A multi-unmanned system formation control method based on specified time convergence

Abstract

The application discloses a multi-unmanned system formation control method based on specified time convergence, and belongs to the field of unmanned system control. The application solves the problem that multi-unmanned systems cannot converge to a common target state at a specified time under arbitrary initial states and dynamically changing environments. The method comprises the following steps: step one, establishing a multi-unmanned system kinematics model containing position, velocity and control input information; step two, regarding each unmanned system as a follower, taking the tracking error of each follower relative to a target position and the tracking error of each follower relative to a target velocity as state variables in a multi-unmanned system formation model of actual followers-virtual leaders, and then designing a formation controller according to the state variables and a reference differential convergence function; and step three, designing a final formation controller of the multi-unmanned system with disturbance based on a sliding mode control and the formation controller designed in step two. The method can be applied to multi-unmanned system formation control.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of unmanned system control, and particularly relates to a multi-unmanned system formation control method based on specified time convergence. BACKGROUND

[0002] In recent years, with the development of robot technology, automatic control theory, computer technology, sensor technology, wireless communication technology and other technologies, unmanned systems, mainly based on unmanned vehicles, have gradually emerged and received widespread attention in various fields, and have been applied in smart agriculture, collaborative assembly and other fields. Unmanned systems are usually equipped with sensors, communication devices, autonomous navigation and control units, and can perform tasks without direct human intervention. Multi-unmanned system clusters refer to multiple unmanned systems working together in a coordinated manner to form a whole to improve efficiency, adaptability and robustness. The cluster can be self-organized to adapt to changing task requirements and environmental conditions. In a multi-unmanned system cluster, individual unmanned system members may need to collaborate, compete or work together to achieve system-level goals such as consistency, optimization, search, monitoring, etc. Among them, the consistency of the multi-unmanned system cluster refers to the final convergence of the states (such as position, speed, direction, etc.) of all unmanned systems to a common target state, which is a key challenge for multi-unmanned system cluster control and the basis for the multi-unmanned system cluster to play to its strengths.

[0003] In actual engineering, when performing formation coordination control on a multi-unmanned system cluster, all unmanned systems in the formation need to converge to a common target state under dynamic changing environments and uncertain conditions. However, due to the influence of factors such as initial formation error, external environmental disturbance and noise, obstacles in the environment, communication delay and bandwidth limitations between multiple unmanned systems, traditional multi-unmanned system formation control methods can only make the states of multiple unmanned systems converge to a common target state within a limited time, which cannot meet the strict time control requirements. At the same time, this may also lead to loss of stability in formation control, increased risk of collision, and increased complexity of control algorithms. Therefore, for the consistency problem in multi-unmanned system formation control, the design method of the formation controller is researched to enable each unmanned system member in the formation to converge to a common target state at a specified time under arbitrary initial states and dynamic changing environments, which has important theoretical research significance and important practical application value. SUMMARY

[0004] The purpose of the present application is to solve the problem that multiple unmanned systems cannot converge to a common target state at a specified time under arbitrary initial states and dynamic changing environments, and a multi-unmanned system formation control method based on specified time convergence is proposed.

[0005] The technical scheme adopted by the present application to solve the above technical problems is: a multi-unmanned system formation control method based on specified time convergence, which specifically comprises the following steps:

[0006] Step one, establishing a multi-unmanned system kinematics model containing position, velocity and control input information;

[0007] Step two, taking each unmanned system as a follower respectively, in the actual follower-virtual leader multi-unmanned system formation model, taking the tracking error of each follower relative to the target position and the tracking error of each follower relative to the target velocity as state variables;

[0008] designing a reference differential convergence function ψ(s, t) based on a reference convergence function ε(t), and then designing a formation controller according to the state variables and the reference differential convergence function ψ(s, t);

[0009] Step three, designing a final formation controller of the multi-unmanned system with disturbance based on the sliding mode control and the formation controller designed in step two.

[0010] Further, the multi-unmanned system kinematics model is established by using a state space method.

[0011] Further, the specific process of step one is:

[0012]

[0013] wherein, x i (t) represents the position of the i-th unmanned system, t is time, x i (t) ∈ R m , R is a real number, m is a dimension, v i (t) represents the velocity of the i-th unmanned system, v i (t) ∈ R m , represents the position change rate of the i-th unmanned system, represents the velocity change rate of the i-th unmanned system, u i (t) represents the control input of the i-th unmanned system, u i (t) ∈ R m , and N is the total number of unmanned systems in the formation.

