A real-time position planning method for multiple robots

Abstract

The present invention discloses a multi-robot real-time position planning method, comprising the following steps: defining a two-dimensional coordinate plane and building a multi-robot position model; determining a leader robot and a follower robot based on a leader-follower strategy, and establishing a multi-robot position planning optimization model by minimizing the distance between the follower robot and the adjacent robot; constructing a time-varying matrix equation using the Lagrange multiplier method according to the multi-robot position planning optimization model; constructing a complex zeroed neural dynamics model for real-time multi-robot position planning, determining the multi-robot position information in real time through the complex zeroed neural dynamics model, and adjusting the left and right wheel speeds and steering angles of the multi-robots according to the multi-robot position information in real time, so that the robots reach the designated positions. The present invention solves the technical problem that the existing methods cannot adapt to the changes in parameters in real time on time-varying problems, thereby generating hysteresis errors that are difficult to eliminate and falling into local minimum values.

Description

Technical Field

[0001] The present invention relates to the field of robot technology, and in particular to a multi-robot real-time position planning method. Background Art

[0002] Multi-robot position planning is to let each robot update its position in real time to achieve the desired formation. In complex scenarios, robots need to be able to avoid obstacles and dangers while ensuring the effectiveness and safety of the path, which requires the support of position planning technology. At present, multi-robot position planning is mostly static planning, which often cannot meet the needs of complex tasks.

[0003] Real-time position planning can help multiple robots achieve effective collaboration and scheduling, and improve the overall efficiency and performance of the system. In early studies, some studies are using artificial potential field methods to achieve robot position planning. This method regards the target and obstacles as objects that have gravity and repulsion on the robot, and the robot moves along the combined force of gravity and repulsion; the most classic method is to regard the robot as a particle and make it move in the direction of gravity, but this method has the problem of gradient vanishing. When all artificial potential fields cancel each other out, such as when the obstacle is exactly between the robot and the target position, this may happen. Although the gradient of these local minima is zero, it is not the target position we want. In addition, the actual situation is complex and changeable. Static planning cannot adapt well to changes in the surrounding environment. The status of dynamic planning is becoming more and more important. Real-time performance is the core of dynamic position planning problems.

[0004] In recent years, researchers have constructed the formation task as a time-varying optimization problem (linear or nonlinear), and ensured real-time performance by solving the optimization problem in real time, thereby realizing dynamic programming. There are currently two methods. One is the numerical iteration method, which has serial processing characteristics. As the dimension of the matrix equation increases, it is difficult to quickly and efficiently process high-dimensional matrix equations, and thus cannot meet real-time tasks. The other is the neural network method, in which each process operates in parallel in a distributed manner. Due to the inherent characteristics of parallel distributed information processing of neural networks, the convergence speed will not slow down with the increase in the number of problems. The core idea of ​​neural dynamics optimization is to set The learning rule of the neural network is designed so that the neural network converges to its equilibrium point, which just corresponds to the global optimal solution of the optimization problem; the main design methods of neural dynamics optimization include projection method, Lagrangian function method, penalty function method, etc. Most neural network designs are based on a convergence factor along the negative gradient descent, which can achieve good results in solving time-invariant problems, but cannot adapt to parameter changes in real time for time-invariant problems, resulting in lag errors that are difficult to eliminate. That is, traditional methods show lag errors that are difficult to eliminate in real-time processing, resulting in inaccurate solution results and difficulty in ensuring that the robot can move to the specified position. Therefore, it is urgent to propose a multi-robot real-time position planning method to solve the technical problem that the existing methods cannot adapt to parameter changes in real time for time-varying problems, resulting in lag errors that are difficult to eliminate and falling into local minimum values. Summary of the invention

[0005] The main purpose of the present invention is to propose a multi-robot real-time position planning method, which aims to solve the technical problem that the existing methods cannot adapt to the changes of parameters in real time in time-varying problems, thereby generating lag errors that are difficult to eliminate and falling into local minimums.

