Tracking control method for movable vehicle-mounted flexible arm aiming at asymmetric gap

Abstract

The invention relates to the technical field of mechanical arms, in particular to a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap, which comprises the following steps of: establishing a kinetic model of the movable vehicle-mounted flexible arm of a moving trolley, and constructing a mathematical model of the asymmetric reverse gap; constructing a tracking control algorithm of the movable vehicle-mounted flexible arm according to the asymmetric reverse gap and a disturbance observer; a Lyapunov function is constructed, Matlab is used for simulation, and the performance of the tracking control algorithm is analyzed; the tracking control stability of the movable vehicle-mounted flexible arm is determined 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 requirement, the boundary control force at the load at the tail end of the movable vehicle-mounted flexible arm is adjusted; and if the tracking accuracy does not meet the requirement, the control torque at the position of a hub of the movable vehicle-mounted flexible arm is adjusted. According to the invention, the tracking control stability of the movable vehicle-mounted flexible arm is improved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical arms, and in particular to a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap. Background Art

[0002] With the rapid development of control technology and computer technology, the research on robotic arms has made significant progress. Flexible robotic arms have been widely used in industrial automation, logistics handling, resource exploration, service industry, rescue, aerospace and other fields due to their advantages in energy consumption, portability and flexibility. Different from the traditional fixed robotic arm system, the vehicle-mounted mobile flexible robotic arm can expand the operating space and has a wider range of application scenarios.

[0003] As a nonlinear system, the strong coupling between the mobile car and the flexible robotic arm poses certain difficulties to the control of the system. At the same time, in the actual application process, it also faces various nonlinear input constraints caused by the limitations of mechanical design, mechanical manufacturing, technical conditions, etc. The reverse clearance caused by the incomplete contact of the mechanical actuator gears and the friction between different components is a common nonlinear input constraint problem, which will inevitably reduce the control performance of the system and even affect the stability of the system. However, the existing technology only considers the impact of the clearance input on the flexible robotic arm system, and uses a smooth inverse compensation operator for controller design. It does not consider how to deal with the influence of asymmetric reverse clearance based on the disturbance observer technology for the movable vehicle-mounted mobile flexible robotic arm system, which has certain limitations.

[0004] Chinese Patent Publication No.: CN118456424A discloses a tracking control method for a flexible robotic arm, including the following steps: S1. Construct a model of the flexible robotic arm system; S2. Construct various order tracking errors; S3. Describe the control target and design a feedback controller; S4. Construct a neural network model; S5. Design a virtual controller; S6. Combine Lyapunov's second method to ensure that the Lyapunov function is semi-positive definite and the time derivative of the function is negative semi-definite. It can be seen that the tracking control method applied to the flexible robotic arm has the problem that the parts at the joints of the vehicle-mounted flexible arm will wear out, and the forces on both sides of the joints are different during movement, resulting in asymmetric gaps that will increase with the increase of use time, causing the tracking control stability of the movable vehicle-mounted flexible arm to decrease. Summary of the invention

[0005] To this end, the present invention provides a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap, so as to overcome the problem in the prior art that due to wear of parts at the joints of the vehicle-mounted flexible arm, the force conditions on both sides of the joints are different during movement, resulting in the asymmetric gap being aggravated with the increase of usage time, causing the tracking control stability of the movable vehicle-mounted flexible arm to decrease.

[0006] To achieve the above-mentioned purpose, the present invention provides a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap, comprising: establishing a dynamic model of the movable vehicle-mounted flexible arm of a mobile car, constructing a mathematical model of an asymmetric backlash, and constructing a tracking control algorithm for the movable vehicle-mounted flexible arm according to the asymmetric backlash and a disturbance observer; constructing a Lyapunov function and applying Matlab to perform simulation, and analyzing 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 wheel hub of the movable vehicle-mounted flexible arm, or adjusting the control force of the movable car based on the maximum offset difference of the displacement of the mobile car.

[0007] Further, the tracking control stability of the movable vehicle-mounted flexible arm is determined, including:

[0008] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm with a 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, 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 movable vehicle-mounted flexible arm is determined, including:

[0011] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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 whether the tracking accuracy of the movable vehicle-mounted flexible arm meets the requirements is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm.

