performance analysis on bio-inspired neurodynamic models and designs their upper and lower limit parameters.

[0077] According to the neurodynamic model:

[0078]

[0079] When x>0, solving the differential equation yields: Furthermore, as x(t) → +∞, we have Although the properties of bio-inspired neurodynamic models allow ψ1 and ψ3 to remain constant However, its boundary value is often only attainable when x approaches infinity, while in practice, the upper bound of the output signal is approximately equal to... Therefore, directly using ε i Using the boundary value of the output signal is an overly conservative strategy that fails to bring out the controller's optimal performance.

[0080] In addition to being affected by ψ1 and ψ3, the system's control variables v and w are also influenced by control parameters such as k1, k2, and k3, as well as the desired tracking speed v. r w r And the influence of the heading angle tracking error cose3. If these parameters are not set properly, the system's control variables v and w will still exceed their constraint range, therefore the parameters ε of the neurodynamic model need to be adjusted. i and To carry out the design.

[0081] Since DWMR is a nonholonomic constrained mobile robot, its control variables v and w are formed by the coordination of the angular velocities of the two drive wheels, and they are not independent of each other, and the following constraint relationship exists:

[0082]

[0083]

[0084] Where v max and w max Find the maximum linear velocity and angular velocity of the robot as a whole. L ,v R These represent the linear velocities of the left and right drive wheels, respectively. The distance between the two rear drive wheels of the robot is 2b.

[0085] Upper and lower limit parameters ε i , The design is as follows:

[0086]

[0087] Where ε1 and ε3 represent the upper bound of the output of the neurodynamic model when calculating intermediate variables in equation (12), k1, k2, and k3 are controller parameters, and v max w max v represents the maximum velocity and angular velocity. r w r For the expected velocity and angular velocity, e 1max ,e 3max Here, δ1 and δ3 are preset upper bounds for lateral and heading angle errors, respectively; e1 and e3 are passive decay rates of neurodynamics; and e1 and e3 are error values ​​that vary with the robot's movement. Since the robot's forward and backward motion patterns are identical, it is possible to set... Under the constraints of equation (15), it can be ensured that the control quantity remains within the constraint range.

[0088] In terms of parameter ε i and After imposing constraints, the controller output is ensured to remain within the constrained range. However, the system's response speed and tracking accuracy are affected to some extent when faced with tracking errors of varying magnitudes. To improve control performance, fuzzy logic inference is used to adaptively adjust the passive decay rate δ of the neurodynamic model. i .

[0089] S4 constructs fuzzy rules to complete the adaptive passive decay rate design.

[0090] Select the error amount |e i |As a fuzzy input, the passive decay rate δ of the neurodynamic model i As the fuzzy output. The input and output fuzzy subsets of the fuzzy controller are defined as {ZO, PS, PM, PB}. The l-th fuzzy rule of this fuzzy controller can be written as:

[0091] R i :if|e|is B l ,thenδ i is C l (16)

[0092] Among them, B l C l All are fuzzy sets, and their corresponding fuzzy membership functions. The associations are given by l = 1, 2, 3, 4.

[0093] Based on control experience, when |e| is large, the vehicle deviates significantly from the expected trajectory, requiring a smaller δ. i Values ​​should be set to avoid drastic changes in output; as the vehicle gradually returns to the predetermined trajectory, the tracking error |e i | Gradually decrease, at which point a larger δ is selected. i The value of can be chosen to appropriately increase the convergence speed without affecting the system's stability. Therefore, the fuzzy rule table is designed as follows:

[0094] Table 1 Fuzzy Rules

[0095]

[0096] The fuzzy input and output are divided into four regions: ZO is zero, PS is positive small, PM is positive center, and PB is positive large.

[0097] The triangular membership function selected by the fuzzy membership function has the following specific form:

[0098]

[0099] Where |e i |(i=1,3) represents the absolute value of the tracking error, α, β, γ are important parameters determining the form of the membership function, and α≤β≤γ. Let the membership function of the set μ on the universe of discourse U be μ(δ ij ),δ ij ∈U. The passive attenuation rate δ is obtained by deblurring using the area center method. i :

[0100]

[0101] Proof of S5 stability;

[0102] The Lyapunov function is selected as follows:

[0103]

[0104] Clearly, V1(t)≥0 and V1(t)=0 holds if and only if e1=e2=e3=ψ1=ψ3=0. Therefore, if a constant is set... make Taking the time derivative of V1, we get:

[0105]

[0106] When e1≥0, then:

[0107]

[0108] When e1 < 0, then:

[0109]

[0110] Similarly, regardless of whether sine3≥0 or sine3<0, we have:

[0111]

[0112] therefore:

[0113]

[0114] Where k1, k2, and k3 are controller parameters, v r As a reference velocity, δ1 and δ3 are the negative decay rates of neuronal activity, both positive real numbers. Since V1 ≥ 0 and Therefore, the entire system can achieve global asymptotic stability.

