Time delay double-arm collaborative robot control method based on Udwadia-Kalaaba and cooperative game theory

Abstract

The invention relates to the technical field of robot control, in particular to a time delay double-arm collaborative robot control method based on Udwadia-Kalaaba and a cooperative game theory, and the method mainly comprises the following steps: obtaining the control input of a double-arm collaborative robot system obeying servo constraint according to the uncertainty of the system; a dynamic model is simplified by adopting a time delay estimation method so as to realize time delay estimation and double-mechanical-arm cooperative impedance control, a self-adaptive robust controller is established according to time-varying uncertainty existing in a system in combination with a self-adaptive updating law, and optimal control parameters of the robust controller are obtained through a cooperative game method. By the adoption of the method, control parameters can be optimized, performance maximization is achieved, it is guaranteed that the robot can be effectively balanced among different performance targets, and optimization of the overall control performance of the system is promoted.

Description

Technical Field

[0001] The invention relates to the technical field of robot control, and in particular to a time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory. Background Art

[0002] In recent years, robotic manipulators have played an important role in industrial applications. Compared with a single manipulator, multiple manipulators have a larger load-bearing capacity and can perform more functional tasks. When multiple manipulators jointly manipulate an object, a set of kinematic and dynamic constraints are imposed on the manipulator's motion due to the formation of a closed kinematic chain. Therefore, the control of multiple robotic manipulators is much more complicated than the control of a single robotic manipulator.

[0003] In order to solve the complete and incomplete trajectory tracking problem, UK theory is used to solve this problem. The remarkable feature of UK theory is that it can solve both complete constraint problems and incomplete constraint problems. In addition, no linearization of the nonlinear system is required, and no quasi-variables and auxiliary variables are required. It is for these reasons that we apply UK theory to multi-manipulator tracking control. However, if the system is controlled as a whole only by UK theory, the system will be unstable because the inevitable uncertainty in the system is not taken into account, and the existence of uncertainty will limit the control performance of the system.

[0004] In the design process of robust control, the description of uncertainty is a crucial process. Generally speaking, the commonly used uncertainty description methods can be summarized into three types: deterministic methods, probabilistic methods and fuzzy methods. Among them, the fuzzy method is another uncertainty description method. So far, the application of fuzzy methods is mainly concentrated on control design based on fuzzy logic theory. In order to further optimize the control of dual-arm collaborative robots, it is also necessary to provide a time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory. Summary of the invention

[0005] The present invention aims at the deficiencies in the prior art and provides the following technical solutions:

[0006] The control method of a time-delay dual-arm collaborative robot based on Udwadia-Kalaba and cooperative game theory includes the following steps:

[0007] S10. Establish a dynamic model of the dual-arm collaborative robot system.

[0008] S20. Based on Udwadia-Kalaba, the trajectory tracking control is converted into servo constraints for the dual-arm collaborative robot system.

[0009] S30. According to the uncertainty of the system, obtain the control input of the dual-arm collaborative robot system to obey the servo constraint.

[0010] S40. Using the time delay estimation method to simplify the dynamic model to achieve impedance control based on time delay estimation and dual-manipulator collaboration.

[0011] S50. Establish an adaptive robust controller based on the time-varying uncertainty in the system and the adaptive update law.

[0012] S60: Obtaining optimal control parameters of the robust controller through a cooperative game method.

[0013] As an improvement of the above technical solution, the kinetic model includes the following formula:

[0014]

[0015] Where t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joint in the dual-arm collaborative robot system, γ represents the uncertain parameters in the mechanical system, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, g is the gravity term of the system, and u is the control torque.

[0016] As an improvement of the above technical solution, step S20 includes the following steps:

[0017] S21: Obtain the motion trajectory of two planar two-degree-of-freedom manipulators grasping an object, convert the trajectory into motion constraints and express it in matrix form.

[0018] S22: Obtain first-order constraints and second-order constraints according to the motion constraints in matrix form of the motion trajectory.

