A collaborative control method for heterogeneous multi-agent system formation

Abstract

The present invention discloses a method for cooperative control of a heterogeneous multi-agent system formation, which relates to the field of cooperative control technology, and includes the following steps: S1, constructing a second-order multi-dimensional heterogeneous multi-agent system, and constructing a kinematic model and a dynamic model for the leader and the follower in the second-order multi-dimensional heterogeneous multi-agent system; S2, determining a controller model; S3, determining the auxiliary control law of the follower; S4, completing the cooperative control of the heterogeneous multi-agent system formation according to the auxiliary control law of the follower. The present invention utilizes a contraction constraint formula to design an auxiliary control rate to optimize the heterogeneous multi-agent system online, and can control the formation to converge in a very short time, and the formation can quickly and effectively construct and transform the formation, and the formation remains stable, the error fluctuation is very small, and the accuracy is high.

Description

Technical Field

[0001] The present invention relates to the field of collaborative control technology, and in particular to a collaborative control method for a heterogeneous multi-agent system formation. Background Art

[0002] In heterogeneous multi-agent systems, different agents usually have different state space dimensions. This brings inherent difficulties to the problem of formation cooperative control. Existing research aims to construct appropriate outputs in the same dimension so that agents with different dimensions can reach an output consensus. In this way, high-dimensional agents can adapt to low-dimensional agents, which leads to a lack of cooperation between high-dimensional agents. For example, the formation control applied to drones and ground vehicles in the horizontal direction, in which the coordination of the vertical position and speed of drones faces the problem of possible failure. In other words, for second-order multi-dimensional heterogeneous agent systems, most of the existing control strategies can only allow agents to track low-dimensional moving targets when forming the desired formation. Therefore, in order to cooperatively track the movement of the leader in higher dimensions, some new cooperative control methods need to be developed. Although the second-order multi-dimensional agent system cannot form a specific formation in the same dimension, the low-dimensional agent can form a lower-dimensional formation to track part of the leader's state, and the cooperation between the low-dimensional and high-dimensional agents can also be guaranteed, which meets the requirements of many tracking tasks in practical applications. The formation scenario mentioned above is called cross-dimensional formation. At sea, some complex tracking tasks require the joint participation of unmanned boats and underwater robots. The underwater robot sails under the three-dimensional sea surface, while the unmanned boat moves on the two-dimensional sea surface. The coordination of unmanned boats and underwater robots can be regarded as a cross-dimensional formation coordination control problem.

[0003] More and more studies have shown that model predictive control strategies can effectively handle the control problems of complex systems and have strong reliability and robustness. However, traditional model predictive control requires local linearization of the system model. However, when faced with strongly coupled nonlinear systems such as unmanned boat-underwater robot heterogeneous multi-agent systems, using local linearization to construct local auxiliary feedback control laws to optimize the system is obviously inefficient. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a formation collaborative control method for a heterogeneous multi-agent system.

[0005] The technical solution of the present invention is: a method for coordinated control of a heterogeneous multi-agent system formation comprises the following steps:

[0006] S1. Construct a second-order multi-dimensional heterogeneous multi-agent system, and construct kinematic and dynamic models for the leader and follower in the second-order multi-dimensional heterogeneous multi-agent system;

[0007] S2, determining a controller model according to the kinematic model and dynamic model of the leader and the kinematic model and dynamic model of the follower;

[0008] S3, construct the Lyapunov function and determine the auxiliary control law of the follower according to the controller model;

[0009] S4. According to the auxiliary control law of the followers, the coordinated control of the heterogeneous multi-agent system formation is completed.

[0010] Furthermore, in S1, the second-order multi-dimensional heterogeneous multi-agent system includes a leader and several followers.

[0011] Furthermore, the kinematic model of leaders The expression is:

[0012]

[0013] In the formula, R g (t) represents the first coefficient matrix, v0(t) represents the velocity state vector of the leader;

[0014] The dynamics model of leadership The expression is:

[0015]

[0016] In the formula, A g (t) represents the second coefficient matrix, B g (t) represents the third coefficient matrix, η0(t) represents the position state vector of the leader, C g (t) represents the fourth coefficient matrix.

[0017] Furthermore, the kinematic model of the follower The expression is:

[0018]

[0019] In the formula, represents the fifth coefficient matrix, v i (t) represents the velocity state vector of agent i;

[0020] Dynamic model of the follower The expression is:

[0021]

[0022] In the formula, represents the sixth coefficient matrix, represents the seventh coefficient matrix, η i(t) represents the position state vector of agent i, represents the eighth coefficient matrix, u i (t) represents the control input vector of agent i.

