A time synchronization control method and system for a dual-arm robot for biochemical experiment operation

Abstract

A biochemical experiment operation-oriented dual-arm robot time synchronization control method and system, the method comprising the following steps: establishing a whole coupling dynamics model of the dual-arm robot-object; defining a compensation tracking error, the compensation tracking error comprising a compensation tracking error variable, constructing an optimization equation of a derivative of the compensation tracking error variable and a calculation equation of the derivative of the compensation tracking error variable; designing a time synchronization controller, constructing the optimization equation of the compensation tracking error variable, solving a derivative of a Lyapunov function, and completing theoretical verification of the dual-arm robot time synchronization control. The application can not only avoid the problem of "dimension explosion", but also design a time synchronization controller, realize synchronous convergence of tracking errors in each dimension to the origin in a limited time, and thus ensure the precision and synchronization of the dual-arm robot operation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dual-arm robot cooperative control, and in particular to a dual-arm robot time synchronization control method and system for biochemical experiment operation. BACKGROUND

[0002] With the rapid development of life science and biological medicine research, biochemical experiment operation presents a trend of high frequency, complexity and refinement. Experimental tasks such as reagent distribution, sample mixing and instrument replacement put forward higher operation requirements for intelligent robots. Traditional single-arm robots have significant limitations in flexibility and task adaptability, while dual-arm robots have stronger cooperative operation capability and can simulate human hands to complete fine experiments. However, the operation process of dual-arm robots often shows strong nonlinearity and high coupling characteristics, and at the same time, the synchronization and coordination of dual-arm actions must be maintained, so that the existing single-arm robot control technology cannot be directly applied. On the other hand, as a core index of control system, the convergence performance directly determines the execution effect and overall performance of the control strategy. In cooperative operation tasks, dual-arm robots must achieve the synchronization convergence of multi-joint states within a limited time to ensure the consistency of trajectory tracking and posture transformation in the work space, which puts higher requirements on the convergence performance of the system. Therefore, it is of great theoretical and practical significance to study the cooperative control technology of dual-arm robots for complex experiment operation.

[0003] Although the traditional finite time control method can guarantee the convergence of system states within a limited time, the convergence time depends on the convergence time of the last stable state component of the system, which is difficult to meet the control requirements of dual-arm robots for multi-dimensional state synchronization stability. In recent years, the time synchronization control method has attracted widespread attention. This method not only makes each state component keep proportional coordination during the convergence process, but also ensures the synchronization of multi-dimensional states to reach the equilibrium point. It is worth emphasizing that the application object of the existing time synchronization control scheme still stays on the simplified nonlinear system, and the time synchronization control algorithm based on Backstepping (Backstepping) will cause the "dimension explosion" problem due to repeated derivation of virtual controllers, resulting in a sharp increase in the complexity of the control algorithm. Therefore, it is urgent to design a time synchronization control strategy that can not only guarantee the synchronization convergence of multi-dimensional states at the same time, but also effectively reduce the complexity of the controller design, in order to improve the stability and execution efficiency of dual-arm robots in cooperative operation tasks. SUMMARY

[0004] The present application provides a dual-arm robot time synchronization control method and system for biochemical experiment operation to solve the technical problems mentioned in the background art.

[0005] To achieve the above purpose, the technical solution of the present application is as follows:

[0006] This invention provides a time synchronization control method for a dual-arm robot for biochemical experiments, comprising the following steps:

[0007] S1. For a dual-arm robot, based on the dynamic model of a single robotic arm, and combined with the dynamic model characteristics of the manipulated object, a final overall coupled dynamic model of the dual-arm robot and the object is established.

[0008] S2. Based on the final coupled dynamic model of the dual-arm robot-object, construct the error transformation formula and define the compensation tracking error. The compensation tracking error includes the compensation tracking error variable. , Based on the error transformation formula, a compensation tracking error variable is constructed. The optimization equation for the derivative and the compensation tracking error variable The equation for calculating the derivative;

[0009] S3. Design a time synchronization controller, and construct a compensation tracking error variable based on the time synchronization controller. The optimization equation is based on the compensation tracking error variable. The optimization equation for the derivative and the compensation tracking error variable The derivative of the Lyapunov function was obtained by solving the optimization equation, thus completing the theoretical verification of the time synchronization control of the dual-arm robot.

[0010] Furthermore, step S1 specifically includes the following steps:

[0011] S11. Based on the structure, posture, speed, and force information of the dual-arm robot, construct a system with... A dynamic model of a single robotic arm with one degree of freedom;

[0012] S12. Based on the dynamic model of a single robotic arm and the assumptions in S11, establish the overall dynamic model of the dual-arm robot; the assumptions are that the connection between the dual-arm robot and the grasped object is rigid, and there is no relative displacement at the grasping point during the movement.

