Method for designing high-performance hierarchical synchronous controller of 2R1T motion redundancy parallel robot based on time delay estimation

Abstract

The invention relates to the technical field of motion redundancy parallel robot control, in particular to a method for designing a 2R1T motion redundancy parallel robot high-performance hierarchical synchronous controller based on time delay estimation, which enables a system to estimate current kinetic parameters in real time by introducing a time delay estimation technology, and enables the current kinetic parameters to be estimated in real time in a high-speed motion state. On the basis of the problems of uncertainty, nonlinearity and the like of robot dynamic parameters, dynamic data predicted in real time is used as feed-forward input, so that excessive redundant calculation is avoided, and the efficiency of a control algorithm is optimized; by introducing hierarchical synchronous control, the error difference between redundant degrees of freedom is overcome, the motion precision of a hierarchical driver and the stability of the system are ensured, and the dynamic response of the robot and the robustness of the system are optimized by taking a time delay estimation technology as dynamic feed-forward compensation; and the coordination problem of redundant degrees of freedom is disassembled into a plurality of sub-problems through layered synchronous control, so that the motion coordination and control precision of the robot is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of motion redundant parallel robot control, and specifically to a design method for a high-performance hierarchical synchronization controller of a 2R1T motion redundant parallel robot based on time delay estimation. Background Art

[0002] As a new type of high-degree-of-freedom parallel mechanism, the 2R1T kinematically redundant parallel robot demonstrates significant technological advantages in modern advanced manufacturing thanks to its unique configuration of two rotational degrees of freedom and one translational degree of freedom. By introducing kinematic redundancy, this mechanism effectively expands the workspace dimensions, reduces the force required by individual actuators, and enhances its ability to avoid singular configurations, while maintaining the high stiffness and precision advantages of traditional parallel mechanisms. This makes it irreplaceable in high-end applications such as precision aerospace assembly, minimally invasive surgical instrument manipulation, and complex surface machining.

[0003] Although motion redundancy can provide robots with greater flexibility and operating space, it also introduces complexity in the control system. In the motion control process of motion-redundant parallel robots, the control difficulty is greatly increased due to the highly nonlinear coupling between multiple degrees of freedom and the multiple solution problems caused by redundant degrees of freedom. How to coordinate the motion of each degree of freedom to achieve high-precision trajectory tracking, especially in dynamic environments and high loads, is still a difficult problem that needs to be solved. Currently, there are few reports on the research of motion control of motion-redundant robots. Redundant degrees of freedom provide the system with higher flexibility, but how to effectively manage these redundant degrees of freedom and avoid motion conflicts and instability caused by redundant control has become a key research direction of current control technology;

[0004] Existing control strategies include synchronous control and time delay estimation techniques. Synchronous control is a control method that can synchronize the coordinated motion of different actuators and can be used to reduce the error amplification caused by asynchronous actuators acting on the same target. Time delay estimation, as an effective nonlinear control strategy, has been widely used in various fields. Existing dynamic feedforward systems mostly rely on control strategies based on dynamic models to improve control accuracy. However, while synchronous control and time delay estimation techniques can achieve significant control effects in non-kinematic redundant parallel robot systems, they face two challenges when applied to kinematic redundant parallel robot control: First, the dimensional expansion of the joint motion solution space introduced by redundant degrees of freedom makes it difficult for traditional synchronous control methods to achieve optimal distribution of joint motions (i.e., the joint synchronization partitioning problem); second, time delay estimation techniques must be compatible with the redundant degrees of freedom characteristics of kinematic redundant systems. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of the present invention is to provide a high-performance hierarchical synchronous controller design method for a 2R1T motion redundant parallel robot based on delay estimation, and to optimize the dynamic response and system robustness of the robot by using delay estimation technology as dynamic feedforward compensation; through hierarchical synchronous control, the coordination problem of redundant degrees of freedom is decomposed into multiple sub-problems to improve the robot's motion coordination and control accuracy.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for designing a high-performance hierarchical synchronization controller for a 2R1T motion redundant parallel robot based on time delay estimation, comprising the following steps:

[0007] (1) Solve the kinematic inverse model of the 2PUPR-PRPU motion redundant parallel robot using the closed-loop vector method and solve the dynamic inverse model using the virtual work principle;

[0008] (2) For the robot in high-speed motion, an augmented PD controller based on time delay estimation technology is proposed for generalized coordinate control;

[0009] (3) Based on the mechanical characteristics of robot motion redundancy, the drive layer is divided and the synchronization error and synchronization error deviation of each drive layer are calculated;

[0010] (4) According to the division of the driving layer, the cross-coupling error within the layer is designed as a sliding surface and dynamically introduced into the control law;

[0011] (5) introducing the control input of step (2) into different driving layers respectively;

[0012] (6) According to the division of the driving layer, synchronous controllers are designed for the first-layer driving and the second-layer driving respectively, and a hierarchical synchronous controller based on delay estimation is obtained.

[0013] In some embodiments, the 2PUPR-PRPU motion redundant parallel robot is composed of a moving platform, a fixed platform and three drive branches.