[0023] Furthermore, in S2, the expression of the controller model is:

[0024]

[0025] Where Ji represents the performance function of the follower i controller, represents the predictive control input of follower i, S(δ) represents the piecewise function of the sampling period, δ represents the sampling period, T represents the prediction time domain, N represents the total number of followers, and a ij represents the adjacency weight between followers i and j, represents the state error of follower i relative to follower j, s represents the independent variable of the integrated term, Q i1 represents the first weight coefficient matrix corresponding to follower i, b i0 represents the adjacency weight between follower i and the leader, represents the state error of follower i relative to the leader, Q i0 represents the second weight coefficient matrix corresponding to follower i, represents the collision avoidance cost function of follower i relative to follower j, represents the predictive control input of follower i with s as the independent variable, R i represents the third weight coefficient matrix of follower i, represents the terminal state error of follower i relative to follower j, P i1 represents the third weight coefficient matrix corresponding to follower i, b i0 represents the adjacency weight between follower i and the leader, represents the terminal state error of follower i relative to the leader, P i0 represents the fourth weight coefficient matrix corresponding to follower i, represents the current state of follower i, x i (t0) represents the current state of follower i, t0 represents the current time, represents the current state of follower j, x j (t0) represents the current state of follower j, represents the predicted state of follower i, represents the first-order derivative of the predicted state of follower i, represents the predictive control input of follower i, represents the predicted state of follower j, represents the first-order derivative of the predicted state of follower j, represents the predictive control input of follower j, V i represents the control Lyapunov function of follower i, x i represents the state of follower i, represents the first-order derivative of the current state of follower i, represents the current control input of follower i, represents the first-order derivative of the current state of follower i based on the auxiliary control law, represents the auxiliary control law of follower i at the current state, u i max represents the maximum control input of follower i, Represented as the set of followers.

[0026] Furthermore, S3 includes the following sub-steps:

[0027] S31, constructing a first Lyapunov function and a second Lyapunov function;

[0028] S32. Determine an auxiliary control law of the follower according to the first Lyapunov function, the second Lyapunov function and the controller model.

[0029] Furthermore, in S31, the first Lyapunov function V 1i The expression is:

[0030]

[0031] In the formula, represents the transpose of the state vector error of the position of agent i, K ηi represents the first positive definite diagonal matrix, Represents the position state vector error of agent i.

[0032] Furthermore, in S31, the second Lyapunov function V 2i The expression is:

[0033]

[0034] In the formula, represents the transpose of the velocity state vector error of agent i, K vi represents the second positive definite diagonal matrix, represents the velocity state vector error of agent i, V 1i represents the first Lyapunov function.

[0035] Furthermore, in S32, the auxiliary control law h of the follower i The expression is:

[0036]

[0037] In the formula, K 2i represents the positive definite gain coefficient matrix, K ηi represents the first positive definite diagonal matrix, K vi represents the second positive definite diagonal matrix, represents the velocity state vector error of agent i, represents the fifth coefficient matrix of the kinematic model of follower i, represents the position state vector error of agent i, represents the sixth coefficient matrix of the dynamic model of follower i, v i represents the velocity state vector of agent i, represents the seventh coefficient matrix of the follower i dynamics model, η i represents the position state vector of agent i, represents the eighth coefficient matrix of the follower i dynamics model, represents the first-order derivative of the auxiliary stabilization quantizer of agent i.

[0038] The beneficial effects of the present invention are:

[0039] (1) The present invention designs a formation cooperative control method for heterogeneous multi-agent systems, which enables high-dimensional agents to adopt the global information of low-dimensional agents; for low-dimensional agents, only partial information of high-dimensional neighbors is used; based on this method, agents in the same dimensional group can form a time-varying formation pattern in their own dimension, and agents in different dimensional groups can move cooperatively in multiple dimensions, so that followers in different dimensions can cooperatively track the leader, effectively solving the problem of partial dimensional function failure that high-dimensional agents may face;

[0040] (2) The present invention utilizes the contraction constraint formula to design the auxiliary control rate for online optimization of the heterogeneous multi-agent system, which can control the formation to converge in a very short time, and the formation can quickly and effectively construct and transform the formation, and the formation remains stable, with very small error fluctuations and high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the cooperative control method of heterogeneous multi-agent system formation;

[0042] Figure 2 The schematic diagram of the structure of the formation cooperative control of a heterogeneous multi-agent system consisting of three unmanned boats;

[0043] Figure 3 The schematic diagram of the structure of the formation cooperative control of a heterogeneous multi-agent system composed of three underwater robots;

[0044] Figure 4It is the 3D space trajectory diagram of the unmanned boat-underwater robot heterogeneous multi-agent system;

[0045] Figure 5 It is the projection diagram of the spatial trajectory onto the 2D plane xy plane;

[0046] Figure 6 This is the position error diagram of the unmanned boat in the formation;

[0047] Figure 7 is the position error diagram of the underwater robot in the formation;

[0048] Figure 8 This is the control input diagram of the unmanned boat;

[0049] Fig. 9 Control input diagram for underwater robot. DETAILED DESCRIPTION

[0050] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0051] like Figure 1 As shown, the present invention provides a method for coordinated control of a heterogeneous multi-agent system formation, comprising the following steps:

[0052] S1. Construct a second-order multi-dimensional heterogeneous multi-agent system, and construct kinematic and dynamic models for the leader and follower in the second-order multi-dimensional heterogeneous multi-agent system;

[0053] S2, determining a controller model according to the kinematic model and dynamic model of the leader and the kinematic model and dynamic model of the follower;

[0054] S3, construct the Lyapunov function and determine the auxiliary control law of the follower according to the controller model;

[0055] S4. According to the auxiliary control law of the followers, the coordinated control of the heterogeneous multi-agent system formation is completed.