[0014] Further, in the multi-unmanned system formation model, the kinematics model of the virtual leader is a second-order system:

[0015]

[0016] wherein x0(t) represents a position of the virtual leader, x0(t)∈R m , v0(t) represents a speed of the virtual leader, v0(t)∈R m , represents a position change rate of the virtual leader, represents a speed change rate of the virtual leader, u0(t) is an acceleration of the virtual leader.

[0017] Further, the tracking error of each follower relative to the target position and the tracking error of each follower relative to the target speed are taken as state variables, and the state variables are specifically:

[0018]

[0019] wherein e i represents a state variable of the i-th unmanned system, e ix represents a position tracking error of the i-th unmanned system, e iv represents a speed tracking error of the i-th unmanned system, h i represents an ideal formation position vector from the i-th unmanned system to the virtual leader, x i is a short form of x i (t), v i is a short form of v i (t), x0 is a short form of x0(t), v0 is a short form of v0(t), 0 m is an m-dimensional 0 vector.

[0020] Further, the reference differential convergence function ψ(s, t) is designed based on the reference convergence function ε(t), and specifically:

[0021]

[0022] wherein ε(t) is a reference convergence function, t f is a specified time, η is a regulation parameter, η>1, and ψ(s, t) is a reference differential convergence function.

[0023] Further, the formation controller is designed according to the state variable and the reference differential convergence function ψ(s, t), and specifically:

[0024]

[0025] wherein u i represents a control input of the i-th unmanned system, u i is a short form of u i (t), e i2,d is a speed tracking error e ivthe expected value of e i2,d = - ψ1(σ i1 , t), ψ1(σ i1 , t) = η1σ i1 / (t f -t), σ i1 is the actual position tracking error of the i-th unmanned system, η1is a tuning parameter, is the first order derivative of e i2,d , ψ2(σ i2 , t) = η2σ i2 / (t f -t), σ i2 is the actual velocity tracking error of the i-th unmanned system, η2is a tuning parameter, and t0is the control starting time.

[0026] Further, the tuning parameters satisfy: η1> 2 and η2> 1.

[0027] Further, the specific process of step three is:

[0028] The kinematic model of the multi-unmanned system with disturbance is:

[0029]

[0030] where d i (t) is the disturbance of the i-th unmanned system, and |d i (t)|≤ C1, |·| represents taking the absolute value, C1is the upper limit value of |d i (t)|, is the first order derivative of d i (t), C2is the upper limit value of ;

[0031] Then the final formation controller u i ' of the i-th unmanned system is:

[0032] u i ' = u i + u i,disc (7)

[0033] where u i,disc is the control for disturbance constraint imposed according to the sliding mode control;

[0034]

[0035] where k i,1 and k i,2 are positive constants, s i,1 is the sliding mode variable of the i-th unmanned system, sign(·) is the sign function, and τ is the integral variable.

[0036] Further, the sliding variable s of the ith unmanned system i,1 is:

[0037]

[0038] wherein, is the first order derivative of e i .

[0039] The beneficial effects of the present application are:

[0040] The present application establishes the kinematic model of multi-unmanned system with position, velocity and control input information by using state space method, adopts the system formation control mode of virtual leader-follower, takes the tracking error of each follower in the formation relative to its target position as the state variable, and designs the controller based on the reference convergence function and the reference differential convergence function, so that the specified state variable in the multi-unmanned system can converge to the target state at the specified time, and the initial state of each unmanned system does not need to be considered, therefore, the controller designed by the present application can make the multi-unmanned system strictly complete the ideal formation at the specified time without being affected by the initial formation error.

[0041] Meanwhile, the method of the present application also adopts the sliding mode control to design the matching anti-disturbance function for the controller, so that when the dynamic changing environment brings disturbance, it can still converge to the target state at the specified time, and the robustness of the formation control method is improved. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is the formation trajectory diagram of multi-unmanned system under strict specified time convergence control;

[0043] Figure 2 is the X direction position error of unmanned aircraft follower under strict specified time convergence control;

[0044] Figure 3 is the Y direction position error of unmanned aircraft follower under strict specified time convergence control;

[0045] Figure 4 is the X direction velocity error of unmanned aircraft follower under strict specified time convergence control;

[0046] Figure 5 is the Y direction velocity error of unmanned aircraft follower under strict specified time convergence control;