[0014] The two drive branches are symmetrically distributed, and both are PUPR branches, and are connected to the fixed platform and the moving platform in sequence through a universal hinge U pair and a rotating pair R pair. The universal hinge U pair is connected to the guide rail on the fixed platform through the slider moving pair P pair, and the universal hinge U pair is connected to the rotating pair R pair on the moving platform through the moving pair P pair, forming two driven PUPR branches on a branch chain;

[0015] The other driving branch is the PRPU branch chain, which connects the fixed platform and the moving platform in sequence through a rotating pair R and a universal hinge U; the rotating pair R is connected to the guide rail on the fixed platform through the slider moving pair P, and the rotating pair R is connected to the universal hinge U on the moving platform through the moving pair P, forming a PRPU branch with two drives on a branch chain.

[0016] In some embodiments, according to step (1), the specific method is:

[0017] By closed-loop vector method O q i = O P m + O a i - O p i (i=1,2,3), the inverse kinematic solution of the 2PUPR-PRPU motion redundant parallel robot is obtained, and the expression is as follows:

[0018]

[0019] Let a=(a q T ,a p T ) T =(q1,q2,q3,p1,p2,p3) T represents the driven joint, η=(z,α,β,p1,p2,p3) T represents generalized coordinates;

[0020] The general equation of dynamics in the form of rigid body virtual work:

[0021]

[0022] The inverse dynamic solution of the 2PUPR-PRPU motion redundant parallel robot is obtained, and the expression is as follows:

[0023]

[0024] in, is the generalized driving force of the 2PUPR-PRPU kinematic redundant parallel robot, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the robot's gravity vector.

[0025] In some embodiments, according to step (2), the specific method is:

[0026] Assume that the driving force of the driving pair and the moving pair is the non-active active force τa ,

[0027] Through the mapping relationship between driving force and generalized driving force, we can get:

[0028]

[0029] in, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the gravity vector of the robot; J represents the velocity Jacobian between the driven joint and the generalized coordinates;

[0030] The linear driving force of the parallel robot is converted from the torque output by the servo motor through the screw transmission system. Through the influence of the friction force of the screw system, the effective radius of the screw and the rotational inertia of the motor, the torque required to be output by the corresponding servo motor is obtained from the driving force of the driving pair:

[0031]

[0032] in, Output torque for each driving pair servo motor, is the moment of inertia of each motor, represents the angular acceleration of the motor, f is the friction between each screw and nut, r eff is the effective radius of each screw, B em Indicates the motor damping coefficient, D em (t) represents the external disturbance to each motor;

[0033] The mapping relationship between the screw rod length and the motor rotation is defined as:

[0034]

[0035] but:

[0036]

[0037] Where M(a)=r eff J -1 M η (η), G(a)=r eff J -1 G η (η),

[0038] F friction =r eff f,I a =I em / N,B a =B em / N.

[0039] In some embodiments, according to step (3), the specific method is:

[0040] Based on the characteristics of the 2PUPR-PRPU kinematic redundant parallel robot structure and combined with the fixed joint method, the robot's drive is divided into two layers: the first layer consists of the drive with guide rails placed on a fixed platform; the second layer consists of the moving pair drives between the universal joints and the revolute pairs in the three branches. Controllers are designed for each of the two drive layers.

[0041] Introducing a positive constant coefficient matrix definition:

[0042]

[0043] Combining formulas (3) and (8), the dynamic model of the parallel robot can be written as:

[0044]

[0045] in, is a positive constant coefficient matrix, is a set of nonlinear terms, including model uncertainty terms, interference terms, friction and other nonlinear terms;

[0046] Therefore, get The motion state under generalized coordinates can be obtained, and the nonlinear term set can be estimated online in real time using the time delay estimation technology. The size of Indicates an estimated value;

[0047] The designed time delay estimation control law (TDC) is:

[0048]

[0049] Where u is the designed input control quantity; the estimated value L is the estimated delay time.

[0050] From formula (10), the dynamic equation at time tL can be obtained:

[0051]

[0052] Therefore, the system control law of the robot is derived as follows:

[0053]

[0054] right Real-time acquisition, that is, predicting the control input at the current moment based on the generalized coordinates of the past moments in a continuous system;

[0055] Compute the generalized coordinate acceleration at past times using the central difference method:

[0056]

[0057] Define the expected generalized coordinate as η d (t), the real-time generalized coordinate is η(t), and the expected generalized coordinate velocity is The real-time generalized coordinate velocity is Therefore, the trajectory error and velocity error during trajectory tracking are:

[0058]

[0059] Therefore, when using PD control based on time delay estimation technology, the control law is:

[0060]

[0061] Among them, K p With K d are non-negative constant gain matrices respectively;

[0062] The simultaneous equations (9), (12), and (15) yield:

[0063]

[0064] in, The error caused by the delay estimation, when χ is a bounded parameter, only the appropriate constant control gain K needs to be selected. p With K d , then the tracking error e η It is also bounded, and the conditions that need to be met are:

[0065]

[0066] Therefore, it is only necessary to use the smallest possible delay estimation time L and select an appropriate positive constant coefficient matrix This ensures good performance of delay estimation control;

[0067] Map the control law from the trajectory task space back to the drive space:

[0068]

[0069] The position error of the driven joint in trajectory tracking control is defined as:

[0070]

[0071] Considering the particularity of the 2PUPR-PRPU motion redundant parallel robot structure, that is, the two-layer drive can independently complete the number of degrees of freedom of the terminal output, the layered synchronization error is defined as:

[0072]

[0073] In some embodiments, according to step (4), the specific method is:

[0074] According to the cross-coupling error control technology, the layered tracking error e p With e q and layer synchronization error ε p With ε q The comprehensive definition is coupling error and

[0075]

[0076] Among them, c p =(ε p1 -ε p3 ,ε p2 -ε p1 ,ε p3 -ε p2 ) T , c q =(ε q1 -ε q3 ,ε q2 -ε q1 ,ε q3 -ε q2 ) T are the deviation vectors between the synchronization errors of the first layer and the second layer respectively; P and Q are the positive real number cross-coupling parameters of the first layer and the second layer respectively;

[0077] The corresponding coupling velocity error is and

[0078]

[0079] Define the layered sliding surface:

[0080]

[0081] in and is a positive constant matrix, the sliding surface s(t)=0 is a linear differential equation system. When the initial expected value is equal to the actual value, that is, p d (0) = p(0) and q d (0)=q(0), then the system of equations has only one solution e *= 0, then the problem of simultaneous convergence of the coupling error and the coupling velocity error is represented by the problem of the sliding surface s(t) approaching 0;

[0082] Derivative of formula (23):

[0083]

[0084] According to the sliding surface, the reference velocity vector and reference acceleration vector are defined as:

[0085]

[0086] In some embodiments, according to steps (5) and (6), the specific method is:

[0087] make Combining the controllers (7) and (15) for the motor output torque and generalized coordinates, and then designing synchronization controllers for the first-layer drive and the second-layer drive respectively, we obtain a hierarchical synchronization controller based on delay estimation:

[0088]

[0089] Among them, the motor output is driven by the augmented PD control based on delay estimation to drive the auxiliary driving force r eff τ a , screw friction compensation F friction , compensation for motor inertia and motor damping And the external disturbance term D on each motor em (t) composition;

[0090]

[0091] In the generalized coordinate control law τ η Where τ1 is the dynamic compensation term inferred by the time delay estimation technology; τ2 is the generalized coordinate PD controller; τ3 is the first-layer drive coupling error elimination term and synchronization error elimination term; τ4 is the second-layer drive coupling error elimination term and synchronization error elimination term;

[0092] According to the error definition, Equation (28) can be expanded as follows:

[0093]

[0094] From the control law (27), we can know that:

[0095]

[0096] Among them, Δ p =χ p +D em_p (t), Δ q =χq +D em_q (t) represents the estimation error caused by the time delay estimation technique and the error caused by the external disturbance to the corresponding motor;

[0097] Design Lyapunov function:

[0098]

[0099] Derivative of the Lyapunov function with respect to time:

[0100]

[0101] Multiply the first and second terms of Equation (30) by s on the left p T With s q T Substitute into formula (32):

[0102]

[0103] in,

[0104]

[0105] Substituting formula (34) into formula (33), we get:

[0106]

[0107] According to the Lyapunov stability criterion, as long as the appropriate parameter K is selected sp With K sq , making At this point, the system is asymptotically stable and all the errors mentioned above converge to 0.

[0108] Compared with the prior art, the beneficial effects of the present invention are: it has significant beneficial technical effects in solving the control problem of 2R1T motion redundant parallel robots. First, the controller compensates by estimating the dynamics in real time, thereby greatly improving the trajectory tracking accuracy of the end effector, especially in dynamic and complex environments. Secondly, based on the characteristics of hierarchical drive, the robustness of the system is enhanced by adopting synchronous control, and the control strategy can be adjusted in real time to effectively respond to external disturbances, load changes, system uncertainties and other factors, ensuring stable operation under high-speed motion and changing conditions. In short, the control scheme provided by the present invention has demonstrated excellent performance under high-dynamic, multi-constraint complex working conditions, and has proposed new ideas for the industrial and high-precision applications of motion redundant parallel robots.

[0109] Details of one or more embodiments of the present application are presented in the following drawings and descriptions to make other features, purposes and advantages of the present application more concise and easy to understand, and the present application is fully described and understood through the embodiments of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 This is a flow chart of the hierarchical synchronization control method of the present invention;

[0111] Figure 2 This is a schematic diagram of the structure of the 2PUPR-PRPU motion redundant parallel robot.

[0112] Figure 3 A hierarchical schematic diagram of a kinematically redundant 2R1T parallel robot.

[0113] Figure 4 This is the control block diagram of hierarchical synchronization control based on delay estimation technology.

