A tracking control method for a movable vehicle-mounted flexible arm for an asymmetric gap

Abstract

The present application relates to the technical field of mechanical arm, especially relates to a tracking control method for movable vehicle-mounted flexible arm of asymmetric gap, comprising: establishing the dynamics model of the movable vehicle-mounted flexible arm of the mobile trolley, constructing the mathematical model of asymmetric reverse gap, constructing the tracking control algorithm of the movable vehicle-mounted flexible arm according to the asymmetric reverse gap and disturbance observer; constructing Lyapunov function and applying Matlab for simulation, analyzing the performance of the tracking control algorithm; determining the tracking control stability of the movable vehicle-mounted flexible arm based on the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm; if the tracking control stability does not meet the requirements, adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm; if the tracking accuracy does not meet the requirements, adjusting the control torque at the hub of the movable vehicle-mounted flexible arm. The present application improves the tracking control stability of the movable vehicle-mounted flexible arm.

Description

Technical Field

[0001] This invention relates to the field of robotic arm technology, and in particular to a tracking control method for a mobile vehicle-mounted flexible arm with asymmetric gaps. Background Technology

[0002] With the rapid development of control and computer technologies, significant progress has been made in robotic arm research. Flexible robotic arms, due to their advantages in energy consumption, portability, and flexibility, have been widely applied in various fields such as industrial automation, logistics handling, resource exploration, service industries, rescue, and aerospace. Unlike traditional fixed robotic arm systems, vehicle-mounted mobile flexible robotic arms can expand the operating space and have a wider range of applications.

[0003] As a nonlinear system, the strong coupling between the mobile vehicle and the flexible robotic arm poses certain challenges to system control. Furthermore, in practical applications, it faces various nonlinear input constraints caused by limitations in mechanical design, manufacturing, and technical conditions of the actuator. Backlash, caused by the incomplete contact of gears in the mechanical actuator and friction between different components, is a common nonlinear input constraint problem that inevitably reduces the system's control performance and even affects its stability. However, existing technologies only consider the impact of backlash input on the flexible robotic arm system and employ smoothing inverse compensation operators for controller design. They do not consider how to handle the effects of asymmetric backlash based on disturbance observer technology for mobile, vehicle-mounted flexible robotic arm systems, thus exhibiting certain limitations.

[0004] Chinese Patent Publication No. CN118456424A discloses a tracking control method for a flexible robotic arm, comprising the following steps: S1. Constructing a model of the flexible robotic arm system; S2. Constructing tracking errors of various orders; S3. Describing the control objective and designing a feedback controller; S4. Constructing a neural network model; S5. Designing a virtual controller; S6. Combining the Lyapunov second method to ensure that the Lyapunov function is positive semi-definite and that the time derivative of the function is negative semi-definite. It is evident that the aforementioned tracking control method for a flexible robotic arm suffers from a problem where the asymmetric gap worsens with increasing usage time due to wear on components at the joints of the vehicle-mounted flexible arm and different force conditions on both sides of the joint during movement, leading to a decrease in the tracking control stability of the mobile vehicle-mounted flexible arm. Summary of the Invention

[0005] To address this issue, the present invention provides a tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps. This method overcomes the problem in the prior art where wear occurs at the joints of the vehicle-mounted flexible arm, resulting in different force conditions on both sides of the joint during movement. Consequently, the asymmetric gaps worsen with increasing usage time, leading to a decrease in the tracking control stability of the movable vehicle-mounted flexible arm.

[0006] To achieve the above objectives, this invention provides a tracking control method for a movable vehicle-mounted flexible arm with asymmetric clearance, comprising: establishing a dynamic model of the movable vehicle-mounted flexible arm of the mobile vehicle; constructing a mathematical model of the asymmetric backlash; constructing a tracking control algorithm for the movable vehicle-mounted flexible arm based on the asymmetric backlash and a disturbance observer; constructing a Lyapunov function and performing simulation using Matlab to analyze the performance of the tracking control algorithm; obtaining the vibration intensity of the movable vehicle-mounted flexible arm within a single operating cycle; determining the tracking control stability of the movable vehicle-mounted flexible arm based on the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm; if the tracking control stability does not meet the requirements, adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm, or determining the tracking accuracy of the movable vehicle-mounted flexible arm based on the rotation angle deviation of the movable vehicle-mounted flexible arm; if the tracking accuracy does not meet the requirements, adjusting the control torque at the hub of the movable vehicle-mounted flexible arm, or adjusting the control force of the mobile vehicle based on the maximum offset difference of the mobile vehicle displacement.

[0007] Furthermore, the tracking control stability of the mobile vehicle-mounted flexible arm was determined, including:

[0008] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset first fluctuation amplitude.

[0009] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude, then it is determined that the tracking control stability of the movable vehicle-mounted flexible arm does not meet the requirements.

