A heavy-load robot adaptive tracking and following control method for solid-phase addition

Abstract

The application discloses a heavy-load robot adaptive tracking and following control method for solid-phase additive, and relates to the technical field of robot control. The method comprises the following steps: performing dynamic modeling on the joint module of the heavy-load robot; based on the uncertainty in the solid-phase additive process, adjusting the dynamic model; modeling the performance requirements of the heavy-load robot as servo constraints, and calculating the second-order form of the servo constraints; based on the second-order form, solving the servo constraint force by using the Udwadia-Kalaba method; based on the servo constraint force, the adjusted dynamic model and preset assumption requirements, constructing a robust controller that fuses feedforward compensation, robust feedback and online parameter adaptation, so as to realize trajectory tracking control of the heavy-load robot. Thus, by fusing the U-K constraint framework and adaptive robust control, high-precision and strong-robust tracking of a complex trajectory required by the solid-phase additive process can be realized under multiple uncertainties, and the forming quality and stability can be ensured.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to an adaptive tracking and following control method for heavy-duty robots used in solid additive manufacturing. Background Technology

[0002] With the increasing demands for performance of large and complex metal components in high-end manufacturing fields such as aerospace and energy equipment, solid-state additive manufacturing technology has become a key technology for achieving efficient forming of high-performance components due to its advantages such as high metallurgical bonding quality and low residual stress. Heavy-duty robots, with their large workspace, high flexibility, and strong load capacity, are considered ideal execution platforms for realizing large-scale solid-state additive manufacturing. However, this process involves complex physical field interactions and dynamic load changes, placing extremely high demands on the robot's trajectory tracking accuracy and dynamic disturbance rejection capabilities.

[0003] Currently, most control methods applied to robot additive manufacturing are based on ideal dynamic models, failing to fully account for the combined effects of uncertainties such as joint friction, parameter perturbations, external disturbances, and time-varying loads during the additive manufacturing process. This leads to decreased tracking accuracy and insufficient stability in actual operations. Furthermore, existing control strategies typically treat trajectory tracking as a general servo control problem, failing to systematically model the specific performance requirements of additive manufacturing processes, such as speed and force / position coupling, as servo constraints and integrate them into the controller design, thus limiting further improvements in process quality. In addition, for the strongly coupled, nonlinear, and highly uncertain characteristics of heavy-duty robots, there is a lack of integrated control solutions that can simultaneously guarantee accurate trajectory tracking, strong robustness, and adaptive capabilities.

[0004] Therefore, there is an urgent need for an adaptive control method for heavy-duty robots in solid-state additive manufacturing processes, which can accurately achieve high-performance tracking of complex trajectories under conditions of multiple uncertainties in the system, and meet the specific process constraints of the additive manufacturing process, thereby ensuring the forming quality and process stability. Summary of the Invention

[0005] The purpose of this invention is to propose an adaptive tracking and following control method for heavy-duty robots in solid-state additive manufacturing, so as to achieve high-precision and robust tracking of the complex trajectory required for solid-state additive manufacturing processes under multiple uncertainties, thereby ensuring the forming quality and stability.

[0006] This invention proposes an adaptive tracking and following control method for heavy-duty robots using solid additive manufacturing, comprising the following steps: performing dynamic modeling of the joint modules of the heavy-duty robot; adjusting the dynamic model based on uncertainties in the solid additive manufacturing process; modeling the performance requirements of the heavy-duty robot as servo constraints and calculating the second-order form of the servo constraints; solving the servo constraint force using the Udwadia-Kalaba method based on the second-order form; and designing a robust controller based on the servo constraint force, the adjusted dynamic model, and preset assumptions to achieve trajectory tracking control of the heavy-duty robot.

