A multi-robot cooperative immune network control method

Abstract

This invention discloses a multi-robot collaborative immune network control method. First, a single-robot time-varying quadratic optimization model is established based on the kinematics of the single robot. Then, a multi-robot collaborative controller is designed based on decision variables for real-time recursion of a recursive neural network. Finally, a fitness evaluation criterion and a recursive error compensation term are integrated into the immune recursive network, and a vaccine operation is introduced to output the optimal joint angle. This invention solves the joint angle during multi-robot trajectory tracking, enabling adaptive tracking of different trajectories by multiple robots. This improves the precision, coordination, and repeatability of multi-robot control, and is of great significance for achieving multi-robot collaborative control in intelligent manufacturing.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing automation, and in particular to a multi-robot collaborative immune network control method. Background Art

[0002] Collaborative control technology is the key to ensuring the safe and efficient operation of multiple robots. It has always been a difficult point in the field of industrial robotics technology and is particularly important for complex systems of multiple robots. High-precision collaborative control enables robots to execute predetermined paths and achieve adaptive tracking of different trajectories, thereby reducing tracking errors and improving the accuracy, coordination and repeatability of multi-robot control.

[0003] With the rapid development of intelligent manufacturing, robots have become an indispensable component of automated production lines. Compared to single robots, multi-robot systems offer advantages such as high redundant degrees of freedom, strong coupling, and flexible tracking, attracting significant attention and application in areas such as collaborative welding and handling.

[0004] Traditional pseudo-inverse methods for solving robot inverse kinematics require matrix inversion. However, at certain moments, the robot may move to singular positions. Numerical algorithms for solving inverse kinematics cannot guarantee accurate solutions, are complex, and are unsuitable for online control. In recent years, intelligent optimization algorithms have been applied to solving inverse kinematics. By rationally setting basic algorithm parameters or improving algorithm structure, the relevant factors involved in solving the real-time joint angles during multi-robot trajectory tracking are used as optimization indicators and an objective function is established. Through multiple iterations of the optimization algorithm, the optimal joint angles with the smallest trajectory tracking error are ultimately obtained. While these improved intelligent algorithms speed up the solution, they lack consideration of the collaborative control accuracy and repeatability of the joint angles during the collaborative control process. Therefore, research on optimization methods for multi-robot collaborative immune network control is crucial for ensuring high-precision collaborative control of multiple robots, achieving repeatable motion, and improving efficiency. Summary of the Invention

[0005] The purpose of the present invention is to provide a multi-robot collaborative immune network control method to improve the problems of large tracking error, easy collision with obstacles, easy generation of joint angle drift during multi-robot collaborative control, thereby reducing the production cycle and manufacturing cost.

[0006] In order to achieve the above object, the present invention provides a multi-robot cooperative immune network control method, comprising the following steps:

[0007] A single-robot time-varying quadratic optimization model is established based on the kinematics of the single robot, wherein the single-robot time-varying quadratic optimization model includes a convex set of cooperative control target description, equality constraints for trajectory tracking, inequality constraints for real-time obstacle avoidance, and joint physical constraints;

[0008] Design a multi-robot collaborative controller based on decision variables, including the multi-robot time-varying quadratic optimization model and the definition of decision variables;

[0009] Design of cooperative immune network control algorithm based on fitness evaluation criteria and recursive error compensation, including network topology design, fitness evaluation criteria description, recursive error compensation term design and vaccine operation;

[0010] Real-time solution of joint angles for multi-robot trajectory tracking based on improved immune optimization algorithm.

[0011] Optionally, the single-robot time-varying quadratic optimization model is:

[0012]

[0013]

[0014]

[0015]

[0016] Where, represents the i-th joint angle of the j-th robot, represents the angular velocity of the i-th joint of the j-th robot, and q j ={q1 j ,q2 j ,…,q6 j}, j∈{1,2,…,N}, i∈{1,2,…,6}; p j =λ j (q j (t)-q j (0)), λ j is the joint offset coefficient of robot j;

[0017] The collaborative control objective is described as:

[0018] φ(q 1 (t))=…=φ(q N (t))=r d (t)

[0019] Where φ() is the nonlinear function mapping from the action space to the joint space, r d is the expected trajectory;

