An asymmetric constraint boundary control method for vehicle-mounted mobile flexible manipulator

Abstract

The present invention relates to the field of automatic control technology, and in particular to an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible robotic arm; comprising: establishing a dynamic model of the vehicle-mounted mobile flexible robotic arm; constructing an asymmetric output constraint control algorithm; constructing an asymmetric input constraint control algorithm; performing system stability analysis; using Matlab to digitally simulate the system, and respectively judging whether the control effects of the input asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet preset standards; if both meet the preset standards, then judging that the model establishment is complete. The present invention designs a control algorithm under the premise of considering asymmetric input and output constraints, which can achieve effective suppression of vibration of the mobile flexible robotic arm system, as well as precise control of the angular position of the mobile trolley and the robotic arm, and can ensure the stability of the system under asymmetric constraint conditions.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and in particular to an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm. Background Art

[0002] With the improvement of industrial automation and intelligence, flexible robotic arms have become a hot topic of research due to their advantages such as light weight and high flexibility. However, the high flexibility of the robotic arm also makes it extremely susceptible to external environmental interference and vibration, thus affecting the stability of the system. As a typical industrial control system, the vehicle-mounted mobile flexible robotic arm system is usually also affected by various external factors during actual application. For example, environmental interference, nonlinear input constraints of the actuator due to mechanical design and manufacturing or technical conditions, various output constraints on the position of the mobile platform, the rotation angle of the robotic arm, and the vibration displacement at the end due to the particularity of the working environment of the robotic arm, etc., all of these factors will affect the stability of the vehicle-mounted mobile flexible robotic arm system.

[0003] Chinese patent application publication number: CN110687787A discloses an adaptive control method for a robotic arm system based on a time-varying asymmetric obstacle Lyapunov function. The controller is designed by combining the backstepping method with the time-varying asymmetric obstacle Lyapunov constraint function, which can realize an adaptive control method for a robotic arm servo system including an asymmetric output constraint.

[0004] It can be seen that the existing control methods are difficult to overcome the influence of asymmetric input constraints and asymmetric output constraints on the vehicle-mounted mobile flexible robotic arm, cannot ensure the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric input and output constraints, and it is difficult to achieve high-precision control goals for the vehicle-mounted mobile flexible robotic arm system. Summary of the invention

[0005] To this end, the present invention provides an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible robotic arm, so as to overcome the problem in the prior art that the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric constraint conditions cannot be ensured due to the influence of asymmetric input constraints and asymmetric output constraints on the vehicle-mounted mobile flexible robotic arm.

[0006] To achieve the above object, the present invention provides an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm, comprising:

[0007] Step S1, establishing a dynamic model of the vehicle-mounted mobile flexible robotic arm, including a main control equation of the vehicle-mounted mobile flexible robotic arm and a boundary condition equation of the vehicle-mounted mobile flexible robotic arm;

[0008] Step S2, constructing an asymmetric output constraint control algorithm according to the asymmetric tracking position deviation constraint and the vibration deviation constraint of the vehicle-mounted mobile flexible manipulator, and designing a corresponding Lyapunov function to process the asymmetric tracking position deviation constraint and the vibration deviation constraint;

[0009] Wherein, the asymmetric tracking position deviation includes the rotation angle position deviation of the robot arm and the motion position deviation of the moving vehicle, and the vibration deviation includes the vibration displacement deviation at the end load of the robot arm;

[0010] Step S3, constructing an auxiliary system based on the state variables, constructing an asymmetric input constraint control algorithm according to the asymmetric input constraint and the auxiliary system, and designing a corresponding Lyapunov function;

[0011] Step S4, performing system stability analysis using the Lyapunov direct method according to the Lyapunov function;

[0012] Step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm, using Matlab to perform digital simulation on the system, and respectively judging whether the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet the preset standards;

[0013] If the control effect of any control algorithm does not meet the preset standard, the corresponding control algorithm is re-established by adjusting the parameters of the corresponding control algorithm until the control effect meets the preset standard;

[0014] Step S6: When the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm both meet preset standards, it is determined that the dynamic model of the vehicle-mounted mobile flexible robotic arm is established.

[0015] Furthermore, in the step S1, it includes:

[0016] Step S11, defining the system state of the vehicle-mounted mobile flexible mechanical arm; wherein, represents the elastic vibration displacement of the robot arm, Indicates the rotation angle of the robot arm, represents the moving position of the mobile car, and They represent the desired rotation angle position of the robot arm and the desired motion position of the mobile car, respectively. , and They represent the external environmental disturbances acting on the mobile car, the rotating hub of the robot arm and the end load respectively. represents the boundary control torque applied at the hub of the robot arm, and represent the boundary control forces applied by the mobile car and the load at the end of the robot arm respectively;

[0017] Step S12, constructing the motion equation of the vehicle-mounted mobile flexible robotic arm; performing dynamic analysis on the vehicle-mounted mobile flexible robotic arm system,

[0018] Its kinetic energy is determined by formula (1):

[0019] (1);

[0020] in, represents the mass of the mobile trolley, represents the moment of inertia of the robot joint, represents the material density of the robot arm, represents the length of the robot arm, Indicates the mass of the load at the end of the robot arm,

[0021] ;

[0022] Its potential energy is determined by formula (2):

[0023] (2);

[0024] in, represents the bending stiffness of the robot arm, Indicates the constant tension of the robot arm;

[0025] The virtual work on the system is determined by equation (3):

[0026] (3);

[0027] Step S13, calculating the main control equation and the boundary condition equation according to the Hamilton principle and the motion equation;

[0028] Among them, Hamilton's principle is: , and is the time constant , is the variation symbol, variable The integral range is and Substituting equations (1)-(3) into the Hamiltonian principle, the main control equation of the vehicle-mounted mobile flexible robotic arm system can be obtained as equation (4):

[0029] (4);

[0030] The boundary condition equations include equations (5)-(10),

[0031] (5),

[0032] (6),

[0033] (7),

[0034] (8),

[0035] (9),

[0036] (10),

[0037] in, Depend on About Time Taking the first-order derivative, we get: Depend on About Time Taking the second-order derivative, we get:

[0038] Depend on For state variables Taking the first-order derivative, we get: Depend on For state variables Taking the second-order derivative, we get: Depend on For state variables Taking the third-order derivative, we get: Depend on For state variables Taking the fourth-order derivative we get .