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

[0014] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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] Further, the increase amplitude of 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 a preset second fluctuation amplitude.

[0017] Further, the control torque at the hub of the movable vehicle-mounted flexible arm is adjusted, including:

[0018] Comparing the rotation angle deviation of the movable vehicle-mounted flexible arm 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, increasing the control torque at the hub of the movable vehicle-mounted flexible arm;

[0021] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is preliminarily determined that the movement smoothness of the movable vehicle-mounted flexible arm does not meet the requirements, and whether the movement smoothness of the movable vehicle-mounted flexible arm meets the requirements is determined based on the maximum offset difference of the displacement of the moving trolley.

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

[0023] Furthermore, the increase amplitude of the control torque at the wheel 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, the control force of the mobile vehicle is adjusted, including:

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

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

[0027] Furthermore, the increase range of the control force of the moving vehicle is determined by the difference between the maximum offset difference of the displacement of the moving vehicle and a preset difference.

[0028] Compared with the prior art, the beneficial effect of the present invention lies in that 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 of the movable vehicle-mounted flexible arm. When the mechanical arm moves, the space on one side of the gap is different from that on the other side, which makes the force conditions of the joints different during forward and reverse movements, causing the mechanical arm to vibrate. As time goes by, small vibrations continue to 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 can return to the desired trajectory faster, and the excess energy generated by the vibration can be consumed, thereby reducing the vibration amplitude. The control torque at the wheel hub of the movable vehicle-mounted flexible arm is adjusted according to the rotation angle deviation of the movable vehicle-mounted flexible arm. When the wheel hub applies a rotational torque, the elastic deformation of the flexible arm will change the force transmission path and magnitude, which may cause the actual wheel hub to The rotation angle is different from the expected angle, and the repeated elastic deformation of the flexible arm will cause the continuous change of the wheel hub angle, which will eventually lead to a serious deviation from the expected angle position. By increasing the control torque at the wheel hub of the movable vehicle-mounted flexible arm, a greater correction force can be generated to make the wheel hub return to the expected angle position faster, effectively reducing the time required for angle deviation recovery. The control force of the mobile car is adjusted according to the maximum offset difference of the mobile car displacement. Since the mechanical arm is affected by the gap when performing the action, its displacement deviates, which will change the relative position relationship between the mechanical arm and the car. When the motion deviation of the mechanical arm is coupled with the motion control of the car, it will make it difficult for the car to move as expected, and as time goes by, the deviation gradually increases. By increasing the control force of the mobile car, the position lag caused by the deviation can be compensated, or a larger lateral control force can be used to correct the lateral offset caused by the coupling, thereby 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. When the mechanical arm moves, the space on one side of the gap is different from that on the other side, so that the force conditions of the joints during forward and reverse movements are different, causing the mechanical arm to vibrate. As time goes by, tiny vibrations continue to 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 can return to the desired trajectory faster, and the excess energy generated by the vibration can be consumed, 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 wheel hub of the movable vehicle-mounted flexible arm by setting a preset first deviation and a preset second deviation. When the wheel hub applies a rotational torque, 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 continuous changes in the wheel hub angle, and ultimately lead to a serious deviation from the expected angle position. By increasing the control torque at the wheel hub of the movable vehicle-mounted flexible arm, a greater corrective force can be generated, so that the wheel hub can return to the expected angle position faster, 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 cart by setting a preset difference. Since the displacement of the robotic arm is deviated by the gap when performing an action, the relative position relationship between the robotic arm and the cart will change. When the movement deviation of the robotic arm is coupled with the movement control of the cart, it will make it difficult for the movement position of the cart to proceed as expected, and the deviation will gradually increase with the passage of time. By increasing the control force of the mobile cart, the position lag caused by the deviation can be compensated, or a larger lateral control force can be used to correct the lateral deviation caused by the coupling, thereby further improving the tracking control stability of the movable vehicle-mounted flexible arm. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0033] Figure 2 It is a logic flow chart of a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to an embodiment of the present invention;

[0034] Figure 3A specific flow chart of the process of adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm in the tracking control method of the movable vehicle-mounted flexible arm with an asymmetric gap according to an embodiment of the present invention;

[0035] Figure 4 The present invention is a specific flow chart of 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 an asymmetric gap according to an embodiment of the present invention. DETAILED DESCRIPTION

[0036] In order to make the objects and advantages of the present invention more clearly understood, the present invention is further described below in conjunction with embodiments; it should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0037] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0038] It should be noted that, in the description of the present invention, terms such as "up", "down", "left", "right", "inside" and "outside" indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings. This is merely for the convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the present invention.