[0019] As an improvement of the above technical solution, the motion trajectory of the two planar two-degree-of-freedom manipulators grasping the object includes the following formula:

[0020]

[0021] The first-order constraint is expressed as follows:

[0022]

[0023] The second-order constraint is expressed as follows:

[0024]

[0025] Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, a=[a1,a2,…,a h ] T is the expected second-order constraint, b=[b1,b2,…,b h ] T is the expected first-order constraint.

[0026] As an improvement of the above technical solution, the acquisition of the control input depends on the following formula:

[0027]

[0028] Wherein, the symbol “+” represents the Moore-Penrose inverse, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, and g is the gravity term of the system.

[0029] As an improvement of the above technical solution, step S40 includes the following steps:

[0030] S41: Introduce the estimated value of the inertia matrix and obtain the nonlinear part in the dynamic model based on the estimated value.

[0031] S42: When the sampling time interval is small enough, the state of the system is estimated according to the actual angular acceleration of the manipulator joint under the control torque at the previous moment, and the dynamic equation based on the time delay estimation is obtained.

[0032] Among them, the dynamic equation based on time delay estimation includes the following:

[0033]

[0034] in, is a positive constant diagonal matrix, ΔN is defined as the time delay estimation error, express The estimated value of , β represents the position of the joints in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, is the nonlinear part in the dynamic model, L is the sampling time interval, t is the time in the dual-arm collaborative robot system, and u is the control torque.

[0035] As an improvement of the above technical solution, step S50 includes the following steps:

[0036] S51: Obtain a servo constraint following error value, and obtain an adaptive update law by estimation.

[0037] S52: Establishing an adaptive robust controller based on the adaptive update law.

[0038] As an improvement of the above technical solution, the acquisition of the servo constraint following error value depends on the following formula:

[0039]

[0040] Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the velocity of the joints in the dual-arm collaborative robot system, and b is a second-order constraint.

[0041] The acquisition of the adaptive update law depends on the following formula:

[0042]

[0043] Among them, k1, ξ1, ξ2 are control parameters in the adaptive law and are positive constants. is a preset function, χ is the servo-constrained following error, and β represents the position of the joints in the dual-arm collaborative robot system, represents the velocity of the joints in the dual-arm collaborative robot system, and t is the time in the dual-arm collaborative robot system.

[0044] The adaptive robust controller includes the following formula:

[0045]

[0046] Among them, τ0 and τ1 are the control items of the controller based on the Udwadia-Kalaba principle, τ2 is the control item of the controller obtained by time delay estimation and dual-manipulator collaborative impedance control, and τ3 is the control item for adaptive compensation of system uncertainty. is the adaptive update law.

[0047] As an improvement of the above technical solution, step S60 includes the following steps:

[0048] S61: Establishing a cost function model of control parameters at any time;

[0049] S62: performing D-operation on the cost function model;

[0050] S63: Using cooperative game method to optimize the control parameters of the cost function model and obtain the minimum performance index;

[0051] S64: Obtaining the optimal control parameter corresponding to the minimum performance indicator.

[0052] As an improvement of the above technical solution, the cost function model in step S61 includes the following formula:

[0053]

[0054] Among them, J1 reflects the cumulative error of the system from the initial moment to infinity, and J2 reflects the error level of the system at infinity. It reflects the transient performance of the system. reflects the steady-state performance of the system, t S is any initial moment, k1 and k2 are constant control parameters, is the adaptive update law.

[0055] The method for obtaining the minimum performance index depends on the following formula:

[0056]

[0057] Among them, γ1>0 and γ2>0, and γ1+γ2=1, is the optimal control parameter

[0058] Beneficial effects of the present invention:

[0059] The method described in the present invention can optimize control parameters and maximize performance. Based on the performance indicators constructed by cooperative game theory, the optimal control parameters that can balance two key performance indicators are found through the "Pareto optimal" method. This process not only ensures that the robot achieves effective trade-offs between different performance objectives, but also promotes the optimization of the overall control performance of the system. Compared with traditional methods, the present invention can provide more refined control parameter settings, so that the robot can perform at its best under various operating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The figure is a schematic diagram of the structure of two planar two-degree-of-freedom manipulators controlling the same object according to the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below. 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.