[0013] S13. Construct a dynamic model of the manipulated object based on its position, velocity, and force information;

[0014] S14. Define the formula for calculating the resultant force of a dual-arm robot acting on the manipulated object;

[0015] S15. Decompose the total force exerted on the object by the dual-arm robot into internal and external forces to obtain the decomposition formula;

[0016] S16, by introducing the overall dynamics model of the dual-arm robot into the dynamics model of the operated object, combining the resultant force calculation formula in S14 and the splitting formula in S15, an initial overall coupling dynamics model of the dual-arm robot-object is constructed;

[0017] S17, the initial overall coupling dynamics model of the dual-arm robot-object is simplified to obtain a simplified overall coupling dynamics model of the dual-arm robot-object;

[0018] S18, the simplified overall coupling dynamics model of the dual-arm robot-object is converted to obtain a final overall coupling dynamics model of the dual-arm robot-object.

[0019] Further, the single-arm dynamics model in S11 is as follows:

[0020] (1)

[0021] Wherein, represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm, ; represents the i-th mechanical arm; T represents the transpose of the matrix; represents the real set;

[0022] The overall dynamics model of the dual-arm robot in S12 is as follows:

[0023] (2)

[0024] Wherein, represents the inertia matrix of the dual-arm robot, and ; represents a diagonal matrix; denote the inertia matrix of the first and second robot arms, respectively; denote the joint angles of the dual-arm robot; denote the angular velocity of the dual-arm robot; denote the angular acceleration of the dual-arm robot; denote the Coriolis and centrifugal force matrix of the dual-arm robot, and denote the Coriolis and centrifugal force matrix of the first and second robot arms, respectively; denote the gravity vector of the dual-arm robot, and denote the gravity vector of the first and second robot arms, respectively; denote the Jacobian matrix of the dual-arm robot, and denote the Jacobian matrix of the first and second robot arms, respectively; denote the total force exerted by the dual-arm robot on the object, and denote the total force exerted by the first and second robot arms on the object, respectively; denote the joint torque of the dual-arm robot;

[0025] The dynamic model of the object operated in the S13 is specifically as follows:

[0026] (3)

[0027] wherein, denotes the position of the object, denotes the velocity of the object, denotes the acceleration of the object, denotes the inertia matrix of the object, denotes the Coriolis and centrifugal force matrix of the object, denotes the gravity vector of the object, denotes the total force acting on the object;

[0028] The formula for calculating the total force exerted by the dual-arm robot on the object in the S14 is specifically as follows:

[0029] (4)

[0030] wherein, denotes the grasp matrix of the dual-arm robot, and denote the grasp matrix related to the object centroid and the grasp point, respectively;

[0031] ​​​​​​​​The splitting formula in S15 is as follows:

[0032] (5)

[0033] wherein, represents internal force, and satisfies , represents external force, and , represents the pseudo-inverse of a matrix;

[0034] The initial overall coupled dynamics model of the dual-arm robot-object in S16 is as follows:

[0035] (6)

[0036] wherein, represents a first intermediate quantity, and ; represents a second intermediate quantity; and ; represents a third intermediate quantity, ;

[0037] The simplified overall coupled dynamics model of the dual-arm robot-object in S17 is as follows:

[0038] (7)

[0039] wherein, represents a fourth intermediate quantity, and ; represents a fifth intermediate quantity, and ; represents a sixth intermediate quantity, and ; represents a control input; ;

[0040] The final overall coupled dynamics model of the dual-arm robot-object in S18 is as follows:

[0041] (8)

[0042] wherein, and represent system state variables, and ; , is a system output.

[0043] Further, S2 specifically comprises the following steps:

[0044] S21, constructing an error transformation formula according to the final overall coupling dynamics model of the dual-arm robot-object;

[0045] S22, designing a finite-time command filter;

[0046] S23, designing an error compensation mechanism in order to suppress the influence of the finite-time command filter error;

[0047] S24, defining a compensation tracking error according to the error compensation mechanism;

[0048] S25, constructing a calculation equation of the derivative of the compensation tracking error variable according to the overall dynamics model of the dual-arm robot, the dynamics model of the operated object, and the error transformation formula;

[0049] S26, designing an expression of a virtual control signal;

[0050] S27, substituting the expression of the virtual control signal into the calculation equation of the derivative of the compensation tracking error variable, to obtain an optimization equation of the derivative of the compensation tracking error variable;

[0051] S28, constructing a calculation equation of the derivative of the compensation tracking error variable according to the overall dynamics model of the dual-arm robot, a calculation formula of the resultant force of the dual-arm robot acting on the operated object, and the error transformation formula.