[0006] To achieve the above object, the present invention provides a multi-robot real-time position planning method, wherein the multi-robot real-time position planning method comprises the following steps:

[0007] S1. Define the two-dimensional coordinate plane and build a multi-robot position model;

[0008] S2. Based on the leader-follower strategy, the leader robot and the follower robot are determined, and a multi-robot position planning optimization model is established by minimizing the distance between the follower robot and the adjacent robots;

[0009] S3, based on the multi-robot position planning optimization model, the Lagrange multiplier method is used to construct the time-varying matrix equation;

[0010] S4. Construct a complex-zero neural dynamics model for real-time multi-robot position planning, determine the multi-robot position information in real time through the complex-zero neural dynamics model, and adjust the left and right wheel speeds and steering angles of the multi-robots according to the real-time feedback of the multi-robot position information, so that the robots reach the specified position.

[0011] In one preferred solution, the multi-robot position model in step S1 is:

[0012] Z j (t) = x j (t)+y j (t)i

[0013] Among them, Z j (t) is the position information of the jth robot in the two-dimensional plane at time t, x j (t) is the x-axis coordinate of the j-th robot at time t, y j (t) is the y-axis coordinate of the j-th robot at time t, and i is an imaginary unit.

[0014] In one of the preferred solutions, step S2 is specifically:

[0015] S21. Based on the leader-follower strategy, the robots at the border and center positions are used as leader robots, and the remaining robots are used as follower robots;

[0016] S22, each follower robot exchanges information with two adjacent robots;

[0017] S23. Establish a multi-robot position planning optimization model by minimizing the distance between the follower robot and the adjacent robots.

[0018] In one preferred solution, step S21 is specifically as follows:

[0019] Z c =k1Z0+(1-k1)Z N+1 +d

[0020] Among them, Z c is the position information of the robot at the center, k1 is the variable scaling factor, Z0 and Z N+1 are the position information of the robot located at the boundary positions on both sides, and d is the translation coefficient.

[0021] In one of the preferred solutions, the multi-robot position planning optimization model is:

[0022]

[0023] Where D is the distance between the follower robot and the adjacent robot at time t, N is the number of robots, and Zj (t) is the position information of the jth robot in the two-dimensional plane at time t, Z j+1 (t) is the position information of the j+1th robot on the two-dimensional plane at time t, Z j-1 (t) is the position information of the j-1th robot in the two-dimensional plane at time t.

[0024] In one preferred solution, the time-varying matrix equation in step S3 is:

[0025] AZ(t)+B(t)=0

[0026] Where A is the coefficient matrix, Z(t) is the position information of the follower robot at time t, Z(t) = [Z1(t), Z2(t), ..., Z N (t),λ(t)] T , Z N (t) is the position information of the Nth follower robot at time t, λ is the Lagrangian factor, B(t) is the position information of the leader robot at time t, B(t)=[-Z0(t),0,0,...,-Z N+1 (t), -Z c (t)] T , Z0(t) and Z N+1 (t) are the position information of the leader robot at the boundary positions on both sides at time t, Z c (t) is the position information of the leader robot located at the center.

[0027] One of the preferred solutions, step S4 constructs a complex zeroing neural dynamics model for real-time multi-robot position planning, specifically:

[0028] Construct an error function; the error function is:

[0029] E(t) = AZ(t) + B(t);

[0030] Among them, E(t) is the error function, A is the coefficient matrix, Z(t) is the position information of the follower robot at time t, and B(t) is the position information of the leader robot at time t;

[0031] A complex zeroing neural dynamics model for real-time robot position planning is constructed based on zeroing neural dynamics; the complex zeroing neural dynamics model is:

[0032]

[0033] in, is the first-order derivative of Z(t), ζ is the convergence factor, is the first-order derivative of B(t).

[0034] In one of the preferred solutions, the position information of the robot includes the x-axis coordinate, y-axis coordinate and steering angle of the robot.