[0062] In the design process of robust control, the description of uncertainty is a crucial process. Generally speaking, the commonly used uncertainty description methods can be summarized into three types: deterministic methods, probabilistic methods and fuzzy methods. Among them, the fuzzy method is another uncertainty description method. So far, the application of fuzzy methods is mainly concentrated on control design based on fuzzy logic theory. In order to further optimize the control of dual-arm collaborative robots, it is also necessary to provide a time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory.

[0063] Before explaining the specific scheme of this embodiment, it is also necessary to calculate the control parameters of two planar two-degree-of-freedom manipulators controlling an ordinary object along the expected trajectory in order to illustrate the performance of the proposed controller.

[0064] Assume that the base positions of the two robot manipulators are (0, 0) and (1, 0) respectively. Figure 1 Middle ij , and I ij (i,j=1,2) represent the length, mass and inertia of the jth link of the ith robot manipulator respectively.

[0065] Define βi j is the joint angle of the jth link of the i-th robot manipulator, and the position and direction of the center of mass of the grasped object are p o =[x o ,y o ,θ] T , the position of the end effector of the i-th robot manipulator is p i =[x i ,y i ] T The kinematic relationship between the joint angle of each robot manipulator in the joint space and the position of the end effector in the Cartesian space is:

[0066]

[0067] In the formula, [d i ,0] T is the base position of the i-th robot manipulator, x i is the x-coordinate position of the i-th robot manipulator, y i is the y coordinate position of the i-th robot manipulator.

[0068] End effector position and posture p i The center of mass position and posture p of the grasped object o The kinematic relationship between them is:

[0069]

[0070] Based on the above theory, the specific solution of this embodiment includes the following steps:

[0071] S10. Establish a dynamic model of the dual-arm collaborative robot system.

[0072] The kinetic model includes the following formula:

[0073]

[0074] Where t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joint in the dual-arm collaborative robot system, γ represents the uncertain parameters in the mechanical system, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, g is the gravity term of the system, and u is the control torque.

[0075] S20. Based on Udwadia-Kalaba, the trajectory tracking control is converted into servo constraints for the dual-arm collaborative robot system.

[0076] Specifically, step S20 includes the following steps:

[0077] S21: Obtain the motion trajectory of two planar two-degree-of-freedom manipulators grasping an object, convert the trajectory into motion constraints and express it in matrix form.

[0078] S22: Obtain first-order constraints and second-order constraints according to the motion constraints in matrix form of the motion trajectory.

[0079] like Figure 1 As shown, the motion trajectory of the two planar two-degree-of-freedom manipulators grasping objects includes the following formula:

[0080]

[0081] The first-order constraint is expressed as follows:

[0082]

[0083] By taking the derivative of equation 2, we get its second-order constraint, which is specifically expressed as follows:

[0084]

[0085] Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, a=[a1,a2,…,a h ] T is the expected second-order constraint, b=[b1,b2,…,b h ] T is the expected first-order constraint.

[0086] S30. According to the uncertainty of the system, obtain the control input of the dual-arm collaborative robot system to obey the servo constraint.

[0087] If we assume that: when Ψ(β,t) and If Ψ(β,t) and is known, then there is at least one solution in Equation 3

[0088] Considering the case where the unconstrained system is constrained, the acquisition of the control input depends on the following formula:

[0089]

[0090] Wherein, the symbol “+” represents the Moore-Penrose inverse, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, and g is the gravity term of the system.

[0091] S40: The time delay estimation method is used to simplify the dynamic model to achieve time delay estimation-based and dual-manipulator collaborative impedance control.

[0092] The specific steps include:

[0093] S41: Introduce the estimated value of the inertia matrix and obtain the nonlinear part in the dynamic model based on the estimated value.

[0094] In order to obtain the relationship between the control torque u and the joint angular acceleration, an estimated value of the inertia matrix is ​​introduced Substituting into equation 1 and transforming it, we can get:

[0095]

[0096] In the formula, is a positive constant diagonal matrix, β represents the position of the joints in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, It is the nonlinear part in the dynamic model, which can be adjusted by the user in practical applications and satisfies the following formula:

[0097]

[0098] For nonlinear parts of dynamic models Its partial linear characteristics can be utilized to make a more accurate estimate of this part using time delay estimation.

