Self-adaptive neural network distributed control system and method for mechanical arm

Abstract

The invention discloses a self-adaptive neural network distributed control system and method for a mechanical arm, and belongs to the technical field of automatic control. Comprising a multi-mechanical-arm system which has position and attitude constraints and is provided with a sensor, a three-dimensional rigid body dynamic model for receiving sensor data from the multi-mechanical-arm system, and a universal time-varying asymmetric barrier function integrated with the three-dimensional rigid body dynamic model, the adaptive neural network is used for estimating unknown kinetic parameters in the system online; and the distributed cooperative tracking controller is designed based on estimation of the adaptive neural network. According to the method, a new universal time-varying asymmetric barrier function of an output constraint multi-mechanical-arm system containing unknown dynamics is constructed, and an online learning module based on a feedforward neural network is established, so that the problem of asymmetric time-varying output constraint of insensitive parameter online estimation is solved; the dynamic estimation problem insensitive to an initial value and limited by asymmetric time-varying output can be solved at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field of automatic control, and in particular relates to a mechanical arm adaptive neural network distributed control system and method. Background Art

[0002] A multi-robot system is a group of two or more robots that collaborate to complete specific tasks. These robots can be homogeneous or heterogeneous, and can have different functions and sensors. Multi-robot systems usually involve communication, coordination, planning, and control between robots in order to perform tasks effectively. Through collaboration, a multi-robot system can complete tasks that are difficult or impossible for a single robot to complete, such as moving large objects, search and rescue in complex environments, etc. Collaborative work can achieve optimal allocation of resources, reduce the execution cost of a single task, and better adapt to diverse tasks and environments. Through the collaborative work of robots with different functions, it can cope with more complex situations.

[0003] In recent years, the technology of cooperative operation of multi-robot systems has made significant progress. However, the design of these cooperative controllers usually requires a precise understanding of the dynamic model of the robot system, which makes the control scheme unable to cope with parameter uncertainty and reduces the stability of the system. In order to overcome this problem, adaptive techniques with the ability to estimate unknown parameters online have been proposed to cope with the uncertainty of system parameters. However, existing adaptive techniques are usually susceptible to external controllers and unmodeled dynamics, and are very sensitive to changes in initial values, which limits their scope of application to a certain extent. Therefore, it is necessary to design a model-free learning controller based on a multilayer feedforward neural network that is insensitive to initial values ​​in order to remove the assumption of linearity of system parameters and improve the robustness of the control scheme.

[0004] In addition, when the multi-robot system performs tasks, it is necessary to ensure the safety of the robots themselves and the surrounding environment. In order to avoid collision or damage, the robot's actions must be within its physical capabilities, such as speed, strength, and range of motion. Therefore, it is necessary to constrain the robot's position and posture in the design of the controller to achieve the purpose of safe production.

[0005] In summary, for output-constrained multi-robot systems with unknown dynamic parameters, there is a need for a manipulator adaptive neural network distributed control system and method 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 the present invention is to provide a robot arm adaptive neural network distributed control system and method, which can simultaneously solve the dynamic estimation problems of insensitivity to initial values ​​and asymmetric time-varying output limitations.

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

[0008] A robotic arm adaptive neural network distributed control system comprises a multi-robotic arm system with position and posture constraints and equipped with sensors, a three-dimensional rigid body dynamics model receiving sensor data from the multi-robotic arm system, a universal time-varying asymmetric potential 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 designed based on the estimation of the adaptive neural network.

[0009] A method for adaptive neural network distributed control of a robot arm is provided, which performs adaptive neural network distributed control of the robot arm based on a control system, and comprises the following steps:

[0010] Step S1: establishing a three-dimensional rigid body dynamics model based on the reference point of the grasped object;

[0011] Step S2: using a universal time-varying asymmetric barrier function to transform the output-limited kinetic equation into a new kinetic equation that takes output boundedness into account;

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

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

[0014] A further improvement of 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 point of the grasped object, as shown in the following formula:

[0016]

[0017] In the formula, Indicates that the grasped object is in a fixed world coordinate system ∑ l The position in and Respectively expressed as Where x is the reference point P in ∑ l The coordinates in the figure are: ω is the angular velocity, which is the same at any position of the rigid body; α is the angular acceleration; represents the inertia matrix, represents the centrifugal-Coriolis matrix, g(X0) represents the gravity matrix, and F ε represents the disturbance force, Ω i represents the grab matrix, represents the control force applied by each robot 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 the l and∑ p The associated rotation matrix, ∑ p Represents the coordinate system of the captured rigid body. For the convenience of notation, let in,

