A mechanical arm adaptive neural network distributed control system and method

Abstract

The application discloses a kind of mechanical arm adaptive neural network distributed control system and method, belong to automation control technical field, including the existence position and pose constraint and equipped with sensor multi-robot arm system, receive three-dimensional rigid body dynamics model from multi-robot arm system sensor data, with three-dimensional rigid body dynamics model integrated general time-varying asymmetric barrier function, adaptive neural network for online estimation unknown dynamics parameters in system and the distributed collaborative tracking controller based on the estimation design of adaptive neural network.The application constructs the new general time-varying asymmetric barrier function of the output constraint multi-robot arm system containing unknown dynamics, and establishes the online learning module based on feedforward neural network, realizes the solution of asymmetric time-varying output constraint problem of online estimation of insensitivity parameter, can simultaneously solve the dynamics estimation problem of initial value insensitivity and asymmetric time-varying output restriction.

Description

Technical Field

[0001] This invention belongs to the field of automation control technology, specifically relating to an adaptive neural network distributed control system and method for robotic arms. Background Technology

[0002] A multi-robot system refers to a group of two or more robots that collaborate to complete a specific task. These robots can be homogeneous or heterogeneous, and may have different functions and sensors. Multi-robot systems typically involve communication, coordination, planning, and control between robots to effectively execute tasks. Through collaboration, multi-robot systems can accomplish tasks that are difficult or impossible for a single robot, such as handling large objects, search and rescue in complex environments, etc. Collaborative work can optimize resource allocation, reduce the execution cost of individual tasks, better adapt to diverse tasks and environments, and cope with more complex situations through the collaborative work of robots with different functions.

[0003] In recent years, significant progress has been made in the cooperative operation technology of multi-robot systems. However, the design of these cooperative controllers typically requires precise knowledge of the robot system's dynamic model, which makes the control scheme unable to cope with parameter uncertainties and reduces system stability. To overcome this challenge, adaptive techniques with the ability to estimate unknown parameters online have been proposed to address system parameter uncertainties. However, existing adaptive techniques are often susceptible to external controllers and unmodeled dynamics, and are highly sensitive to changes in initial values, which limits their application scope to some extent. Therefore, it is necessary to design model-free learning controllers based on multilayer feedforward neural networks that are insensitive to initial values, in order to eliminate the assumption of linearity of system parameters and improve the robustness of the control scheme.

[0004] Furthermore, during the execution of tasks by a multi-robot system, it is necessary to ensure the safety of the robots themselves and their surrounding environment. To avoid collisions or damage, the robot's movements must be within its physical capabilities, such as speed, force, and range of motion. Therefore, the robot's pose needs to be constrained in the controller design to achieve the goal of safe production.

[0005] In summary, for multi-robot systems with output constraints and unknown dynamic parameters, there is a need for an adaptive neural network distributed control system and method for robotic arms that can simultaneously solve the dynamic estimation problems of insensitivity to initial values ​​and asymmetric time-varying output constraints. Summary of the Invention

[0006] The purpose of this invention is to provide an adaptive neural network distributed control system and method for robotic arms, which can simultaneously solve the dynamic estimation problems of insensitivity to initial values ​​and asymmetric time-varying output constraints.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] An adaptive neural network distributed control system for a robotic arm includes a multi-robotic arm system with position and attitude constraints and equipped with sensors, a three-dimensional rigid body dynamics model that receives sensor data from the multi-robotic arm system, a universal time-varying asymmetric barrier function integrated with the three-dimensional rigid body dynamics model, an adaptive neural network for online estimation of unknown dynamic parameters in the system, and a distributed cooperative tracking controller based on the estimation design of the adaptive neural network.

[0009] An adaptive neural network distributed control method for a robotic arm, based on a control system, includes the following steps:

[0010] Step S1: Establish a three-dimensional rigid body dynamics model based on the reference points of the object being grabbed;

[0011] Step S2: Transform the output-constrained dynamic equation into a new dynamic equation that considers the output boundedness using a universal time-varying asymmetric barrier function;

[0012] Step S3: Establish a learning module based on a multi-layer feedforward neural network to estimate the unknown dynamic information in the system;

[0013] Step S4: Design a distributed cooperative tracking controller and verify the stability of the system using Lyapunov functions.