[0039] Furthermore, in the step S2, it includes:

[0040] Step S21, defining the asymmetric tracking position deviation constraint and the vibration deviation constraint,

[0041] ,

[0042] ,

[0043] ;

[0044] in, and They represent the rotation angle position deviation of the robot arm and the motion position deviation of the vehicle, Indicates the vibration displacement deviation at the end load of the robot arm, represents the corresponding asymmetric constraints, and they are all positive definite variable functions;

[0045] Step S22, designing a corresponding Lyapunov function;

[0046] The asymmetric output constraint control algorithm includes (11)-(13),

[0047] (11),

[0048] (12),

[0049] (13),

[0050] Among them, the control parameters are constant parameters. , and Respectively represent disturbance , and The upper bound of is a step function and is defined as in equation (14),

[0051] (14),

[0052] The corresponding Lyapunov function is determined by equation (15):

[0053] (15),

[0054] in,

[0055] (16),

[0056] (17),

[0057] (18),

[0058] (19),

[0059] (20),

[0060] Furthermore, in step S3,

[0061] Step S31, constructing an auxiliary system based on state variables;

[0062] The asymmetric input constraints include: boundary control forces at the mobile cart , the boundary control torque at the hub of the robot and the boundary control force at the end load of the robot arm There are asymmetric saturation constraints, and their mathematical expressions are as follows:

[0063] (twenty one),

[0064] (twenty two),

[0065] (twenty three),

[0066] in, is the asymmetric saturation constraint limit, is the control input;

[0067] The auxiliary system includes equations (24)-(26),

[0068] (twenty four),

[0069] (25),

[0070] (26),

[0071] Among them, the control parameters are constant parameters. , and are state variables, and , , ;

[0072] Step S32, designing a corresponding Lyapunov function;

[0073] The constructed asymmetric input constraint control algorithm includes equations (27)-(29),

[0074] in, , , ;

[0075] The corresponding Lyapunov function is determined by equation (30):

[0076] (30),

[0077] in,

[0078] (31),

[0079] (32),

[0080] (33),

[0081] in, , then the Lyapunov function is a positive definite function.

[0082] Furthermore, in step S4, the asymmetric output constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including:

[0083] for Taking the first-order derivative with respect to time, we can obtain equation (34):

[0084] (34),

[0085] Combining equations (4)-(10), we can obtain equations (35) and (36):

[0086] (35),

[0087] (36),

[0088] Combined with step function and the properties of the logarithmic function, we can calculate formula (37),

[0089] (37),

[0090] Simplifying equation (38),

[0091] (38),

[0092] Similarly, we can get equations (39) and (40):

[0093] (39),

[0094] (40),

[0095] Substituting equations (35), (36), (38), (39) and (40) into equation (34), we can obtain equation (41):

[0096] (41),

[0097] Substituting into equations (11)-(13) and simplifying the calculation results, we can obtain equation (42):

[0098] (42),

[0099] available The semi-negative definiteness of , thus, the stability of the system is obtained.

[0100] Furthermore, in step S4, the asymmetric input constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including:

[0101] for Taking the first-order derivative with respect to time, we can obtain equation (43):

[0102] (43),

[0103] Combining (4)-(10) with state variables , and Definition, we can get formula (44),

[0104] (44),

[0105] At the same time, we can calculate equation (45) and equation (46):

[0106] (45),

[0107] (46),

[0108] Combining the auxiliary systems (24)-(26), the simplified formula (47) can be obtained:

[0109] (47),

[0110] Substituting equations (44)-(47) into equation (43), we can obtain equation (48): (48),

[0111] Substituting into equations (27)-(29) and simplifying the calculation results, we can obtain equation (49): (49),

[0112] When the parameters meet , and hour, It has semi-negative definiteness, thus, the stability of the system is obtained.

[0113] Furthermore, in step S5, during the digital simulation process, firstly, the historical input and output control parameters are used as input and output values, and the parameters of each control algorithm are used as independent variables, and the corresponding control algorithm formulas are substituted to solve the preset value ranges corresponding to the parameters of each control algorithm.

[0114] Furthermore, in step S5, if the control effect of any control algorithm does not meet the preset standard, the parameter value is adjusted within the preset value range corresponding to the parameter of the corresponding control algorithm so that the corresponding control algorithm can achieve the control effect that meets the preset standard.

[0115] Furthermore, in step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm includes:

[0116] Defining system rated parameters of the vehicle-mounted mobile flexible manipulator and defining system extreme value parameters of the vehicle-mounted mobile flexible manipulator;

[0117] Defining the external environmental interference includes defining the working external environmental interference of the vehicle-mounted mobile flexible robotic arm and defining the maximum external environmental interference of the vehicle-mounted mobile flexible robotic arm.

[0118] Furthermore, in step S5, a corresponding preset standard is determined according to the system parameters of the corresponding vehicle-mounted mobile flexible robotic arm and external environmental interference.