[0056] In the embodiment of the present invention, in S1, the second-order multi-dimensional heterogeneous multi-agent system includes a leader and a plurality of followers.

[0057] In this embodiment of the present invention, the kinematic model of the leader The expression is:

[0058]

[0059] In the formula, R g (t) represents the first coefficient matrix, v0(t) represents the velocity state vector of the leader;

[0060] The dynamics model of leadership The expression is:

[0061]

[0062] In the formula, A g (t) represents the second coefficient matrix, B g (t) represents the third coefficient matrix, η0(t) represents the position state vector of the leader, C g (t) represents the fourth coefficient matrix.

[0063] In the embodiment of the present invention, the kinematic model of the follower The expression is:

[0064]

[0065] In the formula, represents the fifth coefficient matrix, v i (t) represents the velocity state vector of agent i;

[0066] Dynamic model of the follower The expression is:

[0067]

[0068] In the formula, represents the sixth coefficient matrix, represents the seventh coefficient matrix, η i (t) represents the position state vector of agent i, represents the eighth coefficient matrix, u i (t) represents the control input vector of agent i.

[0069] In S1, consider a heterogeneous multi-agent system with a leader and N followers. The information exchange between the N followers can be represented by a graph To describe, is a set of N nodes; is the set of edges; is a weighted adjacency matrix, where a ij ≥0, a ij represents the adjacency weight between followers i and j. If (j, i)∈ε, then for any a ij >0; otherwise a ij = 0. A directed edge (j, i)∈ε indicates that agent i receives information from agent j. To exclude self-loops, Definition ii = 0. The neighbor set of node i is recorded as Define the degree matrix as Δ = diag{deg(1), deg(2)...., deg(N)}, where is the degree of agent i. The Laplacian matrix of the directed graph is The directed path from agent j to agent i is (j, i1), (i1, i2)...., (i k-1 , i k ), (i k , i). If then is an undirected graph.

[0070] Suppose there are N followers in g different dimensions. Decompose the N followers into g groups according to the dimensions of their position and velocity vectors. Agents in the same group have the same dimension, and agents in different groups have different dimensions. Let denote the set of g. For any and p ≠ q, it can be seen that ( is an empty set), and Suppose there are m q agents in group q, For any agent Define as the subscript of the subset to which agent i belongs, that is, Denote the number of dimensions contained in the position and velocity vectors of agent i in as The N agents can be redescribed as: for If i < j, then If then From this, it can be obtained that for any and p < q, there is n p < n q . This means that for any If i < j, then Obviously, the agents in group g have the highest dimensions of position and velocity vectors. The dimensions of the position and velocity vectors of the leader are the same as those of the group agents.

[0071] Existing leader-follower cooperative control for multi-agent systems usually requires the assumption that the leader has a direct path to each follower. However, under this assumption, some high-dimensional agents in the present invention may only receive information from low-dimensional agents. Due to insufficient information, the cooperative control between these high-dimensional agents may fail. Therefore, for multi-dimensional multi-agent systems, the present invention requires the following assumption: Assume that there is a directional path from the leader to each follower from high to low.

[0072] Agents are divided into g groups according to their dimensions. Cross-dimensional formation control means that agents in the same dimensional group form a time-varying formation in their own dimension, and agents in different dimensional groups move in coordination in their own dimensions. It requires cooperation of multi-agent systems in multiple dimensions. Its purpose is to drive the followers of the highest dimension (belonging The intelligent agents of the group (in the same dimension) form a time-varying formation to track the leader, and the followers of other dimensions form a lower-dimensional formation to track the partial state of the leader, so that it can not only ensure the consistency of the local state of the formations in different dimensions, but also maintain the consistency of the complete state within the formation of the same dimension. It should be pointed out that the cooperation between intelligent agents of different dimensions is the guarantee for achieving the goal of cross-dimensional group control. This control framework has a wide range of application potential in practical applications. For example, drones flying in three-dimensional space and unmanned surface / ground vehicles moving in two-dimensional space can form cross-dimensional formations to collaboratively track flying targets on the sea / land; unmanned underwater robots sailing in three-dimensional space and unmanned boats moving in two-dimensional space can form cross-dimensional formations to collaboratively track stealth targets in the water.