[0014] A further improvement to the technical solution of the present invention is that step S1 includes the following steps:

[0015] Step S101: Establish a three-dimensional rigid body dynamics model based on the reference points of the object being grabbed, as shown in the following equation:

[0016]

[0017] In the formula, This represents the object being grabbed in a fixed world coordinate system ∑ l The position in the middle, and They are respectively represented as Where x is the reference point P in ∑ l In the coordinate system, ω is the angular velocity, which is constant at any position of the rigid body, and α is the angular acceleration. Represents the inertia matrix. Let g(X0) represent the centrifugal-Coriolis matrix, g(X0) represent the gravity matrix, and F represent the centrifugal-Coriolis matrix. ε Indicates the disturbance force, Ω i Represents the capture matrix. This represents the control force applied by each robotic arm;

[0018] Step S102: In the three-dimensional rigid body dynamics model, X0 = (x0, R), which can be expressed as in,

[0019]

[0020] In the formula, x0 represents the reference point P in ∑ l The position in ∑, R represents the position relative to ∑ l and ∑ p The relevant rotation matrix, ∑ p Let the coordinate system of the captured rigid body be denoted as . For ease of labeling, let . in,

[0021]

[0022] In the formula, (3) is a special Euclidean group, which represents the set of transformation matrices;

[0023] Step S103: In rigid body dynamics, the inertia matrix is ​​defined as:

[0024]

[0025] Where m is the mass of the object being grabbed, and r p The reference point P is in ∑ p Coordinates in;

[0026] The centrifugal-Coriolis matrix is ​​defined as follows:

[0027]

[0028] J p The inertia matrix is ​​based on P and is defined as follows:

[0029]

[0030] Grab the matrix Ω i for:

[0031]

[0032] Where, r i The coordinates of each robotic arm are based on the reference point P;

[0033] Due to the characteristics of the grasping matrix, Ω(X0,r i The inverse of ) is:

[0034]

[0035] Therefore,

[0036]

[0037] In the dynamics of a robotic arm, the matrix M(X0) is symmetric and positive definite, satisfying k1I n ≤M(X0)≤k2I n Where k1 and k2 are positive constants, It is partially symmetrical.

[0038] A further improvement to the technical solution of the present invention is that step S2 includes the following steps:

[0039] Step S201: Addressing output limitations in θ represents the rotation angle of the object during motion, and -A1 and A2 are time-varying functions. A general time-varying asymmetric barrier function is proposed as follows:

[0040]

[0041] In formula (8), the initial conditions are satisfied. And there are as well as

[0042] From the above formula, it can be seen that when When Y approaches -A1 or A2, Y0 approaches infinity. Therefore, when the initial conditions are met, it can be... The constrained problem is transformed into a bounded problem of Y0;

[0043] Step S202: Differentiating with respect to Y0 yields the following equation:

[0044]

[0045] in,

[0046]

[0047] Step S203: Taking the second derivative with respect to Y0 yields the following equation:

[0048]

[0049] Step S204: Substituting formulas (9) and (10) into (1) yields the following formula:

[0050]

[0051] In formula (11), Defined as And we have B = [b1, b2, b3, b4, b5, b6] T , And thus define K = dP / dt, therefore ||P|| F ≤P u P u It is a positive number;

[0052] Step S205: Multiply both sides of equation (11) by P to obtain a new dynamic equation, as shown below:

[0053]

[0054] in,

[0055] E = PMP

[0056] D = PMK + PCP

[0057]

[0058] In the new dynamic equation shown in equation (12), the matrix E is symmetric positive definite and has positive constants l1 and l2 such that l1I n ≤E≤l2I n ,and It is partially symmetric, meaning that the new dynamic equations after transformation by the general time-varying asymmetric barrier function still satisfy the characteristics required by the multi-manipulator system.

[0059] A further improvement to the technical solution of the present invention is that step S3 includes the following steps:

[0060] Step S301: For the new dynamic equation (12), establish a multilayer feedforward neural network as shown in the following equation:

[0061] f i (x)=W i T σ(V i T x)+ε i (13)

[0062] Where, ε i For the approximate error, satisfying ||ε i ||<ε b , and ε b If positive, σ is the activation function, and W... i and V i These are the weights of a neural network.

