A control method for a McNaught wheel mobile robot based on adaptive gain

Abstract

This invention discloses a control method for a Mecanar wheel mobile robot based on adaptive gain, including: S10, sensors acquiring motion parameters of the Mecanar wheel mobile robot; S20, the main controller calculating the error between the desired pose and the actual pose; S30, updating the values ​​of sliding mode variables; and S40, updating the output of the sliding mode controller. This invention consolidates the uncertainties and related disturbances in the system parameters during modeling, making the modeling more accurate and complete. It introduces adaptive parameters, eliminating the need to know the upper bound of the disturbances, adjusting the controller output gain according to the system state, and providing a solution for actuator saturation to achieve better control performance.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of robot trajectory tracking control, and relates to a Mecanum wheel mobile robot control method based on adaptive gain. BACKGROUND

[0002] The Mecanum wheel mobile robot is a kind of omnidirectional mobile robot, which can realize omnidirectional movement and has a zero turning radius compared with traditional mobile robots. In recent years, with the development of society, the Mecanum wheel mobile robot has important application prospects in household service, medical treatment, storage logistics and the like, and therefore scholars continuously research the same.

[0003] In the research of the Mecanum wheel mobile robot, enabling the mobile robot to move along a set trajectory is the first step. As an important control method, the sliding mode control is widely applied due to its strong anti-interference ability, but the conventional sliding mode algorithm often adopts a set disturbance upper limit compensation method to deal with the disturbance, but in fact, it is difficult to obtain an accurate disturbance upper limit, which not only causes a serious chattering phenomenon of the control input, seriously affects the control effect, and also faces the actuator saturation condition when the set disturbance upper limit is too large. In view of the above defects existing in the prior art, it is necessary to make further research to provide a better solution and improve the defects in the prior art. SUMMARY

[0004] To solve the above problems, the technical scheme of the application is a Mecanum wheel mobile robot control method based on adaptive gain, which comprises a sensor, a main control unit and a motor system.

[0005] The sensor is used to collect the motion parameters of the Mecanum wheel mobile robot, and the motion parameters at least include a yaw angle signal, a position signal and a motor speed signal.

[0006] The speed controller for the four motors is arranged in the main control unit, and the main control unit interacts with the upper computer through Bluetooth.

[0007] The motor system comprises four motors and their driving systems for controlling the movement of the Mecanum wheel mobile robot.

[0008] The main control unit is connected with the sensor measurement module and the motor system, and is used to control the movement of the motor system according to the motion parameters collected by the sensor measurement module.

[0009] The main control unit controls the output torque u according to the position signal x q ,y q and the yaw angle signal u=[u1 u2 u3 u4]T The motor is driven to rotate to keep the Mecanum wheel mobile robot moving along the desired trajectory.

[0010] The control method comprises the following steps:

[0011] S10, the sensor collects the motion parameters of the Mecanum wheel mobile robot;

[0012] S20, the host computer calculates the error between the desired pose and the actual pose;

[0013] S30, the value of the sliding mode variable is updated;

[0014] S40, the output of the sliding mode controller is updated.

[0015] Preferably, the motion parameters in S10 include a yaw angle signal, a position signal, and a motor speed signal.

[0016] Preferably, in S20, the host computer calculates the error between the desired pose and the actual pose according to the position signal x q ,y q and the yaw angle signal The control output torque u = [u1 u2 u3 u4] T The motor is driven to rotate to keep the Mecanum wheel mobile robot moving along the desired trajectory.

[0017] Preferably, the sliding mode controller is a Mecanum wheel mobile robot trajectory tracking sliding mode controller based on adaptive gain, and the output equation is:

[0018]

[0019] Wherein, u represents the torque output by the mobile robot, r represents the radius of the mobile robot wheel, and J0 represents the nominal value of the rotational inertia of the mobile robot wheel. Let the desired signal matrix of the control system be P Wherein, x d and y d respectively represent the desired position signal of the mobile robot, represent the desired yaw angle signal of the mobile robot body, represent the second-order derivative of the desired signal matrix P d , and represent the first-order derivative of the error matrix, and the error matrix e represents the pose error of the mobile robot, and is specifically:

[0020]

[0021] Wherein, x q and y q respectively represent the actual position signal of the mobile robot, a signal representing the actual yaw angle of the mobile robot body, the sliding mode variable matrix s is:

[0022]

[0023] wherein m>0, n>0, q>0, p>0, p and q are odd numbers and satisfy 1

[0024] M -1 , N, is a correlation matrix, specifically:

[0025]

[0026]

[0027]

[0028] wherein a and b represent one half of the width of the mobile robot body and one half of the distance between the axles on the same side of the body in the longitudinal direction of the body respectively, represents an adaptive gain matrix, wherein:

[0029]

[0030]

[0031] wherein represent the values of when the actuators are saturated, ε1, ε2, ε3 represent the upper bounds of |s1|, |s2|, |s3| after the system is stable respectively, represent the times when the absolute values |s1|, |s2|, |s3| of the sliding surfaces first reach the corresponding intervals (-ε i , ε i ) from the initial state, η1, η2, η3, ρ1, ρ2, ρ3 are six positive parameters.

[0032] Preferably, it further comprises letting O q X q Y q be the world coordinate system, O l X l Y l be the connected coordinate system, the origin O l be the geometric center of the mobile robot, the y-axis always points to the longitudinal axis of the mobile robot, and the x-axis is perpendicular to the y-axis and forms a right-handed coordinate system; O wi X wi Y wiLet be the wheel train coordinate system for the i-th wheel, with its origin located at the geometric center of the Mecanum wheel of the mobile robot. The x-axis is parallel to the output shaft of the drive motor, and the y-axis is perpendicular to the x-axis, forming a right-handed coordinate system.

[0033] The wheel on the front right side of the mobile robot is designated as wheel number 1, and the order is counter-clockwise. The pose of the mobile robot in the world coordinate system and the connected body coordinate system are respectively represented by... and The kinematic model of the mobile robot is as follows:

[0034]

[0035] Where r represents the radius of the mobile robot's wheels. θ i Let represent the rotation angle of the i-th wheel, and a and b represent half the width of the robot body and half the distance between the axle on the same side of the body along the longitudinal axis of the body, respectively. Starting from O... l X l Y l coordinate system to O q X q Y q The rotation matrix of the coordinate system is:

[0036]

[0037] The velocity transformation between the two coordinate systems is as follows:

[0038]

[0039] Combining equations (1) and (3), we can obtain:

[0040]

[0041] in:

[0042]

[0043] Preferably, it also includes obtaining P from equation (4). q The second derivative:

[0044]

[0045] in for:

[0046]

[0047] Preferably, the dynamic model of the mobile robot is defined as follows:

[0048]

[0049] Where J is the moment of inertia of each wheel of the mobile robot, c is the coefficient of viscous friction of each wheel of the mobile robot, δ is the concentrated uncertainty of each wheel of the mobile robot, and v = [v1 v2 v3 v4] T The input voltages for the four wheels of the mobile robot have the following uncertainties:

[0050] J = J0 + ΔJ (9)

[0051] c = c0 + Δc (10)

[0052] Where J0 and b0 represent the nominal values ​​of the corresponding parameters, and ΔJ and Δc represent the uncertainties of the corresponding parameters, respectively. Substituting equations (10) and (11) into equation (9) yields:

[0053]

[0054] in This represents the concentrated uncertainty of the system.

[0055] Preferably, equation (6) can be modified as follows:

[0056]

[0057] Where G is:

[0058]

[0059] Combining (12) and (13), we get:

[0060]

[0061] The control input v is designed as follows:

[0062]

[0063] Where u = [u1 u2 u3 u4] T To control the output torque, substituting equation (14) into equation (15) yields:

[0064]

[0065] The controller equation u is:

[0066]

[0067] This invention offers at least the following advantages: Traditional sliding mode control often employs a large, constant output gain to handle uncertain parameters. Even with minimal disturbance, the controller maintains a high output gain, leading to chattering and severely impacting control performance. Compared to existing technologies, this invention utilizes adaptive gain control. It increases the output gain when disturbances are significant and decreases it when disturbances are minor, effectively reducing chattering and improving control performance. Furthermore, it considers actuator saturation, providing a solution for when actuator saturation occurs.