[0010] Furthermore, the tracking accuracy of the mobile vehicle-mounted flexible arm was determined, including:

[0011] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset first fluctuation amplitude and the preset second fluctuation amplitude, respectively.

[0012] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude and less than or equal to the preset second fluctuation amplitude, it is preliminarily determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements, and the tracking accuracy of the movable vehicle-mounted flexible arm is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm.

[0013] Furthermore, adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm includes:

[0014] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset second fluctuation amplitude;

[0015] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset second fluctuation amplitude, the boundary control force at the end load of the movable vehicle-mounted flexible arm is increased.

[0016] Furthermore, the increase in the boundary control force at the end load of the movable vehicle-mounted flexible arm is determined by the difference between the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude.

[0017] Furthermore, adjusting the control torque at the hub of the movable vehicle-mounted flexible arm includes:

[0018] The rotation angle deviation of the mobile vehicle-mounted flexible arm is compared with the preset first deviation and the preset second deviation, respectively.

[0019] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation, it is determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements.

[0020] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation and less than or equal to the preset second deviation, then the control torque at the hub of the movable vehicle-mounted flexible arm is increased.

[0021] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is initially determined that the motion stability of the movable vehicle-mounted flexible arm does not meet the requirements, and the motion stability of the movable vehicle-mounted flexible arm is determined based on the maximum offset difference of the mobile trolley displacement.

[0022] Furthermore, the rotation angle deviation of the movable vehicle-mounted flexible arm is the difference between the actual rotation angle and the desired rotation angle of the movable vehicle-mounted flexible arm.

[0023] Furthermore, the increase in the control torque at the hub of the movable vehicle-mounted flexible arm is determined by the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and a preset first deviation.

[0024] Furthermore, adjusting the control force of the mobile vehicle includes:

[0025] Compare the maximum offset difference of the moving trolley with the preset difference;

[0026] If the maximum offset difference of the mobile trolley is greater than the preset difference, it is determined that the motion stability of the mobile vehicle-mounted flexible arm does not meet the requirements, and the control force of the mobile trolley is increased.

[0027] Furthermore, the increase in the control force of the mobile trolley is determined by the difference between the maximum offset difference of the mobile trolley displacement and a preset difference.

[0028] Compared with the prior art, the beneficial effects of the present invention are as follows: The method of the present invention adjusts the boundary control force at the end load of the movable vehicle-mounted flexible arm according to the fluctuation amplitude of the vibration offset. Because the space on one side of the gap differs from that on the other side during the movement of the robotic arm, the force on the joint differs during forward and reverse movements, causing vibration in the robotic arm. Over time, small vibrations accumulate, leading to a gradual increase in the vibration offset at the end load. By increasing the boundary control force at the end load of the movable vehicle-mounted flexible arm, the excessive vibration of the end load can be reversed, allowing the load to return to the vicinity of the desired trajectory more quickly. This consumes excess energy generated by vibration, thereby reducing the vibration amplitude. The control torque at the hub of the movable vehicle-mounted flexible arm is adjusted according to the rotation angle deviation. Since the elastic deformation of the flexible arm changes the force transmission path and magnitude when a rotational torque is applied to the hub, it may affect the actual torque distribution at the hub. When the rotation angle differs from the desired angle, the repeated elastic deformation of the flexible arm causes continuous changes in the hub angle, ultimately leading to a significant deviation from the desired angular position. By increasing the control torque at the hub of the movable vehicle-mounted flexible arm, a greater corrective force can be generated, allowing the hub to return to the desired angular position more quickly and effectively reducing the time required for angular deviation recovery. The control force of the movable vehicle is adjusted according to the maximum offset difference in the displacement of the movable vehicle. Due to the influence of backlash during the execution of actions, the displacement of the robotic arm deviates, changing the relative positional relationship between the robotic arm and the vehicle. When the movement deviation of the robotic arm is coupled with the motion control of the vehicle, the movement position of the vehicle becomes difficult to achieve as desired, and the deviation gradually increases over time. By increasing the control force of the movable vehicle, the positional lag caused by the deviation can be compensated, or the lateral offset caused by the coupling effect can be corrected by using a larger lateral control force, thus improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0029] Furthermore, the method of the present invention adjusts the boundary control force at the end load of the movable vehicle-mounted flexible arm by setting a preset first fluctuation amplitude and a preset second fluctuation amplitude. Because the space on one side of the gap is different from that on the other side when the robotic arm moves, the force on the joint is different when moving in the forward and reverse directions, which causes the robotic arm to vibrate. Over time, the small vibrations accumulate, causing the vibration offset at the end load to gradually increase. By increasing the boundary control force at the end load of the movable vehicle-mounted flexible arm, the excessive vibration of the end load can be reversed, so that the load returns to the vicinity of the desired trajectory more quickly. This can consume the excess energy generated by the vibration, thereby reducing the vibration amplitude and further improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0030] Furthermore, the method of the present invention adjusts the control torque at the hub of the movable vehicle-mounted flexible arm by setting a preset first deviation and a preset second deviation. Since the elastic deformation of the flexible arm changes the force transmission path and magnitude when a rotational torque is applied to the hub, the actual rotation angle of the hub may differ from the desired angle. Repeated elastic deformation of the flexible arm will cause continuous changes in the hub angle, eventually leading to a serious deviation from the desired angle position. By increasing the control torque at the hub of the movable vehicle-mounted flexible arm, a larger corrective force can be generated, allowing the hub to return to the desired angle position more quickly, effectively reducing the time required for angle deviation recovery, and further improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0031] Furthermore, the method of the present invention adjusts the control force of the mobile trolley by setting a preset difference amount. Since the displacement of the robotic arm is affected by the gap when performing the action, it will change the relative positional relationship between the robotic arm and the trolley. When the movement deviation of the robotic arm is coupled with the motion control of the trolley, the movement position of the trolley will be difficult to achieve as expected. Moreover, the deviation gradually increases over time. By increasing the control force of the mobile trolley, the positional lag caused by the deviation can be compensated, or the lateral offset caused by the coupling effect can be corrected by a larger lateral control force, thereby further improving the tracking control stability of the mobile vehicle-mounted flexible arm. Attached Figure Description