[0073] In the embodiment of the present invention, in S2, the expression of the controller model is:

[0074]

[0075]

[0076] Where Ji represents the performance function of the follower i controller, represents the predictive control input of follower i, S(δ) represents the piecewise function of the sampling period, δ represents the sampling period, T represents the prediction time domain, N represents the total number of followers, and a ij represents the adjacency weight between followers i and j, represents the state error of follower i relative to follower j, s represents the independent variable of the integrated term, Q i1 represents the first weight coefficient matrix corresponding to follower i, b i0 represents the adjacency weight between follower i and the leader, represents the state error of follower i relative to the leader, Q i0represents the second weight coefficient matrix corresponding to follower i, represents the collision avoidance cost function of follower i relative to follower j, represents the predictive control input of follower i with s as the independent variable, R i represents the third weight coefficient matrix of follower i, represents the terminal state error of follower i relative to follower j, P i1 represents the third weight coefficient matrix corresponding to follower i, b i0 represents the adjacency weight between follower i and the leader, represents the terminal state error of follower i relative to the leader, P i0 represents the fourth weight coefficient matrix corresponding to follower i, represents the current state of follower i, x i (t0) represents the current state of follower i, t0 represents the current time, represents the current state of follower j, x j (t0) represents the current state of follower j, represents the predicted state of follower i, represents the first-order derivative of the predicted state of follower i, represents the predictive control input of follower i, represents the predicted state of follower j, represents the first-order derivative of the predicted state of follower j, represents the predictive control input of follower j, V i represents the control Lyapunov function of follower i, x i represents the state of follower i, represents the first-order derivative of the current state of follower i, represents the current control input of follower i, represents the first-order derivative of the current state of follower i based on the auxiliary control law, represents the auxiliary control law of follower i at the current state, u i max represents the maximum control input of follower i, Represented as the set of followers.

[0077] In S2, the system model of follower i is established as:

[0078]

[0079] Among them, x i (t) is the state of follower i, u i (t) is the control input of follower i.

[0080] Assume that follower i can receive information from the leader. The dimension of is less than or equal to the state dimension of the leader. To solve the state error of follower i relative to the leader, define is the state that the leader applies to follower i, so that x0(t) has the same i (t) the same dimensions. Assume that follower i can receive information from follower j. When the dimension of is greater than the state dimension of follower j, in order to solve the state error of follower i relative to follower j, define is the state of follower j applied to follower i, where the state of follower j for the dimension missing from follower i is given by x i (t) The state quantity of the current dimension is supplemented so that x j (t) has the same i (t) the same dimensions; when When the dimension of is less than or equal to the state dimension of follower j, define is the state of follower j applied to follower i, so that x j (t) has the same i (t)same in all dimensions.

[0081] The state error of follower i relative to the leader and follower j is defined as follows:

[0082]

[0083] in are the predicted state, predicted control input, current state, and current control input of follower i and follower j respectively; is the predicted status of the leader; J i is the performance function of the follower i controller; Q i1 , Q i0 , R i , P i1 , P i0 is the weighted matrix corresponding to follower i; is the collision avoidance cost function of follower i relative to follower j. i max 、V i , are the maximum control input of follower i, the control Lyapunov function, and the auxiliary control law at the current state. δ is the sampling period, T is the prediction time domain, and S(δ) is the piecewise function system of the sampling period δ. and are the relative expectations of the states between follower i and follower j and the leader, respectively.

[0084] The collision avoidance cost function of follower i relative to follower j is defined as follows:

[0085]

[0086] in and are the predicted spatial position vectors of follower i and follower j respectively, is the weight coefficient. To ensure the sensitivity of the cost function and avoid the situation where the denominator is zero, A small positive number. Set a safe distance constraint Where R is the safety radius of each agent i.

[0087] Change weight coefficient The value of will lead to different replanning trajectories. When the value of is large, the planning result tends to be conservative; that is, the replanned trajectory will increase the distance between the agents to avoid collision. a When , the weight coefficient has no effect on the planning results.

[0088] In this embodiment of the present invention, S3 includes the following sub-steps:

[0089] S31, constructing a first Lyapunov function and a second Lyapunov function;

[0090] S32. Determine an auxiliary control law of the follower according to the first Lyapunov function, the second Lyapunov function and the controller model.

[0091] In the embodiment of the present invention, in S31, the first Lyapunov function V 1i The expression is:

[0092]

[0093] In the formula, represents the transpose of the state vector error of the position of agent i, K ηi represents the first positive definite diagonal matrix, Represents the position state vector error of agent i.

[0094] In the embodiment of the present invention, in S31, the second Lyapunov function V 2i The expression is:

[0095]

[0096] In the formula, represents the transpose of the velocity state vector error of agent i, K virepresents the second positive definite diagonal matrix, represents the velocity state vector error of agent i, V 1i represents the first Lyapunov function.

[0097] In the embodiment of the present invention, in S32, the auxiliary control law h of the follower i The expression is:

[0098]

[0099] In the formula, K 2i represents the positive definite gain coefficient matrix, K ηi represents the first positive definite diagonal matrix, K vi represents the second positive definite diagonal matrix, represents the velocity state vector error of agent i, represents the fifth coefficient matrix of the kinematic model of follower i, represents the position state vector error of agent i, represents the sixth coefficient matrix of the dynamic model of follower i, v i represents the velocity state vector of agent i, represents the seventh coefficient matrix of the follower i dynamics model, η i represents the position state vector of agent i, represents the eighth coefficient matrix of the follower i dynamics model, represents the first-order derivative of the auxiliary stabilization quantizer of agent i.