[0099] When the sampling time interval L is small enough, the nonlinear part of the robot dynamics model at a certain moment can be Approximately:

[0100]

[0101] in, express The estimated value of .

[0102] According to the kinetic model in step S10, we can get

[0103]

[0104] in, is a positive constant diagonal matrix, ΔN is defined as the time delay estimation error, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, is the nonlinear part in the dynamic model, L is the sampling time interval, and t is the time in the dual-arm collaborative robot system.

[0105] S42: When the sampling time interval is small enough, the state of the system is estimated according to the actual angular acceleration of the manipulator joint under the control torque at the previous moment, and the dynamic equation based on the time delay estimation is obtained.

[0106] Among them, the dynamic equation based on time delay estimation includes the following:

[0107]

[0108] in, is defined as the time delay estimation error.

[0109] Based on the above reasons, the time delay estimation error compensation controller based on the desired speed feedback can be designed as:

[0110]

[0111] Among them, β d , It is divided into the expected position and expected acceleration of the joints in the multi-arm robot system, λ∈R 2n×2nis a constant diagonal matrix, v is the intermediate quantity, e is the tracking error of the joint angle, and e = β d -β.

[0112] Based on the above method, it is also necessary to consider the time-varying uncertainty in the system. This uncertainty is bounded and can be characterized by fuzzy set theory to achieve consistent boundedness and consistent final boundedness of the tracking error. Specifically, step S50 is performed.

[0113] S50. Establish an adaptive robust controller based on the time-varying uncertainty in the system and the adaptive update law.

[0114] Usually, the physical parameters of collaborative robot systems are difficult to obtain accurately due to load variations, measurement errors and external disturbances. Therefore, the matrix H(β,γ,t), and g(β,γ,t) can be decomposed into:

[0115] H(β,γ,t)=H0(β,t)+H Δ (β,γ,t)

[0116]

[0117] g(β,γ,t)=g0(β,t)+g Δ (β,γ,t)

[0118] Among them, H0, C0 and g0 represent the nominal part of the dual-arm collaborative robot, H Δ , C Δ and g Δ represents the uncertain part of the dual-arm collaborative robot, and H0, C0, g0, H Δ , C Δ and g Δ They are all continuous.

[0119] Based on the above reasons, specifically, step S50 includes the following steps:

[0120] S51: obtaining a servo constraint following error value, and obtaining an adaptive update law by estimating the value;

[0121] S52: Establishing an adaptive robust controller based on the adaptive update law.

[0122] The acquisition of the servo constraint following error value depends on the following formula:

[0123]

[0124] Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the velocity of the joints in the dual-arm collaborative robot system, and b is the desired first-order constraint.

[0125] Adaptive Update Law The acquisition of depends on the following formula:

[0126]

[0127] Among them, k1, ξ1, ξ2 are control parameters in the adaptive law and are positive constants. is a preset function, χ is the servo-constrained following error, and

[0128] The adaptive robust controller includes the following formula:

[0129]

[0130] Specifically,

[0131]

[0132]

[0133] in,

[0134]

[0135] Wherein, t is the time in the dual-arm collaborative robot system, H0 represents the inertia matrix of the nominal part of the dual-arm collaborative robot, C0 represents the Coriolis / centrifugal force of the nominal part of the dual-arm collaborative robot joint module system, g0 represents the gravity term of the nominal part of the dual-arm collaborative robot system, s and ω are intermediate variables derived during the calculation process. τ0 and τ1 are the control items of the controller based on the Udwadia-Kalaba principle. τ2 is the control item of the controller obtained by time delay estimation and dual-manipulator cooperative impedance control. τ3 is the control item for adaptive compensation of system uncertainty. Q∈R 2×n is a positive definite matrix, Θ is a preset function, k1 and k2 are constant control parameters, and k1>0.