[0063] Step S302: Define f i The estimated value of (x) is shown in the following formula:

[0064]

[0065] in, and W respectively i and V i The estimated value, let As the estimation error, the hidden layer gradient is calculated based on the sigmoid activation function. It is given by the following formula:

[0066]

[0067] Step S303: Define the estimation error as:

[0068]

[0069] in,

[0070]

[0071] definition,

[0072]

[0073] The above formula contains a matrix of all neural network weights; it can be seen that ||Ψ i || F ≤Ψ 1i Ψ 1i It is a positive number; in equation (14), ξ i It is bounded, therefore we can obtain the following formula:

[0074]

[0075] in, and It is a known positive constant;

[0076] Step S304: The tracking error of the transformed new dynamic equation is defined as:

[0077]

[0078] in, For reference trajectory;

[0079] According to formula (13), the filtered tracking error is defined as Therefore, the new dynamic equation (12) can be expressed as:

[0080]

[0081] in,

[0082] From formula (13), the dynamics of the robotic arm can be expressed as:

[0083]

[0084] Step S305: The multilayer feedforward neural network contains the dynamics of the transformed robotic arm E, D, and H. To obtain these unknowns, an adaptive controller is designed as follows:

[0085]

[0086] In the formula, Γ r,i , Γ w,i , Γ v,i It is a positive definite matrix. It is a positive gain parameter.

[0087] A further improvement to the technical solution of the present invention is that step S4 includes the following steps:

[0088] Step S401: Design the distributed controller for each robotic arm, as shown in the following formula:

[0089]

[0090] in,

[0091]

[0092] In the above formula, Θ i For a positive definite matrix, in formula (21) It is caused by material deformation, and satisfies This facilitates the mutual adjustment of internal forces. The parameters in formula (21) satisfy the following conditions:

[0093]

[0094] Where, τ min,i for The minimum singular value, and The details will be provided later in the proof; Step S402: Consider the Lyapunov function:

[0095]

[0096] Differentiating formula (23) yields:

[0097]

[0098] Step S403: Substitute formulas (13) and (18) into formula (24) to obtain:

[0099]

[0100] because It is partially symmetrical, therefore it has In addition, there are and PΩ i P -1 =Ω i Substituting formulas (6), (7), and (21) into the above equation, we obtain:

[0101]

[0102] Meanwhile, substituting formula (14) into the above formula yields:

[0103]

[0104] Since tr(AB) = tr(BA), we can obtain:

[0105]

[0106] because Substituting into formula (16) and the adaptive controller (20), we can obtain:

[0107]

[0108] Step S404: In formula (25), when the sum of the terms in the parentheses is positive, Since it is negative, extracting the terms in the parentheses of formula (25) yields:

[0109]

[0110] in, and Therefore,

[0111]

[0112] or

[0113]

[0114] When the above conditions are met, the term within the parentheses in formula (25) is negative; and In the defining equation, since Ψ 1i , P u and It is bounded. and It is also bounded, therefore the closed set Δ defined by these variables is... z and It is compact, Beyond compact set Δ z Since time is negative, the system is uniformly eventually bounded.

[0115] The technological advancements achieved by this invention due to the adoption of the above technical solutions are as follows:

[0116] This invention proposes an adaptive neural network distributed control system and method for robotic arms. It constructs a new general time-varying asymmetric barrier function for multi-robotic arm systems containing unknown dynamics and output constraints, and establishes an online learning module based on a feedforward neural network. This enables the solution of asymmetric time-varying output constraint problems for online estimation of insensitive parameters, and can simultaneously solve the problems of asymmetric time-varying output constraints and dynamic estimation problems that are insensitive to initial values.

[0117] This invention utilizes an online learning module based on a multi-layer feedforward neural network to estimate unknown geometric and inertial parameters in the system and establishes a distributed tracking control scheme to ensure that the multi-robotic arm system performs tracking control tasks within constraints. The learning module established in this invention can uniformly estimate all unknowns in the system, simplifying controller design, while the consideration of output constraints meets equipment attitude limitations and safe operation requirements.

[0118] This invention addresses multi-manipulator systems by constructing a novel universal asymmetric time-varying barrier function. This function can directly constrain the coordinates of the reference point, avoiding the problem of overly conservative initial conditions for error constraints. While maintaining the original properties of the dynamic equations, the asymmetric time-varying output constraint problem is transformed into a bounded problem through transformation.

[0119] This invention addresses the dynamics of robotic arms utilizing a general asymmetric time-varying barrier function transformation. It employs an online learning module based on a multilayer feedforward neural network. This module is insensitive to changes in initial values ​​and allows for unified online estimation of all parameters of the robotic arm, simplifying controller design.