[0100] In an embodiment of the present invention, a distributed model predictive control method applied to a heterogeneous multi-agent system is specifically:

[0101] 1. For each agent i, Initialize sampling period δ, weight matrix Q i1 , Q i0 , R i , P i1 , P i0 , safety radius R, weight coefficient And other design parameters.

[0102] 2. The current system state x of agent i i (t) Sampling and inputting the objective function J i .

[0103] 3. Receive trajectory states x0(t) and x from the leader and agent j j (t), j≠i, and x0(t) and x j (t) is input to the objective function J i .

[0104] 4. Set x i (t0) = x i (t), solve the optimization problem in the objective function, define is the optimal (suboptimal) control input sequence obtained.

[0105] 5. In the current sampling period, The first control variable in the sequence is κ i (s) as the control input, that is, u i (t) = K i (s), s∈[0,δ].

[0106] 6. Roll the time domain, set t = t + δ, and jump to step 2.

[0107] In the embodiment of the present invention, the system stability analysis is performed. By designing the auxiliary control rate, it can be known that as long as the relationship ||h i (t)|| ∞ ≤u i max Be satisfied, there is always u i (t)≤u i max . Known V 2i (x i ) is continuously differentiable and completely unbounded. According to the inverse Lyapunov stability theory, there must be a Class Functions i (·), (i=1, 2, 3), satisfying Since the optimal solution The solution will be performed in each sampling period, then

[0108] According to the Lyapunov argument, the closed-loop system under this algorithm is globally asymptotically stable in the domain of attraction. In addition, the range of the domain of attraction can be expanded by reducing the control gain. Although the asymptotic stability only depends on the control gain matrix K 1i and K 2i The positive definiteness of the controller function designed by the backstepping method is determined by the size of the control gain. A smaller control gain will lead to slower convergence, so the controller needs to make a certain trade-off between performance and convergence range. The distributed model predictive control technology uses online optimization to enable the controller to generate optimal control about the objective function with a smaller control gain to obtain better control performance.

[0109] The following is a specific application case of this control method.

[0110] The present invention is applied to the formation cooperative control of a heterogeneous multi-agent system consisting of three unmanned vehicles (USVs) and three underwater robots (UUVs). In the subscripts of variables and parameters, S represents the unmanned vehicle and U represents the underwater robot; according to Figure 2 and Figure 3 , unmanned boat ①, unmanned boat ②, unmanned boat ③, underwater robot ④, underwater robot ⑤ and underwater robot ⑥ are represented by subscripts S1, S2, S3, U1, U2, U3 respectively.

[0111] Establish the kinematic and dynamic model of the heterogeneous multi-agent system of unmanned boat and underwater robot:

[0112]

[0113] Among them, η S =[x S y S ψ S ] T ,(x s y S ) and ψ S are the position coordinates and yaw angle of the unmanned boat; v S =[u s v S r S ] T ,u S 、v S and r S are the longitudinal velocity, sway velocity and bow angular velocity of the unmanned boat respectively; η U =[x U y U z U θ U ψ U ] T ,(x U y U z U ), θ U and ψ U are the position coordinates, pitch angle and bow angle of the underwater robot; v U =[u U v U w U q U r U ] T ,u U 、v U 、w U ,q U and r U They are the longitudinal velocity, lateral velocity, vertical velocity, pitch angular velocity and bow angular velocity of the underwater robot.

[0114] is the rotation matrix between the earth coordinate system and the unmanned boat hull coordinate system; is the inertial mass matrix of the unmanned boat; is the Coriolis force and centripetal matrix of the unmanned boat; is the hydrodynamic damping coefficient matrix of the unmanned boat; τ S =[T uS 0 τ rS ] T is the control input of the unmanned boat; T wS =[τ wuS τ wvS τ wrS ] T It is the external environmental disturbance to the unmanned boat.

[0115] M is the rotation matrix between the earth coordinate system and the underwater robot body coordinate system; U =diag{m 11U , m 22U , m 33U , m 44U , m 55U} is the inertial mass matrix of the underwater robot; is the Coriolis force and centripetal force matrix of the underwater robot. U (v U ) = diag{d 11U , d 22U , d 33U , d 44U , d 55U} is the fluid damping matrix of the underwater robot; is the restoring force (torque) of the buoyancy and gravity acting on the underwater robot; τ U =[τ uU τ vU τ wU τ qU τ rU ] T is the control input of the underwater robot; τ wU =[τ wuU τ w v U τ wwU τ wqU τ wrU ] T is the external environmental disturbance to which the underwater robot is subjected.

[0116] The unmanned boat and underwater robot system model is established as follows:

[0117]

[0118] Among them, x S 、x U are the states of the unmanned boat and underwater robot respectively; u S 、u U are the control inputs of the unmanned boat and underwater robot respectively.