[0114] Figure 5 Figure 2 is the tracking error diagram of the driven joints of the hierarchical synchronization control method based on time delay estimation. DETAILED DESCRIPTION

[0115] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0116] In the existing technology, the control methods for 2R1T motion redundant parallel robots have significant limitations: traditional redundant control strategies (such as pseudo-inverse method and optimization algorithm) heavily rely on accurate system dynamics models, and it is difficult to overcome the model mismatch problem caused by nonlinear friction, load mutation and external disturbance in practical applications, and the robustness is seriously insufficient; at the same time, the degree of freedom management scheme based on online optimization has high computational complexity and poor real-time performance, and cannot meet the real-time response requirements of high-speed dynamic tasks (such as rapid obstacle avoidance of surgical instruments), resulting in motion lag or even instability.

[0117] Although the existing hierarchical control improves the coordination of redundant degrees of freedom through task decomposition, its static priority allocation mechanism lacks the ability to dynamically adapt to multi-objective constraints (obstacle avoidance, energy consumption optimization, etc.), which easily leads to control conflicts. It also fails to effectively compensate for time-varying factors such as joint drive delay and sensor sampling lag, resulting in the accumulation of phase deviations of the terminal trajectory under high-speed motion, seriously weakening the contour tracking performance in high-precision scenarios such as precision assembly.

[0118] Furthermore, traditional linear control strategies are inadequate in suppressing strong nonlinear coupling in mechanisms (such as inertial coupling and geometric nonlinearity). Feedforward compensation schemes that rely on parameter identification have poor engineering practicality, and the lack of adaptive compensation mechanisms for time-varying loads and unknown external forces further exacerbates the risk of overshoot and instability in high-disturbance scenarios such as aerospace assembly. These shortcomings make it difficult for existing methods to achieve high-precision and high-robustness control in highly dynamic, multi-constrained, and complex working conditions, becoming a core bottleneck restricting the industrial application of these robots.

[0119] Based on the above description, please refer to Figure 1-5 The present invention provides a technical solution: a design method for a high-performance hierarchical synchronization controller of a 2R1T motion redundant parallel robot based on time delay estimation, the implementation process of which is as follows:

[0120] 1. Solve the kinematic inverse model of the experimental prototype 2PUPR-PRPU motion redundant parallel robot using the closed-loop vector method, and solve the dynamic inverse model using the virtual work principle;

[0121] 2. To address the issues of uncertainty and nonlinearity in robot dynamic parameters under high-speed motion, an augmented PD controller based on time delay estimation technology is proposed for generalized coordinate control.

[0122] 3. Based on the characteristics of the motion redundancy mechanism, the drive layer is divided and the synchronization error and synchronization error deviation of each drive layer are calculated;

[0123] 4. Based on the division of the driving layer, the cross-coupling error within the layer is designed as a sliding surface and dynamically introduced into the control law;

[0124] 5. Introduce the control input of step 2 into different drive layers respectively;

[0125] 6. According to the division of the driving layer, synchronous controllers are designed for the first-layer driving and the second-layer driving respectively, and a hierarchical synchronous controller based on delay estimation can be obtained.

[0126] Among the above schemes, Figure 2The 2PUPR-PRPU kinematic redundant parallel robot shown consists of a moving platform, a fixed platform, and three drive branches. Branches 1 and 2 are symmetrically arranged in pairs. Both branches 1 and 2 are PUPR branches, connecting the fixed platform and the moving platform sequentially via a universal joint (U) and a revolute pair (R). The universal joint U is connected to the guide rail on the fixed platform via a slider-moving pair (P). The universal joint U is connected to the revolute pair R on the moving platform via a moving pair (P), forming a PUPR branch with two drives on one branch. Branch 3 is a PRPU branch, connecting the fixed platform and the moving platform sequentially via a revolute pair (R) and a universal joint (U). The revolute pair R is connected to the guide rail on the fixed platform via a slider-moving pair (P). The revolute pair R is connected to the universal joint U on the moving platform via a moving pair (P), forming a PRPU branch with two drives on one branch.

[0127] By closed-loop vector method O q i = O P m + O a i - O p i (i=1,2,3), the inverse kinematic solution of the 2PUPR-PRPU motion redundant parallel robot can be obtained, and the expression is as follows:

[0128]

[0129] Let a=(a q T ,a p T ) T =(q1,q2,q3,p1,p2,p3) T represents the driven joint, η=(z,α,β,p1,p2,p3) T represents generalized coordinates.

[0130] Since D'Alembert's principle can transform a dynamic problem into an equivalent static problem, including actual external forces and inertial forces, when dealing with equivalent static problems, the principle of virtual work can be used to analyze the equilibrium state of the system and establish a dynamic model. Therefore, the universal dynamic equation in the form of rigid body virtual work can be obtained:

[0131]

[0132] The inverse dynamic solution of the 2PUPR-PRPU motion redundant parallel robot is obtained, and the expression is as follows:

[0133]

[0134] in, is the generalized driving force of the 2PUPR-PRPU kinematic redundant parallel robot, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the gravity vector of the robot.