[0021]

[0022] Where (3) is a special Euclidean group, representing 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 grasped object, r p is the reference point P in ∑ p The coordinates in ;

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

[0027]

[0028] Among them J p is the inertia matrix based on P, defined as:

[0029]

[0030] Grab the matrix Ω i for:

[0031]

[0032] Among them, r i The coordinates of each robot arm based on the reference point P;

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

[0034]

[0035] From this we can see that

[0036]

[0037] In robot dynamics, 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 skewly symmetrical.

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

[0039] Step S201: Output restriction in θ represents the rotation angle of the object during motion, -A1 and A2 are time-varying functions, and the proposed universal time-varying asymmetric barrier function is shown as follows:

[0040]

[0041] In formula (8), the initial condition satisfies And there is as well as

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

[0043] Step S202: Deriving Y0 to obtain the following formula:

[0044]

[0045] in,

[0046]

[0047] Step S203: Calculate the second-order derivative of Y0 to obtain the following formula:

[0048]

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

[0050]

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

[0052] Step S205: Multiply both ends of formula (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 formula (12), the matrix E is symmetric and positive definite, and there exist positive constants l1 and l2 such that l1I n ≤E≤l2I n ,and It is skewly symmetric, that is, the new dynamic equation after transformation by the universal time-varying asymmetric potential barrier function still satisfies the characteristics required by the multi-manipulator system.

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

[0060] Step S301: For the new dynamic equation (12), a multi-layer feedforward neural network is established as shown in the following formula:

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

[0062] Among them, ε i is the approximation error, satisfying ||ε i ||<ε b , and ε b is positive, σ is the activation function, W i and V i is the neural network weight,

[0063] Step S302: define f i The estimated value of (x) is as follows:

[0064]

[0065] in, and W i and V i The estimated value of As the estimation error, according to the sigmoid activation function, the hidden layer gradient Given by:

[0066]

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

[0068]

[0069] in,

[0070]

[0071] definition,

[0072]

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

[0074]

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

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

[0077]

[0078] in, is the reference trajectory;

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

[0080]

[0081] in,

[0082] From formula (13), we can see that the dynamics of the robot arm can be expressed as:

[0083]

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

[0085]

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

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

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

[0089]

[0090] in,

[0091]

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

[0093]

[0094] Among them, τ min,i for The minimum singular value of and It will be designed later in the proof; Step S402: Consider the Lyapunov function:

[0095]

[0096] By taking the derivative of formula (23), we can get:

[0097]

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

[0099]

[0100] because is skewly symmetric, so we have In addition, there are and PΩ i P -1 =Ω i , and substitute formula (6), formula (7) and formula (21) into the above formula to obtain:

[0101]

[0102] At the same time, substituting formula (14) into the above formula yields:

[0103]

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

[0105]

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

[0107]

[0108] Step S404: In formula (25), when the sum of the terms in brackets is positive, is negative, extract the terms in brackets of formula (25) to obtain:

[0109]

[0110] in, and Hence,

[0111]

[0112] or

[0113]

[0114] When the above conditions are met, the term in brackets in formula (25) is negative; and In the definition equation, due to Ψ 1i , P u and is bounded, and is also bounded, so the closed set Δ defined by these variables z and It is a tight set. In the case of exceeding the compact set Δ z When is negative, therefore, the system is uniformly ultimately bounded.

[0115] Due to the adoption of the above technical solution, the technical progress achieved by the present invention is:

[0116] The present invention proposes a robotic arm adaptive neural network distributed control system and method, constructs a new universal time-varying asymmetric potential barrier function for a multi-robotic arm system containing unknown dynamics and output constraints, and establishes an online learning module based on a feedforward neural network, which realizes the solution of the asymmetric time-varying output constraint problem of online estimation of insensitive parameters, and can simultaneously solve the asymmetric time-varying output limitation and the dynamic estimation problem that is insensitive to initial values.

[0117] The present invention uses an online learning module based on a multi-layer feedforward neural network to estimate the unknown geometric and inertial parameters in the system, and establishes a distributed tracking control scheme to ensure that the multi-manipulator system performs tracking control tasks within the constraints. The learning module established by the present invention can uniformly estimate all unknown quantities in the system, simplify the design of the controller, and the consideration of output constraints meets the equipment posture restrictions and safe operation requirements.