[0120] This invention addresses the collaborative tracking task of a multi-robotic arm system by employing a distributed control strategy. This strategy can comprehensively consider the position parameters of the robotic arms and the grasping position, and, in the presence of external interference, set the positions of multiple robotic arms within a limited range to perform trajectory tracking tasks. Attached Figure Description

[0121] Figure 1 This is a flowchart of the adaptive neural network distributed control method for robotic arms of the present invention;

[0122] Figure 2 In this invention, the composite error norm ||z(t)|| and the rotation matrix error are... A schematic diagram;

[0123] Figure 3 This is a schematic diagram illustrating the tracking of the reference point coordinate x0 in this invention;

[0124] Figure 4 This is a schematic diagram illustrating the tracking of the object's rotation angle θ in this invention;

[0125] Figure 5 This is a schematic diagram illustrating the weight changes in the multilayer feedforward neural network of this invention. Detailed Implementation

[0126] The present invention will be further described in detail below with reference to embodiments:

[0127] Example 1

[0128] This embodiment provides an adaptive neural network distributed control system for a robotic arm, including a multi-robotic arm system with position and attitude constraints and equipped with sensors, a three-dimensional rigid body dynamics model that receives sensor data from the multi-robotic arm system, a general time-varying asymmetric barrier function integrated with the three-dimensional rigid body dynamics model, an adaptive neural network for online estimation of unknown dynamic parameters in the system, and a distributed cooperative tracking controller based on the estimation design of the adaptive neural network.

[0129] The multi-arm system comprises multiple robotic arms, each constrained by position and posture during operation. Each arm is equipped with sensors to monitor joint angles, velocity, acceleration, and potential external forces in real time. The arms exchange coordinates, velocities, and disturbance information via communication. A three-dimensional rigid body dynamics model uses the Lagrange equations for robotic arm motion to represent the collaborative task motion equations in three-dimensional space. These equations can also represent the motion of an object on a plane. The model receives sensor data from the multi-arm system, simulates the dynamic behavior of the robotic arms, and provides the control system with the expected kinematics and external force responses of the arms. A general time-varying asymmetric barrier function is integrated with the three-dimensional rigid body dynamics model to handle and control output constraints, ensuring that the robotic arm's motion does not exceed the preset safety range. Considering time-varying and asymmetric constraints improves the flexibility and safety of the control strategy. A learning module composed of an adaptive neural network estimates unknown dynamic parameters in the system online. By learning the difference between the actual behavior of the robotic arms and the model predictions, the parameters of the dynamic model are continuously adjusted and optimized. For common operational scenarios such as industrial production, logistics warehousing, and medical care, a control target for robotic arm grasping and handling with environmental and physical constraints is established. Based on the control target, a distributed cooperative tracking controller is established. This controller generates control commands for each robotic arm based on an adaptive neural network online learning module. As a distributed system, each controller is responsible for the grasping and handling tasks of one or more robotic arms, while working in cooperation with other controllers to achieve coordinated movement of the group.

[0130] Example 2

[0131] This embodiment provides an adaptive neural network distributed control method for a robotic arm, which performs adaptive neural network distributed control of the robotic arm based on the control system of Embodiment 1, and includes the following steps:

[0132] Step S1: For operational scenarios involving multiple robotic arms grasping and handling, such as parts assembly, goods sorting, and surgical assistance, a three-dimensional rigid body dynamics model is established based on the reference points of the grasped object. This includes the following steps:

[0133] Step S101: Establish a three-dimensional rigid body dynamics model based on the reference points of the object being grabbed, as shown in the following equation:

[0134]

[0135] In the formula, This represents the object being grabbed in a fixed world coordinate system ∑ l The position in the middle, and They are respectively represented as Where x is the reference point P in ∑ l In the coordinate system, ω is the angular velocity, which is constant at any position of the rigid body, and α is the angular acceleration. Represents the inertia matrix. Let g(X0) represent the centrifugal-Coriolis matrix, g(X0) represent the gravity matrix, and F represent the centrifugal-Coriolis matrix. ε Indicates the disturbance force, Ω i Represents the capture matrix. This represents the control force applied by each robotic arm.