[0032] Figure 1 This is an overall flowchart of the tracking control method for a movable vehicle-mounted flexible arm with asymmetric gap according to an embodiment of the present invention.

[0033] Figure 2 This is a logic flowchart of a tracking control method for a movable vehicle-mounted flexible arm with asymmetric gap, according to an embodiment of the present invention.

[0034] Figure 3This is a flowchart illustrating the process of adjusting the boundary control force at the end load of the mobile vehicle-mounted flexible arm in the tracking control method for a mobile vehicle-mounted flexible arm with asymmetric gap, according to an embodiment of the present invention.

[0035] Figure 4 This is a flowchart illustrating the process of adjusting the control torque at the hub of a movable vehicle-mounted flexible arm in a tracking control method for a movable vehicle-mounted flexible arm with asymmetric clearance, according to an embodiment of the present invention. Detailed Implementation

[0036] To make the objectives and advantages of the present invention clearer, the present invention will be further described below with reference to embodiments; it should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention.

[0037] Preferred embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0038] It should be noted that in the description of this invention, the terms "upper", "lower", "left", "right", "inner", "outer", etc., which indicate the direction or positional relationship, are based on the direction or positional relationship shown in the drawings. This is only for the convenience of description and is not intended to indicate or imply that the device or element must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of this invention.

[0039] Furthermore, it should be noted that, in the description of this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0040] Please see Figure 1 , Figure 2 , Figure 3 as well as Figure 4 The diagrams shown are, respectively, an overall flowchart, a logic flowchart, a detailed flowchart of the process for adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm, and a detailed flowchart of the process for adjusting the control torque at the hub of the movable vehicle-mounted flexible arm, all according to embodiments of the present invention. The present invention provides a tracking control method for a movable vehicle-mounted flexible arm with asymmetrical clearance, comprising:

[0041] Step S1: Establish a dynamic model of the mobile vehicle-mounted flexible arm of the mobile trolley, construct a mathematical model of the asymmetric backlash, and construct a tracking control algorithm for the mobile vehicle-mounted flexible arm based on the asymmetric backlash and the disturbance observer.

[0042] Step S2: Construct the Lyapunov function and apply Matlab for simulation to analyze the performance of the tracking control algorithm;

[0043] Step S3: Obtain the vibration intensity of the movable vehicle-mounted flexible arm within a single operating cycle;

[0044] Step S4: Determine the tracking control stability of the mobile vehicle-mounted flexible arm based on the fluctuation amplitude of the vibration offset of the mobile vehicle-mounted flexible arm.

[0045] Step S5: If the tracking control stability does not meet the requirements, the boundary control force at the end load of the mobile vehicle-mounted flexible arm is adjusted, or the tracking accuracy of the mobile vehicle-mounted flexible arm is determined based on the rotation angle deviation of the mobile vehicle-mounted flexible arm.

[0046] Step S6: If the tracking accuracy does not meet the requirements, the control torque at the hub of the movable vehicle-mounted flexible arm is adjusted, or the control force of the movable vehicle is adjusted based on the maximum offset difference of the movable vehicle displacement.