[0119] Compared with the prior art, the beneficial effect of the present invention is that, by establishing a dynamic model of a vehicle-mounted mobile flexible mechanical arm system, constructing an asymmetric output constraint control algorithm according to the asymmetric tracking position deviation constraint and vibration deviation constraint of the vehicle-mounted mobile flexible mechanical arm, and constructing an asymmetric input constraint control algorithm according to the asymmetric input constraint and auxiliary system, the reliability and stability of the system under the asymmetric input and output constraint conditions can be guaranteed. By designing the corresponding Lyapunov function, using the Lyapunov direct method to analyze the system stability, using Matlab to perform digital simulation on the system, and respectively judging whether the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet the preset standards, if the control effect of any control algorithm does not meet the preset standards, the corresponding control algorithm is re-established by adjusting the parameters of the corresponding control algorithm until the control effect meets the preset standards, the stability of the model established by the vehicle-mounted mobile flexible mechanical arm system can be ensured, thereby achieving high-precision control of the system.

[0120] Furthermore, the Hamiltonian principle can be used to accurately establish the dynamic model of the vehicle-mounted mobile flexible robotic arm system, providing a theoretical basis for the subsequent construction of asymmetric output constraint control algorithms and asymmetric input constraint control algorithms.

[0121] Furthermore, by considering the asymmetric tracking position deviation constraints and vibration deviation constraints of the vehicle-mounted mobile flexible robotic arm system, an asymmetric constraint control algorithm is constructed. By designing a specific Lyapunov function to process the asymmetric output constraints, it is possible to ensure that the asymmetric constraints on the position of the mobile car, the rotation angle position of the robotic arm and the vibration displacement at the end are satisfied while achieving the vibration attenuation of the robotic arm.

[0122] Furthermore, by considering the boundary control force at the mobile car, the boundary control torque at the robot hub and the boundary control force at the end load of the robot, introducing state variables and three auxiliary systems, and designing a specific Lyapunov function to handle the asymmetric input constraints, it is possible to effectively handle the asymmetric saturation constraints of the control input while ensuring the realization of the position tracking and vibration suppression control objectives of the vehicle-mounted mobile flexible robot arm.

[0123] Furthermore, by using the Lyapunov direct method to analyze the system stability of the asymmetric output constraint control algorithm, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric output constraint conditions can be ensured.

[0124] Furthermore, by using the Lyapunov direct method to analyze the system stability of the asymmetric input constraint control algorithm, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric input constraint conditions can be ensured.

[0125] Furthermore, by solving the preset value intervals corresponding to the parameters of each control algorithm, the accuracy of the solved parameters of each control algorithm can be ensured.

[0126] Furthermore, by adjusting the parameter values ​​within the preset value range of the corresponding control algorithm parameters, the accuracy and efficiency of establishing the system dynamics model can be improved.

[0127] Furthermore, by defining the system parameters of the vehicle-mounted mobile flexible robotic arm and the external environmental interference, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric input and output constraints can be ensured, and it has the characteristics of easy implementation and strong applicability.

[0128] Furthermore, by determining corresponding preset standards according to the system parameters of the corresponding vehicle-mounted mobile flexible robotic arm and external environmental interference, the reliability and stability of the vehicle-mounted mobile flexible robotic arm system can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0129] Figure 1 A flow chart of the asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm provided by the present invention;

[0130] Figure 2 This is a schematic diagram of the operation of the vehicle-mounted mobile flexible robotic arm;

[0131] Figure 3 A three-dimensional vibration curve diagram of the vehicle-mounted mobile flexible mechanical arm without control of the present invention;

[0132] Figure 4is a two-dimensional curve diagram of the rotation angle position of the vehicle-mounted mobile flexible mechanical arm system without control of the present invention;

[0133] Figure 5 A two-dimensional curve diagram of the motion position of the trolley of the vehicle-mounted mobile flexible mechanical arm system without control of the present invention;

[0134] Figure 6 A two-dimensional curve diagram of vibration at the load end of the robot arm of the vehicle-mounted mobile flexible robot arm system without control of the present invention;

[0135] Figure 7 A three-dimensional graph of vibration of a vehicle-mounted mobile flexible mechanical arm to which asymmetric output constraint boundary control is applied according to the present invention;

[0136] Figure 8 A two-dimensional curve diagram of the rotation angle position of the vehicle-mounted mobile flexible mechanical arm system to which the asymmetric output constraint boundary control is applied according to the present invention;

[0137] Fig. 9 A two-dimensional curve diagram of the motion position of the trolley of the vehicle-mounted mobile flexible mechanical arm system to which the asymmetric output constraint boundary control is applied according to the present invention;

[0138] Fig.10 A two-dimensional curve diagram of vibration at the load end of the manipulator arm of the vehicle-mounted mobile flexible manipulator arm system to which the asymmetric output constraint boundary control is applied according to the present invention;

[0139] Fig.11 A diagram of the position deviation of the rotation angle of the robot arm to which the asymmetric output constraint boundary control is applied in the present invention;

[0140] Fig.12 A deviation diagram of the motion position of the trolley for applying asymmetric output constraint boundary control in the present invention;

[0141] Fig.13 A vibration displacement deviation diagram at the load end of the manipulator to which the asymmetric output constraint boundary control is applied according to the present invention;

[0142] Fig.14 The control input of the asymmetric output constraint control algorithm constructed by the present invention is Graph of changes over time;

[0143] Fig.15 Control input of the asymmetric output constraint control algorithm constructed by the present invention Graph of changes over time;