[0020] By taking its derivative, the collaborative control target is transformed from the position layer to the speed layer, that is:

[0021]

[0022] Where, J j is the Jacobian matrix of robot j; is the expected speed;

[0023] The equality constraints for the trajectory tracking are:

[0024]

[0025] Where, α j is the position error feedback coefficient of robot j;

[0026] The real-time obstacle avoidance inequality constraints include a single pair of obstacle-robot critical point obstacle avoidance constraints, robot j's obstacle avoidance speed, robot j's safety speed b j , the inequality constraint for real-time obstacle avoidance is:

[0027]

[0028] Where D j (q j )=[L1(q j ),L2(q j ),...,L l (q j )] T , l is the logarithm of the obstacle-manipulator critical point;

[0029] The single pair of obstacle-critical point obstacle avoidance constraints is:

[0030]

[0031] The obstacle avoidance speed of robot j includes the speed escape vector e of robot j j And matrix L, the obstacle avoidance speed of the robot j is:

[0032]

[0033] The velocity escape vector e of robot j j for:

[0034]

[0035] Where, is the operation space coordinate of obstacle o, is the operating space coordinate of the critical point c on a certain arm of robot j;

[0036] The matrix L is:

[0037] L(q j )=-sgn(e j )ΘJc (q j )

[0038] Where sgn(·) represents the sign function; J c is the Jacobian matrix at the critical point c; the operation rules of the symbol Θ are defined as follows:

[0039]

[0040] Where, represents the x-dimensional column vector, Representation matrix row x;

[0041] The safe speed b of robot j j Including the distance smoothing function s(d), the safe speed b of robot j j for:

[0042]

[0043] Where d is the distance between a robot arm and the obstacle, d1 and d2 are the inner and outer limits of the obstacle's influence space, respectively;

[0044] The distance smoothing function s(d) is:

[0045]

[0046] The convex set of the joint physical constraints includes joint angle constraints and joint angular velocity constraints. The convex set of the joint physical constraints is:

[0047]

[0048] Where, β is a positive level change parameter;

[0049] The joint angle limits are:

[0050]

[0051] The joint angular velocity limit is:

[0052]

[0053] Where, and are the upper and lower bounds of the joint angle and joint angular velocity, respectively.

[0054] Optionally, the multi-robot time-varying quadratic optimization model is defined as follows:

[0055]

[0056] stGz=R

[0057] Az≤B

[0058]

[0059] Where,

[0060]

[0061] ||·||2 represents the vector's two-norm, represents the square of the vector 2 norm, m represents the dimension of the robot end effector operation space, and n represents the dimension of the robot joint space;

[0062]

[0063]

[0064]

[0065] The decision variable u is defined as follows:

[0066] u=[zgh] T ∈R Nn+Nm+Nlm

[0067] Where g is the equality constraint for multi-robot trajectory tracking, and h is the inequality constraint for multi-robot real-time obstacle avoidance.

[0068] Optionally, the network topology design adopts a recursive form of a recursive neural network, by defining the optimization objective function as the antigen and the joint angle obtained by the inverse kinematics solution as the antibody, and designing a recursive immune network including an input layer, a tracking hidden layer, a compensation hidden layer, and an output layer;

[0069] The input layer is the joint angles of multiple robots. The tracking hidden layer defines the actual working space s of the robot according to the joint angles and evaluates it according to the fitness criterion f(). The recursive error e is determined according to the evaluation output, and then the error compensation term Γ(u) is generated after the compensation function Γ() of the compensation hidden layer is activated. k ), based on the error compensation term Γ(u k ) is extracted as vaccine v ac , and at the same time, it realizes error compensation through the network loop recursion, and the optimal vaccine v after the recursion is completed best The input layer is seeded through the outer loop, and the output layer is used to output the optimal joint angular velocity of the multi-robot after the inner loop iteration is completed, and the optimal joint angle of the multi-robot is obtained by integration.