[0118] The present invention constructs a new universal asymmetric time-varying potential barrier function for multi-robotic arm systems, which can directly constrain the coordinates of the reference point, avoiding the problem of overly conservative initial conditions of the error constraint. While keeping the original properties of the dynamic equation unchanged, the asymmetric time-varying output limitation problem is converted into a bounded problem through transformation.

[0119] The present invention aims at the dynamics of the manipulator using the universal asymmetric time-varying barrier function transformation, and adopts an online learning module based on a multi-layer feedforward neural network. The module is insensitive to the change of the initial value and allows a unified online estimation of all parameters of the manipulator, thereby simplifying the design of the controller.

[0120] The present invention adopts a distributed control strategy for the collaborative tracking task of a multi-manipulator system. The strategy can comprehensively consider the position parameters of the manipulators and the grasping position problems, and set multiple manipulator positions to perform trajectory tracking tasks within a limited range in the presence of external interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 is a flow chart of the adaptive neural network distributed control method for a robotic arm of the present invention;

[0122] Figure 2 is the composite error norm ||z(t)|| and the rotation matrix error in the present invention Schematic diagram of

[0123] Figure 3 It is a schematic diagram of the tracking situation of the reference point coordinate x0 in the present invention;

[0124] Figure 4 is a schematic diagram of tracking the angle θ of the object rotation in the present invention;

[0125] Figure 5 It is a schematic diagram of the weight change of the multi-layer feedforward neural network in the present invention. DETAILED DESCRIPTION

[0126] The present invention is further described in detail below in conjunction with embodiments:

[0127] Example 1

[0128] The present embodiment provides a robotic arm adaptive neural network distributed control system, including a multi-robotic arm system with position and posture 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 potential 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 collaborative tracking controller designed based on the estimation of the adaptive neural network.

[0129] Among them, the multi-manipulator system consists of multiple manipulators. Each manipulator is subject to position and posture constraints during operation. The manipulators are equipped with sensors for real-time monitoring of joint angles, speeds, accelerations, and possible external forces. The manipulators exchange information such as coordinates, speeds, and disturbances through communication. The three-dimensional rigid body dynamics model uses the Lagrangian equation of manipulator motion to represent the cooperative task motion equation in three-dimensional space. The motion equation can also represent the motion of an object on a plane. The model receives sensor data from the multi-manipulator system, simulates the dynamic behavior of the manipulator, and provides the control system with the expected kinematics and external force response of the manipulator. The universal time-varying asymmetric barrier function is integrated with the three-dimensional rigid body dynamics model to process and control output restrictions to ensure that the movement of the manipulator does not exceed the preset safety range. The time-varying and asymmetric constraints are taken into account, which improves the flexibility and safety of the control strategy. The learning module composed of an adaptive neural network can estimate the unknown dynamic parameters in the system online, and continuously adjust and optimize the parameters of the dynamic model by learning the difference between the actual behavior of the manipulator and the model prediction. For common operating scenarios such as industrial production, logistics warehousing, and medical care, the control objectives of robotic arm grasping and handling with environmental and physical constraints are established, and a distributed collaborative tracking controller is established based on the control objectives. 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, and works with other controllers to achieve coordinated movement of the group.

[0130] Example 2

[0131] This embodiment provides a method for distributed control of a robot arm using an adaptive neural network. The method performs distributed control of a robot arm using an adaptive neural network based on the control system of Embodiment 1, including the following steps:

[0132] Step S1: For the operation scenarios describing the grasping and handling of multiple robotic arms, such as parts assembly, cargo sorting, and surgical assistance, a three-dimensional rigid body dynamics model is established based on the reference point of the grasped object, which specifically includes the following steps:

[0133] Step S101: Establish a three-dimensional rigid body dynamics model based on the reference point of the grasped object, as shown in the following formula:

[0134]

[0135] In the formula, Indicates that the grasped object is in a fixed world coordinate system ∑ l The position in and Respectively expressed as Where x is the reference point P in ∑ l The coordinates in the figure are: ω is the angular velocity, which is the same at any position of the rigid body; α is the angular acceleration; represents the inertia matrix, represents the centrifugal-Coriolis matrix, g(X0) represents the gravity matrix, and F ε represents the disturbance force, Ω i represents the grab matrix, Represents the control force applied by each robot 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 the l and∑ p The associated rotation matrix, ∑ p Represents the coordinate system of the captured rigid body. For the convenience of notation, let in,