[0144] Fig.16 Control input of the asymmetric output constraint control algorithm constructed by the present invention Graph of changes over time;

[0145] Fig.17 A three-dimensional graph of vibration of a vehicle-mounted mobile flexible manipulator to which asymmetric input constraint boundary control is applied according to the present invention;

[0146] Fig.18 A two-dimensional curve diagram of the rotation angle position of the vehicle-mounted mobile flexible mechanical arm system applying asymmetric input constraint boundary control of the present invention;

[0147] Fig.19 A two-dimensional curve diagram of the motion position of the trolley of the vehicle-mounted mobile flexible mechanical arm system applying asymmetric input constraint boundary control of the present invention;

[0148] Fig. 20 A two-dimensional curve diagram of vibration at the end load of the manipulator of the vehicle-mounted mobile flexible manipulator system to which the asymmetric input constraint boundary control is applied according to the present invention;

[0149] Fig.21 Designing control input for asymmetric input constraint boundary control of the present invention Graph of changes over time;

[0150] Fig. 22 Designing control input for asymmetric input constraint boundary control of the present invention Graph of changes over time;

[0151] Fig.23 Designing control input for asymmetric input constraint boundary control of the present invention Graph of changes over time;

[0152] Fig.24 The actual control input for designing asymmetric input constraint boundary control of the present invention Graph of changes over time;

[0153] Fig.25 The actual control input for designing asymmetric input constraint boundary control of the present invention Graph of changes over time;

[0154] Fig.26 The actual control input for designing asymmetric input constraint boundary control of the present invention Graph of changes over time. DETAILED DESCRIPTION

[0155] 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.

[0156] 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.

[0157] 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.

[0158] 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.

[0159] See also Figure 1 As shown, it is a flow chart of an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm provided by an embodiment of the present invention. The present invention provides an asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm, comprising:

[0160] Step S1, establishing a dynamic model of the vehicle-mounted mobile flexible robotic arm, including a main control equation of the vehicle-mounted mobile flexible robotic arm and a boundary condition equation of the vehicle-mounted mobile flexible robotic arm;

[0161] Step S2, constructing an asymmetric output constraint control algorithm according to the asymmetric tracking position deviation constraint and the vibration deviation constraint of the vehicle-mounted mobile flexible manipulator, and designing a corresponding Lyapunov function to process the asymmetric tracking position deviation constraint and the vibration deviation constraint;

[0162] Wherein, the asymmetric tracking position deviation includes the rotation angle position deviation of the robot arm and the motion position deviation of the moving vehicle, and the vibration deviation includes the vibration displacement deviation at the end load of the robot arm;

[0163] Step S3, constructing an auxiliary system based on the state variables, constructing an asymmetric input constraint control algorithm according to the asymmetric input constraint and the auxiliary system, and designing a corresponding Lyapunov function;

[0164] Step S4, performing system stability analysis using the Lyapunov direct method according to the Lyapunov function;

[0165] Step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm, using Matlab to perform digital simulation on the system, and respectively judging whether the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet the preset standards;

[0166] If the control effect of any control algorithm does not meet the preset standard, the corresponding control algorithm is re-established by adjusting the parameters of the corresponding control algorithm until the control effect meets the preset standard;

[0167] Step S6: When the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm both meet preset standards, it is determined that the dynamic model of the vehicle-mounted mobile flexible robotic arm is established.

[0168] By establishing the dynamic model of the vehicle-mounted mobile flexible manipulator system, and constructing the asymmetric output constraint control algorithm according to the asymmetric tracking position deviation constraint and vibration deviation constraint of the vehicle-mounted mobile flexible manipulator, and constructing the asymmetric input constraint control algorithm according to the asymmetric input constraint and auxiliary system, the reliability and stability of the system under the asymmetric input and output constraint conditions can be guaranteed. By designing the corresponding Lyapunov function, using the Lyapunov direct method to analyze the system stability, using Matlab to perform digital simulation of the system, and judging whether the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet the preset standards, if the control effect of any control algorithm does not meet the preset standard, the corresponding control algorithm is re-established by adjusting the parameters of the corresponding control algorithm until the control effect meets the preset standard, the stability of the model established by the vehicle-mounted mobile flexible manipulator system can be ensured, thereby achieving high-precision control of the system.

[0169] See also Figure 2 As shown, it is a schematic diagram of the operation of the vehicle-mounted mobile flexible mechanical arm of the present invention.

[0170] Specifically, a typical vehicle-mounted mobile flexible robotic arm system includes a flexible robotic arm, an end load and a mobile cart.

[0171] In the step S1, it includes:

[0172] Step S11, defining the system state of the vehicle-mounted mobile flexible mechanical arm;

[0173] in, represents the elastic vibration displacement of the robot arm, Indicates the rotation angle of the robot arm, represents the moving position of the mobile car, and They represent the desired rotation angle position of the robot arm and the desired motion position of the mobile car, respectively. , and They represent the external environmental disturbances acting on the mobile car, the rotating hub of the robot arm and the end load respectively. represents the boundary control torque applied at the hub of the robot arm, and represent the boundary control forces applied by the mobile car and the load at the end of the robot arm respectively;

[0174] Step S12, constructing the motion equation of the vehicle-mounted mobile flexible robotic arm; performing dynamic analysis on the vehicle-mounted mobile flexible robotic arm system,

[0175] Its kinetic energy is determined by formula (1):

[0176] (1);

[0177] in, represents the mass of the mobile trolley, represents the moment of inertia of the robot joint, represents the material density of the robot arm, represents the length of the robot arm, Indicates the mass of the load at the end of the robot arm, ;

[0178] Its potential energy is determined by formula (2):