[0136] Step S102: In the three-dimensional rigid body dynamics model, X0 = (x0, R), which can be expressed as in,

[0137]

[0138] In the formula, x0 represents the reference point P in ∑ l The position in ∑, R represents the position relative to ∑ l and ∑ p The relevant rotation matrix, ∑ p Let the coordinate system of the captured rigid body be denoted as . For ease of labeling, let . in,

[0139]

[0140] In the formula, (3) is a special Euclidean group, which represents the set of transformation matrices;

[0141] Step S103: In rigid body dynamics, the inertia matrix is ​​defined as:

[0142]

[0143] Where m is the mass of the object being grabbed, and r p The reference point P is in ∑ p Coordinates in;

[0144] The centrifugal-Coriolis matrix is ​​defined as follows:

[0145]

[0146] J p The inertia matrix is ​​based on P and is defined as follows:

[0147]

[0148] Grab the matrix Ω i for:

[0149]

[0150] Where, r i The coordinates of each robotic arm are based on the reference point P;

[0151] Due to the characteristics of the grasping matrix, Ω(X0,r i The inverse of ) is:

[0152]

[0153] Therefore,

[0154]

[0155] In the dynamics of a robotic arm, the matrix M(X0) is symmetric and positive definite, satisfying k1I n ≤M(X0)≤k2I n Where k1 and k2 are positive constants, It is partially symmetrical;

[0156] Step S2: Due to environmental and physical limitations, the motion posture of the robotic arm during operation is usually subject to certain restrictions. The output-constrained dynamic equations are transformed into new dynamic equations considering the boundedness of the output using a universal time-varying asymmetric barrier function. This specifically includes the following steps:

[0157] Step S201: Addressing output limitations in θ represents the rotation angle of the object during motion, and -A1 and A2 are time-varying functions. A general time-varying asymmetric barrier function is proposed as follows:

[0158]

[0159] In formula (8), the initial conditions are satisfied. And there are as well as

[0160] From the above formula, it can be seen that when When Y approaches -A1 or A2, Y0 approaches infinity. Therefore, when the initial conditions are met, it can be... The constrained problem is transformed into a bounded problem of Y0;

[0161] Step S202: Differentiating with respect to Y0 yields the following equation:

[0162]

[0163] in,

[0164]

[0165] Step S203: Taking the second derivative with respect to Y0 yields the following equation:

[0166]

[0167] Step S204: Substituting formulas (9) and (10) into (1) yields the following formula:

[0168]

[0169] In formula (11), Defined as And we have B = [b1, b2, b3, b4, b5, b6] T , And thus define K = dP / dt, therefore ||P|| F ≤P u P u It is a positive number;

[0170] Step S205: Multiply both sides of equation (11) by P to obtain a new dynamic equation, as shown below:

[0171]

[0172] in,

[0173] E = PMP

[0174] D = PMK + PCP

[0175]

[0176] In the new dynamic equation shown in equation (12), the matrix E is symmetric positive definite and has positive constants l1 and l2 such that l1In ≤E≤l2I n ,and It is partially symmetric, that is, the new dynamic equation after the transformation by the general time-varying asymmetric barrier function still satisfies the characteristics required by the multi-manipulator system;

[0177] Step S3: In the task of multi-robotic arm collaborative grasping and transporting objects, in order to obtain information such as the mass of the grasped object and the grasping points of each robotic arm, a learning module is established based on a multi-layer feedforward neural network to estimate the unknown dynamic information in the system.

[0178] The robotic arm parameters include the reference point coordinates r. p The coordinates r of each robotic arm's end effector i And the inertial parameter m, which is usually unknown, makes it impossible to obtain accurate E, D, H, P and grasping matrix Ω. i Therefore, it is necessary to construct a feedforward neural network to estimate these unknown dynamic information online, which specifically includes the following steps:

[0179] Step S301: For the new dynamic equation (12), establish a multilayer feedforward neural network as shown in the following equation:

[0180] f i (x)=W i T σ(V i T x)+ε i (13)

[0181] Where, ε i For the approximate error, satisfying ||ε i ||<ε b , and ε b If positive, σ is the activation function, and W... i and V i These are the weights of a neural network.

[0182] Step S302: Define f i The estimated value of (x) is shown in the following formula:

[0183]

[0184] in, and W respectively i and V i The estimated value, let As the estimation error, the hidden layer gradient is calculated based on the sigmoid activation function. It is given by the following formula:

[0185]

[0186] Step S303: Define the estimation error as:

[0187]

[0188] in,

[0189]

[0190] definition,

[0191]

[0192] The above formula contains a matrix of all neural network weights; it can be seen that ||Ψ i || F ≤Ψ 1i Ψ 1i It is a positive number; in equation (14), ξ i It is bounded, therefore we can obtain the following formula:

[0193]

[0194] in, and It is a known positive constant;

[0195] Step S304: The tracking error of the transformed new dynamic equation is defined as:

[0196]

[0197] in, For reference trajectory;

[0198] According to formula (13), the filtered tracking error is defined as Therefore, the new dynamic equation (12) can be expressed as:

[0199]

[0200] in,

[0201] From formula (13), the dynamics of the robotic arm can be expressed as:

[0202]

[0203] Step S305: The multilayer feedforward neural network contains the dynamic information of the transformed robotic arm E, D, and H, which are usually difficult to determine. To obtain these unknowns, an adaptive controller is designed as follows:

[0204]

[0205] In the formula, Γ r,i , Γ w,i , Γ v,i It is a positive definite matrix. It is a positive gain parameter.