[0052] Further, the error transformation formula in S21 is specifically as follows:

[0053] (9)

[0054] wherein, represents a tracking error, represents an error variable, represents an output of a command filter, is a desired tracking trajectory;

[0055] The finite-time command filter in S22 is specifically as follows:

[0056] (10)

[0057] wherein, and are state variables of the command filter, represents a virtual control signal as an input of the command filter; , , , , ​​​​design parameters for the finite-time command filter; and ; ; ; denotes a custom function, and ; is a sign function; denotes or ; when denotes , the custom parameter ; when denotes , the custom parameter ; denotes the nthcomponent of the custom parameter ;

[0058] The error compensation mechanism in S23 is specified as follows:

[0059] (11)

[0060] where and are state variables of the error compensation mechanism, and denote positive design parameters; and denote the derivatives of the state variables and , respectively;

[0061] The compensated tracking error in S24 is specified as follows:

[0062] (12)

[0063] The calculation equation of the derivative of the compensated tracking error variable in S25 is specified as follows:

[0064] (13)

[0065] where denotes the derivative of the desired tracking trajectory; denotes the derivative of the compensated tracking error variable ;

[0066] The expression of the virtual control signal in S26 is:

[0067] (14)

[0068] where , denote design parameters of the virtual control signal represents a norm sign function, and a calculation formula of the norm sign function is specifically as follows:

[0069] ;

[0070] ;

[0071] wherein, represents an input of the norm sign function; represents a Euclidean norm;

[0072] derivative of the compensated tracking error variable in S27 is specifically as follows:

[0073] (15)

[0074] derivative of the compensated tracking error variable in S28 is specifically as follows:

[0075] (16)

[0076] wherein, represents a derivative of the compensated tracking error variable ; represents a derivative of an output of the command filter.

[0077] Further, the S3 specifically comprises the following steps:

[0078] S31, designing a time synchronization controller;

[0079] S32, substituting the time synchronization controller into a calculation formula of the derivative of the compensated tracking error variable , to obtain an optimization equation of the compensated tracking error variable ;

[0080] S33, selecting a Lyapunov function;

[0081] S34, calculating a derivative of the Lyapunov function according to the optimization equation of the derivative of the compensated tracking error variable and the optimization equation of the compensated tracking error variable ; and verifying that the dual-arm robot realizes time synchronization in theory through the derivative of the Lyapunov function.

[0082] Further, the time synchronization controller in the S31 is specifically as follows:

[0083] (17)

[0084] wherein, Design parameters of the time synchronization controller.

[0085] Further, the optimization equation of the compensation tracking error variable in S32 is as follows:

[0086] (18)

[0087] The selected Lyapunov function in S33 is as follows:

[0088] ;

[0089] wherein, the selected Lyapunov function the compensation tracking error variable, i.e. , ;

[0090] The derivative of the Lyapunov function in S34 is as follows:

[0091] (19)

[0092] wherein, a positive design parameter, including a positive design parameter , ; a set parameter, including a design parameter , ; a design parameter, including a design parameter , ; and a seventh intermediate quantity, and ; an eighth intermediate quantity, and .

[0093] Further, the S3 further comprises the following steps:

[0094] S4, actual design parameters are given and substituted into S1 to S3, and the effectiveness of the time synchronization of the dual-arm robot is verified through simulation experiments.

[0095] Another aspect of the present application also provides a time synchronization control system, comprising a dual-arm robot, and the dual-arm robot realizes time synchronization by using the above-mentioned dual-arm robot time synchronization control method.

[0096] The present application has the following advantages:

[0097] ​1. The application discloses a kind of double-arm robot time synchronization control method for biochemical experiment operation, and the final double-arm robot-object overall coupling dynamics model is constructed and used inside, which uniformly describes the dynamics of robot and the dynamics of the object to be operated, and provides accurate model support for the design of time synchronization controller.

[0098] 2, S2 and S3 in the double-arm robot time synchronization control method in the application and the error transformation formula, compensation tracking error, time synchronization controller, finite time command filter and error compensation mechanism used in the two steps constitute a finite time synchronization command filter backstepping design framework, which not only solves the "dimension explosion" problem in finite time, but also effectively suppresses the influence of filter error.

[0099] 3, The application constructs and uses a time synchronization controller, which not only ensures that the tracking error converges to the origin in finite time, but also achieves the tracking error in each dimension reaching the origin at the same time, thereby ensuring the precision and synchronization of double-arm robot operation. BRIEF DESCRIPTION OF DRAWINGS

[0100] Figure 1 The flowchart of the double-arm robot time synchronization control method in the application is shown in the figure.

[0101] Figure 2 The principle diagram of the double-arm robot time synchronization control method in the application is shown in the figure.

[0102] Figure 3 The structure diagram of the double-arm robot in the embodiment of the application is shown in the figure.

[0103] Figure 4 The structure diagram of one of the mechanical arms of the double-arm robot in the embodiment of the application is shown in the figure.

[0104] Figure 5 The trajectory tracking diagram of the embodiment of the application is shown in the figure.

[0105] Figure 6 The tracking error diagram of the embodiment of the application is shown in the figure.