[0068] Compared to traditional sliding mode control, the controller designed in this invention performs better, with smaller errors between the actual and desired poses during trajectory tracking of the Meckner mother wheel mobile robot, smoother controller input, less jitter, and higher robustness. Attached Figure Description

[0069] Figure 1 This is a top view of a model of a Meckner mother-wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0070] Figure 2 This is a flowchart illustrating the steps of a Mecanar wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0071] Figure 3 This is a trajectory tracking effect diagram of a Mecanar wheel mobile robot control method based on adaptive gain according to an embodiment of the present invention;

[0072] Figure 4 This is a diagram illustrating the yaw angle tracking effect during trajectory tracking of a Mecanar wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0073] Figure 5 This is an error diagram during trajectory tracking of a Mecanar wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0074] Figure 6 This is a control input diagram for trajectory tracking in a Meckner mother-wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0075] Figure 7 This is a sliding mode variable fluctuation diagram during trajectory tracking of a Mecanar wheel mobile robot control method based on adaptive gain, according to an embodiment of the present invention.

[0076] Figure 8 This is an error diagram for sliding mode control trajectory tracking using existing control methods.

[0077] Figure 9This is the control input diagram for sliding mode control trajectory tracking using existing control methods. Detailed Implementation

[0078] 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.

[0079] Conversely, this invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of the invention as defined in the claims. Furthermore, to provide a better understanding of the invention, certain specific details are described in detail below. However, those skilled in the art will fully understand the invention even without these detailed descriptions.

[0080] Figure 1 The image shows a top view of a Mechner mother-wheel mobile robot model. Each Mechner mother wheel is driven by an independent DC motor. By adjusting the different speeds of the four motors, omnidirectional movement, such as lateral and longitudinal movement, tilting movement, and zero-turn rotation, can be achieved. The relevant coordinate system of the Mechner mother-wheel mobile robot is as follows: Figure 1 As shown, O q X q Y q For the world coordinate system, O l X l Y l It is a solid coordinate system with its origin O. l Let O be the geometric center of the car, with its y-axis always pointing towards the longitudinal axis of the car body, and its x-axis perpendicular to the y-axis, forming a right-handed coordinate system. wi X wi Y wi Let be the wheel train coordinate system for the i-th wheel, with its origin located at the geometric center of the Mecanum wheel. The x-axis is parallel to the output shaft of the drive motor, and the y-axis is perpendicular to the x-axis, forming a right-handed coordinate system. The wheel at the front right of the vehicle is designated as wheel number 1, and the order is counter-clockwise. The pose of the vehicle in the world coordinate system and the connected coordinate system are respectively represented by […]. and express.

[0081] Control methods include:

[0082] Step S1: Set up a controller for controlling the motor in the Mechner mother wheel mobile robot chip, where the controller's output equation is as follows:

[0083]

[0084] in Let be the adaptive gain matrix, where:

[0085]

[0086]

[0087] Step S2: Collect the pose status of the Mechner mother wheel mobile robot through the sensor module, mainly the position signal collected by the radar and the yaw angle signal collected by the gyroscope, and transmit the signal to the control chip to update the controller output.

[0088] Step S3: After acquiring the input parameters, the adaptive sliding mode controller calculates the output torque required to make the mobile robot move along the desired trajectory based on the control equations set in S1. Then, it drives the motors to rotate, and under the coordinated action of the four Mecanar wheel hubs, the mobile robot moves along the desired trajectory. By continuously obtaining the output through the feedback pose signal, the Mecanar mobile robot completes the trajectory tracking task.