[0119] Design auxiliary control rate of unmanned boat-underwater robot heterogeneous multi-agent system:

[0120] Among them Kv S , Kη S , K vU , K ηU are all positive definite diagonal matrices; K 1S , K 2S , K 1U , K 2U are all positive definite gain coefficient matrices; where the error is defined as follows:

[0121]

[0122] The auxiliary stabilization vector is defined as follows:

[0123]

[0124] Stability analysis of heterogeneous multi-agent system of unmanned boat and underwater robot:

[0125] Theorem 1: Auxiliary control rate of unmanned boat If the following relations are satisfied:

[0126] Then the unmanned boat control system is asymptotically stable, that is, when t≥0, ||h S (t)|| ∞ ≤u S max .

[0127] The theorem is proved as follows: The positive definite matrix K ηS , K vS , K 1S , K 2S Designed as K ηS =diag{k ηSi}, K vS =diag{k vSi}, K 1S =diag{k 1Si}, K2S =diag{k 2Si}. Define K ηS The largest element in Minimum element Define K vS The largest element in Minimum element Define K 1S The largest element in Minimum element Define K 2S The largest element in Minimum element

[0128] Take constant Available Because |m 11S |,|m 22S |,|m 23S |,|m 32S |,|m 33S | are all constants, so we know is bounded, so let the constant Make

[0129] Depend on Knowable Considering Available

[0130] For the matrix R S (ψ S ) takes the infinite norm, we have:

[0131]

[0132] From this we can get the auxiliary stabilization vector α S The infinite norm of :

[0133]

[0134] Assume that the external disturbance velocity v wS is bounded and satisfies for positive numbers have

[0135] C S (v S ) Take the infinite norm and rearrange it to get:

[0136] set up have to

[0137] Assume that the external disturbance input τ wS is bounded and satisfies for positive numbers have It can be seen that |d 11S |,|d 22S |,|d 23S |,|d 32S |,|d 33S | are bounded, take From this we can get D S (v S )

[0138] From the definition, we know We can get:

[0139] In summary, we can get:

[0140]

[0141] From this we can see that ||h S (t)|| ∞ ≤u S max . The proof is complete.

[0142] Theorem 2: For the auxiliary control rate of underwater robots If the following relations are satisfied:

[0143]

[0144] Then the underwater robot control system is asymptotically stable, that is, when t≥0, ||h U (t)|| ∞ ≤u U max .

[0145] The proof of the theorem is as follows:

[0146] Positive definite matrix K ηU , K vU , K 1U , K 2U Designed as K ηU =diag{k ηUi}, K vU =diag{k vUi}, K 1U =diag{k 1Ui}, K 2U =diag{k 2Ui}. Define KηU The largest element in Minimum element Define K vU The largest element in Minimum element Define K 1U The largest element in Minimum element Define K 2U The largest element in Minimum element

[0147] It is worth noting that the inertial mass matrix of the underwater robot is a symmetric positive definite matrix with an upper bound, namely Take a constant Available Because |m 11U |,|m 22U |,|m 33U |,|m 44U |,|m 55U | are all constants, so we know is bounded, so let the constant Make The restoring force (torque) of buoyancy and gravity on the underwater robot is bounded: is a constant.

[0148] Depend on Knowable Considering Available

[0149] According to the actual working conditions, the pitch angle θ of the underwater robot is U Constraints are imposed, and 0≤θ U ≤π / 4. The matrix J is obtained U (η U )and The infinite norm of :

[0150]

[0151] From this we can get the auxiliary stabilization vector α U The infinite norm of :

[0152]

[0153] We can get:

[0154]

[0155] Assume that the external disturbance velocity v wU is bounded and satisfies for positive numbers have

[0156] C U (v U ) Take the infinite norm and rearrange it to get: set up have to

[0157] Assume that the external disturbance input τ wU is bounded and satisfies for positive numbers have

[0158] Take a constant Right D U (v U ) Take the infinite norm and rearrange it to get:

[0159] set up have to

[0160] From the definition, we know We can get:

[0161] In summary, we can get: From this we can get ||h U (t)|| ∞ ≤u U max . The proof is complete.

[0162] The simulation settings of the unmanned boat-underwater robot heterogeneous multi-agent system are as follows:

[0163] (1) Communication diagram setting: Based on the control method of the invention, the heterogeneous multi-agent system can realize the time-varying communication chain. The system changes the communication topology at a time of 30 seconds. Figure 2 This is the system communication diagram 30 seconds ago. Figure 3 This is the system communication diagram after 30 seconds. is a virtual leader, ①, ②, ③ are unmanned boats, ④, ⑤, ⑥ are underwater robots.