[0070] Optionally, the fitness evaluation criterion description includes the actual workspace s of the robot, and the fitness evaluation criterion f() is:

[0071]

[0072] Where s∈R η (η=Nn+Nm+Nlm), and its upper and lower bounds are defined as follows:

[0073]

[0074] The actual working space s of the robot is:

[0075] s=u-(Mu+σ)

[0076] Where,

[0077] Optionally, the recursive error compensation term design includes the recursive error e calculation, the error compensation term Γ(u k ) is calculated, the recursive error e is:

[0078] e(u k )=u k -f(s k )

[0079] Where k is the iteration step length;

[0080] The error compensation term Γ(u k )for:

[0081] Γ(u k )=(M T +I)e(u k )

[0082] Where I is the identity matrix and Γ() is the compensation activation function.

[0083] Optionally, the vaccine operation includes the following steps:

[0084] Vaccine selection, the error compensation term Γ(u k ) for vaccine extraction, namely:

[0085]

[0086] Vaccination, introduction of the vaccine ac , perform the network loop recursion of the decision variable u, that is:

[0087] u k+1 =u k -v ac ·Γ(u k ).

[0088] Optionally, the real-time solution of joint angles for multi-robot trajectory tracking based on the improved immune optimization algorithm includes the following steps:

[0089] Step a: Convert the multi-robot intelligent collaborative control objective into a QP problem;

[0090] Input antibody q into the input layer 1 (t),q 2 (t),…,q N (t) and vaccine v ac (t);

[0091] Step b: Calculate the actual working space s of the robot, and then obtain the output value of the tracking hidden layer after evaluating it with the fitness criterion f();

[0092] Step c: Calculate the recursive error e and pass it to the compensation hidden layer to obtain the compensation hidden layer output as the error compensation term Γ(u k );

[0093] Step d: The error compensation term Γ(u k ) extract as the vaccine vac;

[0094] Step e: Based on the error compensation term Γ(u k ) and the vaccine vac and recursively perform the next generation of the decision variable u;

[0095] Step f: Determine whether the recursion meets the given recursive error accuracy or number of iterations. If so, output the optimal vaccine v best and the optimal joint angular velocity of multiple robots and the optimal joint angle q j , otherwise return to step d;

[0096] Step g: Determine whether the multi-robots have completed the collaborative task. If so, end the task. Otherwise, return to step b and use the optimal vaccine v best Vaccination of the input layer is carried out.

[0097] The present invention has the following beneficial effects:

[0098] (1) Based on the kinematic analysis of robots, the present invention transforms the collaborative control problem of multiple robots into a quadratic optimization problem, which can avoid the complex inversion of matrices in inverse kinematics and improve the efficiency of solving the optimal joint angles of multiple robots.

[0099] (2) Based on the good real-time optimization performance of recursive neural networks and the excellent information processing mechanism of artificial immunity, the present invention transforms the collaborative control problem of multiple robots into a problem-solving method of recursive neural networks, constructs a collaborative immune network controller, realizes the solution of joint angles in the process of multi-robot trajectory tracking, and satisfies the adaptive tracking of multiple robots on different trajectories.

[0100] (3) The present invention uses the immune neural network to track the recursive error generated by the hidden layer output, and obtains the error compensation term by compensating the hidden layer activation through the network. Through network recursion and vaccination of the network input layer, the accuracy of obtaining the optimal joint angle of multiple robots is improved, thereby improving the accuracy, coordination and repeatability in the control of multiple robots, which is of great significance to the realization of intelligent manufacturing automation. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0102] Figure 1 A flowchart of a multi-robot collaborative immune network control method provided by an embodiment of the present invention;

[0103] Figure 2 A diagram of a six-degree-of-freedom robot model provided by an embodiment of the present invention;

[0104] Figure 3 A block diagram of multi-robot collaborative control provided by an embodiment of the present invention;

[0105] Figure 4 A topological structure diagram of a recursive immune network provided by an embodiment of the present invention;

[0106] Figure 5 A flowchart for solving a multi-robot collaborative control problem based on CINCABEC provided in an embodiment of the present invention;

[0107] Figure 6a A comparison chart of D-shaped trajectory tracking corresponding to the three algorithms provided in the embodiment of the present invention;

[0108] Figure 6b The vaccine value of CINCABEC corresponding to the D-shaped trajectory provided in the embodiment of the present invention;