[0007] In some embodiments, the joint module includes a permanent magnet synchronous motor and a harmonic reducer, and the dynamic model of the joint module is represented by the following equation:

[0008]

[0009] in, , , These represent the inertial torque, viscous friction coefficient, and output electromagnetic torque of the permanent magnet synchronous motor, respectively. These represent the angular velocity and angular acceleration of the rotor in the permanent magnet synchronous motor, respectively. , These represent the transmission ratio and transmission efficiency of the harmonic reducer, respectively. This indicates the load torque on the joint module. This represents the nonlinear frictional torque in the harmonic reducer.

[0010] In some embodiments, the nonlinear frictional torque is obtained by the following formula:

[0011]

[0012] in, , These represent the viscous friction coefficient and the Coulomb friction coefficient, respectively. This indicates the relative speed between the load side and the motor side of the harmonic reducer. Represents a symbolic function.

[0013] In some embodiments, the adjusted dynamic model is represented by the following equation:

[0014]

[0015] in, Indicates an uncertain parameter. Represents the system's inertia matrix. Represents the matrix of Coriolis force and centrifugal force. Let represent the gravity matrix, and satisfy:

[0016]

[0017]

[0018]

[0019] in, , , They represent , , The nominal part, , , They represent , , The uncertain part.

[0020] In some embodiments, the second-order form of the servo constraint is expressed by the following equation:

[0021]

[0022] in, express The One element, , This indicates the number of degrees of freedom of a heavy-duty robot; , Indicates the first The first degree of freedom A about The function, , , Indicates the first A about The function, This indicates the number of servo constraints. Not greater than .

[0023] In some embodiments, the preset assumptions include:

[0024] For any and The inertia matrix satisfies ,in, Represent a known compact set;

[0025] The servo constraints are consistent;

[0026] For any ,matrix It is full rank, and and It is reversible;

[0027] There exists a positive definite matrix AND function This makes the following equation true:

[0028]

[0029] And there exists a constant. satisfy:

[0030]

[0031] in, These represent the uncertainty correlation matrix and the system nominal inertia correlation matrix, respectively.

[0032] Existing vector and adjustment function This ensures that the uncertain terms satisfy the following bounded conditions:

[0033]

[0034] in, The maximum value represents the weighted matrix of the uncertainty boundary. The operator representing the norm maximization over an uncertain set of parameters. Denotes the Euclidean vector norm; This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions; This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties.

[0035] function For any vector , The following equation holds true;

[0036] .

[0037] In some embodiments, the servo constraint force is obtained by the following formula:

[0038]

[0039] in, This represents the servo constraint force. This represents the generalized inverse matrix.

[0040] In some embodiments, the robust controller is represented by the following formula:

[0041]

[0042] in,

[0043]

[0044]

[0045]

[0046] in,

[0047]

[0048]

[0049] in, This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions; This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties. This is an adaptive term used to estimate and compensate for the uncertainties of the joint module online; It is the control gain constant, and is a positive real number; For adaptive parameters, This represents the time-varying error threshold.

[0050] In some embodiments, the update law of the adaptive parameters is:

[0051]

[0052] Among them, L , is a positive definite diagonal matrix, and This is to constrain the tracking error.

[0053] In some embodiments, the robust controller adjusts the parameter estimates online through the adaptive update law to achieve real-time compensation for uncertainties in the solid additive manufacturing process and ensure that the closed-loop control of the heavy-duty robot has consistent final bounded stability.

[0054] This invention discloses an adaptive tracking and following control method for heavy-duty robots in solid-state additive manufacturing. First, it performs precise dynamic modeling of the robot's joint modules and then adaptively adjusts the model to address multiple uncertainties in the additive manufacturing process. By systematically modeling process performance requirements as servo constraints and analytically solving for these constraints using the Udwadia-Kalaba equations, a robust controller integrating feedforward compensation, robust feedback, and online parameter adaptation is constructed. This scheme achieves high-precision and robust tracking control of complex process trajectories under conditions of model uncertainty, parameter perturbations, and external disturbances, effectively ensuring the forming quality and process stability of solid-state additive manufacturing, and providing reliable technical support for the precision operation of heavy-duty robots in high-end manufacturing fields. Attached Figure Description

[0055] Figure 1 This is a flowchart of an adaptive tracking and following control method for a heavy-duty robot used in solid-phase additive manufacturing, according to an embodiment of the present invention.