[0039] In addition, it should be noted that in the description of the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For those skilled in the art, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0040] See also Figure 1 , Figure 2 , Figure 3 as well as Figure 4 As shown, they are respectively an overall flow chart of a tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap, a logic flow chart, a specific flow chart of a process for adjusting the boundary control force at the end load of the movable vehicle-mounted flexible arm, and a specific flow chart of a process for adjusting the control torque at the hub of the movable vehicle-mounted flexible arm. A tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to the present invention comprises:

[0041] Step S1, establishing a dynamic model of a movable vehicle-mounted flexible arm of a mobile vehicle, constructing a mathematical model of an asymmetric backlash, and constructing a tracking control algorithm for the movable vehicle-mounted flexible arm according to the asymmetric backlash and a disturbance observer;

[0042] Step S2, constructing a Lyapunov function and applying Matlab to perform simulation to analyze the performance of the tracking control algorithm;

[0043] Step S3, obtaining the vibration intensity of the movable vehicle-mounted flexible arm in a single operation cycle;

[0044] Step S4, 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;

[0045] Step S5, if the tracking control stability does not meet the requirements, the boundary control force at the end load of the movable vehicle-mounted flexible arm is adjusted, or 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;

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

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

[0048] To simplify the representation, the present invention uniformly adopts It means that (·) takes the first-order derivative with respect to t; means (·) finds the second-order derivative with respect to t; (·)' means (·) finds the first-order derivative with respect to x, (·)" means (·) finds the second-order derivative with respect to x; (·)"' means (·) finds the third-order derivative with respect to x, (·)"" means (·) finds the fourth-order derivative 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 and ρ represent the unit moment of inertia and unit length mass of the robot; t represents the time variable, which is a positive constant; α(t) represents the rotation angle of the robot; L represents the length of the robot; x represents the spatial position variable, and x∈[0,L]; J(x,t) is the absolute displacement vector of the robot 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; m a and mv Represent the load mass at the end of the robot arm and the mass of the trolley respectively;

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

[0053]

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

[0055] The virtual work on the system is expressed as:

[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 car and the external unknown disturbance respectively; n(t) and q n (t) represent the control torque acting on the hub of the robot and the external unknown disturbance respectively; f(t) and q f (t) represent the control force and external unknown disturbance acting on the end load of the robot arm respectively;

[0058] Combining the kinetic energy, potential energy and virtual work expressions of the vehicle-mounted mobile flexible robotic arm, and applying the Hamiltonian principle, the dynamic model of the vehicle-mounted mobile flexible robotic arm 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 of asymmetric backlash is:

[0064] Taking into account the nonlinear, non-differentiable and non-smooth characteristics of the backlash, the present invention describes the asymmetric backlash input as a desired control input and a nonlinear input error, and regards the nonlinear input error and the external disturbance as a quasi-disturbance term and processes them 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 is a positive constant slope, parameter B 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 reverse gap input variable, y(t - ),n(t - ),f(t - ) means that y(t), n(t) and f(t) remain unchanged.

[0067] Describing the above asymmetric gap input as the desired control input and the nonlinear input error, 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) is the nonlinear error of the reverse gap input, and y o (t), n o (t) and f o (t) are all bounded.