[0109] Figure 7a A tracking comparison diagram of the quincunx trajectory corresponding to the three algorithms provided in the embodiment of the present invention;

[0110] Figure 7b The vaccine value of CINCABEC corresponding to the plum blossom trajectory provided in the embodiment of the present invention;

[0111] Figure 8a A schematic diagram of three-dimensional tracking of a D-shaped trajectory of two robots provided in an embodiment of the present invention;

[0112] Figure 8b A schematic diagram of three-dimensional tracking of a quincunx-shaped trajectory of two robots provided in an embodiment of the present invention;

[0113] Figure 9 Three-dimensional tracking of circular trajectories of three robots provided by an embodiment of the present invention;

[0114] Figure 10 Three-dimensional tracking of a square trajectory of four robots provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0115] To make the purpose and technical solutions of the embodiments of the present invention more clear, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0116] like Figure 1 As shown, a multi-robot collaborative immune network control method of the present invention includes the following steps:

[0117] Step S1: establishing a single robot time-varying quadratic optimization model based on the single robot kinematics, wherein the single robot time-varying quadratic optimization model includes a convex set of collaborative control target description, trajectory tracking equality constraints, real-time obstacle avoidance inequality constraints, and joint physical constraints;

[0118] Step S2: Designing a multi-robot collaborative controller based on the decision variables, including the multi-robot time-varying quadratic optimization model and the definition of the decision variables;

[0119] Step S3: designing a cooperative immune network control algorithm based on the fitness evaluation criterion and recursive error compensation, including network topology design, fitness evaluation criterion description, recursive error compensation term design and vaccine operation;

[0120] Step S4: Solve the joint angles of multi-robot trajectory tracking in real time based on the improved immune optimization algorithm.

[0121] This embodiment first establishes a single-robot time-varying quadratic optimization model based on single-robot kinematics, then designs a multi-robot collaborative controller based on decision variables for real-time recursion of recursive neural networks, and finally outputs the optimal joint angle based on a collaborative immune network control algorithm with error compensation.

[0122] like Figure 2 、 Figure 3 As shown, the single robot time-varying quadratic optimization model is:

[0123]

[0124]

[0125]

[0126]

[0127] Where, represents the i-th joint angle of the j-th robot, represents the angular velocity of the i-th joint of the j-th robot, and q j ={q1 j ,q2 j ,…,q6 j}, j∈{1,2,…,N}, i∈{1,2,…,6}; p j =λ j (q j (t)-q j (0)), λ j is the joint offset coefficient of robot j;

[0128] The collaborative control objective is described as:

[0129] φ(q 1 (t))=…=φ(q N (t))=r d (t)

[0130] Where φ() is the nonlinear function mapping from the action space to the joint space, r d is the expected trajectory;

[0131] By taking its derivative, the collaborative control target is transformed from the position layer to the speed layer, that is:

[0132]

[0133] Where, J j is the Jacobian matrix of robot j; is the expected speed;

[0134] The equality constraints for the trajectory tracking are:

[0135]

[0136] Where, α j is the position error feedback coefficient of robot j;

[0137] The real-time obstacle avoidance inequality constraints include a single pair of obstacle-robot critical point obstacle avoidance constraints, robot j's obstacle avoidance speed, robot j's safety speed b j , the inequality constraint for real-time obstacle avoidance is:

[0138]

[0139] Where D j (q j )=[L1(q j ),L2(q j ),...,L l (q j )] T , l is the logarithm of the obstacle-manipulator critical point;

[0140] The single pair of obstacle-critical point obstacle avoidance constraints is:

[0141]

[0142] The obstacle avoidance speed of robot j includes the speed escape vector e of robot j j And matrix L, the obstacle avoidance speed of the robot j is:

[0143]

[0144] The velocity escape vector e of robot j j for:

[0145]

[0146] Where, is the operation space coordinate of obstacle o, is the operating space coordinate of the critical point c on a certain arm of robot j;

[0147] The matrix L is:

[0148] L(q j )=-sgn(e j )ΘJ c (q j )

[0149] Where sgn(·) represents the sign function; J c is the Jacobian matrix at the critical point c; the operation rules of the symbol Θ are defined as follows:

[0150]