[0106] Figure 7 The three-dimensional trajectory diagram of the embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0107] In order to facilitate understanding of the application, the application will be described more fully below with reference to the accompanying drawings. The preferred embodiments of the application are shown in the drawings. However, the application can be realized in many other different forms, and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the application more thorough and comprehensive.

[0108] Furthermore, the terms "first", "second", etc. are used herein only to describe different instances, and do not imply or suggest relative importance or a number of the technical features indicated. Thus, the features defined with "first", "second", etc. can explicitly or implicitly include one or more of the features. In the description of the present application, the meaning of "a plurality" is two or more, unless otherwise explicitly and specifically limited.

[0109] With reference to Figure 1 and Figure 2 , the embodiments of the present application provide a time synchronization control method for a dual-arm robot in biochemical experiment operation, comprising the following steps:

[0110] S1, for the dual-arm robot, on the basis of a single mechanical arm dynamics model, combined with the dynamics model characteristics of the object being operated, an overall coupling dynamics model of the dual-arm robot-object is established;

[0111] S2, according to the overall coupling dynamics model of the dual-arm robot-object, an error transformation formula is constructed, a compensation tracking error is defined, and the compensation tracking error includes compensation tracking error variables 、 , according to the error transformation formula, an optimization equation of the derivative of the compensation tracking error variable and a calculation equation of the derivative of the compensation tracking error variable are constructed;

[0112] S3, a time synchronization controller is designed, and according to the time synchronization controller, an optimization equation of the compensation tracking error variable is constructed, the derivative of the optimization equation of the compensation tracking error variable and the optimization equation of the compensation tracking error variable are used to solve the derivative of the Lyapunov function, and the theoretical verification of the time synchronization control of the dual-arm robot is completed.

[0113] In some embodiments, the S1 specifically comprises the following steps:

[0114] S11, according to the structure, posture, speed information and force information of the dual-arm robot, a single mechanical arm dynamics model with degrees of freedom is constructed;

[0115] S12, on the basis of the single mechanical arm dynamics model and the assumed conditions in S11, an overall dynamics model of the dual-arm robot is established; the assumed conditions are that the connection between the dual-arm robot and the object being grabbed is rigid, and there is no relative displacement at the grabbing point during the movement;

[0116] S13. Construct a dynamic model of the manipulated object based on its position, velocity, and force information;

[0117] S14. Define the formula for calculating the resultant force of a dual-arm robot acting on the manipulated object;

[0118] S15. Decompose the total force exerted on the object by the dual-arm robot into internal and external forces to obtain the decomposition formula;

[0119] S16. By introducing the overall dynamic model of the dual-arm robot into the dynamic model of the manipulated object, and combining the resultant force calculation formula in S14 and the split formula in S15, an initial overall coupled dynamic model of the dual-arm robot and the object is constructed.

[0120] S17. The initial global coupled dynamics model of the dual-arm robot-object is simplified to obtain the simplified global coupled dynamics model of the dual-arm robot-object.

[0121] S18. Transform the simplified overall coupled dynamics model of the dual-arm robot-object to obtain the final overall coupled dynamics model of the dual-arm robot-object.

[0122] In some embodiments, the dynamic model of a single robotic arm in S11 is specifically as follows:

[0123] (1)

[0124] in, Indicates the first One robotic arm, ; Indicates the first The joint angles of a robotic arm Indicates the first The angular velocity of the robotic arm Indicates the first The angular acceleration of the robotic arm, Indicates the first The inertia matrix of a robotic arm, Indicates the first Coriolis force and centrifugal force matrix of a robotic arm Indicates the first The gravity vector of each robotic arm. Indicates the first The joint torque of a robotic arm Indicates the application of the first The force vector of the end effector of the robotic arm Indicates the first The Jacobian matrix of the robotic arms; T denotes the transpose of the matrix; Represents the set of real numbers;

[0125] The overall dynamics model of the dual-arm robot in S12 is specifically as follows:

[0126] (2)

[0127] wherein, represents the inertia matrix of the dual-arm robot, and ; represents a diagonal matrix; , respectively represent the inertia matrix of the first and second mechanical arms; represents the joint angle of the dual-arm robot; represents the angular velocity of the dual-arm robot; represents the angular acceleration of the dual-arm robot; represents the Coriolis force and centrifugal force matrix of the dual-arm robot, and ; , respectively represent the Coriolis force and centrifugal force matrix of the first and second mechanical arms; represents the gravity vector of the dual-arm robot, and , , respectively represent the gravity vector of the first and second mechanical arms; represents the Jacobian matrix of the dual-arm robot, and , respectively represent the Jacobian matrix of the first and second mechanical arms; represents the total force applied by the dual-arm robot on the object, and , respectively represent the total force applied by the first and second mechanical arms on the object; represents the joint torque of the dual-arm robot;