[0206] Step S4: Design a distributed cooperative tracking controller and verify the system's stability using Lyapunov functions to achieve the goal of grasping and transporting objects. This includes the following steps:

[0207] Step S401: Design the distributed controller for each robotic arm, as shown in the following formula:

[0208]

[0209] in,

[0210]

[0211] In the above formula, Θ i For a positive definite matrix, in formula (21) It is caused by material deformation, and satisfies This facilitates the mutual adjustment of internal forces. The parameters in formula (21) satisfy the following conditions:

[0212]

[0213] Where, τ min,i for The minimum singular value, and The design will be provided later in the proof;

[0214] Step S402: Consider the Lyapunov function:

[0215]

[0216] Differentiating formula (23) yields:

[0217]

[0218] Step S403: Substitute formulas (13) and (18) into formula (24) to obtain:

[0219]

[0220] because It is partially symmetrical, therefore it has In addition, there are and PΩ i P -1 =Ω iSubstituting formulas (6), (7), and (21) into the above equation, we obtain:

[0221]

[0222] Meanwhile, substituting formula (14) into the above formula yields:

[0223]

[0224] Since tr(AB) = tr(BA), we can obtain:

[0225]

[0226] because Substituting into formula (16) and the adaptive controller (20), we can obtain:

[0227]

[0228] Step S404: In formula (25), when the sum of the terms in the parentheses is positive, Since it is negative, extracting the terms in the parentheses of formula (25) yields:

[0229]

[0230] in, and Therefore,

[0231]

[0232] or

[0233]

[0234] When the above conditions are met, the term within the parentheses in formula (25) is negative; and In the defining equation, since Ψ 1i , P u and It is bounded. and It is also bounded, therefore the closed set Δ defined by these variables is... z and It is compact, Beyond compact set Δ z Since time is negative, the system is uniformly eventually bounded.

[0235] That is, because and initial conditions We can conclude that V is bounded. In formula (26), since... and Both are bounded, thus we obtain the boundedness of z. From formula (17), It is bounded, therefore Y0 is bounded, combined with P -1 and The boundedness of u can be obtained i It is bounded. Therefore, all signals within the closed loop of the system are bounded.

[0236] The original dynamic equation (1) is transformed into a new dynamic equation (12) by using the time-varying asymmetric barrier function (8). The constraint problem is transformed into the boundedness problem of Y0, which is a common problem encountered in the tracking performance analysis of nonlinear systems. After the above boundedness statement, the boundedness of Y0 is proved, that is, the solution is obtained. The constraint problem.

[0237] Therefore, the collaborative controller proposed in this invention can solve problems such as the constraints on the motion posture of the robotic arm caused by environmental and physical constraints, and the inability to accurately describe the grasping model due to the unknown mass and shape of the grasped object, and can realize the grasping and handling tasks for unknown objects.

[0238] Experimental Example

[0239] The experimental example uses a group of 6 robots to collaboratively transport a rocket body. The performance of the proposed online learning module and cooperative operation controller is verified through the following simulation. Consider a cylindrical rigid body controlled by 6 robots, tracking a periodic trajectory with ideal angular and linear velocities. The parameters in the tracking task are set as m = 8.56 kg, r = 0.32 m, h = 0.1 m, ρ = 266 kg / m. 3 J xx =0.23 kg·m 2 J yy =0.23 kg·m 2 J zz =0.43 kg·m 2 p1 = [0, 0, 0.05] T p2 = [0, 0, -0.05] T p1 = [0.32, 0, 0] T p4 = [-0.32, 0, 1.5] T p5 = [0, 0.32, 0] T And p6 = [0, -0.32, 0] T .