[0139]

[0140] Where (3) is a special Euclidean group, representing 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 grasped object, r p is the reference point P in ∑ p The coordinates in ;

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

[0145]

[0146] Among them J p is the inertia matrix based on P, defined as:

[0147]

[0148] Grab the matrix Ω i for:

[0149]

[0150] Among them, r i The coordinates of each robot arm based on the reference point P;

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

[0152]

[0153] From this we can see that

[0154]

[0155] In robot dynamics, 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 skewly symmetrical;

[0156] Step S2: Due to environmental and physical limitations, the motion posture of the robot arm in operation is usually limited to a certain extent. The output-constrained dynamic equation is transformed into a new dynamic equation that takes into account the boundedness of the output using a universal time-varying asymmetric potential barrier function, which specifically includes the following steps:

[0157] Step S201: Output restriction in θ represents the rotation angle of the object during motion, -A1 and A2 are time-varying functions, and the proposed universal time-varying asymmetric barrier function is shown as follows:

[0158]

[0159] In formula (8), the initial condition satisfies And there is as well as

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

[0161] Step S202: Deriving Y0 to obtain the following formula:

[0162]

[0163] in,

[0164]

[0165] Step S203: Calculate the second-order derivative of Y0 to obtain the following formula:

[0166]

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

[0168]

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

[0170] Step S205: Multiply both ends of formula (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 formula (12), the matrix E is symmetric and positive definite, and there exist positive constants l1 and l2 such that l1In ≤E≤l2I n ,and It is skewly symmetric, that is, the new dynamic equation after transformation by the universal time-varying asymmetric potential barrier function still satisfies the characteristics that the multi-manipulator system needs to satisfy;

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

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

[0179] Step S301: For the new dynamic equation (12), a multi-layer feedforward neural network is established as shown in the following formula:

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

[0181] Among them, ε i is the approximation error, satisfying ||ε i ||<ε b , and ε b is positive, σ is the activation function, W i and V i is the neural network weight,

[0182] Step S302: define f i The estimated value of (x) is as follows:

[0183]

[0184] in, and W i and V i The estimated value of As the estimation error, according to the sigmoid activation function, the hidden layer gradient Given by:

[0185]

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

[0187]

[0188] in,

[0189]

[0190] definition,

[0191]

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

[0193]

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

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

[0196]

[0197] in, is the reference trajectory;

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

[0199]

[0200] in,

[0201] From formula (13), we can see that the dynamics of the robot arm can be expressed as:

[0202]

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

[0204]

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

[0206] Step S4: Design a distributed cooperative tracking controller and verify the stability of the system through the Lyapunov function to achieve the purpose of grasping and moving objects. Specifically, it includes the following steps:

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

[0208]

[0209] in,

[0210]

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

[0212]

[0213] Among them, τ min,i for The minimum singular value of and This will be devised later in the proof;

[0214] Step S402: Consider the Lyapunov function:

[0215]

[0216] By taking the derivative of formula (23), we can get:

[0217]

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

[0219]

[0220] because is skewly symmetric, so we have In addition, there are and PΩ i P -1 =Ω i, and substitute formula (6), formula (7) and formula (21) into the above formula to obtain:

[0221]

[0222] At the same time, substituting formula (14) into the above formula yields:

[0223]

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

[0225]

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

[0227]

[0228] Step S404: In formula (25), when the sum of the terms in brackets is positive, is negative, extract the terms in brackets of formula (25) to obtain:

[0229]

[0230] in, and Hence,

[0231]

[0232] or

[0233]

[0234] When the above conditions are met, the term in brackets in formula (25) is negative; and In the definition equation, due to Ψ 1i , P u and is bounded, and is also bounded, so the closed set Δ defined by these variables z and It is a tight set. In the case of exceeding the compact set Δ z When is negative, therefore, the system is uniformly ultimately bounded.

[0235] That is, due to and initial conditions It can be obtained that V is bounded. In formula (26), due to and are all bounded, thus z is bounded. From formula (17), is bounded, so Y0 is bounded. Combined with P -1 and The boundedness of u i is bounded. Therefore, all signals within the closed loop of the system are bounded.