[0164] (2) Model parameter setting

[0165] Table 1

[0166]

[0167]

[0168] The state equation of the horizontal position of the known virtual leader The trajectory state of the virtual leader is set to η0 = [10sin(0.1t+π / 12); -10cos(0.1t+π / 12)+10; 3; 0; 0.1t+π / 12]. To set the formation, we take the position state of the virtual leader (x0, y0, z0) = (10sin(0.1t+π / 12), -10cos(0.1t+π / 12)+10, 3), thus setting:

[0169] When time t≤30 seconds, unmanned boat ①, unmanned boat ②, unmanned boat ③, underwater robot ④, underwater robot ⑤, underwater robot ⑥ and the leader The relative expectations of the positions between are: (-2sin(0.1t+π / 12), 2coS(0.1t+π / 12), -3), (0, 0, -3), (2sin(0.1t+π / 12), -2cos(0.1t+π / 12), -3), (-2sin(0.1t+π / 12), 2coS(0.1t+π / 12), 2sin(t+π / 2-π / 12)), (0, 0, 0), (2sin(0.1t+π / 12), -2cos(0.1t+π / 12), 2sin(t-π / 2-π / 12)).

[0170] When time t≥30 seconds, unmanned boat ①, unmanned boat ②, unmanned boat ③, underwater robot ④, underwater robot ⑤, underwater robot ⑥ and the leader The relative expectations of the positions between are: (-2sin(0.1t+π / 12), 2cos(0.1t+π / 12), -3), (0, 0, -3), (2sin(0.1t+π / 12), -2cos(0.1t+π / 12), -3), (-2sin(0.1t+π / 12)coS(2t-60), 2coS(0.1t+π / 12)coS(2t-60), 2sin(2t-60)), (0, 0, 0), (2sin(0.1t+π / 12)coS(-2t+60), -2cos(0.1t+π / 12)coS(-2t+60), 2sin(-2t+60)).

[0171] An underwater robot ⑤ and an unmanned boat ② are set to track the leader The spatial position state and horizontal position state of the unmanned boat ① and the unmanned boat ③ are arranged in a straight line with an interval of about 2 meters relative to the unmanned boat ②. When the time t≤30 seconds, the underwater robot ④ and the underwater robot ⑥ maintain the same horizontal position state as the unmanned boat ① and the unmanned boat ③ respectively, and the vertical direction is set to the sine function of time t, with an amplitude of 2 meters and a period of 2π seconds. When the time t≥30 seconds, the underwater robot ④ and the underwater robot ⑥ perform a circular motion about the underwater robot ⑤. In the hull coordinate system of the underwater robot ⑤, the underwater robot ④ and the underwater robot ⑥ always have the same horizontal axis coordinate as the underwater robot ⑤, and the straight-line distance between them and the underwater robot ⑤ in the plane composed of the longitudinal axis and the vertical axis is always set to 2 meters, and the angular velocity is set to 2rad / s.

[0172] Set the initial state of agents ① to ⑥: [0.500000] T , [000000] T , [-0.500000] T , [00.52000000000] T , [0.51.52.5000000000] T , [2-0.53.5000000000] T .

[0173] (4) System parameter settings

[0174] The system parameters are set as follows: δ = 0.1, N t =5, T = 0.5, u S max =400,u U max =800,σ J =0.01, S J =10, R=1, D a =2, Q S1 =P S1 =diag(10 3 , 10 3 , 10 2 ,10,10,10),Q S0 =P S0 =diag(10 4 , 10 4 , 10 2 , 10, 10, 10), R S =diag(10 -4 , 10 -4 , 10 -4 ), Q U1 =P U1 =diag(10 3 , 10 3 , 10 3, 10 2 , 10 2 ,10,10,10,10,10),Q U0 =P U0 =diag(10 4 , 10 4 , 10 4 , 10 2 , 10 2 ,10,10,10,10,10),R U =diag(10 -4 , 10 -4 , 10 -4 , 10 -4 , 10 -4 ), K ηS =diag(1.2,1.2,1.2),K vS =diag(1,1,1),K 1S =diag(0.8,0.8,0.8),K 2S =diag(0.2,0.2,0.2),K ηU =diag(1.2, 1.2, 1.2, 1.2, 1.2), Kv U =diag(1,1,1,1,1),K 1U =diag(0.8, 0.8, 0.8, 0.8, 0.8), K 2U =diag(0.2, 0.2, 0.2, 0.2, 0.2).

[0175] Time-varying external disturbances are simulated using trigonometric functions:

[0176]

[0177] Figure 4 It is the 3D space trajectory diagram of the unmanned boat-underwater robot heterogeneous multi-agent system. Figure 5 for Figure 4 The projection of the spatial trajectory onto the 2D plane xy. Figure 4 and Figure 5 ,It can be seen that both the unmanned boat and the underwater robot can track the leader well, transform the communication topology and change the formation, and the motion trajectory is relatively smooth. Figure 6 and Figure 7 is the position error diagram of the unmanned boat and the underwater robot in the formation, (Xe, Ye, Ze) is the coordinate error of the follower's current position relative to its position in the formation, Xe is the error of the x-coordinate, Ye is the error of the y-coordinate, and Ze is the error of the z-coordinate. Figure 6 and Figure 7It can be seen that the heterogeneous multi-agent system can quickly and effectively construct and transform the formation, and the formation remains stable, with small error fluctuations and high accuracy. Figure 8 and Fig. 9 Provides control input for unmanned boats and underwater robots.