[0047] Specifically, the process of establishing the dynamic model of the movable vehicle-mounted flexible arm is as follows:

[0048] For the sake of simplicity, the present invention uses the following uniform approach. This represents the first derivative of (·) with respect to t; ∠(·) represents the second derivative of (·) with respect to t; ∠(·)' represents the first derivative of (·) with respect to x; ∠(·)” represents the second derivative of (·) with respect to x; ∠(·)”' represents the third derivative of (·) with respect to x; and ∠(·)”” represents the fourth derivative of (·) with respect to x.

[0049] The kinetic energy of the vehicle-mounted mobile flexible robotic arm is expressed as:

[0050]

[0051] Among them, J a ρ represents the unit moment of inertia and unit mass of the robotic arm; t represents the time variable, which is a positive constant; α(t) represents the rotation angle of the robotic arm; L represents the length of the robotic arm; x represents the spatial position variable, and x∈[0,L]; J(x,t) is the absolute displacement vector of the robotic arm in the XOY coordinate system, and Where s(t) and p(x,t) represent the displacement of the trolley and the elastic vibration displacement of the robotic arm, respectively; m a and mv These represent the end-effector load mass and the cart mass, respectively.

[0052] The potential energy of the vehicle-mounted mobile flexible robotic arm is expressed as:

[0053]

[0054] Among them, EI and T e This represents the bending stiffness and tension of the robotic arm;

[0055] The virtual work performed on the system is represented as follows:

[0056] B d (t)=[y(t)+q y (t)]s(t)+[n(t)+q n (t)]α(t)+[f(t)+q f (t)]p(L,t) (3)

[0057] Where y(t) and q y (t) represent the control force acting on the vehicle and the unknown external disturbance, respectively; n(t) and q n f(t) and q(t) represent the control torque acting on the hub of the robotic arm and the unknown external disturbance, respectively; f (t) represent the control force and the unknown external disturbance acting on the end effector of the robotic arm, respectively;

[0058] Combining the expressions for the kinetic energy, potential energy, and virtual work of the vehicle-mounted mobile flexible manipulator, and applying Hamilton's principle, the dynamic model of the vehicle-mounted mobile flexible manipulator system can be calculated as follows:

[0059] p(0,t)=p'(0,t)=0 (4)

[0060] p"(L,t)=0 (5)

[0061]

[0062]

[0063] Specifically, the process of constructing the mathematical model for the asymmetric reverse gap is as follows:

[0064] Considering the nonlinear, nondifferentiable, and nonsmooth characteristics of the backlash, this invention describes the asymmetric backlash input as a desired control input and a nonlinear input error. This nonlinear input error, along with external disturbances, is considered a disturbance-like term and processed by designing a suitable disturbance observer. Therefore, the control inputs y(t), n(t), and f(t) are described as follows:

[0065]

[0066] Where: m y ,m n ,m f The slope is a positive constant, and the parameter B is... yr B nr B fr >0,B yl B nl B fl <0,y b (t), n b (t) and f b (t) is the input variable for the reverse gap, y(t) - ),n(t - ),f(t - Let f(t) represent y(t), n(t) and f(t) remain unchanged.

[0067] Describing the above asymmetric gap input as the desired control input and nonlinear input error respectively, we can obtain y(t) = B(y b (t))=m y y b (t)+y o (t),

[0068]

[0069] n(t) = B(n b (t))=m n n b (t)+n o (t),

[0070]

[0071] f(t) = B(f b (t))=m f f b (t)+f o (t),

[0072]

[0073] Where y o (t), n o (t) and f o (t) represents the nonlinear error of the backlash input, and y o (t), n o (t) and f o (t) are all bounded.

[0074] The nonlinear error of the backlash input acting on the trolley, the hub of the robotic arm, and the end-effector load, along with external disturbances, are collectively considered as a disturbance term and defined as follows:

[0075]

[0076] It is known that Q y (t), Q n (t) and Q f (t) are all bounded, and the bounding values ​​are positive constants Q. uy Q un Q uf Based on the above representation of asymmetric backlash, the system boundary conditions (6)-(8) can be further expressed as:

[0077]

[0078] Specifically, the process of constructing the tracking control algorithm for the mobile vehicle-mounted flexible arm is as follows:

[0079] For the above-mentioned vehicle-mounted mobile flexible robotic arm system with asymmetric backlash, in order to achieve vibration control of the robotic arm and position tracking of the vehicle's movement position and the robotic arm's angular position, and to effectively handle the influence of asymmetric backlash, this invention proposes the following tracking control algorithm:

[0080]

[0081] Among them, the control parameters μ1, μ2, μ3, κ1, κ2, κ3, and γ are all positive constants, and s i and α i This represents the desired displacement of the trolley and the desired rotation angle of the robotic arm. Represents the perturbation term Q y (t),Q n (t),Q f (t) Each boundary value Q uy Q un Q uf The estimated quantity is obtained, and based on this, the following perturbation observer is designed:

[0082]

[0083] Among them, the control parameters ω1, ω2, and ω3 are all positive numbers.