[0074] The above backlash input nonlinear error and external disturbance acting on the trolley, the robot arm wheel hub, and the end load of the robot arm are considered as quasi-disturbance terms and defined as follows:

[0075]

[0076] Know Q y (t), Q n (t) and Q f (t) are bounded, and the bounds are positive numbers Q uy ,Q un ,Q uf Based on the above representation of asymmetric backlash, the boundary conditions (6)-(8) of the system can be further expressed as:

[0077]

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

[0079] For the above 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 motion position and the robotic arm angle position, and effectively deal with the influence of asymmetric backlash, the present invention proposes the following tracking control algorithm:

[0080]

[0081] Among them, the control parameters μ1, μ2, μ3, κ1, κ2, κ3, γ are all positive constants, s i and α i Represents the expected displacement of the car and the expected rotation angle of the robot arm, Represents the pair-like disturbance term Q y (t),Q n (t),Q f (t) respective threshold value Q uy ,Q un ,Q uf The estimator of is obtained, and based on this, the following disturbance observer is designed:

[0082]

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

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

[0085] The composite energy Lyapunov function 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] The control parameters are c,ξ1,ξ2, are all normal numbers, Respectively represent Q uy ,Q un ,Q uf The estimation error of is defined as follows:

[0091]

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

[0093] By taking the derivative of the Lyapunov function H(t), we can obtain:

[0094]

[0095] Combining equations (17)-(19) with the tracking control algorithm (20), we can get

[0096]

[0097] Combining equations (28)-(32), we can get

[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 vehicle-mounted mobile flexible robotic arm system is asymptotically stable, and all signals in the system are uniformly and ultimately bounded.

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

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

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

[0107] In implementation, 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 of the movable vehicle-mounted flexible arm. When the mechanical arm moves, the space on one side of the gap is different from that on the other side, which makes the force conditions of the joints different during forward and reverse movements, causing the mechanical arm to vibrate. As time goes by, 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 desired trajectory faster, and the excess energy generated by the vibration can be consumed, thereby reducing the vibration amplitude. The control torque at the wheel hub of the movable vehicle-mounted flexible arm is adjusted according to the rotation angle deviation of the movable vehicle-mounted flexible arm. When the wheel hub applies a rotational torque, 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 deviate from the desired angle. At different angles, the repeated elastic deformation of the flexible arm will cause continuous changes in the wheel hub angle, eventually leading to a serious deviation from the desired angle position. By increasing the control torque at the wheel hub of the movable vehicle-mounted flexible arm, a greater corrective force can be generated to make the wheel hub return to the desired angle position faster, effectively reducing the time required for angle deviation recovery. The control force of the mobile trolley is adjusted according to the maximum offset difference of the mobile trolley displacement. Since the robotic arm is affected by the gap when performing an action, its displacement deviates, which will change the relative position relationship between the robotic arm and the trolley. When the motion deviation of the robotic arm is coupled with the motion control of the trolley, it will make it difficult for the trolley to move as expected, and as time goes by, the deviation gradually increases. By increasing the control force of the mobile trolley, the position lag caused by the deviation can be compensated, or a larger lateral control force can be used to correct the lateral offset caused by the coupling, thereby improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0108] Specifically, the tracking control stability of the movable vehicle-mounted flexible arm is determined, including:

[0109] Obtaining the vibration intensity of the movable vehicle-mounted flexible arm within a single operating cycle, and calculating the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm;

[0110] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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, it is determined that the tracking control stability of the movable vehicle-mounted flexible arm does not meet the requirements.

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

[0113] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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 whether the tracking accuracy of the movable vehicle-mounted flexible arm meets the requirements is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm.

[0115] It can be understood that the three intervals corresponding to the preset first fluctuation range and the preset second fluctuation range correspond to three situations respectively:

[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, corresponding to the situation that the tracking control stability of the movable vehicle-mounted flexible arm meets the requirements;

[0117] The second interval is that 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. When the rotational torque is applied to the wheel hub, the elastic deformation of the flexible arm will change the transmission path and magnitude of the force, which may make the actual rotation angle of the wheel hub different from the expected angle. The repeated elastic deformation of the flexible arm will cause the continuous change of the wheel hub angle, and finally lead 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. When the corresponding robotic arm moves, the space on one side of the gap is different from that on the other side, which makes the force conditions of the joints during forward and reverse movements different, causing the robotic arm to vibrate. As time goes by, tiny vibrations continue to accumulate, causing the vibration offset at the end load to gradually increase.