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

[0237] Therefore, the collaborative controller proposed in the present invention can solve problems such as the robot arm's motion posture constraints caused by environmental and physical constraints, and the unknown mass and shape of the grasped object that make it impossible to accurately describe the grasping model, and can realize grasping and handling tasks for unknown objects.

[0238] Experimental example

[0239] The experimental example uses a group of robots (N = 6) to collaboratively carry a rocket body. The performance of the proposed online learning module and collaborative operation controller is verified by the following simulation. Consider a cylindrical rigid body controlled by 6 robots, tracking a periodic trajectory with ideal angular velocity and linear velocity. The parameters in the tracking task are set to m = 8.56 kg, r = 0.32 m, h = 0.1 m, ρ = 266 kg / m 3 ,J xx =0.23kg·m 2 ,J yy =0.23kg·m 2 ,J zz =0.43kg·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:

[0241]

[0242] The simulation step size is set to h = 0.01s. In order to keep the rotation matrix within the Lie group SO(3), an exponential mapping is used. Considering the physical environment and safe operation constraints, There are 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 the neural network, the hidden layer has 12 neurons and the activation function is f(x)=1 / (1+e -x ), and The elements in come from the standard normal distribution N(0,1). Set γ 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 to Ψ 1i =225,θ i =2I6. The internal force caused by material deformation is:

[0248]

[0249] The simulation results of this example are as follows Figure 2-Figure 5 shown. Figure 2 The tracking error of the collaborative task and the tracking of the rotation matrix are given, and it can be seen that the proposed distributed controller has good tracking performance. Figure 3 and Figure 4 It can be seen that when the attitude and coordinates of the controlled object are restricted, the proposed controller allows the controlled object to be within the restricted range. Figure 5 It shows the change of neural network weights by obtaining and The dynamics of all unknown objects in the system can be obtained. Therefore, the proposed adaptive collaborative controller based on multi-layer feedforward neural network can well realize the multi-manipulator gripping function.

[0250] In summary, the present invention can effectively improve the control accuracy, robustness and collaborative operation capability of the multi-robot system. The proposed example can be applied to a variety of production operation scenarios and has important engineering application value.

[0251] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A robotic arm adaptive neural network distributed control system, characterized in that: It includes a multi-manipulator system equipped with sensors with position and posture constraints, a three-dimensional rigid body dynamics model that receives sensor data from the multi-manipulator system, a general time-varying asymmetric potential 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 collaborative tracking controller designed based on the estimation of the adaptive neural network.

2. A distributed control method of a robotic arm using an adaptive neural network, characterized in that: The control system according to claim 1 performs adaptive neural network distributed control of a robot arm, comprising the following steps: Step S1: establishing a three-dimensional rigid body dynamics model based on the reference point of the grasped object; Step S2: using a universal time-varying asymmetric barrier function to transform the output-limited kinetic equation into a new kinetic equation that takes output boundedness into account; Step S3: Establishing a learning module based on a multi-layer feedforward neural network to estimate unknown dynamic information in the system; Step S4: Design a distributed cooperative tracking controller and verify the stability of the system through the Lyapunov function.

3. The method for distributed control of a robot arm using an adaptive neural network according to claim 2, characterized in that: The step S1 comprises the following steps: Step S101: Establish a three-dimensional rigid body dynamics model based on the reference point of the grasped object, as shown in the following formula: In the formula, Indicates that the grasped object is in a fixed world coordinate system ∑ l The position in and Respectively expressed as Where x is the reference point P in ∑ l The coordinates in the figure are: ω is the angular velocity, which is the same at any position of the rigid body; α is the angular acceleration; represents the inertia matrix, represents the centrifugal-Coriolis matrix, g(X0) represents the gravity matrix, and F ε represents the disturbance force, Ω i represents the grab matrix, represents the control force applied by each robot 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 l and∑ p The associated rotation matrix, ∑ p Represents the coordinate system of the captured rigid body. For the convenience of notation, let in, Where (3) is a special Euclidean group, representing the set of transformation matrices; Step S103: In rigid body dynamics, the inertia matrix is ​​defined as: Where m is the mass of the grasped object, r p is the reference point P in ∑ p The coordinates in ; The centrifugal-Coriolis matrix is ​​defined as: Among them J p is the inertia matrix based on P, defined as: Grab the matrix Ω i for: Among them, r i The coordinates of each robot arm based on the reference point P; Due to the characteristics of the grab matrix, Ω(X0,r i ) is: From this we can see that In robot dynamics, 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 skewly symmetrical.