[0084] Specifically, the process of constructing a Lyapunov function is as follows:

[0085] The Lyapunov function for composite energy is designed as follows:

[0086] H(t)=H a (t)+H b (t)+H c (t)+H d (t) (22)

[0087] in,

[0088]

[0089]

[0090] Where the control parameters are c, ξ1, ξ2, All are positive numbers. They represent the values ​​for Q respectively. uy Q un Q uf The estimation error is defined as follows:

[0091]

[0092] Clearly, the Lyapunov function H(t) is positive definite.

[0093] Taking the derivative of the Lyapunov function H(t), we get:

[0094]

[0095] Combining equations (17)-(19) with the tracking control algorithm (20), the following can be calculated:

[0096]

[0097] Combining equations (28) and (32), we can calculate that...

[0098]

[0099] in,

[0100]

[0101] d1, d2 are positive constants, χ0=min{χ, χ+ω1, χ+ω2, χ+ω3}=χ>0,

[0102]

[0103] Therefore, it can be proved that the considered vehicle-mounted mobile flexible robotic arm system is asymptotically stable, and all signals in the system are uniformly bounded.

[0104] Specifically, the fluctuation range of the vibration offset of the movable vehicle-mounted flexible arm is the range of changes in the degree to which the flexible arm deviates from its equilibrium position during vibration.

[0105] Specifically, the rotation angle deviation of the movable vehicle-mounted flexible arm is the difference between the actual angular position and the desired angular position of the flexible arm hub rotation.

[0106] Specifically, the maximum displacement difference of the mobile trolley is the maximum value of the difference between the actual displacement and the expected displacement of the trolley during the operation of the on-board flexible arm.

[0107] In implementation, the method of this invention adjusts the boundary control force at the end load of the movable vehicle-mounted flexible arm based on the fluctuation amplitude of the vibration offset. Because the space on one side of the gap differs from the other during the movement of the robotic arm, the force on the joint differs during forward and reverse movements, causing vibration. Over time, these minute vibrations accumulate, leading to a gradual increase in the vibration offset at the end load. By increasing the boundary control force at the end load of the movable vehicle-mounted flexible arm, excessive vibration of the end load can be counteracted, allowing the load to return to the desired trajectory more quickly. This consumes excess energy generated by the vibration, thereby reducing the vibration amplitude. The control torque at the hub of the movable vehicle-mounted flexible arm is adjusted based on the rotation angle deviation. Since the elastic deformation of the flexible arm changes the force transmission path and magnitude when a rotational torque is applied to the hub, the actual rotation angle of the hub may deviate from the desired value. Different angles cause repeated elastic deformation of the flexible arm, leading to continuous changes in the hub angle and ultimately resulting in a significant deviation from the desired angle position. By increasing the control torque at the hub of the movable vehicle-mounted flexible arm, a greater corrective force can be generated, allowing the hub to return to the desired angle position more quickly and effectively reducing the time required for angle deviation recovery. The control force of the movable vehicle is adjusted according to the maximum deviation difference in the displacement of the movable vehicle. Due to the influence of gaps during the execution of actions, the displacement of the robotic arm deviates, which changes the relative positional relationship between the robotic arm and the vehicle. When the motion deviation of the robotic arm is coupled with the motion control of the vehicle, it becomes difficult for the vehicle to move as expected, and the deviation gradually increases over time. By increasing the control force of the movable vehicle, the positional lag caused by the deviation can be compensated, or the lateral offset caused by the coupling effect can be corrected by using a larger lateral control force, thereby improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0108] Specifically, determining the tracking control stability of the mobile vehicle-mounted flexible arm includes:

[0109] The vibration intensity of the movable vehicle-mounted flexible arm within a single operating cycle is obtained, and the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is calculated.

[0110] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with a preset first fluctuation amplitude;

[0111] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude, then it is determined that the tracking control stability of the movable vehicle-mounted flexible arm does not meet the requirements.

[0112] Specifically, determining the tracking accuracy of the mobile, vehicle-mounted flexible arm includes:

[0113] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset first fluctuation amplitude and the preset second fluctuation amplitude, respectively.

[0114] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude and less than or equal to the preset second fluctuation amplitude, it is preliminarily determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements, and the tracking accuracy of the movable vehicle-mounted flexible arm is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm.

[0115] It is understandable that the three intervals corresponding to the preset first fluctuation range and the preset second fluctuation range correspond to three different scenarios:

[0116] The first interval is when the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is less than or equal to the preset first fluctuation amplitude, which corresponds to the situation where the tracking control stability of the movable vehicle-mounted flexible arm meets the requirements.