[0047] Figure 6 is the X direction position error of unmanned surface vessel follower under strict specified time convergence control;

[0048] Figure 7is the position error of the follower in Y direction of the unmanned surface vehicle under the strict specified time convergence control. DETAILED DESCRIPTION

[0049] Embodiment I: The method comprises the following steps:

[0050] Step 1: Establish a kinematic model of the multi-unmanned system containing position, velocity and control input information;

[0051] Step 2: Take each unmanned system as a follower, and take the tracking error of each follower relative to the target position and the tracking error of each follower relative to the target velocity as state variables in the actual follower-virtual leader multi-unmanned system formation model;

[0052] Design a reference differential convergence function ψ(s, t) based on the reference convergence function ε(t), and then design a formation controller according to the state variables and the reference differential convergence function ψ(s, t);

[0053] Step 3: Design a final formation controller of the multi-unmanned system with disturbance based on the sliding mode control and the formation controller designed in Step 2.

[0054] Embodiment II: The difference between this embodiment and Embodiment I is that the kinematic model of the multi-unmanned system is established by using the state space method.

[0055] The other steps and parameters are the same as those in Embodiment I.

[0056] Embodiment III: The difference between this embodiment and Embodiment I or II is that the specific process of Step 1 is as follows:

[0057]

[0058] wherein, x i (t) represents the position of the i-th unmanned system, t is time, x i (t) ∈ R m , R is a real number, m is the dimension, v i (t) represents the velocity of the i-th unmanned system, v i (t) ∈ R m , represents the rate of change of the position of the i-th unmanned system, represents the rate of change of the velocity of the i-th unmanned system, u i (t) represents the control input of the i-th unmanned system, u i (t) ∈ R mN is the total number of unmanned systems in the formation.

[0059] The other steps and parameters are the same as those in embodiment one or two.

[0060] Embodiment four: different from one of embodiments one to three, in the multi-unmanned system formation model, the second-order system kinematics model of the virtual leader is:

[0061]

[0062] wherein x0(t) represents the position of the virtual leader, x0(t)∈R m v0(t) represents the speed of the virtual leader, v0(t)∈R m represents the position change rate of the virtual leader, represents the speed change rate of the virtual leader, u0(t) is a given speed change function, i.e., the acceleration of the virtual leader.

[0063] The other steps and parameters are the same as those in one of embodiments one to three.

[0064] The formation model adopted in the application is a multi-unmanned system formation model of "actual follower-virtual leader", wherein the information of the virtual leader is shared by each unmanned system, and each unmanned system can realize its own movement by acquiring the information of the virtual leader and the information of the neighbor node, so as to achieve the final formation purpose. By designing the control signal u0(t) of the leader, the movement trajectory of the leader is specified, and the movement trajectory of the formation is indirectly designed. In the process of formation, the role of the leader is to control the travel route of the whole formation, and the relative deviation between the members as followers and the leader can control the formation shape. In the actual formation model, the leader can be a real individual member or a virtual leader. The leader considered in the application is a virtual leader, and since there is no leader entity, there is no need to worry about the problem of leader failure.

[0065] Embodiment five: different from one of embodiments one to four, the tracking error of each follower relative to the target position and the tracking error of each follower relative to the target speed are taken as state variables, and the state variables are specifically:

[0066]

[0067] wherein e i represents the state variable of the i-th unmanned system, e ix represents the position tracking error of the i-th unmanned system, e iv ​is the velocity tracking error of the ith unmanned system, h i is the ideal formation position vector of the ith unmanned system to the virtual leader, x i is the short form of x i (t), v i is the short form of v i (t), x0 is the short form of x0(t), v0 is the short form of v0(t), 0 m is a 0 vector of m dimensions.

[0068] The other steps and parameters are the same as one of the first to fourth embodiments.

[0069] When e i = 0, i = 1, 2, …, N, it means that the multi-unmanned system has achieved the desired formation shape at this time.

[0070] The sixth embodiment is different from one of the first to fifth embodiments in that the reference differential convergence function ψ(s, t) is designed based on the reference convergence function ε(t), specifically:

[0071]

[0072] wherein ε(t) is the reference convergence function, t f is the specified time, η is the adjustment parameter, η > 1, and ψ(s, t) is the reference differential convergence function.

[0073] The other steps and parameters are the same as one of the first to fifth embodiments.