[0128] The dynamics model of the object being operated in S13 is specifically as follows:

[0129] (3)

[0130] wherein, represents the position of the object, represents the velocity of the object, represents the acceleration of the object, represents the inertia matrix of the object, represents the Coriolis force and centrifugal force matrix of the object, represents the gravity vector of the object, represents the resultant force acting on the object;

[0131] The formula for calculating the resultant force of the dual-arm robot acting on the object in S14 is as follows:

[0132] (4)

[0133] wherein, represents the grasp matrix of the dual-arm robot, and , respectively represent the grasp matrix related to the object centroid and the grasp point;

[0134] The splitting formula in S15 is as follows:

[0135] (5)

[0136] wherein, represents the internal force, and satisfies , represents the external force, and , represents the pseudo-inverse of a matrix;

[0137] The initial overall coupled dynamics model of the dual-arm robot-object in S16 is as follows:

[0138] (6)

[0139] wherein, represents the first intermediate quantity, and ; represents the second intermediate quantity; and ; represents the third intermediate quantity, ;

[0140] The simplified overall coupled dynamics model of the dual-arm robot-object in S17 is as follows:

[0141] (7)

[0142] wherein, represents the fourth intermediate quantity, and ; represents the fifth intermediate quantity, and ; represents the sixth intermediate quantity, and ; represents the control input; ;

[0143] The final overall coupled dynamics model of the dual-arm robot-object in S18 is as follows:

[0144] (8)

[0145] wherein, and denote two system state variables, and ; , is the system output.

[0146] In some embodiments, the S2 specifically comprises the following steps:

[0147] S21, constructing an error transformation formula according to a final overall coupling dynamics model of the dual-arm robot-object;

[0148] S22, designing a finite-time command filter;

[0149] S23, designing an error compensation mechanism in order to suppress the influence of the finite-time command filter error;

[0150] S24, defining a compensation tracking error according to the error compensation mechanism;

[0151] S25, constructing a calculation equation of the derivative of the compensation tracking error variable according to the overall dynamics model of the dual-arm robot, the dynamics model of the operated object, and the error transformation formula;

[0152] S26, designing an expression of a virtual control signal;

[0153] S27, substituting the expression of the virtual control signal into the calculation equation of the derivative of the compensation tracking error variable to obtain an optimization equation of the derivative of the compensation tracking error variable ;

[0154] S28, constructing a calculation equation of the derivative of the compensation tracking error variable according to the overall dynamics model of the dual-arm robot, a calculation formula of the resultant force of the dual-arm robot acting on the operated object, and the error transformation formula.

[0155] In some embodiments, the error transformation formula in the S21 is specifically as follows:

[0156] (9)

[0157] wherein, denotes a tracking error, denotes an error variable, denotes an output of the command filter, is a desired tracking trajectory;

[0158] The finite-time command filter in the S22 is specifically as follows:

[0159] (10)

[0160] where, and are state variables of the command filter, represents a virtual control signal as the input of the command filter; , , , , are design parameters of the finite-time command filter; and ; ; ; represents a custom function, and ; is a sign function; represents or ; when represents , the custom parameter ; when represents , ; represents the nth component of the custom parameter ;

[0161] The error compensation mechanism in S23 is as follows:

[0162] (11)

[0163] where, and are state variables of the error compensation mechanism, and represent positive design parameters; and respectively represent the derivative of the state variable and the state variable ;

[0164] The compensation tracking error in S24 is as follows:

[0165] (12)

[0166] The calculation equation of the derivative of the compensation tracking error variable in S25 is as follows:

[0167] (13)

[0168] where, represents the derivative of the desired tracking trajectory; denotes the derivative of the compensated tracking error variable ;

[0169] The expression of the virtual control signal in S26 is:

[0170] (14)

[0171] wherein, denotes the design parameter of the virtual control signal; denotes the norm sign function, and the calculation formula of the norm sign function is specifically as follows:

[0172] ;

[0173] ;

[0174] wherein, denotes the input of the norm sign function; denotes the Euclidean norm;

[0175] The optimization equation of the derivative of the compensated tracking error variable in S27 is specifically as follows:

[0176] (15)

[0177] The calculation equation of the derivative of the compensated tracking error variable in S28 is specifically as follows:

[0178] (16)

[0179] wherein, denotes the derivative of the compensated tracking error variable ; denotes the derivative of the output of the command filter.

[0180] In some embodiments, the S3 specifically comprises the following steps:

[0181] S31, designing a time synchronization controller;

[0182] S32, substituting the time synchronization controller into the calculation equation of the derivative of the compensated tracking error variable , to obtain the optimization equation of the derivative of the compensated tracking error variable ;

[0183] S33, selecting a Lyapunov function;

[0184] S34, according to the optimization equation of the derivative of the compensated tracking error variable and the compensated tracking error variable The optimization equation calculates the derivative of the Lyapunov function; and the derivative of the Lyapunov function verifies that the dual-arm robot theoretically realizes time synchronization.