[0135] Assume that only the driving force of the driving pair (moving pair) is the non-active active force τ a , which is consistent with the force information contained in the generalized driving force. Therefore, through the mapping relationship between the driving force and the generalized driving force, we can get:

[0136]

[0137] in, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the gravity vector of the robot; J represents the velocity Jacobian between the driven joint and the generalized coordinates.

[0138] The linear driving force of the parallel robot is converted from the torque output by the servo motor through the screw transmission system. Considering the influence of the friction of the screw system, the effective radius of the screw and the rotational inertia of the motor, the torque required to be output by the corresponding servo motor can be calculated from the driving force of the driving pair:

[0139]

[0140] in, Output torque for each driving pair servo motor, is the moment of inertia of each motor, represents the angular acceleration of the motor, f is the friction between each screw and nut, r eff is the effective radius of each screw, B em Indicates the motor damping coefficient, D em (t) represents the external disturbance to each motor.

[0141] The mapping relationship between the screw rod length and the motor rotation is defined as:

[0142]

[0143] but:

[0144]

[0145] Where M(a)=r eff J -1 M η (η), G(a)=r eff J -1 G η(η),

[0146] F friction =r eff f,I a =I em / N,B a =B em / N.

[0147] like Figure 3 As shown in the figure, the number of drive pairs of the motion-redundant parallel robot is greater than the number of degrees of freedom of the terminal output, so there are infinite drive solutions corresponding to the terminal output. The non-uniqueness of the inverse solution requires selection and optimization among multiple degrees of freedom during trajectory planning, which makes the control algorithm very complicated. The existing control algorithm is not well applicable to this type of robot due to the existence of redundant degrees of freedom. Therefore, based on the characteristics of the 2PUPR-PRPU motion-redundant parallel robot structure and combined with the fixed joint method proposed by some scholars, this paper divides the robot's drive into two layers: the first layer consists of a drive placed on a fixed platform with a guide rail; the second layer consists of a mobile pair drive between the universal joint and the rotating pair in the three branches (both layers of drive can independently complete the number of degrees of freedom of the terminal output), and the controller is designed in the two-layer drive space.

[0148] In the dynamic model, it is not easy to accurately obtain the real-time inertia parameters. In order to avoid a lot of calculations and to more conveniently obtain the control signal, a positive constant coefficient matrix is ​​introduced here. definition:

[0149]

[0150] Combining formulas (3) and (8), the dynamic model of the parallel robot can be written as:

[0151]

[0152] in, is a positive constant coefficient matrix, is a set of nonlinear terms, including model uncertainty terms, interference terms, friction and other nonlinear terms.

[0153] Therefore, get The motion state under generalized coordinates can be obtained. However, due to the online real-time acquisition of accurate It is not easy. Therefore, we use the time delay estimation technology to estimate the nonlinear term set online in real time. The size of Indicates an estimated value.

[0154] The designed time delay estimation control law (TDC) is:

[0155]

[0156] Where u is the designed input control quantity; the estimated value L is the estimated delay time.

[0157] From (10), we can get the dynamic equation at time tL:

[0158]

[0159] Therefore, the system control law of the robot is derived as follows:

[0160]

[0161]

[0162] So just need to Real-time acquisition, that is, predicting the control input at the current moment based on the generalized coordinates of the past moments in a continuous system.

[0163] The generalized coordinate acceleration at past times can be calculated using the central difference method:

[0164]

[0165] Define the expected generalized coordinate as η d (t), the real-time generalized coordinate is η(t), and the expected generalized coordinate velocity is The real-time generalized coordinate velocity is Therefore, the trajectory error and velocity error during trajectory tracking are:

[0166]

[0167] Therefore, when using PD control based on time delay estimation technology, the control law is:

[0168]

[0169] Among them, K p With K d are non-negative constant gain matrices respectively.

[0170] Combining equations (9), (12), and (15), we get:

[0171]

[0172] in, The error caused by the delay estimation, when χ is a bounded parameter, only the appropriate constant control gain K needs to be selected. p With K d , then the tracking error e ηIt is also bounded, and the conditions that need to be met are:

[0173]

[0174] Therefore, it is only necessary to use the smallest possible delay estimation time L and select an appropriate positive constant coefficient matrix This ensures good performance of delay estimation control.

[0175] Since the direct object of the motor output is the driven joint during actual control, the control law is mapped from the trajectory task space back to the drive space:

[0176]

[0177] The position error of the driven joint in trajectory tracking control is defined as:

[0178]

[0179] Due to the characteristics of parallel robots, traditional controllers fail to consider the fact that parallel robots have multiple kinematic branches in their mechanical structure, and therefore neglect the coordinated motion between these branches. As a result, at high speeds, traditional controllers cannot guarantee the motion accuracy of the parallel robot's end effector.

[0180] When designing a controller, the synchronization behavior of a parallel robot can be described by introducing an additional error signal, synchronization error. This error represents the coordination relationship between the driven joints. For a parallel robot, the synchronization error of each active joint contains information about both its own joint and that of its neighboring joints.