[0035] One of the preferred solutions, the real-time determination of multi-robot position information by using a complex zeroing neural dynamics model is specifically as follows:

[0036] The position information of multiple robots is determined in real time through the complex zeroing neural dynamics model, and the left and right wheel speeds of multiple robots are adjusted in real time based on the position information of multiple robots and the robot dynamics equations;

[0037] The kinetic equation is:

[0038]

[0039] in, is the first-order derivative of the x-axis coordinate of the robot at time t, b is the radius of the robot wheel, d is the wheelbase between the two wheels of the robot, and v l (t) is the left wheel speed of the robot at time t, v r (t) is the right wheel speed of the robot at time t, θ(t) is the steering angle of the robot at time t, is the first-order derivative of the y-axis coordinate of the robot at that moment, is the first-order derivative of the steering angle of the robot at time t.

[0040] In one of the preferred solutions, the left and right wheel speeds of the robot are:

[0041]

[0042] in, is the second-order derivative of the x-axis coordinate of the robot at time t, is the second derivative of the y-axis coordinate of the robot at that moment.

[0043] In the above technical solution of the present invention, the multi-robot real-time position planning method includes the following steps: defining a two-dimensional coordinate plane and building a multi-robot position model; based on the leader-follower strategy, determining the leader robot and the follower robot, and establishing a multi-robot position planning optimization model by minimizing the distance between the follower robot and the adjacent robot; according to the multi-robot position planning optimization model, using the Lagrange multiplier method to construct a time-varying matrix equation; constructing a complex zeroed neural dynamics model for real-time multi-robot position planning, determining the multi-robot position information in real time through the complex zeroed neural dynamics model, and adjusting the left and right wheel speeds and steering angles of the multi-robots in real time according to the multi-robot position information, so that the robots reach the specified position. The present invention solves the technical problem that the existing methods cannot adapt to the changes in parameters in real time in time-varying problems, thereby generating hysteresis errors that are difficult to eliminate and falling into local minimum values.

[0044] In the present invention, based on the optimization idea, a multi-robot position planning optimization model is established by minimizing the distance between robots, and the ground is regarded as a Cartesian plane. The position of a single robot can be represented by a two-dimensional Cartesian coordinate system, and the multi-robot position planning optimization model is further converted into an equivalent complex matrix form. Real-time position planning is achieved by solving the matrix in real time.

[0045] In the present invention, the time-varying solution can be effectively tracked by the complex zeroing neural dynamics model. The complex zeroing neural dynamics model has global convergence, avoiding the problems of poor real-time performance of existing methods, difficulty in effectively tracking time-varying solutions, lag errors, and falling into local minima, thereby improving the robot's task execution efficiency, reducing waiting time, as well as the safety and reliability of operation, thereby enabling the robot to adapt to diverse working scenarios in different terrains and environments, that is, satisfying the dynamic planning of multiple robots.

[0046] In the present invention, based on the traditional matrix space representation, the increase in dimension leads to an increase in the dimension of the matrix. For example, in a two-dimensional space, the positions of n robots are usually represented by an n×2 matrix. The present invention adopts a complex number representation and only requires an n×1 matrix representation, which effectively reduces the matrix dimension and improves the calculation speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying any creative work.

[0048] Figure 1 A schematic diagram of a multi-robot real-time position planning method according to an embodiment of the present invention;

[0049] Figure 2 Schematic diagram of a two-wheel differential robot according to an embodiment of the present invention;

[0050] Figure 3 This is a first schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0051] Figure 4 A first curve diagram of the speed change of the left and right wheels of the follower robot according to an embodiment of the present invention;

[0052] Figure 5 A first curve diagram showing the change of the error function of the zeroed neural dynamics model according to an embodiment of the present invention;

[0053] Figure 6A first curve diagram of real-time change of phase angle of a follower robot according to an embodiment of the present invention;

[0054] Figure 7 A second schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0055] Figure 8 A third schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0056] Fig. 9 A fourth schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0057] Fig.10 is a fifth schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0058] Fig.11 is a sixth schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0059] Fig.12 is a seventh schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0060] Fig.13 A second curve diagram of the speed change of the left and right wheels of the follower robot according to an embodiment of the present invention;

[0061] Fig.14 The second curve diagram of the real-time change of the phase angle of the follower robot according to the embodiment of the present invention is

[0062] Fig.15 A second curve diagram showing the variation of the error function of the zeroed neural dynamics model according to an embodiment of the present invention;

[0063] Fig.16 is an eighth schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention;

[0064] Fig.17 This is the ninth schematic diagram of the motion trajectory of the robot according to an embodiment of the present invention.