[0178] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for coordinated control of a heterogeneous multi-agent system formation, characterized in that: The following steps are involved: S1. Construct a second-order multi-dimensional heterogeneous multi-agent system, and construct kinematic and dynamic models for the leader and follower in the second-order multi-dimensional heterogeneous multi-agent system; S2, determining a controller model according to the kinematic model and dynamic model of the leader and the kinematic model and dynamic model of the follower; S3, construct the Lyapunov function and determine the auxiliary control law of the follower according to the controller model; S4, according to the auxiliary control law of the follower, complete the coordinated control of the heterogeneous multi-agent system formation; In S2, the expression of the controller model is: ； ； ； ； ； ； In the formula, Indicates followers The performance function of the controller, Indicates followers The predictive control input, represents the piecewise function of the sampling period, represents the sampling period, represents the prediction time domain, Represents the total number of followers, Indicates followers With followers The adjacency weight between Indicates followers Relative to followers The state error, represents the independent variable of the integrated term, Indicates followers The corresponding first weight coefficient matrix, Indicates followers The adjacency weight with the leader, Indicates followers The state error relative to the leader, represents the second weight coefficient matrix corresponding to follower 𝑖, Indicates followers Relative to followers The collision avoidance cost function is: Indicates followers by is the predictive control input of the independent variable, represents the third weight coefficient matrix of follower 𝑖, Indicates followers Relative to followers The terminal state error, represents the third weight coefficient matrix corresponding to follower 𝑖, Indicates followers The adjacency weight with the leader, Indicates followers The terminal state error relative to the leader, Indicates followers The corresponding fourth weight coefficient matrix, Indicates followers The current status of Indicates followers The current status of Indicates the current moment, Indicates followers The current status of Indicates followers The current status of Indicates followers The predicted state of Indicates followers Predict the first derivative of the state, Indicates followers The predictive control input, Indicates followers The predicted state of Indicates followers Predict the first derivative of the state, Indicates followers The predictive control input, Indicates followers The controlling Lyapunov function, Indicates followers status, Indicates followers The first-order derivative of the current state, Indicates followers The current control input, Indicates followers The first-order derivative of the current state based on the auxiliary control law, Indicates followers The auxiliary control law under the current state, Indicates followers The maximum control input, Represented as the set of followers.

2. The method for coordinated control of heterogeneous multi-agent system formation according to claim 1, characterized in that: In S1, the second-order multi-dimensional heterogeneous multi-agent system includes a leader and several followers.

3. The method for coordinated control of heterogeneous multi-agent system formation according to claim 2, characterized in that: Kinematic model of the leader The expression is: ； In the formula, represents the first coefficient matrix, represents the velocity state vector of the leader; The leader dynamics model The expression is: ； In the formula, represents the second coefficient matrix, represents the third coefficient matrix, represents the position state vector of the leader, represents the fourth coefficient matrix.

4. The method for coordinated control of heterogeneous multi-agent system formation according to claim 2, characterized in that: The follower Kinematic model The expression is: ； In the formula, represents the fifth coefficient matrix, Representing an Agent The velocity state vector of The follower The dynamic model The expression is: ； In the formula, represents the sixth coefficient matrix, represents the seventh coefficient matrix, Representing an Agent The position state vector, represents the eighth coefficient matrix, Representing an Agent The control input vector.

5. The method for coordinated control of heterogeneous multi-agent system formation according to claim 1, characterized in that: The S3 comprises the following sub-steps: S31, constructing a first Lyapunov function and a second Lyapunov function; S32. Determine an auxiliary control law of the follower according to the first Lyapunov function, the second Lyapunov function and the controller model.

6. The method for coordinated control of heterogeneous multi-agent system formation according to claim 5, characterized in that: In S31, the first Lyapunov function The expression is: ； In the formula, Representing an Agent The transpose of the position state vector error, represents the first positive definite diagonal matrix, Representing an Agent The position state vector error.

7. The method for coordinated control of heterogeneous multi-agent system formation according to claim 5, characterized in that: In S31, the second Lyapunov function The expression is: ； In the formula, Representing an Agent The transpose of the velocity state vector error, represents the second positive definite diagonal matrix, Representing an Agent The velocity state vector error, represents the first Lyapunov function.

8. The method for coordinated control of heterogeneous multi-agent system formation according to claim 5, characterized in that: In S32, the auxiliary control law of the follower The expression is: ； In the formula, represents the positive definite gain coefficient matrix, represents the first positive definite diagonal matrix, represents the second positive definite diagonal matrix, Representing an Agent The velocity state vector error, Indicates followers The fifth coefficient matrix of the kinematic model, Representing an Agent The position state vector error, Indicates followers The sixth coefficient matrix of the kinetic model, Representing an Agent The velocity state vector, Indicates followers The seventh coefficient matrix of the dynamic model, Representing an Agent The position state vector, Indicates followers The eighth coefficient matrix of the kinetic model, Representing an Agent First derivative of the auxiliary stabilization quantity.

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