[0151] Where, represents the x-dimensional column vector, Representation matrix row x;

[0152] The safe speed b of robot j j Including the distance smoothing function s(d), the safe speed b of robot j j for:

[0153]

[0154] Where d is the distance between a robot arm and the obstacle, d1 and d2 are the inner and outer limits of the obstacle's influence space, respectively;

[0155] The distance smoothing function s(d) is:

[0156]

[0157] The convex set of the joint physical constraints includes joint angle constraints and joint angular velocity constraints. The convex set of the joint physical constraints is:

[0158]

[0159] Where, β is a positive level change parameter;

[0160] The joint angle limits are:

[0161]

[0162] The joint angular velocity limit is:

[0163]

[0164] Where, and are the upper and lower bounds of the joint angle and joint angular velocity, respectively.

[0165] The multi-robot time-varying quadratic optimization model is defined as follows:

[0166]

[0167] stGz=R

[0168] Az≤B

[0169]

[0170] Where,

[0171]

[0172] ||·||2 represents the vector's two-norm, represents the square of the vector 2 norm, m represents the dimension of the robot end effector operation space, and n represents the dimension of the robot joint space;

[0173]

[0174]

[0175]

[0176] The decision variable u is defined as follows:

[0177] u=[zgh] T ∈R Nn+Nm+Nlm

[0178] Where g is the equality constraint for multi-robot trajectory tracking, and h is the inequality constraint for multi-robot real-time obstacle avoidance.

[0179] like Figure 4 As shown, the network topology design adopts the recursive form of recursive neural network. By defining the optimization objective function as antigen and the joint angle obtained by inverse kinematics as antibody, a recursive immune network including input layer, tracking hidden layer, compensation hidden layer and output layer is designed.

[0180] The input layer is the joint angles of multiple robots. The tracking hidden layer defines the actual working space s of the robot according to the joint angles and evaluates it according to the fitness criterion f(). The recursive error e is determined according to the evaluation output, and then the error compensation term Γ(u) is generated after the compensation function Γ() of the compensation hidden layer is activated. k ), based on the error compensation term Γ(u k ) is extracted as vaccine v ac , and at the same time, it realizes error compensation through the network loop recursion, and the optimal vaccine v after the recursion is completed best The input layer is seeded through the outer loop, and the output layer is used to output the optimal joint angular velocity of the multi-robot after the inner loop iteration is completed, and the optimal joint angle of the multi-robot is obtained by integration.

[0181] The fitness evaluation criterion description includes the actual workspace s of the robot, and the fitness evaluation criterion f() is:

[0182]

[0183] Where s∈R η (η=Nn+Nm+Nlm), and its upper and lower bounds are defined as follows:

[0184]

[0185] The actual working space s of the robot is:

[0186] s=u-(Mu+σ)

[0187] Where,

[0188] The recursive error compensation term design includes the recursive error e calculation, the error compensation term Γ(u k ) is calculated, the recursive error e is:

[0189] e(u k )=u k -f(s k )

[0190] Where k is the iteration step length;

[0191] The error compensation term Γ(u k )for:

[0192] Γ(u k )=(M T +I)e(u k )

[0193] Where I is the identity matrix and Γ() is the compensation activation function.

[0194] The vaccine operation comprises the following steps:

[0195] Vaccine selection, the error compensation term Γ(u k ) for vaccine extraction, namely:

[0196]

[0197] Vaccination, introduction of the vaccine ac , perform the network loop recursion of the decision variable u, that is:

[0198] u k+1 =u k -v ac ·Γ(u k )

[0199] Then error compensation is achieved and the optimal vaccine v after the recursion is completed best The network input layer is inoculated through the outer loop, so that the network output layer is obtained to realize the optimal joint angular velocity output of the multi-robot after the inner loop iteration is completed, and the optimal joint angle of the multi-robot is obtained by integration.