[0117] The second range is where the vibration offset of the movable vehicle-mounted flexible arm fluctuates more than the preset first fluctuation amplitude and less than or equal to the preset second fluctuation amplitude. When a rotational torque is applied to the corresponding wheel hub, the elastic deformation of the flexible arm will change the force transmission path and magnitude, which may cause the actual rotation angle of the wheel hub to be different from the expected angle. The repeated elastic deformation of the flexible arm will cause the wheel hub angle to change continuously, eventually leading to a serious deviation from the expected angle position.

[0118] The third interval is when the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset second fluctuation amplitude. This corresponds to the situation where, when the robotic arm moves, the space on one side of the gap is different from that on the other side, resulting in different forces on the joint during forward and reverse movements, causing the robotic arm to vibrate. Over time, the tiny vibrations accumulate, leading to a gradual increase in the vibration offset at the end load.

[0119] Preferably, the preset first fluctuation amplitude is generally selected in the range of [0.2mm, 0.4mm], and the preset second fluctuation amplitude is generally selected in the range of [0.5mm, 0.7mm].

[0120] Preferably, the first fluctuation amplitude is 0.3 mm in a preferred embodiment, and the second fluctuation amplitude is 0.6 mm in a preferred embodiment.

[0121] Specifically, the fluctuation range of the vibration offset of the movable vehicle-mounted flexible arm is the range of changes in the degree to which the vibration of the movable vehicle-mounted flexible arm deviates from the equilibrium position within a single operating cycle.

[0122] In practice, the method of the present invention determines the tracking control stability of the mobile vehicle-mounted flexible arm by setting a preset first fluctuation amplitude and a preset second fluctuation amplitude, thereby reducing the impact of the decrease in the tracking control accuracy of the mobile vehicle-mounted flexible arm due to the inaccurate determination of the tracking control stability of the mobile vehicle-mounted flexible arm, and further improving the tracking control stability of the mobile vehicle-mounted flexible arm.

[0123] Specifically, adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm includes:

[0124] The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset second fluctuation amplitude;

[0125] If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset second fluctuation amplitude, the boundary control force at the end load of the movable vehicle-mounted flexible arm is increased.

[0126] Specifically, the increase in the boundary control force at the end load of the movable vehicle-mounted flexible arm is determined by the difference between the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude.

[0127] Specifically, when the difference between the vibration offset amplitude of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude is within 0.2 mm, the boundary control force at the load end of the movable vehicle-mounted flexible arm increases to 1.1 times the original value; when the difference between the vibration offset amplitude of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude exceeds 0.2 mm, the boundary control force at the load end of the movable vehicle-mounted flexible arm increases by 1 N for every 0.1 mm exceeding the preset second fluctuation amplitude. For example, if the difference between the vibration offset amplitude of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude is 0.4 mm, and the current boundary control force at the load end of the movable vehicle-mounted flexible arm is 10 N, the reduced boundary control force at the load end of the movable vehicle-mounted flexible arm will be 10 × 1.1 + 1 × 2 = 13 N.

[0128] In practice, the method of the present invention adjusts the boundary control force at the end load of the mobile vehicle-mounted flexible arm by setting a preset first fluctuation amplitude and a preset second fluctuation amplitude. As the space on one side of the gap is different from that on the other side when the robotic arm moves, the force on the joint is different when it moves in the forward and reverse directions, which causes the robotic arm to vibrate. Over time, the small vibrations accumulate, causing the vibration offset at the end load to gradually increase. By increasing the boundary control force at the end load of the mobile vehicle-mounted flexible arm, the excessive vibration of the end load can be reversed, so that the load returns to the vicinity of the desired trajectory more quickly. This can consume the excess energy generated by the vibration, thereby reducing the vibration amplitude and further improving the tracking control stability of the mobile vehicle-mounted flexible arm.

[0129] Specifically, adjusting the control torque at the hub of the movable vehicle-mounted flexible arm includes:

[0130] The actual and expected angles of the rotation of the wheel hub of the movable vehicle-mounted flexible arm are obtained respectively, and the deviation of the rotation angle of the movable vehicle-mounted flexible arm is calculated.

[0131] The rotation angle deviation of the movable vehicle-mounted flexible arm is compared with a preset first deviation and a preset second deviation, respectively.

[0132] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation, it is determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements.

[0133] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation and less than or equal to the preset second deviation, then the control torque at the hub of the movable vehicle-mounted flexible arm is increased.

[0134] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is initially determined that the motion stability of the movable vehicle-mounted flexible arm does not meet the requirements, and the motion stability of the movable vehicle-mounted flexible arm is determined based on the maximum offset difference of the mobile trolley displacement.

[0135] It is understandable that the three intervals corresponding to the preset first deviation and the preset second deviation correspond to three different scenarios:

[0136] The first interval is when the rotation angle deviation of the movable vehicle-mounted flexible arm is less than or equal to the preset first deviation, which corresponds to the situation where the tracking accuracy of the movable vehicle-mounted flexible arm meets the requirements.