[0065] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with the implementation methods and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0066] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0067] The technical solutions between the various embodiments of the present invention can be combined with each other, but they must be based on the fact that they can be implemented by ordinary technicians in the field. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0068] See also Figure 1-Figure 2 According to one aspect of the present invention, the present invention provides a multi-robot real-time position planning method, wherein the multi-robot real-time position planning method comprises the following steps:

[0069] S1. Define the two-dimensional coordinate plane and build a multi-robot position model;

[0070] S2. Based on the leader-follower strategy, the leader robot and the follower robot are determined, and a multi-robot position planning optimization model is established by minimizing the distance between the follower robot and the adjacent robots;

[0071] S3, based on the multi-robot position planning optimization model, the Lagrange multiplier method is used to construct the time-varying matrix equation;

[0072] S4. Construct a complex-zero neural dynamics model for real-time multi-robot position planning, determine the multi-robot position information in real time through the complex-zero neural dynamics model, and adjust the left and right wheel speeds and steering angles of the multi-robots according to the real-time feedback of the multi-robot position information, so that the robots reach the specified position.

[0073] Specifically, in this embodiment, a two-dimensional coordinate plane is defined, where there are N robots, and the position of the jth robot in the two-dimensional coordinate plane is:

[0074] Z j =x j +y j i

[0075] The real part and imaginary part of the complex number Z represent the x-axis coordinate and y-axis coordinate of the robot respectively. Therefore, the calculation of the complex number Z is equivalent to determining the position of the robot. The complex number representation can effectively reduce the matrix dimension, thereby improving the calculation efficiency. Since the real-time position planning of the robot is a dynamic problem, each robot has different position coordinates at different times t. The multi-robot position model in step S1 is:

[0076] Z j (t) = x j (t)+y j (t)i

[0077] Among them, Z j (t) is the position information of the jth robot in the two-dimensional plane at time t, x j(t) is the x-axis coordinate of the j-th robot at time t, y j (t) is the y-axis coordinate of the j-th robot at time t, and i is an imaginary unit.

[0078] Specifically, in this embodiment, the step S2 is specifically:

[0079] S21. Based on the leader-follower strategy, the robots at the edge and center are used as leader robots, and the remaining robots are used as follower robots; specifically:

[0080] Z c =k1Z0+(1-k1)Z N+1 +d

[0081] Among them, Z c is the position information of the robot at the center, k1 is the variable scaling factor, the closer k1 is to 1, the closer the center robot is to Z0, and vice versa. N+1 , Z0 and Z N+1 are the position information of the robots located at the boundary positions on both sides, and d is the translation coefficient;

[0082] S22, each follower robot exchanges information with two adjacent robots;

[0083] S23, establishing a multi-robot position planning optimization model by minimizing the distance between the follower robot and the adjacent robot; the multi-robot position planning optimization model is:

[0084]

[0085] Where D is the distance between the follower robot and the adjacent robot at time t, N is the number of robots, and Z j (t) is the position information of the jth robot in the two-dimensional plane at time t, Z j+1 (t) is the position information of the j+1th robot on the two-dimensional plane at time t, Z j-1 (t) is the position information of the j-1th robot in the two-dimensional plane at time t.

[0086] Specifically, in this embodiment, the time-varying matrix equation in step S3 is:

[0087] AZ(t)+B(t)=0

[0088] Where Z(t) is the position information of the follower robot at time t, Z(t) = [Z1(t), Z2(t), ..., Z N (t),λ(t)] T , Z N(t) is the position information of the Nth follower robot at time t, λ is the Lagrangian factor, B(t) is the position information of the leader robot at time t, B(t)=[-Z0(t),0,0,...,-Z N+1 (t), -Z c (t)] T , Z0(t) and Z N+1 (t) are the position information of the leader robot at the boundary positions on both sides at time t, Z c (t) is the position information of the leading robot at the center; A is the coefficient matrix, which is a time-invariant matrix and does not change with time. The coefficient matrix is:

[0089]

[0090] Specifically, in this embodiment, the step S4 constructs a complex zeroing neural dynamics model for real-time multi-robot position planning, specifically:

[0091] Construct an error function; the error function is:

[0092] E(t) = AZ(t) + B(t);

[0093] Among them, E(t) is the error function, A is the coefficient matrix, Z(t) is the position information of the follower robot at time t, and B(t) is the position information of the leader robot at time t;

[0094] Based on zeroing neural dynamics

[0095] Constructing a complex zeroed neural dynamics model for real-time robot position planning;

[0096] The complex zeroing neural dynamics model is:

[0097]

[0098] in, is the first-order derivative of Z(t), ζ is the convergence factor, is the first-order derivative of B(t).

[0099] Specifically, in this embodiment, the position information of the robot includes the x-axis coordinate, y-axis coordinate and steering angle of the robot; the time-varying variables of the two-wheel differential robot in the two-dimensional coordinate plane at time t are expressed as: R(t)=[x(t),y(t),θ(t)] T ∈R 3 , where x(t), y(t), and θ(t) represent the x-axis coordinate, y-axis coordinate, and steering angle of the robot at time t, respectively.

[0100] Specifically, in this embodiment, the multi-robot position information is determined in real time by using the zeroing neural dynamics model, specifically:

[0101] The position information of multiple robots is determined in real time through the complex zeroing neural dynamics model, and the left and right wheel speeds of multiple robots are adjusted in real time based on the position information of multiple robots and the robot dynamics equations;

[0102] The kinetic equation is:

[0103]

[0104] in, is the first-order derivative of the x-axis coordinate of the robot at time t, b is the radius of the robot wheel, d is the wheelbase between the two wheels of the robot, and v l (t) is the left wheel speed of the robot at time t, v r (t) is the right wheel speed of the robot at time t, θ(t) is the steering angle of the robot at time t, is the first-order derivative of the y-axis coordinate of the robot at that moment, is the first-order derivative of the steering angle of the robot at time t.

[0105] Specifically, in this embodiment, the left and right wheel speeds of the robot are adjusted by real-time feedback of the position information so that the robot moves to the specified position, that is, the left and right wheel speeds of the robot can be represented by the finite-order differentials of the position information; the left and right wheel speeds of the robot are:

[0106]

[0107] in, is the second-order derivative of the x-axis coordinate of the robot at time t, is the second derivative of the y-axis coordinate of the robot at that moment.

[0108] Specifically, in this embodiment, the desired position of the leader robot is set, and the position information of the follower robots is calculated in real time through the complex zeroing neural dynamics model. The left and right wheel speeds and steering angles of the robots are fed back and adjusted in real time through the position information, so that all robots move to the desired position; the wheelbase d between the two wheels of the two-wheel differential robot of the present invention is set to 2, the wheel radius b is set to 1, and the convergence factor ζ is set to 1. The present invention does not make specific limitations and can be set as needed; N robots are set in a two-dimensional coordinate plane. In the present invention, 7 robots are randomly set in a two-dimensional coordinate plane as an example, where the two robots located at the boundary position are used as leader robots Z0 and Z5, and the remaining four are follower robots. The position information matrix of the leader robot is:

[0109] [-1-i 0 0 -1-7i]T , indicating that the position coordinates of the two leader robots are (1,1) and (1,7) respectively, and the position information Z of the robot at the center is taken c =1+4i, the position information matrix of the follower robot is Z(t)=[Z1(t),Z2(t),Z3(t),Z4(t),λ(t)] T , transformed into a complex time-varying problem, that is:

[0110] AZ(t)+B(t)=0

[0111] in,

[0112] Z(t) takes a random value, the direction angle θ of the follower robot is set to a random value, the variable scaling factor k1 of the robot at the center is set to 0.5, and the translation factor d is set to 0. Figure 3 , the two leader robots are fixed at (1,1) and (1,7), and the remaining follower robots can effectively move to the desired position Sports, among them In the figure, "+" indicates the position of each follower robot at time t = 0, and "*" indicates the position of each follower robot at time t = 1. Indicates the position of the follower robot at the final moment; see Figure 4 is the speed change curve of the left and right wheels of the follower robot. Each follower robot adjusts the speed of the left and right wheels according to the feedback of the current position information until it moves to the desired position; see Figure 5 is the real-time error function change curve of each follower robot. It can be seen that the error function of the zeroing neural dynamics model proposed in the present invention can achieve global convergence; see Figure 6 is the real-time change curve of the phase angle of each follower robot. Through the real-time feedback of the expected position and the current position, the forward direction is adjusted in real time; see Figure 7 , set the variable scaling factor k1 of the robot at the center to 0.3 and the translation factor d to 0, so that the robot at the center moves closer to the Z5 robot; see Figure 8 , set the variable scaling factor k1 of the robot at the center to 0.7 and the translation factor d to 0, so that the robot at the center moves closer to the Z0 robot; see Fig. 9 , set the variable scaling factor k1 of the robot at the center to 0.5 and the translation factor d to 2 to achieve arc distribution; see Fig.10 , set the variable scaling factor k1 of the robot at the center to 0.3 and the translation factor d to 2 to achieve arc distribution; see Fig.11, the variable scaling coefficient k1 of the robot located at the center position is set to 0.7, and the translation coefficient d is set to 2 to achieve arc distribution; in the present invention, by introducing a central robot, that is, the robot located at the center position, and by changing the variable scaling coefficient and translation coefficient of the robot located at the center position, more variable formations can be achieved.

[0113] Specifically, in this embodiment, N robots are set on the two-dimensional coordinate plane. In the present invention, 7 robots are randomly set on the two-dimensional coordinate plane as an example, wherein a fixed leader robot and a dynamic leader robot are set, and the position information of the leader robot is Z0=1+7i, Z5=5+0.5i respectively. Correspondingly, Z c =3+3.5i, which means that the leader robot Z5 starts from position (5, 0) and moves along the x-axis at a uniform speed. It is converted into a complex time-varying problem, that is,

[0114] AZ(t)+B(t)=0

[0115] Where, B(t) = [-1-7i, 0, 0, -5-0.5i] T ,

[0116] See also Figure 12-Figure 15 For detailed experimental results, see Fig.12 , the leader robot Z0 is fixed at the coordinate (1, 7), the leader robot Z5 starts from the coordinate (5, 0) and moves in a uniform straight line in the y-axis direction with a speed of 0.5m / s. At the same time, from the random initial range [0,1+i] 4×1 At the beginning, the four follower robots are dynamically and evenly distributed between the leader robots Z0 and Z5, that is, the real-time state solution Z(t) of the zeroed neural dynamics model can quickly and accurately find the theoretical solution Z * (t); see Fig.13 The driving speeds of the left and right wheels of all follower robots are given and stabilized after 5s; see Fig.14 is the real-time change of the phase angle during the movement of each follower robot. Finally, each robot gradually converges to 0, indicating that the direction of each robot is opposite to the x-axis at this time; see Fig.15 The dynamic errors of all follower robots converged to 0 quickly, indicating that the annulized neural dynamics model has excellent convergence performance when dealing with position planning tasks under the condition of a dynamic leader robot; see Fig.16 , set the variable scaling factor k1 of the robot at the center to 0.7 and the translation factor d to 2 to achieve dynamic arc distribution; see Fig.17 , set the variable scaling coefficient k1 of the robot at the center to 0.3 and the translation coefficient d to 2 to achieve dynamic arc distribution.

[0117] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. All equivalent structural changes made using the contents of the present invention's specification and drawings, or directly / indirectly applied in other related technical fields, are included in the patent protection scope of the present invention.