[0200] like Figure 5 As shown, the real-time solution of joint angles for multi-robot trajectory tracking based on the improved immune optimization algorithm includes the following steps:

[0201] Step a: Convert the multi-robot intelligent collaborative control objective into a QP problem;

[0202] Input antibody q into the input layer 1 (t),q 2 (t),…,q N (t) and vaccine v ac (t);

[0203] Step b: Calculate the actual working space s of the robot, and then obtain the output value of the tracking hidden layer after evaluating it with the fitness criterion f();

[0204] Step c: Calculate the recursive error e and pass it to the compensation hidden layer to obtain the compensation hidden layer output as the error compensation term Γ(u k );

[0205] Step d: The error compensation term Γ(u k ) extract as the vaccine vac;

[0206] Step e: Based on the error compensation term Γ(u k ) and the vaccine vac and recursively perform the next generation of the decision variable u;

[0207] Step f: Determine whether the recursion meets the given recursive error accuracy or number of iterations. If so, output the optimal vaccine v best and the optimal joint angular velocity of multiple robots and the optimal joint angle q j , otherwise return to step d;

[0208] Step g: Determine whether the multi-robots have completed the collaborative task. If so, end the task. Otherwise, return to step b and use the optimal vaccine v best Vaccination of the input layer is carried out.

[0209] To verify the effectiveness and superiority of the multi-robot cooperative immune network control method provided in this embodiment, we first conducted a dual-robot tracking performance test for two types of trajectories, D-shaped and plum blossom-shaped, and compared the test results with those of the GNN algorithm and the SPDNN algorithm. The comparative performance index is defined as:

[0210] The tracking error of robot j is

[0211] The collaborative error of the two robots is

[0212] The joint offset of robot j is

[0213] The tracking error of robot j is the average of the two-norm error between the actual tracking position of robot j and the expected trajectory position. The smaller the value, the higher the tracking accuracy. The collaborative error of the two robots is the average of the two-norm error between the actual tracking position of the two robots. The smaller the value, the higher the collaboration. The joint offset of robot j is the angular deviation between the final state and the initial state of the joint of robot j. The smaller the value, the smaller the joint angle offset of the robotic arm, which means the robot has higher repeatability.

[0214] Set the basic parameters of CINCABEC: m is 3, n is 6, β is 8, α is 1 is 6, α 2 is 6, λ 1 is 1, λ 2 = 1, d1 = 0.05, d2 = 0.1, and l = 2. This embodiment tests the tracking performance of two trajectories for the three algorithms respectively. The test results are shown in Table 1.

[0215] As can be seen in Table 1, although the GNN algorithm has small joint offsets and high robot repeatability, GNNs trained using gradient descent often fail to achieve a global optimal solution. Therefore, their tracking error and coordination error are 0.46 and 0.16 higher than those of the CINCABEC algorithm, respectively. Although the SPDNN algorithm has smaller tracking and coordination errors than the GNN, it does not consider joint offsets, resulting in higher joint offsets and low robot tracking repeatability. Compared to the above two algorithms, the CINCABEC algorithm in this embodiment, on the one hand, introduces a joint angle offset coefficient, reducing joint offset to 29.73%, effectively achieving repeatable multi-robot motion; on the other hand, vaccination reduces tracking error and coordination error to 17.74% and 18.63%, respectively. These test results demonstrate that the method in this embodiment achieves high-precision, highly coordinated, and highly repeatable control performance for multiple robots.

[0216] like Figures 6a to 7b As shown in the figure, the tracking results of the three algorithms under two different trajectories are compared, as well as the vaccine changes of the CINCABEC algorithm in this embodiment. From the comprehensive tracking comparison of the two trajectories, it can be seen that although the three algorithms all achieve trajectory tracking, the tracking errors are quite different, especially in places such as corner discontinuities, where the differences are most obvious. The tracking error of GNN is the largest, while the tracking error of CINCABEC in this embodiment is the smallest. This also verifies the shortcomings of local optimization based on gradient descent, as well as the effectiveness and superiority of considering joint angle offset and vaccination. From the comprehensive changes of CINCABEC in the tracking process of the two trajectories, it can be seen that as the trajectory to be tracked changes, in order to enable the method in this embodiment to track the upper trajectory quickly, effectively and with high precision, vaccination is also changed in a timely manner. Figure 6bThe D-shaped trajectory is composed of a semicircular and a straight line trajectory. The vaccine value in the semicircular trajectory decreases as the absolute value of the slope of the trajectory tangent decreases, while the vaccine value in the straight line trajectory changes relatively steadily. Figure 7b The plum blossom trajectory is composed of three identical plum blossom leaves, so the vaccine value roughly shows periodic changes. From the changes in the vaccine during the above trajectory tracking process, it can be seen that in order to effectively track the changing trajectory, especially the trajectory with turning mutations, the vaccine in this embodiment can be adjusted in time according to the iterative error to achieve adaptive tracking adjustment of various trajectories. Figures 6a to 7b The tracking results also verified the effectiveness of vaccine extraction and vaccination in this embodiment.