[0056] Figure 2 This is a schematic diagram of the structure of a joint module according to an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of the robust controller according to an embodiment of the present invention;

[0058] Figure 4 This is a schematic diagram of simulation results showing the tracking effect of the method of the present invention and other methods on a given trajectory, which is an example of the present invention.

[0059] Figure 5 This is a schematic diagram illustrating the simulation results of the tracking effect of the method of the present invention and other methods on a given trajectory, which is another example of the present invention. Detailed Implementation

[0060] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0061] This invention provides an adaptive tracking and following control method for heavy-duty robots in solid additive manufacturing. By integrating the Udwadia-Kalaba (UK) framework with adaptive robust control theory, this method systematically solves the problem of how to accurately meet the specific performance requirements of additive manufacturing processes and achieve high-precision trajectory tracking under the influence of multiple uncertainties.

[0062] An adaptive tracking and following control method for heavy-duty robots using solid additive manufacturing, according to an embodiment of the present invention, is described below with reference to the accompanying drawings.

[0063] like Figure 1 As shown, an adaptive tracking and following control method for heavy-duty robots used in solid-phase additive manufacturing includes the following steps:

[0064] S11 performs dynamic modeling of the joint modules of the heavy-duty robot.

[0065] Heavy-duty robots can have multiple degrees of freedom, such as six degrees of freedom, which includes multiple joint modules.

[0066] In some embodiments of the present invention, each joint module includes a permanent magnet synchronous motor and a harmonic reducer, such as... Figure 2 As shown, a single joint of the robotic arm of a heavy-duty robot can be considered as a motor-gear system composed of a permanent magnet synchronous motor and a harmonic reducer. The dynamic model of the joint module is expressed by the following equation:

[0067]

[0068] in, , , These represent the inertial torque, viscous friction coefficient, and output electromagnetic torque of the permanent magnet synchronous motor, respectively. These represent the angular velocity and angular acceleration of the rotor in a permanent magnet synchronous motor, respectively. , These represent the transmission ratio and transmission efficiency of the harmonic reducer, respectively. This indicates the load torque on the joint module. This represents the nonlinear frictional torque in a harmonic reducer.

[0069] For example, the nonlinear frictional torque is obtained by the following equation:

[0070]

[0071] in, , These represent the viscous friction coefficient and the Coulomb friction coefficient, respectively. This indicates the relative speed between the load side and the motor side of the harmonic reducer. Represents a symbolic function.

[0072] By combining the dynamic models of all joint modules, the overall joint space dynamic model of the heavy-duty robot can be obtained.

[0073] Specifically, for any joint module, the mathematical model of the permanent magnet synchronous motor is described by the following equation (1):

[0074] (1)

[0075] in, Indicates permanent magnet synchronous motor exist shaft and Components of the axis Indicates permanent magnet synchronous motor exist shaft and Components of the axis Indicates permanent magnet synchronous motor exist shaft and Components of the axis, This indicates the number of electrode pairs in a permanent magnet synchronous motor. These represent the angular velocity and angular acceleration of the rotor of the permanent magnet synchronous motor, respectively. R Indicates the resistance of the stator. Indicates the magnetic flux linkage of the rotor. , , , These represent the inertial torque, viscous friction coefficient, output electromagnetic torque, and external load torque of the permanent magnet synchronous motor, respectively.

[0076] Based on equation (1), Represented as equation (2):

[0077] (2)

[0078] According to the FOC (Field-Oriented Control) algorithm, the mathematical model (1) of a synchronous motor equipped with permanent magnets (i.e., a permanent magnet synchronous motor) can be rewritten as equation (3):

[0079] (3)

[0080] Based on equation (3), Represented as equation (4):

[0081] (4)

[0082] in, This represents the torque coefficient.