[0181] Considering the particularity of the 2PUPR-PRPU motion redundant parallel robot structure, that is, the two-layer drive can independently complete the number of degrees of freedom of the terminal output. Therefore, the layer synchronization error is defined as:

[0182]

[0183] According to the cross-coupling error control technology, the layered tracking error e p With e q and layer synchronization error ε p With ε q The comprehensive definition is coupling error and

[0184]

[0185] Among them, c p =(ε p1 -ε p3 ,ε p2 -εp1 ,ε p3 -ε p2 ) T , c q =(ε q1 -ε q3 ,ε q2 -ε q1 ,ε q3 -ε q2 ) T are the deviation vectors between the synchronization errors of the first layer and the second layer respectively; P and Q are the positive real number cross-coupling parameters of the first layer and the second layer respectively.

[0186] The corresponding coupling velocity error is and

[0187]

[0188] Define the layered sliding surface:

[0189]

[0190] in and is a positive constant matrix. In fact, the sliding surface s(t)=0 is a linear differential equation system. When the initial expected value is equal to the actual value, that is, p d (0) = p(0) and q d (0)=q(0), then the system of equations has only one solution e * = 0. Then the problem of the coupling error and the coupling velocity error converging simultaneously can be represented by the problem of the sliding surface s(t) approaching 0.

[0191] Derivative of formula (23):

[0192]

[0193] According to the sliding surface, the reference velocity vector and reference acceleration vector are defined as:

[0194]

[0195] and expected speed and expected acceleration Compared to the reference velocity vector With the reference acceleration vector It not only contains the expected trajectory information, but also the actual tracking error and synchronization error. Therefore, when tracking the trajectory, using the reference velocity and reference acceleration is more conducive to high-precision trajectory tracking control.

[0196] make Combining the controllers (7) and (15) for motor output torque and generalized coordinates, and then designing synchronization controllers for the first layer drive and the second layer drive respectively, we can obtain a hierarchical synchronization controller based on delay estimation (control block diagram as shown in Figure 4 shown):

[0197]

[0198] Among them, the motor output is driven by the augmented PD control based on delay estimation to drive the auxiliary driving force r eff τ a , screw friction compensation F friction , compensation for motor inertia and motor damping And the external disturbance term D on each motor em (t) Composition.

[0199]

[0200] In the generalized coordinate control law τ η where τ1 is the dynamic compensation term inferred by the time delay estimation technology; τ2 is the generalized coordinate PD controller; τ3 is the first-layer drive coupling error elimination term and synchronization error elimination term; τ4 is the second-layer drive coupling error elimination term and synchronization error elimination term.

[0201] According to the error definition, Equation (28) can be expanded as follows:

[0202]

[0203] From the control law (27), we can know that:

[0204]

[0205] Among them, Δ p =χ p +D em_p (t), Δ q =χ q +D em_q (t) represents the estimation error caused by the time delay estimation technology and the error caused by the external disturbance of the corresponding motor.

[0206] Design Lyapunov function:

[0207]

[0208] Derivative of the Lyapunov function with respect to time:

[0209]

[0210] Multiply the first and second terms of Equation (30) by s on the left pT With s q T Substitute into formula (32):

[0211]

[0212] in,

[0213]

[0214] Substituting formula (34) into formula (33), we get:

[0215]

[0216] According to the Lyapunov stability criterion, as long as the appropriate parameter K is selected sp With K sq , making At this point, the system is asymptotically stable and all the errors mentioned above converge to 0.

[0217] According to the designed controller formula (27), a simulation experiment was built and the joint tracking error was obtained as follows: Figure 5 As shown in the figure, it can be seen that the method proposed in the present invention has a very obvious effect on the tracking accuracy of the desired trajectory, and the tracking error of each joint is within 0.02mm. Therefore, the motion redundant hierarchical synchronization control method based on delay estimation proposed in the present invention is effective and superior.

[0218] The technical solution of this application aims to address the difficulty in achieving high-precision control of redundant 2R1T parallel robots under certain speed and acceleration conditions. Traditional PD dynamics control schemes for redundant mechanisms suffer from insufficient robustness due to factors such as time-varying system parameters, load variations, and external interference.

[0219] Therefore, the present invention proposes a hierarchical synchronous controller based on time delay estimation, which is used to solve the control difficulties caused by redundant degrees of freedom of the motion redundant 2R1T parallel robot and the control problem of coordinated combination of time delay estimation technology and motion redundant system. First, the kinematic inverse model of the experimental prototype 2PUPR-PRPU motion redundant parallel robot is solved by the closed-loop vector method, and the dynamic inverse model is solved by the principle of virtual work; in order to solve the problems of uncertainty and nonlinearity of the robot dynamic parameters under high-speed motion state, an augmented PD controller based on time delay estimation technology is proposed for the control of generalized coordinates; according to the mechanism characteristics of motion redundancy, the drive layer is divided, and the cross-coupling error within the layer is designed as a sliding surface and dynamically introduced into the control law; hierarchical synchronous control is proposed to make the drive layer move in a coordinated manner, overcome the error difference between the redundant degrees of freedom, ensure the motion accuracy of the hierarchical drive and the stability of the drive, and finally achieve the goal of high-precision control of the terminal under certain speed and acceleration conditions.