[0240] The ideal trajectory is set as follows:

[0241]

[0242] The simulation step size was set to h = 0.01s. To keep the rotation matrix within the Lie group SO(3), an exponential mapping was used. Considering the constraints of the physical environment and safe operation, It has certain limitations, namely,

[0243] A1=[1.5-0.06cos2t,1.75-0.06cos2t,1.8-0.06cos2t,

[0244] 1.75-0.04cos2t,1.75-0.04cos2t,1.75-0.04cos2t] T

[0245] A2=[-1.25-0.06sin2t,-1-0.06sin2t,-1.5-0.06sin2t,

[0246] -1.5-0.04cos2t,-1.5-0.04cos2t,-1.5-0.04cos2t] T

[0247] In a neural network, the hidden layer has 12 neurons, and the activation function is f(x) = 1 / (1+e^x). -x ), and The elements in the matrix are derived from the standard normal distribution N(0,1). Let γ be... i =1 / 6、Γ r,i =0.3I3、Γ w,i =3.6、Γ v,i =3.6 and To complete the tracking task, the parameters of the cooperative controller are set as follows: Ψ 1i =225, Θ i =2I6. The internal forces caused by material deformation are:

[0248]

[0249] The simulation results for this example are as follows: Figures 2-5 As shown. Figure 2 The tracking error and tracking performance of the rotation matrix for the cooperative task are presented, demonstrating that the proposed distributed controller exhibits excellent tracking performance. From... Figure 3 and Figure 4 It can be seen that when the posture and coordinates of the controlled object are restricted, the proposed controller allows the controlled object to remain within the restricted range. Figure 5 This demonstrates how the weights of the neural network change, by obtaining... and The dynamics of all unknown objects in the system can be obtained. Therefore, the proposed adaptive cooperative controller based on a multi-layer feedforward neural network can effectively realize the multi-arm gripping function.

[0250] In summary, this invention can effectively improve the control accuracy, robustness, and collaborative operation capability of multi-robotic arm systems. The proposed examples can be applied to various production operation scenarios and have significant engineering application value.

[0251] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. An adaptive neural network distributed control system for a robotic arm, characterized in that: This includes a multi-arm system with position and attitude constraints and equipped with sensors, a three-dimensional rigid body dynamics model that receives sensor data from the multi-arm system, a general time-varying asymmetric barrier function integrated with the three-dimensional rigid body dynamics model, an adaptive neural network for online estimation of unknown dynamic parameters in the system, and a distributed cooperative tracking controller based on the estimation design of the adaptive neural network. The control method for adaptive neural network distributed control of a robotic arm based on a control system includes the following steps: Step S1: Establish a three-dimensional rigid body dynamics model based on the reference points of the object being grabbed; specifically including the following steps: Step S101: Establish a three-dimensional rigid body dynamics model based on the reference points of the object being grabbed, as shown in the following equation: In the formula, This indicates that the object being grabbed is in a fixed world coordinate system Σ. l The position in the middle, and They are respectively represented as Where x is the reference point P in ∑ l In the coordinate system, ω is the angular velocity, which is constant at any position of the rigid body, and α is the angular acceleration. Represents the inertia matrix. Let g(X0) represent the centrifugal-Coriolis matrix, g(X0) represent the gravity matrix, and F represent the centrifugal-Coriolis matrix. ε Indicates the disturbance force, Ω i Represents the capture matrix. This represents the control force applied by each robotic arm; Step S102: In the three-dimensional rigid body dynamics model, X0 = (x0, R), which can be expressed as in, In the formula, R represents the relationship with Σ l and Σ p The relevant rotation matrix, Σ p Let the coordinate system of the captured rigid body be denoted as . For ease of labeling, let . in, In the formula, (3) is a special Euclidean group, which represents the set of transformation matrices; Step S103: In rigid body dynamics, the inertia matrix is ​​defined as: Where m is the mass of the object being grabbed, and r p The reference point P is in Σ p The coordinates in the matrix; the eccentric-Coriolis matrix is ​​defined as: J p The inertia matrix is ​​based on P and is defined as follows: Grab the matrix Ω i for: Where, r i The coordinates of each robotic arm are based on the reference point P; Due to the characteristics of the grasping matrix, Ω(X0,r i The inverse of ) is: Therefore, In the dynamics of a robotic arm, the matrix M(X0) is symmetric and positive definite, satisfying k1I n ≤M(X0)≤k2I n Where k1 and k2 are positive constants, It is partially symmetrical; Step S2: Transform the output-constrained dynamic equation into a new dynamic equation that considers the output boundedness using a universal time-varying asymmetric barrier function; Step S3: Establish a learning module based on a multi-layer feedforward neural network to estimate the unknown dynamic information in the system; Step S4: Design a distributed cooperative tracking controller and verify the stability of the system using Lyapunov functions.