[0217] like Figure 8a and Figure 8b As shown, based on the method in this embodiment, a three-dimensional effect of dual-robot collaborative tracking for D-shaped and plum blossom-shaped trajectories is given.

[0218] Figure 9 The three-dimensional effect of three-robot collaborative tracking on a circular trajectory is given.

[0219] Figure 10 The three-dimensional effect of four robots' coordinated tracking of a square trajectory is shown. As can be seen from the figures, in an obstacle environment, the CINCABEC algorithm in this embodiment achieves accurate tracking of multiple robots' different trajectories, further verifying the effectiveness of this embodiment.

[0220] Table 1

[0221]

[0222] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be included in the scope of protection of the claims of the present invention.

Claims

1. A multi-robot cooperative immune network control method, characterized in that: The steps include: A single-robot time-varying quadratic optimization model is established based on the kinematics of the single robot, wherein the single-robot time-varying quadratic optimization model includes a convex set of cooperative control target description, equality constraints for trajectory tracking, inequality constraints for real-time obstacle avoidance, and joint physical constraints; Design a multi-robot collaborative controller based on decision variables, including the multi-robot time-varying quadratic optimization model and the definition of decision variables; Design of cooperative immune network control algorithm based on fitness evaluation criteria and recursive error compensation, including network topology design, fitness evaluation criteria description, recursive error compensation term design and vaccine operation; Real-time solution of joint angles for multi-robot trajectory tracking based on improved immune optimization algorithm; The single robot time-varying quadratic optimization model is: Where, represents the i-th joint angle of the j-th robot, represents the angular velocity of the i-th joint of the j-th robot, and q j ={q1 j ,q2 j ,…,q6 j }, p j =λ j (q j (t)-q j (0)), λ j is the joint offset coefficient of robot j; The collaborative control objective is described as: φ(q 1 (t))=…=φ(q N (t))=r d (t) Where φ() is the nonlinear function mapping from the action space to the joint space, r d is the expected trajectory; By taking its derivative, the collaborative control target is transformed from the position layer to the speed layer, that is: Where, J j is the Jacobian matrix of robot j; is the expected speed; The equality constraints for the trajectory tracking are: Where, α j is the position error feedback coefficient of robot j; The real-time obstacle avoidance inequality constraints include a single pair of obstacle-robot critical point obstacle avoidance constraints, robot j's obstacle avoidance speed, robot j's safety speed b j , the inequality constraint for real-time obstacle avoidance is: Where D j (q j )=[L1(q j ),L2(q j ),...,L l (q j )] T , l is the logarithm of the obstacle-manipulator critical point; The single pair of obstacle-critical point obstacle avoidance constraints is: The obstacle avoidance speed of robot j includes the speed escape vector e of robot j j And matrix L, the obstacle avoidance speed of the robot j is: The velocity escape vector e of robot j j for: In the formula, (x o j ,y o j ,z o j ) is the operation space coordinate of obstacle o, (x c j ,y c j ,z c j ) is the operating space coordinate of the critical point c on a certain arm of robot j; The matrix L is: L(q j )=-sgn(e j )ΘJ c (q j ) Where sgn(·) represents the sign function; J c is the Jacobian matrix at the critical point c; the operation rules of the symbol Θ are defined as follows: Where, represents the x-dimensional column vector, Representation matrix row x; The safe speed b of robot j j Including the distance smoothing function s(d), the safe speed b of robot j j for: Where d is the distance between a robot arm and the obstacle, d1 and d2 are the inner and outer limits of the obstacle's influence space, respectively; The distance smoothing function s(d) is: The convex set of the joint physical constraints includes joint angle constraints and joint angular velocity constraints. The convex set of the joint physical constraints is: Where, β is a positive level change parameter; The joint angle limits are: The joint angular velocity limit is: Where, and are the upper and lower bounds of the joint angle and joint angular velocity, respectively.