[0179] (2);

[0180] in, represents the bending stiffness of the robot arm, Indicates the constant tension of the robot arm;

[0181] The virtual work on the system is determined by equation (3):

[0182] (3);

[0183] Step S13, calculating the main control equation and the boundary condition equation according to the Hamilton principle and the motion equation;

[0184] Among them, Hamilton's principle is: , and is the time constant , is the variation symbol, variable The integral range is and Substituting equations (1)-(3) into the Hamiltonian principle, the main control equation of the vehicle-mounted mobile flexible robotic arm system can be obtained as equation (4):

[0185] (4);

[0186] The boundary condition equations include equations (5)-(10),

[0187] (5),

[0188] (6),

[0189] (7),

[0190] (8),

[0191] (9),

[0192] (10),

[0193] in, Depend on About Time Taking the first-order derivative, we get: Depend on About Time Taking the second-order derivative, we get:

[0194] Depend on For state variables Taking the first-order derivative, we get: Depend on For state variables Taking the second-order derivative, we get: Depend on For state variables Taking the third-order derivative, we get: Depend on For state variables Taking the fourth-order derivative we get .

[0195] Specifically, the Hamiltonian principle can be used to accurately establish the dynamic model of the vehicle-mounted mobile flexible robotic arm system, providing a theoretical basis for the subsequent construction of an asymmetric output constraint control algorithm and an asymmetric input constraint control algorithm.

[0196] In the step S2, it includes:

[0197] Step S21, defining the asymmetric tracking position deviation constraint and the vibration deviation constraint, , , ;

[0198] in, and They represent the rotation angle position deviation of the robot arm and the motion position deviation of the vehicle, Indicates the vibration displacement deviation at the end load of the robot arm, represents the corresponding asymmetric constraints, and they are all positive definite variable functions;

[0199] Step S22, designing a corresponding Lyapunov function, the asymmetric output constraint control algorithm includes equations (11)-(13),

[0200] (11),

[0201] (12),

[0202] (13),

[0203] Among them, the control parameters are constant parameters. , and Respectively represent disturbance , and The upper bound of is a step function and is defined as in equation (14),

[0204] (14),

[0205] The corresponding Lyapunov function is determined by equation (15):

[0206] (15),

[0207] in,

[0208] (16),

[0209] (17),

[0210] (18),

[0211] (19),

[0212] (20),

[0213] Specifically, by considering the asymmetric tracking position deviation constraints and vibration deviation constraints of the vehicle-mounted mobile flexible robotic arm system, an asymmetric constraint control algorithm is constructed. By designing a specific Lyapunov function to process the asymmetric output constraints, it is possible to achieve robotic arm vibration attenuation while ensuring that the asymmetric constraints on the position of the mobile car, the rotation angle position of the robotic arm, and the vibration displacement at the end are met.

[0214] In the step S3, step S31, constructing an auxiliary system based on the state variables;

[0215] The asymmetric input constraints include: boundary control forces at the mobile cart , the boundary control torque at the hub of the robot and the boundary control force at the end load of the robot arm There are asymmetric saturation constraints, and their mathematical expressions are as follows:

[0216] (twenty one),

[0217] (twenty two),

[0218] (twenty three),

[0219] in, is the asymmetric saturation constraint limit, is the control input;

[0220] The auxiliary system includes equations (24)-(26),

[0221] (twenty four),

[0222] (25),

[0223] (26),

[0224] Among them, the control parameters are constant parameters. , and are state variables, and , , ;

[0225] Step S32, designing the corresponding Lyapunov function,

[0226] The constructed asymmetric input constraint control algorithm includes equations (27)-(29),

[0227]

[0228] in, , , ;

[0229] The corresponding Lyapunov function is determined by equation (30):

[0230] (30),

[0231] in,

[0232] (31),

[0233] (32),

[0234] (33),

[0235] in, , then the Lyapunov function is a positive definite function.

[0236] Specifically, by considering the boundary control force at the mobile car, the boundary control torque at the robot hub and the boundary control force at the end load of the robot, introducing state variables and three auxiliary systems, and designing a specific Lyapunov function to handle the asymmetric input constraints, it is possible to effectively handle the asymmetric saturation constraints of the control input while ensuring the realization of the position tracking and vibration suppression control objectives of the vehicle-mounted mobile flexible robot arm.

[0237] In step S4, the asymmetric output constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including:

[0238] for Taking the first-order derivative with respect to time, we can obtain equation (34):

[0239] (34),

[0240] Combining equations (4)-(10), we can obtain equations (35) and (36):

[0241] (35),

[0242] (36),

[0243] Combined with step function and the properties of the logarithmic function, we can calculate formula (37),

[0244] (37),

[0245] Simplifying equation (38),

[0246] (38),

[0247] Similarly, we can get equations (39) and (40):

[0248] (39),

[0249] (40),

[0250] Substituting equations (35), (36), (38), (39) and (40) into equation (34), we can obtain equation (41):

[0251] (41),

[0252] Substituting into equations (11)-(13) and simplifying the calculation results, we can obtain equation (42), where equation (42) is

[0253] (42),

[0254] available The semi-negative definiteness of , thus, the stability of the system is obtained.

[0255] Specifically, by using the Lyapunov direct method to analyze the system stability of the asymmetric output constraint control algorithm, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric output constraint conditions can be ensured.