2. The adaptive neural network distributed control system for a robotic arm according to claim 1, characterized in that: Step S2 includes the following steps: Step S201: Addressing output limitations in θ represents the rotation angle of the object during motion, and -A1 and A2 are time-varying functions. A general time-varying asymmetric barrier function is proposed as follows: In formula (8), the initial conditions are satisfied. And there are as well as From the above formula, it can be seen that when When Y approaches -A1 or A2, Y0 approaches infinity. Therefore, when the initial conditions are met, it can be... The constrained problem is transformed into a bounded problem of Y0; Step S202: Differentiating with respect to Y0 yields the following equation: in, Step S203: Taking the second derivative with respect to Y0 yields the following equation: Step S204: Substituting formulas (9) and (10) into (1) yields the following formula: In formula (11), Defined as And we have B1 = [b1, b2, b3, b4, b5, b6] T , And thus define K = dP / dt, therefore ||P|| F ≤P u P u It is a positive number; Step S205: Multiply both sides of equation (11) by P to obtain a new dynamic equation, as shown below: in, E = PMP D = PMK + PCP In the new dynamic equation shown in equation (12), the matrix E is symmetric positive definite and has positive constants l1 and l2 such that l1I n ≤E≤l2I n ,and It is partially symmetric, meaning that the new dynamic equations after transformation by the general time-varying asymmetric barrier function still satisfy the characteristics required by the multi-manipulator system.

3. The adaptive neural network distributed control system for a robotic arm according to claim 2, characterized in that: Step S3 includes the following steps: Step S301: For the new dynamic equation (12), establish a multilayer feedforward neural network as shown in the following equation: f i (x)=W i T σ(V i T x)+e i (13) Where, ε i For the approximate error, satisfying ||ε i ||<ε b , and ε b If positive, σ is the activation function, and W... i and V i These are the weights of a neural network. Step S302: Define f i The estimated value of (x) is shown in the following formula: in, and W respectively i and V i The estimated value, let As the estimation error, the hidden layer gradient is calculated based on the sigmoid activation function. It is given by the following formula: Step S303: Define the estimation error as: in, definition, The above formula contains a matrix of all neural network weights; it can be seen that ||Ψ i || F ≤Ψ 1i Ψ 1i It is a positive number; in equation (14), ξ i It is bounded, therefore we can obtain the following formula: in, and It is a known positive constant; Step S304: The tracking error of the transformed new dynamic equation is defined as: in, For reference trajectory; According to formula (13), the filtered tracking error is defined as Therefore, the new dynamic equation (12) can be expressed as: in, From formula (13), the dynamics of the robotic arm can be expressed as: Step S305: The multilayer feedforward neural network contains the dynamics of the transformed robotic arm E, D, and H. To obtain these unknowns, an adaptive controller is designed as follows: In the formula, Γ r,i , Γ w,i , Γ v,i It is a positive definite matrix. It is a positive gain parameter.

4. The adaptive neural network distributed control system for a robotic arm according to claim 3, characterized in that: Step S4 includes the following steps: Step S401: Design the distributed controller for each robotic arm, as shown in the following formula: in, In the above formula, Θ i For a positive definite matrix, in formula (21) It is caused by material deformation, and satisfies This facilitates the mutual adjustment of internal forces. The parameters in formula (21) satisfy the following conditions: Where, τ min,i for The smallest singular value of i = 1, ..., N. and This will be designed in the proof later; Step S402: Consider the Lyapunov function: Differentiating formula (23) yields: Step S403: Substitute formulas (13) and (18) into formula (24) to obtain: because It is partially symmetrical, therefore it has In addition, there are and PΩ i P -1 =Ω i Substituting formulas (6), (7), and (21) into the above equation, we obtain: Meanwhile, substituting formula (14) into the above formula yields: Since tr(AB) = tr(BA), we can obtain: because Substituting into formula (16) and the adaptive controller (20), we can obtain: Step S404: In formula (25), when the sum of the terms in the parentheses is positive, Since it is negative, extracting the terms in the parentheses of formula (25) yields: in, and Therefore, or When the above conditions are met, the term within the parentheses in formula (25) is negative; and In the defining equation, since Ψ 1i , P u and It is bounded. and It is also bounded, therefore the closed set Δ defined by these variables is... z and It is compact, Beyond compact set Δ z Since time is negative, the system is uniformly eventually bounded.

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