2. A multi-robot cooperative immune network control method according to claim 1, characterized in that: The multi-robot time-varying quadratic optimization model is defined as follows: stGz=R Az≤B Where, ‖·‖2 represents the vector's two-norm, represents the square of the vector 2 norm, m represents the dimension of the robot end effector operation space, and n represents the dimension of the robot joint space; The decision variable u is defined as follows: u=[z g h] T ∈R Nn+Nm+Nlm Where g is the equality constraint for multi-robot trajectory tracking, and h is the inequality constraint for multi-robot real-time obstacle avoidance.

3. The multi-robot cooperative immune network control method according to claim 1, characterized in that: The network topology design adopts the recursive form of recursive neural network, by defining the optimization objective function as antigen and the joint angle obtained by inverse kinematics as antibody, and designing a recursive immune network including input layer, tracking hidden layer, compensation hidden layer and output layer; The input layer is the joint angles of multiple robots. The tracking hidden layer defines the actual working space s of the robot according to the joint angles and evaluates it according to the fitness criterion f(). The recursive error e is determined according to the evaluation output, and then the error compensation term Γ(u) is generated after the compensation function Γ() of the compensation hidden layer is activated. k ), based on the error compensation term Γ(u k ) is extracted as vaccine v ac , and at the same time, it realizes error compensation through the network loop recursion, and the optimal vaccine v after the recursion is completed best The input layer is seeded through the outer loop, and the output layer is used to output the optimal joint angular velocity of the multi-robot after the inner loop iteration is completed, and the optimal joint angle of the multi-robot is obtained by integration.

4. A multi-robot cooperative immune network control method according to claim 3, characterized in that: The fitness evaluation criterion description includes the actual workspace s of the robot, and the fitness evaluation criterion f() is: Where s∈R η (η=Nn+Nm+Nlm), and its upper and lower bounds are defined as follows: The actual working space s of the robot is: s=u-(Mu+σ) Where, 5. The multi-robot cooperative immune network control method according to claim 4 is characterized in that: The recursive error compensation term design includes the recursive error e calculation, the error compensation term Γ(u k ) is calculated, the recursive error e is: e(u k )=u k -f(s k ) Where k is the iteration step length; The error compensation term Γ(u k )for: Γ(u k )=(M T +I)e(u k ) Where I is the identity matrix and Γ() is the compensation activation function.

6. A multi-robot cooperative immune network control method according to claim 5, characterized in that: The vaccine operation comprises the following steps: Vaccine selection, the error compensation term Γ(u k ) for vaccine extraction, namely: Vaccination, introduction of the vaccine ac , perform the network loop recursion of the decision variable u, that is: in k+1 =in k -v ac ·Γ(in k )。 7. The multi-robot cooperative immune network control method according to claim 6, characterized in that: The method of solving the joint angles in real time for multi-robot trajectory tracking based on the improved immune optimization algorithm comprises the following steps: Step a: Convert the multi-robot intelligent collaborative control objective into a QP problem; Input antibody q into the input layer 1 (t),q 2 (t),…,q N (t) and vaccine v ac (t); Step b: Calculate the actual working space s of the robot, and then obtain the output value of the tracking hidden layer after evaluating it with the fitness criterion f(); Step c: Calculate the recursive error e and pass it to the compensation hidden layer to obtain the compensation hidden layer output as the error compensation term Γ(u k ); Step d: The error compensation term Γ(u k ) extract as the vaccine vac; Step e: Based on the error compensation term Γ(u k ) and the vaccine vac and recursively perform the next generation of the decision variable u; Step f: Determine whether the recursion meets the given recursive error accuracy or number of iterations. If so, output the optimal vaccine v best and the optimal joint angular velocity of multiple robots and the optimal joint angle q j , otherwise return to step d; Step g: Determine whether the multi-robots have completed the collaborative task. If so, end the task. Otherwise, return to step b and use the optimal vaccine v best Vaccination of the input layer is carried out.

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