[0083] Based on equation (3), the dynamic model of the permanent magnet synchronous motor can be described by equation (5):

[0084] (5)

[0085] The dynamic model of the harmonic reducer can be described by equation (6):

[0086] (6)

[0087] in, This indicates the transmission ratio of the harmonic reducer. This indicates the transmission efficiency of the harmonic reducer. This indicates the load torque on the joint module.

[0088] Combining equations (5) and (6), and taking into account the frictional force inside the harmonic reducer, the dynamic model of the joint module can be described by equation (7):

[0089] (7)

[0090] in, The nonlinear frictional torque in the harmonic reducer is represented by equation (8):

[0091] (8)

[0092] Equation (7) can be written in Lagrange form as equation (9):

[0093] (9)

[0094] in, ， ， .

[0095] The core purpose of rewriting equation (7) as equation (9) is to incorporate the system into a unified and rigorous theoretical framework, so that subsequent advanced control theories based on this framework (especially the Udwadia-Kalaba method) can be directly applied, and it can provide the necessary mathematical model foundation for proving that the robust controller can guarantee "uniform eventual bounded stability".

[0096] S12, the dynamic model is adjusted based on the uncertainties in solid-state additive manufacturing.

[0097] In solid-state additive manufacturing, heavy-duty robots face multiple uncertainties, including: 1) uncertainties in model parameters, such as the joint friction coefficient. , 1) Changes with temperature and wear; 2) Unmodeled dynamics, such as the flexibility and high-frequency vibration modes of transmission components; 3) Bounded external disturbances, such as time-varying loads caused by uneven plastic flow of materials during additive manufacturing. Fluctuations. To address this, the nominal dynamic model in step S11 is adjusted to include lumped uncertainties.

[0098] In some embodiments of the present invention, the adjusted dynamics model in task space (or joint space) in compact matrix form is represented by the following equation:

[0099] (10)

[0100] in, Represents an uncertain parameter, belonging to a known compact set. (A bounded and closed set) may include the joint friction coefficient. , The actual value, the unknown part of the load mass / inertia, the fluctuation of the transmission efficiency of the harmonic reducer, the amplitude of external disturbances, etc. The inertia matrix represents the joint module. Represents the matrix of Coriolis force and centrifugal force. Let gravitational force be the matrix. The above matrix can be decomposed into the sum of the nominal and uncertain parts as follows:

[0101] (11)

[0102] (12)

[0103] (13)

[0104] in, , , They represent , , The nominal part in , , They represent , , The uncertain part.

[0105] S13, model the performance requirements of the heavy-duty robot as servo constraints, and calculate the second-order form of the servo constraints.

[0106] For solid-state additive manufacturing processes, performance requirements are not limited to end-effector position tracking. For example, in friction stir additive manufacturing, the end-effector stirring head is required to: 1) move along a predetermined spatial path (position constraint); 2) maintain a constant travel speed (velocity constraint); 3) maintain a constant posture perpendicular to the substrate (posture constraint); and 4) apply stable axial pressure (force constraint). These performance requirements are systematically modeled as a set of parameters relating to the robot's end-effector pose, velocity, and even force. There are several servo constraint equations. These constraint equations are mapped to constraint equations concerning joint variables, and second-order time derivatives are performed to obtain the acceleration level constraints:

[0107] In some embodiments of the present invention, the second-order form of the servo constraint is expressed by the following equation:

[0108]

[0109] in, express The One element, n is the number of degrees of freedom of the heavy-duty robot; , is the constraint Jacobian matrix; Indicates the first The first degree of freedom A about The function, , For the number of servo constraints, , is a vector related to velocity, position, and time; Indicates the first A about The function; ,and Full rank is used to ensure that constraints are compatible and independent.