[0136] S60: Obtaining optimal control parameters of the robust controller through a cooperative game method.

[0137] According to Equation 4 and its derivation process, it can be concluded that the size of the control input is affected by the control parameters ν and ∈. In addition, the size of the uniformly bounded region is also affected by the control parameters k1 and k2. Therefore, in order to achieve an acceptable balance between control workload and system performance, it is necessary to seek the optimal k1 and k2.

[0138] Specifically, step S60 includes the following steps:

[0139] S61: Establish a cost function model of control parameters at any time.

[0140] The cost function model in step S61 includes the following formula:

[0141]

[0142] Among them, J1 reflects the cumulative error of the system from the initial moment to infinity, and J2 reflects the error level of the system at infinity. It reflects the transient performance of the system. reflects the steady-state performance of the system, t S is any initial moment, k1 and k2 are constant control parameters, is the adaptive update law.

[0143] S62: Perform D-operation on the cost function model.

[0144] S63: Use cooperative game method to optimize the control parameters of the cost function model and obtain the minimum performance index.

[0145] S64: Obtaining the optimal control parameter corresponding to the minimum performance indicator.

[0146] Since there is a fuzzy part in the cost function, the D-operation is used (D-operation can be regarded as a defuzzification method). By performing the D-operation on the previous formula, we can get:

[0147]

[0148] Among them, the performance index J1 reflects the system at the initial time t s The cumulative error to infinity time takes into account the deviation of the system state, such as position, speed, etc., and the influence of control parameters k1 and k2 on these deviations, where σ1, σ2, σ3, σ4, σ5, σ6, σ7, σ8, σ9, σ 10 Adaptive parameters to satisfy uniform boundedness;

[0149] Similarly, we can get

[0150]

[0151] The performance index J2 thus obtained reflects the error level of the system at infinity, that is, the final error state of the system. It is usually related to the steady-state performance of the system and measures whether the system can reach or approach the expected state after a long period of operation. Among them, λ1, λ2, λ3, λ4, λ5, and λ6 are adaptive parameters that satisfy uniform boundedness;

[0152] The control parameter optimization problem can be solved by the following cooperative game.

[0153] First, find the optimal So for any Both have:

[0154]

[0155] To find Use Lemma 1: Decision pair is Pareto optimal if there exist weighting factors γ1>0 and γ2>0, and γ1+γ2=1, such that:

[0156]

[0157] The cost function is as follows:

[0158]

[0159] Therefore, the control parameter optimization problem is transformed into a constrained optimization problem, namely

[0160] For any time t s And the given decision set satisfy

[0161]

[0162] To obtain this solution, we apply the partial differential operator to J(k1,k2) and obtain:

[0163]

[0164]

[0165] Next,

[0166]

[0167] Among them, k1∈D1, k2∈D2.

[0168] Then, Equation 5 is minimized by the solution of Equation 6 and Equation 7, and the solution is the Pareto optimal solution;

[0169] Based on the above analysis, the minimum performance index obtained after calculation is expressed as follows:

[0170]

[0171] Among them, γ1>0 and γ2>0, and γ1+γ2=1, is the optimal control parameter.

[0172] After completing the calculation of the minimum performance index, the optimal control parameters Applied in the controller to complete the uncertainty control of the collaborative robot system.

[0173] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them.

Claims

1. A time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory, characterized in that: The steps include: S10. Establish a dynamic model of the dual-arm collaborative robot system; S20, based on Udwadia-Kalaba, the trajectory tracking control is converted into a servo constraint for the dual-arm collaborative robot system; S30, obtaining a control input of the dual-arm collaborative robot system that obeys the servo constraint according to the uncertainty of the system; S40, simplifying the dynamic model by using a time delay estimation method to achieve dual-manipulator coordinated impedance control based on time delay estimation; S50, establishing an adaptive robust controller according to the time-varying uncertainty in the system and combining the adaptive update law; S60: Obtaining optimal control parameters of the robust controller through a cooperative game method.

2. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 1 is characterized in that: The kinetic model includes the following formula: Where t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joint in the dual-arm collaborative robot system, γ represents the uncertain parameters in the mechanical system, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, g is the gravity term of the system, and u is the control torque.

3. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 1 is characterized in that: The step S20 comprises the following steps: S21: obtaining the motion trajectory of two planar two-degree-of-freedom manipulators grasping an object, converting the trajectory into motion constraints and expressing it in matrix form; S22: Obtain first-order constraints and second-order constraints according to the motion constraints in matrix form of the motion trajectory.

4. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 3 is characterized in that: The motion trajectories of the two planar two-degree-of-freedom manipulators grasping objects include the following formula: The first-order constraint is expressed as follows: The second-order constraint is expressed as follows: Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, a=[a1,a2,…,a h ] T is the expected second-order constraint, b=[b1,b2,…,b h ] T is the expected first-order constraint.

5. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 4 is characterized in that: The acquisition of the control input depends on the following formula: Where the symbol "+" represents the Moore-Penrose inverse, H is the inertia matrix of the system, C is the Coriolis / centrifugal force of the joint module system, and g is the gravity term of the system.

6. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 1 is characterized in that: The step S40 includes the following steps: S41: introducing an estimated value of the inertia matrix and obtaining the nonlinear part of the dynamic model based on the estimated value; S42: when the sampling time interval is small enough, the state of the system is estimated according to the actual angular acceleration of the manipulator joint under the control torque at the previous moment, and a dynamic equation based on time delay estimation is obtained; Among them, the dynamic equation based on time delay estimation includes the following: in, is a positive constant diagonal matrix, ΔN is defined as the time delay estimation error, express The estimated value of , β represents the position of the joints in the dual-arm collaborative robot system, represents the speed of the joints in the dual-arm collaborative robot system, represents the acceleration of the joints in the dual-arm collaborative robot system, is the nonlinear part in the dynamic model, L is the sampling time interval, and t is the time in the dual-arm collaborative robot system.

7. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 1, characterized in that: The step S50 comprises the following steps: S51: obtaining a servo constraint following error value, and obtaining an adaptive update law by estimating the value; S52: Establishing an adaptive robust controller based on the adaptive update law.

8. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 7, characterized in that: The acquisition of the servo constraint following error value depends on the following formula: Where Ψ is the constraint matrix, t is the time in the dual-arm collaborative robot system, β represents the position of the joint in the dual-arm collaborative robot system, represents the velocity of the joints in the dual-arm collaborative robot system, and b is a second-order constraint. The acquisition of the adaptive update law depends on the following formula: Among them, k1, ξ1, ξ2 are control parameters in the adaptive law and are positive constants. is a preset function, χ is the servo-constrained following error, and β represents the position of the joints in the dual-arm collaborative robot system, represents the velocity of the joints in the dual-arm collaborative robot system, and t is the time in the dual-arm collaborative robot system. The adaptive robust controller includes the following formula: Among them, τ0 and τ1 are the control items of the controller based on the Udwadia-Kalaba principle, τ2 is the control item of the controller obtained by time delay estimation and dual-manipulator collaborative impedance control, and τ3 is the control item for adaptive compensation of system uncertainty. is the adaptive update law.

9. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 8, characterized in that: The step S60 includes the following steps: S61: Establishing a cost function model of control parameters at any time; S62: performing D-operation on the cost function model; S63: Using cooperative game method to optimize the control parameters of the cost function model and obtain the minimum performance index; S64: Obtaining the optimal control parameter corresponding to the minimum performance indicator.

10. The time-delay dual-arm collaborative robot control method based on Udwadia-Kalaba and cooperative game theory according to claim 9, characterized in that: The cost function model in step S61 includes the following formula: Among them, J1 reflects the cumulative error of the system from the initial moment to infinity, and J2 reflects the error level of the system at infinity. It reflects the transient performance of the system. reflects the steady-state performance of the system, t S is any initial moment, k1 and k2 are constant control parameters, is the adaptive update law; The method for obtaining the minimum performance index depends on the following formula: Among them, γ1>0 and γ2>0, and γ1+γ2=1, is the optimal control parameter.

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