4. The method for distributed control of a robot arm using an adaptive neural network according to claim 3, characterized in that: The step S2 comprises the following steps: Step S201: Output restriction in θ represents the rotation angle of the object during motion, -A1 and A2 are time-varying functions, and the proposed universal time-varying asymmetric barrier function is shown as follows: In formula (8), the initial condition satisfies And there is as well as From the above formula, we can see that when When Y0 approaches -A1 or A2, it approaches infinity. Therefore, when the initial conditions are met, The restricted problem of is transformed into the bounded problem of Y0; Step S202: Deriving Y0 to obtain the following formula: in, Step S203: Calculate the second-order derivative of Y0 to obtain the following formula: Step S204: Substituting formula (9) and formula (10) into formula (1) yields the following formula: In formula (11), Defined as And B1=[b1,b2,b3,b4,b5,b6] T , And thus defined K=dP / dt, we know ||P|| F ≤P u , P u is a positive number; Step S205: Multiply both ends of formula (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 formula (12), the matrix E is symmetric and positive definite, and there exist positive constants l1 and l2 such that l1I n ≤E≤l2I n ,and It is skewly symmetric, that is, the new dynamic equation after transformation by the universal time-varying asymmetric potential barrier function still satisfies the characteristics that the multi-manipulator system needs to satisfy.

5. The method for distributed control of a robot arm using an adaptive neural network according to claim 4, characterized in that: The step S3 comprises the following steps: Step S301: For the new dynamic equation (12), a multi-layer feedforward neural network is established as shown in the following formula: f i (x)=W i T σ(V i T x)+e i (13) Among them, ε i is the approximation error, satisfying ||ε i ||<ε b , and ε b is positive, σ is the activation function, W i and V i is the neural network weight, Step S302: define f i The estimated value of (x) is as follows: in, and W i and V i The estimated value of As the estimation error, according to the sigmoid activation function, the hidden layer gradient Given by: Step S303: define the estimation error as: in, definition, The above formula contains the matrix of all neural network weights; it can be seen that ||Ψ i || F ≤Ψ 1i , where Ψ 1i is a positive number; in formula (14), ξ i is bounded, so we can get the following formula: in, and is a known positive constant; Step S304: The tracking error of the converted new dynamic equation is defined as: in, is the reference trajectory; According to formula (13), the filtered tracking error is defined as Therefore, the new kinetic equation (12) can be expressed as: in, From formula (13), we can see that the dynamics of the robot arm can be expressed as: Step S305: The multilayer feedforward neural network contains the transformed dynamics of the robot arms E, D and H. To obtain these unknown quantities, an adaptive controller is designed as follows: In the formula, Γ r,i , Γ w,i , Γ v,i is a positive definite matrix, is the positive gain parameter, 6. The method for distributed control of a robot arm using an adaptive neural network according to claim 5, characterized in that: The step S4 comprises the following steps: Step S401: Design a distributed controller for each robotic arm, as shown in the following formula: in, In the above formula, Θ i is a positive definite matrix, and in formula (21) is caused by material deformation, satisfying It is helpful for the mutual regulation of internal forces. The parameters in formula (21) satisfy the following conditions: Among them, τ min,i for The minimum singular value of and This will be designed in a later proof; Step S402: Consider the Lyapunov function: By taking the derivative of formula (23), we can get: Step S403: Substitute formula (13) and formula (18) into formula (24) to obtain: because is skewly symmetric, so we have In addition, there are and PΩ i P -1 =Ω i , and substitute formula (6), formula (7) and formula (21) into the above formula to obtain: At the same time, substituting formula (14) into the above formula yields: Since tr(AB)=tr(BA), we can get: because Substituting into formula (16) and adaptive controller (20) we can get: Step S404: In formula (25), when the sum of the terms in brackets is positive, is negative, extract the terms in brackets of formula (25) to obtain: in, and Hence, or When the above conditions are met, the term in brackets in formula (25) is negative; and In the definition equation, due to Ψ 1i , P u and is bounded, and is also bounded, so the closed set Δ defined by these variables z and It is a tight set. In the case of exceeding the compact set Δ z When is negative, therefore, the system is uniformly ultimately bounded.

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