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

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

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

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

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

[0124] Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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 amplitude of 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 fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude is within 0.2mm, the boundary control force at the end load of the movable vehicle-mounted flexible arm increases to 1.1 times the original; when the difference between the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude exceeds 0.2mm, the boundary control force at the end load of the movable vehicle-mounted flexible arm increases by 1N for every 0.1mm exceeding, for example, the difference between the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm and the preset second fluctuation amplitude is 0.4mm, the current boundary control force at the end load of the movable vehicle-mounted flexible arm is 10N, and the reduced boundary control force at the end load of the movable vehicle-mounted flexible arm is 10×1.1+1×2=13N.

[0128] In implementation, 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. When the mechanical arm moves, the space on one side of the gap is different from that on the other side, so that the force conditions of the joints during forward and reverse movements are different, causing the mechanical arm to vibrate. As time goes by, tiny vibrations continue to 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 can return to the desired trajectory faster, and the excess energy generated by the vibration can be consumed, thereby reducing the vibration amplitude, and further improving the tracking control stability of the movable vehicle-mounted flexible arm.

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

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

[0131] Comparing the rotation angle deviation of the movable vehicle-mounted flexible arm 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, increasing the control torque at the hub of the movable vehicle-mounted flexible arm;

[0134] If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is preliminarily determined that the movement smoothness of the movable vehicle-mounted flexible arm does not meet the requirements, and whether the movement smoothness of the movable vehicle-mounted flexible arm meets the requirements is determined based on the maximum offset difference of the displacement of the moving trolley.

[0135] It can be understood that the three intervals corresponding to the preset first deviation amount and the preset second deviation amount correspond to three situations respectively:

[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, corresponding to the situation where the tracking accuracy of the movable vehicle-mounted flexible arm meets the requirements;

[0137] The second interval 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 wheel hub, the elastic deformation of the flexible arm will change the force transmission path and magnitude, which may make the actual rotation angle of the wheel hub different from the expected angle. The repeated elastic deformation of the flexible arm will cause the continuous change of the wheel hub angle, and eventually lead 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. When the corresponding robotic arm is performing 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 car. When the motion deviation of the robotic arm is coupled with the motion control of the car, it will make the movement position of the car difficult to proceed as expected, and the deviation will gradually increase with the passage of 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 preferred embodiment of the preset first deviation is 5°, and the preferred embodiment of the preset second deviation is 8°.

[0141] In implementation, the method of the present invention determines the tracking accuracy of the movable vehicle-mounted flexible arm by setting a preset first deviation and a preset second deviation, thereby reducing the impact of the decreased tracking control stability of the movable vehicle-mounted flexible arm due to inaccurate determination of the tracking accuracy of the movable vehicle-mounted flexible arm, and further improving the tracking control stability of the movable 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 of the movable vehicle-mounted flexible arm and the expected angle in a single operation cycle.

[0143] Specifically, the increase amplitude of the control torque at the wheel 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 the 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 wheel 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 wheel hub of the movable vehicle-mounted flexible arm increases by 2N·m for every 1° exceeding. For example, the difference between the rotation angle deviation of the movable vehicle-mounted flexible arm and the preset first deviation is 5°, the current control torque at the wheel hub of the movable vehicle-mounted flexible arm is 20N·m, and the reduced control torque at the wheel hub of the movable vehicle-mounted flexible arm is 20×1.2+2×2=28N·m.

[0145] In implementation, the method of the present invention adjusts the control torque at the wheel hub of the movable vehicle-mounted flexible arm by setting a preset first deviation and a preset second deviation. When the wheel hub applies a rotational torque, 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 continuous changes in the wheel hub angle, and ultimately lead to a serious deviation from the expected angle position. By increasing the control torque at the wheel hub of the movable vehicle-mounted flexible arm, a greater corrective force can be generated, so that the wheel hub can return to the expected angle position faster, 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] Get the maximum offset difference of the mobile car displacement;

[0148] Comparing the maximum offset difference of the displacement of the mobile carriage with a preset difference;

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

[0150] It can be understood that the two intervals corresponding to the preset difference amount correspond to two 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, corresponding to the situation where 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 mobile car's displacement is greater than the preset difference. When the corresponding robotic arm is performing 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 car. When the motion deviation of the robotic arm is coupled with the motion control of the car, it will make the movement position of the car difficult to proceed as expected, and the deviation will gradually increase over time.