[0185] In some embodiments, the time synchronization controller in S31 is specifically as follows:

[0186] (17)

[0187] wherein, denotes a design parameter of the time synchronization controller.

[0188] In some embodiments, the compensation tracking error variable in S32 is specifically as follows: The optimization equation is specifically as follows:

[0189] (18)

[0190] The selected Lyapunov function in S33 is specifically as follows:

[0191] ;

[0192] wherein, denotes the selected Lyapunov function; denotes the compensation tracking error variable, i.e., the compensation tracking error variable , ;

[0193] The derivative of the Lyapunov function in S34 is specifically as follows:

[0194] (19)

[0195] wherein, denotes a positive design parameter, including the positive design parameter , ; denotes a set parameter, including the design parameter , ; denotes a design parameter, including the design parameter , ; and ; denotes a seventh intermediate quantity, and ; denotes an eighth intermediate quantity, and .

[0196] In some embodiments, S3 further comprises the following steps:

[0197] S4, actual design parameters are given and substituted into S1 to S3, and the effectiveness of the time synchronization of the dual-arm robot is verified through simulation experiments.

[0198] In some embodiments, S4 specifically includes the following steps:

[0199] S41, the number of degrees of freedom of each mechanical arm in the dual-arm robot is selected, and actual design parameters of each mechanical arm in the dual-arm robot and the object being operated are given;

[0200] Specifically, referring to Figure 3 and Figure 4 , the dual-arm robot system in the embodiment of the application is composed of two three-degree-of-freedom mechanical arms, the structures of the two mechanical arms are completely the same, each mechanical arm includes a first connecting rod, a second connecting rod and a third connecting rod, wherein the first connecting rod is rotationally connected with a base, the second connecting rod is rotationally connected with the first connecting rod, and the third connecting rod is rotationally connected with the second connecting rod, and the design parameters of each mechanical arm are as follows: the mass of the first connecting rod , the moment of inertia of the first connecting rod , the length of the first connecting rod , the center of mass position of the first connecting rod ; the mass of the second connecting rod , the moment of inertia of the second connecting rod , the length of the second connecting rod , the center of mass position of the second connecting rod ; the mass of the third connecting rod , the moment of inertia of the third connecting rod , the length of the third connecting rod , and the center of mass position of the third connecting rod .

[0201] The actual design parameters of the object being operated are as follows: the mass , the length , the moment of inertia , and the gravitational acceleration .

[0202] S42, the desired tracking trajectory of the object being operated and the initial state of the object being operated are set;

[0203] In this embodiment, the desired tracking trajectory of the object being operated is specifically as follows:

[0204] ;

[0205] wherein, and represent the desired position of the object, represents the desired attitude angle of the object; represents time.

[0206] The initial state of the object to be operated is: ;

[0207] S43, given other parameter specific values, as follows: set the design parameters , design parameters , design parameters , design parameters , design parameters , design parameters ;

[0208] S44, the relevant data of S41 to S43 is substituted into the finite time synchronization instruction filter backstepping method design framework composed of S2 and S3, and the effectiveness of the time synchronization control of the dual-arm robot is verified through simulation experiments.

[0209] Figure 5 The comparison between the expected trajectory and the actual trajectory of the object to be operated in position and attitude is given. From the position tracking results in the direction, although there is a deviation between the actual trajectory and the expected trajectory in the initial stage, the stable tracking is realized with the change of time; in the tracking process of the attitude angle , the actual trajectory also quickly tracks the expected trajectory in a short time. It can be seen that the proposed time synchronization control method of the dual-arm robot can realize the rapid tracking of the object position and attitude, and shows good tracking performance. Figure 6 The tracking error curves of position and attitude are given. From the figure, it can be seen that there is a certain error in the initial moment of position and attitude, among which the error in the direction is the largest, and the error in the direction is relatively small. With the passage of time, the three error curves all show a rapid downward trend, and converge to the origin at about 1 second. This shows that the proposed time synchronization control method of the dual-arm robot can ensure the synchronous convergence of the position and attitude tracking errors of the system. Figure 7 The motion trajectory curve of the object to be operated in three-dimensional space is given, and the object forms a continuous and smooth space curve in the position and attitude dimensions. In summary, the proposed control method can not only ensure the accurate tracking of the position trajectory, but also maintain good tracking performance in the attitude dimension, so as to realize the precise collaborative control of the dual-arm robot on the object.

[0210] Another aspect of the present application also provides a time synchronization control system, comprising a dual-arm robot, and the dual-arm robot adopts the above-mentioned dual-arm robot time synchronization control method to realize time synchronization.