[0137] The second range is when the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation and less than or equal to the preset second deviation. When a rotational torque is applied to the corresponding wheel hub, the elastic deformation of the flexible arm will change the force transmission path and magnitude, which may cause the actual rotation angle of the wheel hub to be different from the expected angle. The repeated elastic deformation of the flexible arm will cause the wheel hub angle to change continuously, eventually leading to a serious deviation from the expected angle position.

[0138] The third interval is when the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation. This corresponds to the fact that when the robotic arm performs an action, its displacement is affected by the gap, which will change the relative position relationship between the robotic arm and the vehicle. When the movement deviation of the robotic arm is coupled with the motion control of the vehicle, the movement position of the vehicle will be difficult to achieve as expected, and the deviation will gradually increase over time.

[0139] In practice, the preset first deviation is generally selected in the range of [4°, 6°], and the preset second deviation is generally selected in the range of [7°, 9°].

[0140] Preferably, the first deviation is 5° and the second deviation is 8°.

[0141] In practice, the method of the present invention determines the tracking accuracy of the mobile vehicle-mounted flexible arm by setting a preset first deviation amount and a preset second deviation amount, thereby reducing the impact of the decrease in tracking control stability of the mobile vehicle-mounted flexible arm due to inaccurate determination of the tracking accuracy, and further improving the tracking control stability of the mobile vehicle-mounted flexible arm.

[0142] Specifically, the rotation angle deviation of the movable vehicle-mounted flexible arm is the difference between the actual rotation angle and the expected angle of the movable vehicle-mounted flexible arm within a single operating cycle.

[0143] Specifically, the increase in control torque at the hub of the movable vehicle-mounted flexible arm is determined by the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and a preset first deviation.

[0144] Specifically, when the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and the preset first deviation is within 3°, the control torque at the hub of the movable vehicle-mounted flexible arm increases to 1.2 times the original value. When the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and the preset first deviation exceeds 3°, the control torque at the hub of the movable vehicle-mounted flexible arm increases by 2 N·m for every 1° exceeding the preset first deviation. For example, if the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and the preset first deviation is 5°, and the current control torque at the hub of the movable vehicle-mounted flexible arm is 20 N·m, the reduced control torque at the hub of the movable vehicle-mounted flexible arm is 20 × 1.2 + 2 × 2 = 28 N·m.

[0145] In practice, the method of the present invention adjusts the control torque at the hub of the movable vehicle-mounted flexible arm by setting a preset first deviation and a preset second deviation. Since the elastic deformation of the flexible arm changes the force transmission path and magnitude when a rotational torque is applied to the hub, the actual rotation angle of the hub may differ from the desired angle. Repeated elastic deformation of the flexible arm will cause continuous changes in the hub angle, eventually leading to a serious deviation from the desired angle position. By increasing the control torque at the hub of the movable vehicle-mounted flexible arm, a larger corrective force can be generated, allowing the hub to return to the desired angle position more quickly, effectively reducing the time required for angle deviation recovery, and further improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0146] Specifically, adjusting the control force of the mobile vehicle includes:

[0147] Obtain the maximum offset difference of the moving trolley;

[0148] The maximum offset difference of the moving trolley displacement is compared with a preset difference.

[0149] If the maximum offset difference of the mobile trolley is greater than the preset difference, it is determined that the motion stability of the mobile vehicle-mounted flexible arm does not meet the requirements, and the control force of the mobile trolley is increased.

[0150] It is understandable that the two intervals corresponding to the preset difference amount correspond to two different situations:

[0151] The first interval is when the maximum offset difference of the mobile trolley displacement is less than or equal to the preset difference, which corresponds to the condition that the motion stability of the mobile vehicle-mounted flexible arm meets the requirements.

[0152] The second interval is when the maximum offset difference of the moving trolley is greater than the preset difference. This corresponds to the fact that when the robotic arm performs an action, it is affected by the gap, and its displacement deviates, which will change the relative position relationship between the robotic arm and the trolley. When the movement deviation of the robotic arm is coupled with the movement control of the trolley, it will be difficult for the trolley to move as expected, and the deviation will gradually increase over time.

[0153] In practice, the preset difference is generally selected within the range of [0.2m, 0.4m].

[0154] Preferably, the preferred embodiment of the preset difference amount is 0.3m.

[0155] In practice, the method of the present invention determines the motion stability of the movable vehicle-mounted flexible arm by setting a preset difference amount, thereby reducing the impact of the decrease in the tracking control stability of the movable vehicle-mounted flexible arm due to the inaccurate determination of the motion stability of the movable vehicle-mounted flexible arm, and further improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0156] Specifically, the increase in the control force of the mobile trolley is determined by the difference between the maximum displacement difference of the mobile trolley and a preset difference.