[0110] Specifically, the performance requirements are modeled as servo constraints (i.e., system constraint forces are used as control inputs). Assuming the system is subject to m constraints, the first-order expression is given by equation (14):

[0111] , (14)

[0112] in, express The One element, and All are continuously differentiable functions. .

[0113] Equation (14) can be expressed in matrix form as follows:

[0114] (15)

[0115] in, , .

[0116] Equation (15) for time Differentiating the expression yields the second-order form of the constraint:

[0117] (16)

[0118] in,

[0119] (17)

[0120] (18)

[0121] The second-order constraint form (16) is rewritten as equation (19):

[0122] (19)

[0123] Equation (16) can be expressed in matrix form as shown in equation (20):

[0124] (20)

[0125] S14, Solve the servo constraint force using the Udwadia-Kalaba method based on the second-order form.

[0126] S15, based on servo constraints, an adjusted dynamic model, and preset assumptions, constructs a robust controller that integrates feedforward compensation, robust feedback, and online parameter adaptation to control a heavy-duty robot used in solid-phase additive manufacturing.

[0127] In some embodiments of the present invention, the preset assumptions are required to be obtained based on the characteristics of the joint module and the servo constraint characteristics, including:

[0128] 1) For any and The inertia matrix satisfies ,in, Represent a known compact set;

[0129] 2) The servo constraints (Equation (17)) are consistent;

[0130] 3) For any ,matrix It is full rank, and and It is reversible;

[0131] 4) A positive definite matrix exists. AND function This makes the following equation true:

[0132] (twenty one)

[0133] And there exists a constant. satisfy:

[0134] (twenty two)

[0135] in, These represent the uncertainty correlation matrix and the system nominal inertia correlation matrix, respectively.

[0136] 5) There exists a vector sum function This ensures that the uncertain terms satisfy the following bounded conditions:

[0137] (twenty three)

[0138] in, The maximum value represents the weighted matrix of the uncertainty boundary. The operator representing the norm maximization over an uncertain set of parameters. Denotes the Euclidean vector norm; This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions; This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties.

[0139] 6) Function For any vector , The following equation holds true;

[0140] (twenty four)

[0141] It should be noted that the "consistency" in 2) above refers to the core characteristic of servo constraints for heavy-duty robots in solid-state additive manufacturing. Its meaning can be understood by combining control theory with practical application scenarios. Specifically, it means that the servo constraint system is mathematically compatible, physically feasible, and there are no conflicts between the constraints. It can find a motion trajectory (including joint position, velocity, and acceleration) that satisfies all constraints within the robot's dynamic capabilities. This can be understood from two levels: mathematically, the constraint equations are compatible and have solutions; physically, the constraint equations conform to the robot's dynamic capabilities and the actual process requirements. In short, this consistency ensures that the servo constraints are not "ideal but unrealizable assumptions," but rather effective constraints that are mathematically solvable, physically feasible, and process-coordinated. This is the foundation for the subsequent controller to accurately track the trajectory and meet process requirements.

[0142] In some embodiments of the present invention, the servo constraint force is solved using the UK equation, as shown in the following formula:

[0143] (25)

[0144] in, Indicates servo constraint force. This represents the generalized inverse matrix.

[0145] Due to uncertainties in solid-state additive control of heavy-duty robots, direct application cannot guarantee tracking performance. Therefore, a robust controller is designed as follows:

[0146] (26)

[0147] in,

[0148] (27)

[0149] (28)

[0150] (29)

[0151] in,

[0152] (30)

[0153] (31)

[0154] in, This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions, that is, to ensure that the system can approximately follow the target task when it is not affected by uncertainties. This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties, i.e., it considers the case where the system does not meet constraints in the initial time. This is an adaptive term used to estimate and compensate for the uncertainties of the joint module online; It is the control gain constant, and is a positive real number; For adaptive parameters, This represents the time-varying error threshold.

[0155] and, , , .