[0220] The main contributions are: proposing a new synchronization control strategy, namely, utilizing the cross-coupling errors within the hierarchical drive layers of the motion redundant mechanism to optimize the coupling of the hierarchical drive with the terminal output error, thereby improving the tracking accuracy and stability of the mechanism; combining the augmented PD control based on the time delay estimation technology of the terminal output generalized coordinates with the sliding mode variable structure control based on the synchronization error of the hierarchical drive, effectively solving the uncertainty between the output generalized coordinates and the redundant degrees of freedom; by judging the stability of the designed controller, the asymptotic stability of the system is rigorously proved; finally, by experimentally verifying the control effect on the 2PUPR-PRPU motion redundant parallel robot, it is proved that the designed controller is effective in improving the control accuracy and system robustness.

[0221] The above embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art could make various modifications and improvements without departing from the spirit of the present application, all of which fall within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be determined by the appended claims.

[0222] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A high-performance hierarchical synchronization controller design method for a 2R1T kinematic redundant parallel robot based on time delay estimation, characterized by: The steps are: (1) Solve the kinematic inverse model of the 2PUPR-PRPU motion redundant parallel robot using the closed-loop vector method and solve the dynamic inverse model using the virtual work principle; (2) For the robot in high-speed motion, an augmented PD controller based on time delay estimation technology is proposed for generalized coordinate control; (3) Based on the mechanical characteristics of robot motion redundancy, the drive layer is divided and the synchronization error and synchronization error deviation of each drive layer are calculated; (4) According to the division of the driving layer, the cross-coupling error within the layer is designed as a sliding surface and dynamically introduced into the control law; (5) introducing the control input of step (2) into different driving layers respectively; (6) According to the division of the driving layer, synchronous controllers are designed for the first-layer driving and the second-layer driving respectively, and a hierarchical synchronous controller based on delay estimation is obtained.

2. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 1 is characterized by: The 2PUPR-PRPU motion redundant parallel robot consists of a moving platform, a fixed platform and three drive branches. The two drive branches are symmetrically distributed, and both are PUPR branches, and are connected to the fixed platform and the moving platform in sequence through a universal hinge U pair and a rotating pair R pair. The universal hinge U pair is connected to the guide rail on the fixed platform through the slider moving pair P pair, and the universal hinge U pair is connected to the rotating pair R pair on the moving platform through the moving pair P pair, forming two driven PUPR branches on a branch chain; The other driving branch is the PRPU branch chain, which connects the fixed platform and the moving platform in sequence through a rotating pair R and a universal hinge U; the rotating pair R is connected to the guide rail on the fixed platform through the slider moving pair P, and the rotating pair R is connected to the universal hinge U on the moving platform through the moving pair P, forming a PRPU branch with two drives on a branch chain.

3. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 2, characterized in that: According to step (1), the specific method is as follows: By closed-loop vector method O q i = O P m + O a i - O p i (i=1,2,3), the inverse kinematic solution of the 2PUPR-PRPU motion redundant parallel robot is obtained, and the expression is as follows: Let a=(a q T ,a p T ) T =(q1,q2,q3,p1,p2,p3) T represents the driven joint, η=(z,α,β,p1,p2,p3) T represents generalized coordinates; The general equation of dynamics in the form of rigid body virtual work: The inverse dynamic solution of the 2PUPR-PRPU motion redundant parallel robot is obtained, and the expression is as follows: in, is the generalized driving force of the 2PUPR-PRPU kinematic redundant parallel robot, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the robot's gravity vector.

4. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 3 is characterized by: According to step (2), the specific method is: Assume that the driving force of the driving pair and the moving pair is the non-active active force τ a , Through the mapping relationship between driving force and generalized driving force, we can get: in, is the mass matrix of the robot, are the centrifugal and G-force vectors of the robot, is the gravity vector of the robot; J represents the velocity Jacobian between the driven joint and the generalized coordinates; The linear driving force of the parallel robot is converted from the torque output by the servo motor through the screw transmission system. Through the influence of the friction force of the screw system, the effective radius of the screw and the rotational inertia of the motor, the torque required to be output by the corresponding servo motor is obtained from the driving force of the driving pair: in, Output torque for each driving pair servo motor, is the moment of inertia of each motor, represents the angular acceleration of the motor, f is the friction between each screw and nut, r eff is the effective radius of each screw, B em Indicates the motor damping coefficient, D em (t) represents the external disturbance to each motor; The mapping relationship between the screw rod length and the motor rotation is defined as: but: where M(a) = r eff J -1 M η (η), G(a) = r eff J -1 G η (η), F friction = r eff f, I a = I em / N, B a = B em / N.

5. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 4, characterized in that: According to step (3), the specific method is: Based on the characteristics of the 2PUPR-PRPU kinematic redundant parallel robot structure and combined with the fixed joint method, the robot's drive is divided into two layers: the first layer consists of the drive with guide rails placed on a fixed platform; the second layer consists of the moving pair drives between the universal joints and the revolute pairs in the three branches. Controllers are designed for each of the two drive layers. Introducing a positive constant coefficient matrix definition: Combining formulas (3) and (8), the dynamic model of the parallel robot can be written as: in, is a positive constant coefficient matrix, is a set of nonlinear terms, including model uncertainty terms, interference terms, friction and other nonlinear terms; Therefore, get The motion state under generalized coordinates can be obtained, and the nonlinear term set can be estimated online in real time using the time delay estimation technology. The size of Indicates an estimated value; The designed time delay estimation control law (TDC) is: Where u is the designed input control quantity; the estimated value L is the estimated delay time. From formula (10), the dynamic equation at time tL can be obtained: Therefore, the system control law of the robot is derived as follows: right Real-time acquisition, that is, predicting the control input at the current moment based on the generalized coordinates of the past moments in a continuous system; Compute the generalized coordinate acceleration at past times using the central difference method: Define the expected generalized coordinate as η d (t), the real-time generalized coordinate is η(t), and the expected generalized coordinate velocity is The real-time generalized coordinate velocity is Therefore, the trajectory error and velocity error during trajectory tracking are: Therefore, when using PD control based on time delay estimation technology, the control law is: Among them, K p With K d are non-negative constant gain matrices respectively; The simultaneous equations (9), (12), and (15) yield: in, The error caused by the delay estimation, when χ is a bounded parameter, only the appropriate constant control gain K needs to be selected. p With K d , then the tracking error e η It is also bounded, and the conditions that need to be met are: Therefore, it is only necessary to use the smallest possible delay estimation time L and select an appropriate positive constant coefficient matrix This ensures good performance of delay estimation control; Map the control law from the trajectory task space back to the drive space: The position error of the driven joint in trajectory tracking control is defined as: Considering the particularity of the 2PUPR-PRPU motion redundant parallel robot structure, that is, the two-layer drive can independently complete the number of degrees of freedom of the terminal output, the layered synchronization error is defined as:

6. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 5, characterized in that: According to step (4), the specific method is: According to the cross-coupling error control technology, the layered tracking error e p With e q and layer synchronization error ε p With ε q The comprehensive definition is coupling error and Among them, c p =(ε p1 -ε p3 ,ε p2 -ε p1 ,ε p3 -ε p2 ) T , c q =(ε q1 -ε q3 ,ε q2 -ε q1 ,ε q3 -ε q2 ) T are the deviation vectors between the synchronization errors of the first layer and the second layer respectively; P and Q are the positive real number cross-coupling parameters of the first layer and the second layer respectively; The corresponding coupling velocity error is and Define the layered sliding surface: in and is a positive constant matrix, the sliding surface s(t)=0 is a linear differential equation system. When the initial expected value is equal to the actual value, that is, p d (0) = p(0) and q d (0)=q(0), then the system of equations has only one solution e * = 0, then the problem of simultaneous convergence of the coupling error and the coupling velocity error is represented by the problem of the sliding surface s(t) approaching 0; Derivative of formula (23): According to the sliding surface, the reference velocity vector and reference acceleration vector are defined as:

7. The method for designing a high-performance hierarchical synchronous controller for a 2R1T kinematic redundant parallel robot based on time delay estimation according to claim 6, characterized in that: According to steps (5) and (6), the specific method is: make Combining the controllers (7) and (15) for the motor output torque and generalized coordinates, and then designing synchronization controllers for the first-layer drive and the second-layer drive respectively, we obtain a hierarchical synchronization controller based on delay estimation: Among them, the motor output is driven by the augmented PD control based on delay estimation to drive the auxiliary driving force r eff τ a , screw friction compensation F friction , compensation for motor inertia and motor damping And the external disturbance term D on each motor em (t) composition; In the generalized coordinate control law τ η Where τ1 is the dynamic compensation term inferred by the time delay estimation technology; τ2 is the generalized coordinate PD controller; τ3 is the first-layer drive coupling error elimination term and synchronization error elimination term; τ4 is the second-layer drive coupling error elimination term and synchronization error elimination term; According to the error definition, Equation (28) can be expanded as follows: From the control law (27), we can know that: Among them, Δ p =χ p +D em_p (t), Δ q =χ q +D em_q (t) represents the estimation error caused by the time delay estimation technique and the error caused by the external disturbance to the corresponding motor; Design Lyapunov function: Derivative of the Lyapunov function with respect to time: Multiply the first and second terms of Equation (30) by s on the left p T With s q T Substitute into formula (32): in, Substituting formula (34) into formula (33), we get: According to the Lyapunov stability criterion, as long as the appropriate parameter K is selected sp With K sq , making At this point, the system is asymptotically stable and all the errors mentioned above converge to 0.

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