Claims

1. A multi-robot real-time position planning method, characterized in that: The following steps are involved: S1. Define a two-dimensional coordinate plane and build a multi-robot position model; the multi-robot position model in step S1 is: Z j (t)=x j (t)+y j (t)i Among them, Z j (t) is the position information of the jth robot in the two-dimensional plane at time t, x j (t) is the x-axis coordinate of the j-th robot at time t, y j (t) is the y-axis coordinate of the j-th robot at time t, and i is an imaginary unit; S2. Based on the leader-follower strategy, a leader robot and a follower robot are determined, and a multi-robot position planning optimization model is established by minimizing the distance between the follower robot and the adjacent robots; the step S2 is specifically as follows: S21. Based on the leader-follower strategy, the robots at the border and center positions are used as leader robots, and the remaining robots are used as follower robots. The follower robots are dynamically and evenly distributed among the leader robots. The step S21 is specifically as follows: WITH c =k1Z0+(1-k1)Z N+1 +d Among them, Z c is the position information of the robot at the center, k1 is the variable scaling factor, Z0 and Z N+1 are the position information of the robots located at the boundary positions on both sides, and d is the translation coefficient; S22, each follower robot exchanges information with two adjacent robots; S23, establishing a multi-robot position planning optimization model by minimizing the distance between the follower robot and the adjacent robot; the multi-robot position planning optimization model is: Where D is the distance between the follower robot and the adjacent robot at time t, N is the number of robots, and Z j (t) is the position information of the jth robot in the two-dimensional plane at time t, Z j+1 (t) is the position information of the j+1th robot on the two-dimensional plane at time t, Z j-1 (t) is the position information of the j-1th robot on the two-dimensional plane at time t; S3. According to the multi-robot position planning optimization model, a time-varying matrix equation is constructed using the Lagrange multiplier method; the time-varying matrix equation in step S3 is: AZ(t)+B(t)=0 Where A is the coefficient matrix, Z(t) is the position information of the follower robot at time t, Z(t) = [Z1(t), Z2(t), ..., Z N (t),λ(t)] T , Z N (t) is the position information of the Nth follower robot at time t, λ is the Lagrangian factor, B(t) is the position information of the leader robot at time t, B(t)=[-Z0(t),0,0,...,-Z N+1 (t), -Z c (t)] T , Z0(t) and Z N+1 (t) are the position information of the leader robot at the boundary positions on both sides at time t, Z c (t) is the position information of the leading robot located at the center; S4, constructing a complex zeroing neural dynamics model for real-time multi-robot position planning, determining the multi-robot position information in real time through the complex zeroing neural dynamics model, and adjusting the left and right wheel speeds and steering angles of the multi-robots according to the real-time feedback of the multi-robot position information, so that the robots reach the specified position; The step S4 constructs a complex zeroing neural dynamics model for real-time multi-robot position planning, specifically: Construct an error function; the error function is: E(t) = AZ(t) + B(t); Among them, E(t) is the error function, A is the coefficient matrix, Z(t) is the position information of the follower robot at time t, and B(t) is the position information of the leader robot at time t; A complex zeroing neural dynamics model for real-time robot position planning is constructed based on zeroing neural dynamics; the complex zeroing neural dynamics model is: in, is the first-order derivative of Z(t), ζ is the convergence factor, is the first-order derivative of B(t).

2. A multi-robot real-time position planning method according to claim 1, characterized in that: The position information of the robot includes the x-axis coordinate, y-axis coordinate and steering angle of the robot.

3. A multi-robot real-time position planning method according to claim 1, characterized in that: The real-time determination of multi-robot position information by using the complex zeroing neural dynamics model is specifically as follows: The position information of multiple robots is determined in real time through the complex zeroing neural dynamics model, and the left and right wheel speeds of multiple robots are adjusted in real time based on the position information of multiple robots and the robot dynamics equations; The kinetic equation is: in, is the first-order derivative of the x-axis coordinate of the robot at time t, b is the radius of the robot wheel, d is the wheelbase between the two wheels of the robot, and v l (t) is the left wheel speed of the robot at time t, v r (t) is the right wheel speed of the robot at time t, θ(t) is the steering angle of the robot at time t, is the first-order derivative of the y-axis coordinate of the robot at that moment, is the first-order derivative of the steering angle of the robot at time t.

4. A multi-robot real-time position planning method according to claim 3, characterized in that: The left and right wheel speeds of the robot are: in, is the second-order derivative of the x-axis coordinate of the robot at time t, is the second derivative of the y-axis coordinate of the robot at that moment.

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