[0156] It is a supplementary term for Lyapunov stability analysis, meaning a condition related to... Proportional scalar design parameters. This differential equation describes the time-varying error threshold. The dynamic change pattern, i.e., the initial moment (Upper limit of initial error) The decay rate constant is This indicates that the error threshold decays exponentially over time. Its core function is to balance system robustness and control smoothness. In the initial stage, a larger error threshold is allowed to quickly respond to initial deviations and strong disturbances, and then the threshold is gradually reduced to improve trajectory tracking accuracy.

[0157] Figure 3 The overall structure of the robust controller of the present invention is shown. For example... Figure 2As shown, firstly, the nominal controller p1 of the system is written based on the dynamic equation, objective constraints, and preset assumptions. Then, a controller p2 is proposed to compensate for the problem of unsatisfied initial conditions based on the system error. Finally, a controller p3 is proposed to compensate for the uncertainty of the system by designing an adaptive law.

[0158] In some embodiments of the present invention, the update law of the adaptive parameters is:

[0159] (32)

[0160] Among them, L , is a positive definite diagonal matrix, meaning that each matrix is ​​non-negative; This is to constrain the tracking error.

[0161] In this embodiment, the robust controller adjusts the parameter estimates online through an adaptive update law to achieve real-time compensation for uncertainties in the solid additive manufacturing process and ensure that the closed-loop control of the heavy-duty robot has consistent final bounded stability.

[0162] Specifically, the control signals output by the robust controller are sent to the motor drivers of each joint module (e.g., using FOC-based servo drivers) to drive the heavy-duty robot's movement. During the friction stir additive manufacturing process, adaptive parameters... It can estimate and compensate for uncertainties caused by changes in process load, friction and temperature rise in real time. The feedforward term p1 ensures accurate tracking of complex trajectories, and the feedback term p2 guarantees the transient and steady-state performance of the system.

[0163] In this embodiment of the invention, parameters This is related to the incompatibility of initial compensation conditions. The larger the value, the better the effect, but the greater the control cost; parameter Related to compensation for uncertainty, the impact of parameter adjustment on system control performance and control costs is a comprehensive adjustment process. That is, The larger the value of , the better the control effect, and the greater the corresponding control cost; adaptive control parameters The value of these parameters is a comprehensive consideration and needs to be adjusted in conjunction with the requirements of control effect and control cost. The specific values ​​of these parameters can be determined by the designer based on the actual control accuracy requirements of the system.

[0164] In some embodiments of the present invention, the stability of the designed robust controller is also analyzed using Lyapunov theory, specifically including:

[0165] The final uniform stability bound of the constructed robust controller is analyzed using the Lyapunov function shown in equation (33):

[0166] + (33)

[0167] in, Describe the Lyapunov candidate function. Represents the system state vector. The convergence rate adjustment matrix representing the adaptive parameter update law is the inverse of a positive definite diagonal matrix L, and is also a positive definite diagonal matrix. L is k×k dimensional, and k is the number of adaptive parameters. yes The vector representation of .

[0168] Equation (33) is calculated to obtain the following expression:

[0169] + (34)

[0170] in,

[0171] (35)

[0172] break down , .in, The matrix representing the inverse of the nominal inertia matrix, i.e. .in It is the nominal part of the system inertia matrix. D is used to characterize the inverse mapping relationship of the system's inertial characteristics under ideal operating conditions, and is the feedforward compensation term. The design provides the core parameters; while ΔD is the uncertain part of the inverse of the inertia matrix (i.e., This is used to separate the nominal and uncertain components in inertial characteristics, so as to achieve the desired result through the adaptive term. Targeted compensation.