[0089] The kinematic model of the Mechner mother-wheel mobile robot is as follows:

[0090]

[0091] Where r represents the radius of the mobile robot's wheels. θ i Let a and b represent the angle of rotation of the i-th wheel. Figure 1 The length in O. l X l Y l coordinate system to O q X q Y q The rotation matrix of the coordinate system is as follows:

[0092]

[0093] The velocity transformation between the two coordinate systems is as follows:

[0094]

[0095] Combining equations (1) and (3), we can obtain:

[0096]

[0097] in:

[0098]

[0099] From equation (4), we can obtain P q The second derivative:

[0100]

[0101] in for:

[0102]

[0103] The kinematic model of the mobile robot is as follows:

[0104]

[0105] J is the moment of inertia of each wheel, c is the coefficient of viscous friction of each wheel, δ is the concentrated uncertainty of each wheel, and v = [v1 v2 v3 v4]. T The input voltages for the four wheels have the following parameter uncertainties:

[0106] J = J0 + ΔJ (9)

[0107] c = c0 + Δc (10)

[0108] Where J0 and b0 represent the nominal values ​​of the corresponding parameters, and ΔJ and Δc represent the uncertainties of the corresponding parameters, respectively. Substituting equations (10) and (11) into equation (9) yields:

[0109]

[0110] in This represents the concentrated uncertainty of the system.

[0111] Equation (6) can be changed to:

[0112]

[0113] Where G is:

[0114]

[0115] Combining (12) and (13) yields

[0116]

[0117] The control input v is designed as follows:

[0118]

[0119] Where u = [u1 u2 u3 u4] T Substituting equation (14) into equation (15) to obtain the equivalent control input to be designed later, we get:

[0120]

[0121] The controller equation u is:

[0122]

[0123] The design process is as follows:

[0124] First, the tracking error matrix is ​​designed as follows:

[0125]

[0126] To achieve rapid error convergence, the sliding surface matrix is ​​designed as follows:

[0127]

[0128] Where m > 0, n > 0, q > 0, p > 0, p and q are odd numbers and satisfy 1 < p / q < 2, p / q < m / n, and λ1, λ2, λ3, α1, α2, α3 are six positive parameters.

[0129] Based on the sliding mode design principle and adaptive gain, the expression for the controller can be obtained.

[0130]

[0131] Where u = [u1 u2 u3 u4] T M represents the control input. -1 N The correlation matrix is ​​as follows:

[0132]

[0133]

[0134]

[0135] Where a and b are as follows Figure 1 The length shown

[0136] Let represent the adaptive gain matrix, where:

[0137]

[0138]

[0139] in These represent the actuator saturation conditions. The upper bounds of |s1|, |s2|, and |s3| after the system stabilizes are denoted by ε1, ε2, and ε3, respectively. η1, η2, η3, ρ1, ρ2, and ρ3 represent the time when the absolute values ​​of each sliding surface, |s1|, |s2|, and |s3|, first reach their corresponding upper bounds from the initial state. η1, η2, η3, ρ1, ρ2, and ρ3 are six positive parameters.

[0140] To prove the effectiveness of the designed controller, Lyapunov equations need to be designed. Since the adaptive parameters change with time, two Lyapunov equations need to be designed.

[0141] exist Lyapunov equations:

[0142]

[0143] in k i Let μ1, μ2, and μ3 represent the upper bound of the disturbance corresponding to the sliding surface, where μ1, μ2, and μ3 are three positive numbers. Differentiating the Lyapunov equation, we get:

[0144]

[0145] Substituting the model control expressions, we can obtain:

[0146]

[0147] Where ξ1 is a positive number, we can obtain:

[0148]

[0149] This indicates that, under the control of the controller designed in this invention, the sliding surface can converge to a specified area within a finite time.

[0150] exist Lyapunov's equation:

[0151]

[0152] Similarly, we can obtain:

[0153]

[0154] Where ξ2 is a positive number, it indicates the effectiveness of the controller in this invention.

[0155] See the system workflow diagram. Figure 2 After system initialization, the values ​​of the sliding mode variables are updated based on the error between the desired and actual poses. The corresponding adaptive rate is then selected based on these values, and the controller output is calculated. See simulation results below. Figures 3 to 7 It can be seen that the controller of the present invention performs well, with smooth output, low jitter, and high robustness.

[0156] The above description is only 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 protection scope of the present invention.