[0256] In step S4, the asymmetric input constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including:

[0257] for Taking the first-order derivative with respect to time, we can obtain equation (43):

[0258] (43),

[0259] Combining (4)-(10) with the state variable , ,and Definition, we can get formula (44),

[0260] (44),

[0261] At the same time, we can calculate equation (45) and equation (46):

[0262] (45),

[0263] (46),

[0264] Combining the auxiliary systems (24)-(26), the simplified formula (47) can be obtained:

[0265] (47),

[0266] Substituting equations (44)-(47) into equation (43), we can obtain equation (48):

[0267] (48),

[0268] Substituting into equations (27)-(29) and simplifying the calculation results, we can obtain equation (49):

[0269] (49),

[0270] When the parameters meet , and hour, The semi-negative definiteness of , thus, the stability of the system is obtained.

[0271] Specifically, by using the Lyapunov direct method to analyze the system stability of the asymmetric input constraint control algorithm, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric input constraint conditions can be ensured.

[0272] In step S5, during the digital simulation process, the historical input and output control parameters are first used as input and output values, the parameters of each control algorithm are used as independent variables, and the system parameters of the vehicle-mounted mobile flexible robotic arm are substituted into the corresponding control algorithm formula to solve the preset value range corresponding to the parameters of each control algorithm.

[0273] In implementation, the historical input control parameters are several system states of the vehicle-mounted mobile flexible robotic arm obtained historically, and the historical output control parameters are several system states of the vehicle-mounted mobile flexible robotic arm obtained historically, and their corresponding values ​​are used as input values, and the control results that meet the constraints are used as output values, and the parameters of each control algorithm are used as independent variables to solve the preset value ranges corresponding to the parameters of each control algorithm.

[0274] Specifically, by solving the preset value intervals corresponding to the parameters of each control algorithm, the accuracy of the solved parameters of each control algorithm can be guaranteed.

[0275] In step S5, if the control effect of any control algorithm does not meet the preset standard, the parameter value is adjusted within the preset value range corresponding to the parameter of the corresponding control algorithm so that the corresponding control algorithm can achieve the control effect that meets the preset standard.

[0276] In implementation, the preset standard includes a preset vibration standard of the vehicle-mounted mobile flexible robotic arm and a preset angle deviation standard of the robotic arm arm angle relative to the mobile vehicle, and the preset vibration standard includes a preset amplitude standard and a preset vibration frequency standard. It is understandable that the above corresponding standards can be determined by the working parameters, scene requirements or customization of the system of the vehicle-mounted mobile flexible robotic arm, which is the ideal control standard that the vehicle-mounted mobile flexible robotic arm needs to achieve, and will not be elaborated here.

[0277] In a specific embodiment, when adjusting the parameter values ​​of the parameters of each control algorithm, one or more parameter values ​​can be set as fixed values, and other parameter values ​​are solved according to the control algorithm until the control effect meets the preset standard.

[0278] Specifically, by adjusting the parameter value within the preset value range of the corresponding control algorithm parameter, the accuracy and efficiency of establishing the system dynamics model can be improved.

[0279] In step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm includes:

[0280] Defining system rated parameters of the vehicle-mounted mobile flexible manipulator and defining system extreme value parameters of the vehicle-mounted mobile flexible manipulator;

[0281] Defining the external environmental interference includes defining the working external environmental interference of the vehicle-mounted mobile flexible robotic arm and defining the maximum external environmental interference of the vehicle-mounted mobile flexible robotic arm.

[0282] In a specific embodiment, the system rated parameters of the vehicle-mounted mobile flexible mechanical arm include the mass of the mobile vehicle , the moment of inertia of the robot joint , the material density of the robot arm , the length of the robot arm , the mass of the load at the end of the robot arm , the bending stiffness of the robot arm , the constant tension of the robot arm The external environmental interference of the vehicle-mounted mobile flexible robotic arm includes the external environmental interference acting on the mobile vehicle. , external environmental interference acting on the rotating hub of the robot arm and external environmental disturbances acting on the end load ,The maximum external environmental interference of the vehicle-mounted mobile flexible robotic arm can be determined based on the historical maximum interference of the demand scenario.

[0283] Specifically, by defining the system parameters of the vehicle-mounted mobile flexible robotic arm and the external environmental interference, the stability of the vehicle-mounted mobile flexible robotic arm system under asymmetric input and output constraints can be ensured, and it has the characteristics of easy implementation and strong applicability.

[0284] In step S5, a corresponding preset standard is determined according to the system parameters of the corresponding vehicle-mounted mobile flexible robotic arm and external environmental interference.

[0285] In a specific embodiment, a comparison table of system parameters of the vehicle-mounted mobile flexible robotic arm, external environmental interference and corresponding preset standards can be set up, and the corresponding preset standards can be determined according to the control accuracy requirements of the working scenes corresponding to the system parameters of the vehicle-mounted mobile flexible robotic arm and / or the external environmental interference.

[0286] Specifically, by determining the corresponding preset standard according to the system parameters of the corresponding vehicle-mounted mobile flexible robotic arm and the external environmental interference, the reliability and stability of the vehicle-mounted mobile flexible robotic arm system can be improved.

[0287] Embodiment 1:

[0288] See also Figure 3 - Fig.26 In the first embodiment of the present invention, Matlab is used to perform digital simulation on the system, and the system parameters of the vehicle-mounted mobile flexible mechanical arm system are: , , , , , , , , ;

[0289] The external environmental disturbances acting on the mobile car, the end load of the robot arm and the rotating hub are:

[0290] ;

[0291] The output constraints are: , , , , and ;

[0292] The input constraints are: , , , , and ;

[0293] Figure 3 - Figure 6 They are the vibration three-dimensional curve of the vehicle-mounted mobile flexible manipulator without control, the rotation angle position of the vehicle-mounted mobile flexible manipulator without control, the movement position of the trolley, and the vibration of the load at the end of the manipulator. As shown in the figure, when no control is applied, the vibration displacement of the flexible manipulator is large, and the rotation angle of the manipulator and the movement position of the trolley deviate from their respective expected positions.