[0173] (36)

[0174] for Control items, uncertain parameters ,so, ， ， ， :

[0175] (37)

[0176] (38)

[0177] based on Control items:

[0178] (39)

[0179] based on Control items and :

[0180] (40)

[0181] based on We can obtain:

[0182] (41)

[0183] (42)

[0184] Combining equations (41) and (42):

[0185] (43)

[0186] like Based on formula (30), we can obtain:

[0187] (44)

[0188] like Based on formula (30), we can obtain:

[0189] (45)

[0190] Based on formula (37) (44), for :

[0191] (46)

[0192] exist :

[0193] (47)

[0194] Based on the above requirement 6),

[0195] (48)

[0196] Substituting formula (48) into formulas (46) and (47), we can obtain the result for all... :

[0197] (49)

[0198] Applying the adaptive law (32) to the second term on the right side of formula (34) yields:

[0199] (50)

[0200] based on , , The third term on the right side of formula (34) yields:

[0201] (51)

[0202] Based on formula (49) (51), from formula (34), we can obtain:

[0203] (52)

[0204] The derivative of the Lyapunov function in formula (52) is less than 0, which proves that the proposed adaptive robust control has uniform boundedness and uniform final boundedness.

[0205] Furthermore, this invention also compares the designed robust controller with a controller without adaptive control through numerical simulation. and The controllers are compared to verify the effectiveness of the robust controller of the present invention, including: based on the theoretical proof that the stability of the proposed robust controller has been achieved using the Lyapunov method, a specific analysis of the control effect is performed.

[0206] Based on the heavy-duty robotic arm joint module system model (10) considering the effects of uncertainty, the system is analyzed under adaptive robust control (26) and without adaptive control. and The tracking effect on a given trajectory under controller conditions.

[0207] Figure 4 and Figure 5 The cooperative control (i.e., adaptive control) at p1, p2, and p3 is shown respectively. Under these conditions, compared to those without adaptive control... and The diagram illustrates the simulation results of tracking two different given trajectories under controller conditions. The figure shows that, under conditions of system uncertainty, inputting a sine wave with an amplitude of 30 and a frequency of 0.25 Hz (corresponding to a 53-radian amplitude in a permanent magnet synchronous motor) and a step signal with a frequency of 30° and an amplitude of 30° (corresponding to 53 degrees in a permanent magnet synchronous motor), the force output by the controller enables the joint module to quickly and smoothly follow the expected trajectory. By comparing the simulation results, it can be found that the method in this invention is more accurate and smoother, proving the effectiveness and superiority of the design method of this invention.

[0208] This invention discloses an adaptive tracking and following control method for heavy-duty robots using solid-phase additive manufacturing. It lays the theoretical foundation for subsequent robust controller construction by performing kinematic and dynamic modeling of the joint module system. Simultaneously, it introduces uncertainties into the model, providing a design benchmark for the controller to handle actual system disturbances. Furthermore, performance requirements are transformed into servo constraints and described in second-order form, clarifying the controller's final tracking and adjustment objectives. Reasonable assumptions are proposed by combining system and constraint characteristics, providing necessary physical and mathematical basis for control design. Subsequently, the robust controller designed based on Lyapunov theory not only ensures the global stability of the closed-loop system but also significantly improves the dynamic response accuracy and robustness of the system under uncertainties, external disturbances, and complex servo constraints. Compared to traditional control methods, this invention's method exhibits stronger adaptability, higher control accuracy, and superior constraint satisfaction capability.