[0211] The above merely describes specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Furthermore, the technical solutions of each embodiment of the present application can be combined with each other, but it must be based on the realization of the ordinary skilled in the art, when the combination of the technical solutions appears contradictory or unachievable, it should be considered that the combination of the technical solutions does not exist, and is not within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A time synchronization control method for a dual-arm robot for biochemical experimental operations, characterized in that, Includes the following steps: S1. For a dual-arm robot, based on the dynamic model of a single robotic arm, and combined with the dynamic model characteristics of the manipulated object, a final overall coupled dynamic model of the dual-arm robot and the object is established. S2. Based on the final coupled dynamic model of the dual-arm robot-object, construct the error transformation formula and define the compensation tracking error. The compensation tracking error includes the compensation tracking error variable. , Based on the error transformation formula, a compensation tracking error variable is constructed. The optimization equation for the derivative and the compensation tracking error variable The equation for calculating the derivative; S3. Design a time synchronization controller, and construct a compensation tracking error variable based on the time synchronization controller. The optimization equation is based on the compensation tracking error variable. The optimization equation for the derivative and the compensation tracking error variable Solving the optimization equations to obtain the derivatives of the Lyapunov function completes the theoretical verification of the time synchronization control of the dual-arm robot. S1 specifically includes the following steps: S11. Based on the structure, posture, speed, and force information of the dual-arm robot, construct a system with... A dynamic model of a single robotic arm with one degree of freedom; S12. Based on the dynamic model of a single robotic arm and the assumptions in S11, establish the overall dynamic model of the dual-arm robot; the assumptions are that the connection between the dual-arm robot and the grasped object is rigid, and there is no relative displacement at the grasping point during the movement. S13. Construct a dynamic model of the manipulated object based on its position, velocity, and force information; S14. Define the formula for calculating the resultant force of a dual-arm robot acting on the manipulated object; S15. Decompose the total force exerted on the object by the dual-arm robot into internal and external forces to obtain the decomposition formula; S16. By introducing the overall dynamic model of the dual-arm robot into the dynamic model of the manipulated object, and combining the resultant force calculation formula in S14 and the split formula in S15, an initial overall coupled dynamic model of the dual-arm robot and the object is constructed. S17. The initial global coupled dynamics model of the dual-arm robot-object is simplified to obtain the simplified global coupled dynamics model of the dual-arm robot-object. S18. Transform the simplified global coupled dynamics model of the dual-arm robot-object to obtain the final global coupled dynamics model of the dual-arm robot-object. The specific dynamic model of a single robotic arm in S11 is as follows: （1） in, Indicates the first One robotic arm, ; Indicates the first The joint angles of a robotic arm Indicates the first The angular velocity of the robotic arm Indicates the first The angular acceleration of the robotic arm, Indicates the first The inertia matrix of a robotic arm, Indicates the first Coriolis force and centrifugal force matrix of a robotic arm Indicates the first The gravity vector of each robotic arm. Indicates the first The joint torque of a robotic arm Indicates the application of the first The force vector of the end effector of the robotic arm Indicates the first The Jacobian matrix of the robotic arms; T denotes the transpose of the matrix; Represents the set of real numbers; The overall dynamic model of the dual-arm robot in S12 is as follows: （2） in, Let represent the inertia matrix of the dual-arm robot, and ; Represents a diagonal matrix; , These represent the inertia matrices of the first and second robotic arms, respectively. Indicates the joint angles of a dual-arm robot; This represents the angular velocity of the dual-arm robot; This represents the angular acceleration of the dual-arm robot. Let the matrix represent the Coriolis force and centrifugal force of the dual-arm robot, and ; , These represent the Coriolis force and centrifugal force matrices for the first and second robotic arms, respectively. Let represent the gravity vector of the dual-arm robot, and , , These represent the gravity vectors of the first and second robotic arms, respectively. Let Jacobian matrix represent the two-armed robot, and , Let represent the Jacobian matrices of the first and second robotic arms, respectively; This represents the total force exerted on the object by the dual-armed robot, and , These represent the total forces exerted on the object by the first and second robotic arms, respectively. This represents the joint torque of a dual-arm robot; The dynamic model of the manipulated object in S13 is as follows: （3） in, Indicates the position of an object. Represents the velocity of an object. Represents the acceleration of an object. The inertia matrix representing an object. The matrix representing the Coriolis force and centrifugal force of an object. Represents the gravitational vector of an object. It represents the resultant force acting on an object; The specific formula for calculating the resultant force of the dual-arm robot acting on the manipulated object in S14 is as follows: （4） in, Let represent the grasping matrix of the dual-arm robot, and , These represent the grasping matrices related to the object's centroid and the grasping point, respectively. The specific splitting formula in S15 is as follows: （5） in, Represents internal force, and satisfies , Indicates external force, and , Represents the pseudo-inverse of a matrix; The initial global coupled dynamics model of the dual-arm robot-object in S16 is as follows: （6） in, Indicates the first intermediate quantity, and ; Indicates the second intermediate quantity; and ; Indicates the third intermediate quantity. ; The simplified overall coupled dynamics model of the dual-arm robot-object in S17 is as follows: （7） in, Indicates the fourth intermediate quantity, and ; Indicates the fifth intermediate quantity, and ; Indicates the sixth intermediate quantity, and ; Indicates control input; ; The final overall coupled dynamics model of the dual-arm robot-object within S18 is as follows: （8） in, and Represents the system state variable, and ; , For system output; S2 specifically includes the following steps: S21. Construct an error transformation formula based on the final dual-arm robot-object overall coupled dynamics model; S22. Design a finite-time instruction filter; S23. To suppress the influence of finite-time instruction filtering error, design an error compensation mechanism; S24. Define the compensation tracking error according to the error compensation mechanism; S25. Based on the overall dynamic model of the dual-arm robot, the dynamic model of the manipulated object, and the error transformation formula, construct compensation tracking error variables. The equation for calculating the derivative; S26. Design the expression for the virtual control signal; S27. Substitute the expression for the virtual control signal into the compensation tracking error variable. The equation for calculating the derivative yields the compensation tracking error variable. The optimal equation for the derivative; S28. Construct compensation tracking error variables based on the overall dynamic model of the dual-arm robot, the calculation formula of the resultant force of the dual-arm robot acting on the manipulated object, and the error transformation formula. The equation for calculating the derivative; The error transformation formula in S21 is as follows: （9） in, Indicates tracking error. Represents the error variable. This indicates the output of the instruction filter. It is the expected tracking trajectory; The finite-time instruction filtering in S22 is as follows: （10） in, and It is the state variable of the instruction filter. This represents the virtual control signal used as the input for instruction filtering; , , , , The design parameters are for finite-time instruction filtering; and ; ; ; This indicates a user-defined function, and ; It is a symbolic function; express or ;when express Custom parameters ;when express hour, ; Indicates custom parameters The nth component; The error compensation mechanism in S23 is as follows: （11） in, and These are the state variables of the error compensation mechanism. and Indicates a positive design parameter; and Representing state variables respectively and state variables The derivative; The specific compensation for tracking error in S24 is as follows: （12） S25 Compensation tracking error variable The equation for calculating the derivative is as follows: （13） in, The derivative of the desired tracking trajectory; Represents the variable for compensating for tracking error. The derivative; The expression for the virtual control signal in S26 is: （14） in, , Design parameters representing virtual control signals The norm sign function is represented by the following formula: ； ； in, The input to the norm sign function; Denotes the Euclidean norm; Compensation tracking error variable in S27 The optimization equation for the derivative is as follows: （15） Compensation tracking error variable in S28 The equation for calculating the derivative is as follows: （16） in, Represents the variable for compensating for tracking error. The derivative; This represents the derivative of the output of the instruction filter.