Claims

1. A control method for a Mecanar wheel mobile robot based on adaptive gain, characterized in that, Includes the following steps: S10, the sensor collects the motion parameters of the Mechner mother wheel mobile robot; S20, the main controller calculates the error between the desired pose and the actual pose; S30, Update the value of the sliding mode variable; S40, Update the output of the sliding mode controller; The sliding mode controller is an adaptive gain-based sliding mode controller for tracking the trajectory of a Mecanar driver-wheel mobile robot, and its output equation is: ； in, This represents the torque output by the mobile robot, where r represents the radius of the robot's wheels. Let represent the nominal value of the moment of inertia of the mobile robot's wheels; let the desired signal matrix of the control system be denoted as . ,in and These represent the desired position signals of the mobile robot. This represents the desired yaw angle signal of the mobile robot body. Represents the desired signal matrix The second derivative, The first derivative of the error matrix is ​​given by the error matrix. The pose error of the mobile robot is represented as follows: ； in and These represent the actual position signals of the mobile robot. The sliding mode variable matrix s represents the actual yaw angle signal of the mobile robot body: ； in p and q are odd numbers and satisfy ,at the same time , , , , , There are six positive parameters; , , The correlation matrix is ​​as follows: ； ； ； Where a and b represent half the width of the mobile robot body and half the distance between the axles on the same side of the body along the longitudinal axis of the body, respectively. , Let represent the adaptive gain matrix, where: ； ； in , , These represent the actuator saturation conditions. , , The value, , , These represent the system after it stabilizes. , , The upper realm, , , Representing the absolute values ​​of each sliding surface , , From the initial state, the first arrival at the corresponding interval The time, , , , , , There are six positive parameters.

2. The method according to claim 1, characterized in that, The motion parameters in S10 include yaw angle signal, position signal, and motor speed signal.

3. The method according to claim 2, characterized in that, In S20, the main controller uses the position signal obtained by the sensor. and yaw angle signal Controlling output torque This drives the motor to rotate, keeping the Meckner mother wheel mobile robot moving along the desired trajectory.

4. The method according to claim 1, characterized in that, It also includes making Using the world coordinate system, It is a connected coordinate system, with its origin at... The coordinate system is the geometric center of the mobile robot, with its y-axis always pointing to the vertical axis of the mobile robot, and its x-axis perpendicular to the y-axis, forming a right-handed coordinate system. Let be the wheel train coordinate system for the i-th wheel, with its origin located at the geometric center of the Mecanum wheel of the mobile robot. The x-axis is parallel to the output shaft of the drive motor, and the y-axis is perpendicular to the x-axis, forming a right-handed coordinate system. The wheel on the front right side of the mobile robot is designated as wheel number 1, and the order is counter-clockwise. The pose of the mobile robot in the world coordinate system and the connected body coordinate system are respectively represented by... and The kinematic model of the mobile robot is as follows: (1) in Represents the radius of the mobile robot's wheels. , Let represent the rotation angle of the i-th wheel, and 'a' and 'b' represent half the width of the mobile robot's body and half the distance between the axle on the same side of the body along the longitudinal axis of the body, respectively. coordinate system to The rotation matrix of the coordinate system is: (2) The velocity transformation between the two coordinate systems is as follows: (3) Combining equations (1) and (3), we can obtain: (4) in: (5)。 5. The method according to claim 4, characterized in that, It also includes the result obtained from equation (4) The second derivative: (6) in for: (7)。 6. The method according to claim 5, characterized in that, The dynamic model of the mobile robot is defined as follows: (8) Where J is the moment of inertia of each wheel of the mobile robot, and c is the coefficient of viscous friction of each wheel of the mobile robot. For the concentrated uncertainty of each wheel of the mobile robot, The input voltages for the four wheels of the mobile robot have the following uncertainties: (9) (10) in and These represent the nominal values ​​of the corresponding parameters. and Let Equations (10) and (11) represent the uncertainties of the corresponding parameters respectively. Substituting Equations (10) and (11) into Equation (9) yields: (11) in This represents the concentrated uncertainty of the system.

7. The method according to claim 6, characterized in that, Equation (6) can be modified as follows: (12) Where G is: (13) Combining (12) and (13), we get: (14) The control input v is designed as follows: (15) in To control the output torque, substituting equation (14) into equation (15) yields: (16) The controller equation u is: (17)。

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