[0115] like Figure 1The figure shows a typical differential motion robot model. All wheel radii are represented by r, and the distance between the two driving rear wheels is 2b. OXY is the global coordinate system, and CX... C Y C Let be a local coordinate system fixed on the mobile robot. d is the distance between the robot's center G and the midpoint C of the two rear drive wheels. The robot's current pose can be represented by three generalized coordinates (x, y, θ), where (x, y) is the position of G in the local coordinate system, and the x-axis is perpendicular to the x-axis. C The included angle between the axes is θ.

[0116] like Figure 2 The diagram shows the control block diagram of a fuzzy robust control method for mobile robots based on neurodynamics. In practical applications, the upper-level path planning stage generates the desired path, which includes the pose information of the target point, as well as the desired velocity and angular velocity. In each control cycle, the target point is updated; the target point's pose is the error of the robot's current pose, calculated by subtracting the robot's current pose from its desired pose. This robot pose error serves as the controller's input. First, the passive decay rate δ of the bio-inspired neurodynamics model is calculated using fuzzy rules. i Next, the intermediate variable ψ was calculated using a bio-inspired neurodynamic model. i Finally, the robot's linear velocity v and angular velocity w are calculated using a backstepping controller based on a neurodynamic model. The differential motion robot's kinematic model calculates the robot's pose at the next moment based on the input linear velocity v and angular velocity w.

[0117] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fuzzy robust control method for mobile robots based on neurodynamics, characterized in that, The control method includes the following steps: S1 Establish the dynamic model of the mobile robot to be processed, calculate the pose error of the mobile robot to be processed, and construct the controller that makes the pose error converge to zero. S2 uses a bio-inspired neurodynamics model to improve step S1 and obtain the controller, resulting in the improved neurodynamics controller. S3 Constructs the upper and lower limits of the output conditions of the neurodynamic controller based on the actual situation of the mobile robot to be processed; S4 takes the pose error as input and the passive decay rate of the neurodynamic controller as output, constructs the control equation for the passive decay rate, and uses the control equation to adjust the passive decay rate; and uses this passive decay rate to control the robot to be processed. In step S2, the bio-inspired neurodynamic model is performed according to the following formula: in, It is the neural activity of neurons in relation to time. t The first derivative, It refers to the neural activity of neurons, parameters δ , ε and φ These are the passive decay rate of neurons, the upper limit of neural activity, and the lower limit of neural activity, respectively. and The input signal is converted into either an excitation or a suppression input, respectively. x It is the value of the input signal. sign ( x ) is a sign function, if x If the output value is positive, the output value is 1. x If the value is negative, the output value is -1. x The output value is 0 if the value is 0; In step S3, the upper and lower limits of the output of the neurodynamic controller are determined according to the following conditions: in, k 1. k 2. k 3 represents the controller parameters. v max , w max These are the maximum linear velocity and angular velocity. v r , w r These are the expected linear velocity and angular velocity. e 1max It is the upper bound of the longitudinal error. e 2max It is the upper bound of the lateral error. e 3max This is the upper bound of the heading angle error. δ 1, δ 3 represents the passive decay rate of the neurodynamic model. e 1, e 3. Real-time longitudinal error and heading angle error during robot operation.

2. The fuzzy robust control method for mobile robots based on neurodynamics as described in claim 1, characterized in that, In step S1, the dynamic model is performed according to the following relationship: in,( x , y , θ ) is the robot's current pose, ( x , y () represents the position of the robot's center G in the local coordinate system. θ It is the angle between the X-axis and the XC-axis. d It is the distance between the center of the robot and the midpoint of the two rear drive wheels. v and w These are the robot's linear velocity and angular velocity.

3. A fuzzy robust control method for mobile robots based on neurodynamics as described in claim 1 or 2, characterized in that, In step S1, the controller performs the following: in, e 1 represents the longitudinal error. e 2 represents the lateral error. e 3 represents the heading angle error. v r and w r These are the desired linear velocity and angular velocity, respectively. k a , k b , k c These are the controller parameters, all of which are positive real numbers. v 1 and w 1 represents the linear velocity and angular velocity calculated by the controller.

4. The fuzzy robust control method for mobile robots based on neurodynamics as described in claim 1, characterized in that, In step S2, the neurodynamic controller performs the following: in, e 1 represents the longitudinal error. e 2 represents the lateral error. e 3 represents the heading angle error. and These are intermediate variables calculated by bio-inspired neurodynamic models based on the input. v r and w r These are the desired linear velocity and angular velocity, respectively. k 1, k 2, k 3 represents the parameter of the neurodynamic controller. v 2 and w 2 represents the linear velocity and angular velocity calculated by the neurodynamic controller.

5. The fuzzy robust control method for mobile robots based on neurodynamics as described in claim 1, characterized in that, In step S4, the control equation for constructing the passive attenuation rate is constructed using a fuzzy algorithm.

6. The fuzzy robust control method for mobile robots based on neurodynamics as described in claim 5, characterized in that, In step S4, the passive attenuation rate is determined according to the following formula: in, δi It is the passive decay rate in the neurodynamic model. i =1, 3, δij yes δi The corresponding first in the universe of discourse U j Each region u ( δi )yes δij Membership degree of a location.

7. A system for fuzzy robust control of a mobile robot based on neurodynamics, comprising a processor for executing the control method as described in any one of claims 1-6.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the control method as described in any one of claims 1-6.

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