[0209] The above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and are not intended to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0210] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. An adaptive tracking and following control method for heavy-duty robots used in solid-phase additive manufacturing, characterized in that, Includes the following steps: Dynamic modeling is performed on the joint module of the heavy-duty robot, wherein the joint module includes a permanent magnet synchronous motor; Based on the uncertainties in solid-state additive manufacturing, the dynamic model is adjusted to include both uncertain and nominal components. The uncertainties include changes in the joint friction coefficient and time-varying load fluctuations caused by uneven plastic flow of the material. The performance requirements of the heavy-duty robot are modeled as servo constraints, and the second-order form of the servo constraints is calculated. The performance requirements include position constraints for the end effector to move along a preset spatial path, velocity constraints to maintain a constant travel speed, attitude constraints to maintain a constant posture perpendicular to the substrate, and force constraints to apply stable axial pressure. Based on the second-order form, the servo constraint force is solved using the Udwadia-Kalaba method. Based on the servo constraint force, the adjusted dynamic model, and the preset assumptions, a robust controller integrating feedforward compensation, robust feedback, and online parameter adaptation is constructed to achieve trajectory tracking control of the heavy-duty robot. The online parameter adaptation is used to estimate and compensate for uncertainties in the solid-state additive manufacturing process in real time through adaptive parameters. Furthermore, the robust controller ensures consistent final bounded stability of the closed-loop control of the heavy-duty robot through the update law of the adaptive parameters. The update law of the adaptive parameters is: in, For adaptive parameters, The true value of the adaptive parameter; L , is a positive definite diagonal matrix; For about Constrained tracking error, Denotes the Euclidean vector norm; , These represent the angle and angular velocity of the rotor in the permanent magnet synchronous motor, respectively. Indicates about The adjustment function.

2. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 1, characterized in that, The joint module also includes a harmonic reducer, and the dynamic model of the joint module is expressed by the following equation: in, , , These represent the inertial torque, viscous friction coefficient, and output electromagnetic torque of the permanent magnet synchronous motor, respectively. These represent the angular velocity and angular acceleration of the rotor in the permanent magnet synchronous motor, respectively. , These represent the transmission ratio and transmission efficiency of the harmonic reducer, respectively. This indicates the load torque on the joint module. This represents the nonlinear frictional torque in the harmonic reducer.

3. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 2, characterized in that, The nonlinear frictional torque is obtained by the following formula: in, , These represent the viscous friction coefficient and the Coulomb friction coefficient, respectively. This indicates the relative speed between the load side and the motor side of the harmonic reducer. Represents a symbolic function.

4. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 2, characterized in that, The adjusted dynamic model is expressed by the following equation: in, Indicates an uncertain parameter. Indicates time, Represents the system's inertia matrix. Represents the matrix of Coriolis force and centrifugal force. Let represent the gravity matrix, and satisfy: in, , , They represent , , The nominal part, , , They represent , , The uncertain part.

5. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 4, characterized in that, The second-order form of the servo constraint is expressed by the following equation: in, express The One element, , This indicates the number of degrees of freedom of a heavy-duty robot; , Indicates the first The first degree of freedom A about The function, , , Indicates the first A about The function, the number of constraints Not greater than .

6. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 5, characterized in that, The preset assumptions include: For any and The inertia matrix satisfies ,in, Represent a known compact set; The servo constraints are consistent; For any ,matrix It is full rank, and and It is reversible; There exists a positive definite matrix AND function This makes the following equation true: And there exists a constant. satisfy: in, These represent the uncertainty correlation matrix and the system nominal inertia correlation matrix, respectively. Existing vector and adjustment function This ensures that the uncertain terms satisfy the following bounded conditions: in, The maximum value represents the weighted matrix of the uncertainty boundary. The operator representing the norm maximization over an uncertain set of parameters. Denotes the Euclidean vector norm; This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions; This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties. function For any vector , The following equation holds true; 。 7. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 6, characterized in that, The servo constraint force is obtained by the following formula: in, This represents the servo constraint force. This represents the generalized inverse matrix.

8. The adaptive tracking and following control method for heavy-duty robots in solid-phase additive manufacturing according to claim 7, characterized in that, The robust controller is represented by the following formula: in, in, in, This is a feedforward compensation term based on the nominal model, used to achieve trajectory tracking under ideal conditions; This is a robust feedback term used to handle situations where the initial state does not meet constraints and some uncertainties. This is an adaptive term used to estimate and compensate for the uncertainties of the joint module online; It is the control gain constant, and is a positive real number; For adaptive parameters, This represents the time-varying error threshold.

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