[0294] Figure 7 - Fig.16 They are the three-dimensional curve of the vibration of the vehicle-mounted mobile flexible manipulator with asymmetric output constraint boundary control, the two-dimensional curve of the rotation angle position, the trolley motion position and the vibration at the end load of the manipulator with asymmetric output constraint boundary control, the deviation of the rotation angle position of the manipulator, the deviation of the trolley motion position and the vibration displacement deviation at the end load of the manipulator with asymmetric output constraint boundary control, and the control input diagram of asymmetric output constraint boundary control. As shown in the figure, when the asymmetric output constraint boundary control is applied, the vibration displacement of the flexible manipulator is significantly controlled and reduced, and the rotation angle of the manipulator and the trolley motion position are in line with their respective expected positions. At the same time, the deviation of the rotation angle position of the manipulator, the deviation of the trolley motion position and the vibration displacement deviation at the end load of the manipulator are all within the constraint range.

[0295] Fig.17 - Fig.26 They are the three-dimensional curve of the vibration of the vehicle-mounted mobile flexible manipulator with asymmetric input constraint boundary control, the two-dimensional curve of the rotation angle position, the trolley motion position and the vibration at the end load of the manipulator with asymmetric input constraint boundary control, the control input diagram of the asymmetric input constraint boundary control, and the actual control input diagram of the asymmetric input constraint boundary control. As shown in the figure, when the asymmetric input constraint boundary control is applied, the vibration displacement of the flexible manipulator is also significantly controlled and reduced, and the accurate tracking of the rotation angle position of the manipulator, the trolley motion position and the vibration displacement at the end load of the manipulator can be guaranteed at the same time. In addition, the asymmetric saturation constraint of the control input is also effectively handled.

[0296] 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. An asymmetric constraint boundary control method for a vehicle-mounted mobile flexible robotic arm, characterized in that: include: Step S1, establishing a dynamic model of the vehicle-mounted mobile flexible robotic arm, including a main control equation of the vehicle-mounted mobile flexible robotic arm and a boundary condition equation of the vehicle-mounted mobile flexible robotic arm; Step S2, constructing an asymmetric output constraint control algorithm according to the asymmetric tracking position deviation constraint and the vibration deviation constraint of the vehicle-mounted mobile flexible manipulator, and designing a corresponding Lyapunov function to process the asymmetric tracking position deviation constraint and the vibration deviation constraint; Wherein, the asymmetric tracking position deviation includes the rotation angle position deviation of the robot arm and the motion position deviation of the moving vehicle, and the vibration deviation includes the vibration displacement deviation at the end load of the robot arm; Step S3, constructing an auxiliary system based on the state variables, constructing an asymmetric input constraint control algorithm according to the asymmetric input constraint and the auxiliary system, and designing a corresponding Lyapunov function; Step S4, performing system stability analysis using the Lyapunov direct method according to the Lyapunov function; Step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm, using Matlab to perform digital simulation on the system, and respectively judging whether the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm meet the preset standards; If the control effect of any control algorithm does not meet the preset standard, the corresponding control algorithm is re-established by adjusting the parameters of the corresponding control algorithm until the control effect meets the preset standard; Step S6, when the control effects of the asymmetric output constraint control algorithm and the asymmetric input constraint control algorithm both meet the preset standards, it is determined that the dynamic model of the vehicle-mounted mobile flexible mechanical arm is established; In the step S1, it includes: Step S11, defining the system state of the vehicle-mounted mobile flexible mechanical arm; Among them, y(x,t) represents the elastic vibration displacement of the robot arm, ζ(t) represents the rotation angle of the robot arm, G(t) represents the moving position of the mobile car, ζ d and G d They represent the desired rotation angle position of the robot arm and the desired motion position of the mobile car, respectively. v (t), d j (t) and d p (t) represents the external environmental disturbance acting on the mobile car, the rotating hub of the robot arm and the end load, respectively, μ(t) represents the boundary control torque applied at the hub of the robot arm, r(t) and p(t) represent the boundary control forces applied at the mobile car and the end load of the robot arm, respectively; Step S12, constructing the motion equation of the vehicle-mounted mobile flexible robotic arm; performing dynamic analysis on the vehicle-mounted mobile flexible robotic arm system, Its kinetic energy is determined by formula (1): Where m represents the mass of the mobile car, I h represents the moment of inertia of the robot joint, ρ represents the material density of the robot, L represents the length of the robot, M represents the mass of the load at the end of the robot, Its potential energy is determined by formula (2): Where, EI represents the bending stiffness of the robot arm, T e Indicates the constant tension of the robot arm; The virtual work on the system is determined by equation (3): R v (t)=[r(t)+d v (t)]G(t)+[p(t)+d p (t)]y(L,t)+[μ(t)+d j (t)]ζ(t)(3); Step S13, calculating the main control equation and the boundary condition equation according to the Hamilton principle and the motion equation; Among them, Hamilton's principle is: t1 and t2 are time constants (t1<t2), δ is the variation symbol, and the integral range of variable t is between t1 and t2. Substituting equations (1)-(3) into the Hamiltonian principle, the main control equation of the vehicle-mounted mobile flexible manipulator system can be obtained as equation (4): The boundary condition equations include equations (5)-(10), y(0,t)=0(5), y′(0,t)=0(6), y″(L,t)=0(10), in, By taking the first-order derivative of y with respect to time t, we can obtain: By taking the second-order derivative of y with respect to time t, we can obtain: y′ is obtained by taking the first-order derivative of y with respect to the state variable x, y″ is obtained by taking the second-order derivative of y with respect to the state variable x, y”′ is obtained by taking the third-order derivative of y with respect to the state variable x, and y″″ is obtained by taking the fourth-order derivative of y with respect to the state variable x; In the step S2, it includes: Step S21, defining the asymmetric tracking position deviation constraint condition and the vibration deviation constraint condition, -φ1(t)<e ζ (t)=ζ(t)-ζ d <φ2(t), -φ3(t)<e G (t)=G(t)-G d <φ4(t), -φ5(t)<e y (t)=y(L,t)-0<φ6(t), Among them, e ζ (t) and e G (t) represent the rotation angle position deviation of the robot arm and the motion position deviation of the vehicle, respectively, and e y (t) represents the vibration displacement deviation at the load end of the manipulator, φ1(t)-φ6(t) represent the corresponding asymmetric constraints, and all are positive constant variable functions; Step S22, designing a corresponding Lyapunov function, the asymmetric output constraint control algorithm includes equations (11)-(13), Among them, the control parameters η, α1, α2, α3, β1, β2, β3>0 are all constant parameters, D j ,D v and D p ∈R + Denote the disturbance d j (t), d v (t) and d p (t) is the upper bound. In addition, the function χ(*) is a step function and is defined as in equation (14). The corresponding Lyapunov function is determined by equation (15): K o (t)=K a (t)+K b (t)+K c (t)+K d (t)+K e (t) (15), in, In the step S3, it includes: Step S31, constructing an auxiliary system based on state variables; The asymmetric input constraints include: the boundary control force r(t) at the mobile car, the boundary control torque μ(t) at the robot hub and the boundary control force p(t) at the end load of the robot, all of which have asymmetric saturation constraints, and their mathematical expressions are as follows: Among them, r h ,r l ,μ h ,μ l ,p h ,p l is the asymmetric saturation constraint limit, h r (t),h μ (t),h p (t) is the control input; The auxiliary system includes equations (24)-(26), Among them, the control parameters q0, α0, p0, β0, w0, λ0>0 are all constant parameters, α(t), β(t), λ(t), Δμ(t), Δr(t) and Δp(t) are all state variables, and Δμ(t)=μ(t)-h μ (t),Δr(t)=r(t)-h r (t), Δp(t)=p(t)-h p (t); Step S32, designing a corresponding Lyapunov function; The constructed asymmetric input constraint control algorithm includes equations (27)-(29), among them, e ζ (t)=ζ(t)-ζ d ,e G (t)=G(t)-G d ,e y (t)=y(L,t)-0=y(L,t); The corresponding Lyapunov function is determined by equation (30): R o (t)=R c (t)+R d (t)+R e (t)(30), in, Among them, s1, s2, s3> 0, then the Lyapunov function R o (t) is a positive definite function.

2. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 1, characterized in that: In step S4, the asymmetric output constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including: For K o Taking the first-order derivative of (t) with respect to time, we can obtain equation (34): Combining equations (4)-(10), we can obtain equations (35) and (36): Combining the properties of the step function χ(*) and the logarithmic function, we can calculate equation (37): Simplifying formula (38), Similarly, we can get equations (39) and (40): Substituting equations (35), (36), (38), (39) and (40) into equation (34), we can obtain equation (41): Substituting into equations (11)-(13) and simplifying the calculation results, we can obtain equation (42): available The semi-negative definiteness of , thus, the stability of the system is obtained.

3. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 2, characterized in that: In step S4, the asymmetric input constraint control algorithm is subjected to system stability analysis using the Lyapunov direct method, including: For R o Taking the first-order derivative of (t) with respect to time, we can obtain equation (43): Combining (4)-(10) with the definitions of state variables Δμ(t), Δr(t) and Δp(t), we can obtain equation (44): At the same time, we can calculate equation (45) and equation (46): Combining the auxiliary systems (24)-(26), the simplified formula (47) can be obtained: Substituting equations (44)-(47) into equation (43) yields equation (48), Substituting into equations (27)-(29) and simplifying the calculation results, we can obtain equation (49): When the parameters satisfy q0≥1,p0≥1 and w0≥1, It has semi-negative definiteness, thus, the stability of the system is proved.

4. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 1, characterized in that: In step S5, during the digital simulation process, firstly, the historical input and output control parameters are used as input and output values, and the parameters of each control algorithm are used as independent variables, and the corresponding control algorithm formulas are substituted to solve the preset value ranges corresponding to the parameters of each control algorithm.

5. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 4, characterized in that: In step S5, if the control effect of any control algorithm does not meet the preset standard, the parameter value is adjusted within the preset value range corresponding to the parameter of the corresponding control algorithm so that the corresponding control algorithm can achieve the control effect that meets the preset standard.

6. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 1, characterized in that: In step S5, defining the system parameters and external environmental interference of the vehicle-mounted mobile flexible mechanical arm includes: Defining system rated parameters of the vehicle-mounted mobile flexible manipulator and defining system extreme value parameters of the vehicle-mounted mobile flexible manipulator; Defining the external environmental interference includes defining the working external environmental interference of the vehicle-mounted mobile flexible robotic arm and defining the maximum external environmental interference of the vehicle-mounted mobile flexible robotic arm.

7. The asymmetric constraint boundary control method for a vehicle-mounted mobile flexible mechanical arm according to claim 6, characterized in that: In step S5, a corresponding preset standard is determined according to the system parameters of the corresponding vehicle-mounted mobile flexible robotic arm and external environmental interference.

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