[0074] The seventh embodiment is different from one of the first to sixth embodiments in that the formation controller is designed according to the state quantity and the reference differential convergence function ψ(s, t), specifically:

[0075]

[0076] wherein u i represents the control input of the ith unmanned system, u i is the short form of u i (t), e i2,d is the expected value of the velocity tracking error e iv , e i2,d = -ψ1(σ i1 , t), ψ1(σ i1 , t) = η1σ i1 / (t f -t), σ i1 is the actual position tracking error of the ith unmanned system, η1 is the adjustment parameter, is e i2,dthe first derivative of ψ1(σ i2 ,t)=η1σ i2 (t f -t),σ i2 is the actual speed tracking error of the i-th unmanned system, η1 is a tuning parameter, and t0 is the control starting time.

[0077] The other steps and parameters are the same as one of the first to sixth embodiments.

[0078] The present application takes the differential convergence function as the time-varying feedback function, and designs the controller based on the time-varying feedback function. The controller of the present application can achieve the strict specified time convergence, and solves the problem that the traditional multi-unmanned system formation control method can only make the state of the multi-unmanned system converge to the common target state in a limited time, and cannot converge in a strict specified time, and cannot meet the strict time control requirements. Under the action of the formation controller designed in the present application, when t≥t f , e ix =0, that is, the considered multi-unmanned system can achieve the formation formation in the strict specified time t f .

[0079] The eighth embodiment is different from one of the first to seventh embodiments in that the tuning parameters satisfy: η1>2 and η2>1.

[0080] The other steps and parameters are the same as one of the first to seventh embodiments.

[0081] The ninth embodiment is different from one of the first to eighth embodiments in that the specific process of the step three is:

[0082] The kinematic model of the multi-unmanned system with disturbance is:

[0083]

[0084] wherein d i (t) is the disturbance of the i-th unmanned system, and |d i (t)|≤C1, |·| represents taking the absolute value, C1 is the upper limit value of |d i (t)|, is the first derivative of d i (t), C2 is the upper limit value of ;

[0085] The influence of the disturbance on the formation controller u i ′ of the i-th unmanned system is constrained by using the sliding mode control, and the final formation controller u i ′ of the i-th unmanned system is:

[0086] u i ′=ui +u i,disc (7)

[0087] wherein, u i,disc is the control for disturbance constraint imposed according to the sliding mode control;

[0088]

[0089] wherein, k i,1 and k i,2 are positive constants, s i,1 is the sliding mode variable of the i-th unmanned system, sign(·) is the sign function, and τ is the integral variable.

[0090] The other steps and parameters are the same as one of the first to eighth embodiments.

[0091] The tenth embodiment is different from one of the first to ninth embodiments in that the sliding mode variable s i,1 of the i-th unmanned system is:

[0092]

[0093] wherein, is the first derivative of e i .

[0094] The other steps and parameters are the same as one of the first to ninth embodiments.

[0095] The state trajectory of the multi-unmanned system is initially on the sliding mode surface, and the disturbance is suppressed from the beginning. The multi-unmanned system is controlled by u i to achieve the effect of predetermined transient stability. Under the robust formation control action, when t≥t f , e ix =0, that is, the multi-unmanned system considered can achieve the formation shape at the specified time t f and has strong robustness to the disturbance.

[0096] In order to verify and demonstrate the effectiveness of the formation control algorithm designed by the present application, the present application carries out formation control simulation verification based on the multi-unmanned system cluster composed of four unmanned aerial vehicles and two unmanned surface vessels, and demonstrates the strong robust formation control effect of the multi-unmanned system converging at the specified time of the present application.

[0097] In the task environment, the height of the UAV follower 1 and 2 is fixed as Z1=10m, the height of the UAV follower 3 and 4 is fixed as Z2=5m, and the height of the unmanned surface vehicle follower 1 and 2 is fixed as Z3=0. Meanwhile, the height of the virtual UAV leader is set as Z1=10m, the height of the virtual unmanned surface vehicle leader is set as Z3=0, and the initial horizontal position of the two virtual leaders is set as x0(0)=[0,0] T , and the initial speed is set as v0(0)=[1,1] T . The ideal formation vectors of the six unmanned systems to the virtual leaders are set as Meanwhile, the initial positions of the six unmanned systems are set as

[0098] , and the initial speeds of the six unmanned systems are all set as 0.