[0157] Specifically, when the difference between the maximum displacement difference of the moving trolley and the preset difference is within 0.2m, the control force of the moving trolley increases to 1.3 times the original value; when the difference between the maximum displacement difference of the moving trolley and the preset difference exceeds 0.2m, the control force of the moving trolley increases by 2N for every 0.1m exceeding the preset difference. For example, if the difference between the maximum displacement difference of the moving trolley and the preset difference is 0.4m, and the current control force of the moving trolley is 10N, the increased control force of the moving trolley will be 10×1.3+2×2=17N.

[0158] In practice, the method of the present invention adjusts the control force of the mobile trolley by setting a preset difference amount. Due to the influence of the gap when the robotic arm performs the action, its displacement deviates, which changes the relative positional relationship between the robotic arm and the trolley. When the movement deviation of the robotic arm is coupled with the motion control of the trolley, the movement position of the trolley is difficult to achieve as expected, and the deviation gradually increases over time. By increasing the control force of the mobile trolley, the positional lag caused by the deviation can be compensated, or the lateral offset caused by the coupling effect can be corrected by a larger lateral control force, which further improves the tracking control stability of the mobile vehicle-mounted flexible arm.

[0159] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps, characterized in that, include: A dynamic model of the mobile vehicle-mounted flexible arm of the mobile trolley is established, a mathematical model of the asymmetric backlash is constructed, and a tracking control algorithm for the mobile vehicle-mounted flexible arm is constructed based on the asymmetric backlash and the disturbance observer. The Lyapunov function was constructed and simulated using Matlab to analyze the performance of the tracking control algorithm. Obtain the vibration intensity of the movable vehicle-mounted flexible arm within a single operating cycle; The tracking control stability of the mobile vehicle-mounted flexible arm is determined based on the fluctuation amplitude of the vibration offset of the mobile vehicle-mounted flexible arm. If the tracking control stability does not meet the requirements, the boundary control force at the end load of the mobile vehicle-mounted flexible arm is adjusted, or the tracking accuracy of the mobile vehicle-mounted flexible arm is determined based on the rotation angle deviation of the mobile vehicle-mounted flexible arm. If the tracking accuracy does not meet the requirements, the control torque at the hub of the movable vehicle-mounted flexible arm is adjusted, or the control force of the movable vehicle is adjusted based on the maximum offset difference of the movable vehicle displacement. Determine the tracking control stability of the mobile vehicle-mounted flexible arm, including: The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset first fluctuation amplitude. If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude, it is determined that the tracking control stability of the movable vehicle-mounted flexible arm does not meet the requirements. Determine the tracking accuracy of the mobile, vehicle-mounted flexible arm, including: The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset first fluctuation amplitude and the preset second fluctuation amplitude, respectively. If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset first fluctuation amplitude and less than or equal to the preset second fluctuation amplitude, it is initially determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements, and the tracking accuracy of the movable vehicle-mounted flexible arm is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm. Adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm includes: The fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is compared with the preset second fluctuation amplitude; If the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm is greater than the preset second fluctuation amplitude, the boundary control force at the end load of the movable vehicle-mounted flexible arm is increased.

2. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 1, characterized in that, The increase in the boundary control force at the end load of the movable vehicle-mounted flexible arm is determined by the difference between the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude.

3. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 2, characterized in that, Adjusting the control torque at the hub of the movable vehicle-mounted flexible arm includes: The rotation angle deviation of the mobile vehicle-mounted flexible arm is compared with the preset first deviation and the preset second deviation, respectively. If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation, it is determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements. If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset first deviation and less than or equal to the preset second deviation, then the control torque at the hub of the movable vehicle-mounted flexible arm is increased. If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is initially determined that the motion stability of the movable vehicle-mounted flexible arm does not meet the requirements, and the motion stability of the movable vehicle-mounted flexible arm is determined based on the maximum offset difference of the mobile trolley displacement.

4. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 3, characterized in that, The deviation of the rotation angle of the movable vehicle-mounted flexible arm is the difference between the actual angle of rotation of the movable vehicle-mounted flexible arm and the expected angle.

5. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 4, characterized in that, The increase in control torque at the hub of the movable vehicle-mounted flexible arm is determined by the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and a preset first deviation.

6. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 5, characterized in that, Adjusting the control force of the mobile vehicle includes: Compare the maximum offset difference of the moving trolley with the preset difference; If the maximum offset difference of the mobile trolley is greater than the preset difference, it is determined that the motion stability of the mobile vehicle-mounted flexible arm does not meet the requirements, and the control force of the mobile trolley is increased.

7. The tracking control method for a movable vehicle-mounted flexible arm with asymmetric gaps according to claim 6, characterized in that, The increase in the control force of the mobile trolley is determined by the difference between the maximum displacement difference of the mobile trolley and the preset difference.

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