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

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

[0155] In implementation, the method of the present invention determines the movement smoothness of the movable vehicle-mounted flexible arm by setting a preset difference amount, thereby reducing the impact of the decreased tracking control stability of the movable vehicle-mounted flexible arm due to inaccurate determination of the movement smoothness 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 moving vehicle is determined by the difference between the maximum offset difference of the displacement of the moving vehicle and the preset difference.

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

[0158] In implementation, the method of the present invention adjusts the control force of the mobile cart by setting a preset difference. Since the mechanical arm is affected by the gap when performing an action, its displacement deviates, which will change the relative position relationship between the mechanical arm and the cart. When the movement deviation of the mechanical arm is coupled with the movement control of the cart, it will make it difficult for the movement position of the cart to proceed as expected, and as time goes by, the deviation gradually increases. By increasing the control force of the mobile cart, the position lag caused by the deviation can be compensated, or a larger lateral control force can be used to correct the lateral deviation caused by the coupling, thereby further improving the tracking control stability of the movable vehicle-mounted flexible arm.

[0159] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle 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 fall within the protection scope of the present invention.

Claims

1. A tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap, characterized in that: include: Establishing a dynamic model of a movable vehicle-mounted flexible arm of a mobile vehicle, constructing a mathematical model of an asymmetric backlash, and constructing a tracking control algorithm of the movable vehicle-mounted flexible arm according to the asymmetric backlash and a disturbance observer; Constructing Lyapunov function and applying Matlab to simulate, analyzing the performance of the tracking control algorithm; Obtaining the vibration intensity of the movable vehicle-mounted flexible arm during 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, the boundary control force at the end load of the movable vehicle-mounted flexible arm is adjusted, or 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; If the tracking accuracy does not meet the requirements, the control torque at the hub of the flexible arm of the movable vehicle is adjusted, or the control force of the movable vehicle is adjusted based on the maximum offset difference of the displacement of the movable vehicle.

2. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 1 is characterized in that: Determine the tracking control stability of a movable vehicle-mounted flexible arm, including: Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm with a 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.

3. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 2, characterized in that: Determine the tracking accuracy of a mobile vehicle-mounted flexible arm, including: Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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 preliminarily determined that the tracking accuracy of the movable vehicle-mounted flexible arm does not meet the requirements, and whether the tracking accuracy of the movable vehicle-mounted flexible arm meets the requirements is determined based on the rotation angle deviation of the movable vehicle-mounted flexible arm.

4. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 3 is characterized in that: The boundary control force at the end load of the movable vehicle-mounted flexible arm is adjusted, including: Comparing the fluctuation amplitude of the vibration offset of the movable vehicle-mounted flexible arm 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.

5. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 4, characterized in that: The increase amplitude of 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.

6. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 3, characterized in that: The control torque at the hub of the movable vehicle-mounted flexible arm is adjusted, including: Comparing the rotation angle deviation of the movable vehicle-mounted flexible arm 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, increasing the control torque at the hub of the movable vehicle-mounted flexible arm; If the rotation angle deviation of the movable vehicle-mounted flexible arm is greater than the preset second deviation, it is preliminarily determined that the movement smoothness of the movable vehicle-mounted flexible arm does not meet the requirements, and whether the movement smoothness of the movable vehicle-mounted flexible arm meets the requirements is determined based on the maximum offset difference of the displacement of the moving trolley.

7. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 6, characterized in that: The rotation angle deviation of the movable vehicle-mounted flexible arm is the difference between the actual rotation angle of the movable vehicle-mounted flexible arm and the expected rotation angle.

8. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 7, characterized in that: The increase amplitude of the control torque at the wheel 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 the preset first deviation.

9. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 8, characterized in that: The control force of the mobile vehicle is adjusted, including: Compare the maximum offset difference of the mobile trolley displacement with the preset difference; If the maximum offset difference of the displacement of the moving trolley is greater than the preset difference, it is determined that the movement stability of the movable vehicle-mounted flexible arm does not meet the requirements, and the control force of the moving trolley is increased.

10. The tracking control method for a movable vehicle-mounted flexible arm with an asymmetric gap according to claim 9, characterized in that: The increase in the control force of the moving vehicle is determined by the difference between the maximum offset difference of the moving vehicle displacement and the preset difference.

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