[0099] Under the control of the method of the present application, the specified convergence time is set as t f =2s, the parameters of the UAV follower are set as η1=3 and η2=2, and the parameter of the unmanned surface vehicle is set as μ=3. The multi-unmanned system formation motion trajectory under the control of the method of the present application is shown in Figure 1 , the position error of the UAV follower is shown in Figure 2 and Figure 3 , the speed error of the UAV follower is shown in Figure 4 and Figure 5 , and the position error of the unmanned surface vehicle follower is shown in Figure 6 and Figure 7 .

[0100] The above calculation examples of the present application are only used to illustrate the calculation model and calculation process of the present application, and are not used to limit the embodiments of the present application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the present application are still within the protection scope of the present application.

Claims

1. A multi-unmanned system formation control method based on convergence over a specified time, characterized in that, The method specifically includes the following steps: Step 1: Establish a kinematic model of the multi-unmanned system that includes position, velocity, and control input information; Step 2: Treat each unmanned system as a follower. In the multi-unmanned system formation model of actual follower-virtual navigator, the tracking error of each follower relative to the target position and the tracking error of each follower relative to the target velocity are used as state variables. Based on the reference convergence function Design a reference differential convergence function. Then, based on the state variables and the reference differential convergence function... Design a formation controller; The reference convergence function Design a reference differential convergence function. Specifically: (4) in, It is the reference convergence function. It is a specified time. It's about adjusting parameters. , It is the reference differential convergent function; The convergence function based on the state variables and the reference differential function Design a formation controller, specifically: (5) in, Indicates the first The control input of an unmanned system yes abbreviation, It is speed tracking error Expected value , , It is the first The actual position tracking error of an unmanned system It's about adjusting parameters. yes The first derivative, , It is the first The actual speed tracking error of an unmanned system It's about adjusting parameters. It controls the start time; Step 3: Based on sliding mode control and the formation controller designed in Step 2, design the final formation controller for the multi-unmanned system with disturbances; The specific process of step three is as follows: The kinematic model of a multi-unmanned system with perturbations is as follows: (6) in, Indicates the first The location of an unmanned system. It is time. Indicates the first The rate of change of position of an unmanned system Indicates the first The speed of an unmanned system Indicates the first The control input of an unmanned system For the first Disturbances in unmanned systems, and , This represents taking the absolute value. yes The upper limit, yes The first derivative, , yes The upper limit; Then the first The ultimate formation controller for an unmanned system for: (7) in, It is a control applied for disturbance constraint based on sliding mode control; (8) in, and It is a positive constant. It is the first Sliding mode variables of an unmanned system It is a symbolic function. It is an integral variable.

2. The multi-unmanned system formation control method based on convergence within a specified time according to claim 1, characterized in that, The kinematic model of the multi-unmanned system is established using the state-space method.

3. The multi-unmanned system formation control method based on convergence within a specified time according to claim 1, characterized in that, The specific process of step one is as follows: (1) in, Indicates the first The location of an unmanned system. It is time. , It is a real number. It is a dimension. Indicates the first The speed of an unmanned system , Indicates the first The rate of change of position of an unmanned system , Indicates the first The rate of change of speed of an unmanned system , Indicates the first The control input of an unmanned system , It represents the total number of unmanned systems in the formation.

4. The multi-unmanned system formation control method based on convergence within a specified time according to claim 3, characterized in that, In the aforementioned multi-unmanned system formation model, the second-order system kinematics model of the virtual navigator is as follows: (2) in, Indicates the location of the virtual navigator. , Indicates the speed of the virtual navigator. , This indicates the rate of change of the virtual navigator's position. , This represents the rate of change of the virtual navigator's speed. , Accelerating the virtual navigator.

5. The multi-unmanned system formation control method based on convergence within a specified time according to claim 4, characterized in that, The tracking error of each follower relative to the target position and the tracking error of each follower relative to the target velocity are used as state variables, and the state variables are specifically: (3) in, Indicates the first The state variables of an unmanned system Indicates the first Position tracking error of an unmanned system Indicates the first Speed ​​tracking error of an unmanned system Indicates from the first The ideal formation position vector from an unmanned system to a virtual navigator yes abbreviation, yes abbreviation, yes abbreviation, yes abbreviation, yes A zero-dimensional vector.

6. The multi-unmanned system formation control method based on convergence at a specified time according to claim 5, characterized in that, The adjustment parameters satisfy: and .

7. The multi-unmanned system formation control method based on convergence within a specified time according to claim 6, characterized in that, The first Sliding mode variables of an unmanned system for: (9) in, yes The first derivative.

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