2. The time synchronization control method for a dual-arm robot for biochemical experimental operations according to claim 1, characterized in that, S3 specifically includes the following steps: S31. Design a time synchronization controller; S32, Substitute the time synchronization controller into the compensation tracking error variable. The equation for calculating the derivative yields the compensation tracking error variable. The optimization equation; S33. Choose the Lyapunov function; S34. Based on the compensation tracking error variable The optimization equation for the derivative and the compensation tracking error variable The derivative of the Lyapunov function is calculated using the optimization equation; the derivative of the Lyapunov function is used to verify that the dual-arm robot has theoretically achieved time synchronization.

3. The time synchronization control method for a dual-arm robot for biochemical experimental operations according to claim 2, characterized in that, The time synchronization controller in S31 is specifically as follows: （17） in, This indicates the design parameters of the time synchronization controller.

4. The time synchronization control method for a dual-arm robot for biochemical experimental operations according to claim 3, characterized in that, The compensation tracking error variable in S32 The optimization equation is as follows: （18） The Lyapunov function selected in S33 is as follows: ； in, Lyapunov function representing selection This represents the variable used to compensate for tracking error. , ; The derivatives of the Lyapunov function in S34 are as follows: （19） in, Indicates positive design parameters, including positive design parameters , ; This indicates the setting parameters, including design parameters. , ; Indicates design parameters, including design parameters , ;and Represents the seventh intermediate quantity, and ; Represents the eighth intermediate quantity, and .

5. The time synchronization control method for a dual-arm robot for biochemical experimental operations according to claim 1, characterized in that, The following steps are included after step S3: S4. Provide the actual design parameters and substitute them into S1 to S3. Verify the effectiveness of the time synchronization of the dual-arm robot through simulation experiments.

6. A time synchronization control system, characterized in that, The invention includes a dual-arm robot, wherein the dual-arm robot achieves time synchronization using the dual-arm robot time synchronization control method described in any one of claims 1 to 5.

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