A distributed preset time integral sliding mode control method based on an extended state observer

Abstract

The application discloses a kind of distributed preset time integral sliding mode control methods based on extended state observer, the underactuated kinematic model of each follower in the leader-follower formation is established;Get full drive kinematic model;Design preset time extended state observer, and deduce formation observation error system based on preset time extended state observer;Define the error system of each follower based on preset time extended state observer, and design the switching function of the error system of follower;Design distributed preset time integral sliding mode controller based on switching function, and design distributed preset time integral sliding mode control law, to realize the control of leader-follower formation.The application can make the follower form and keep formation tracking formation within preset time by designing distributed preset time integral sliding mode controller and distributed preset time integral sliding mode control law for making follower form formation tracking formation within preset time, and continue to keep formation after preset time, avoid infinite time control problem, so as to improve the response speed and accuracy of AUV.

Description

Technical Field

[0001] This invention relates to the field of underactuated AUV control technology, and in particular to a distributed preset time integral sliding mode control method based on an extended state observer. Background Technology

[0002] Autonomous Underwater Vehicles (AUVs) have been widely used in marine resource surveys, maritime rescue, and underwater reconnaissance missions. Faced with complex maritime tasks, a single AUV is often insufficient to meet the requirements; therefore, multiple AUVs need to work collaboratively to complete the mission. Formation control is the fundamental guarantee for achieving multi-AUV collaborative operations. The core of achieving the predetermined mission objectives is ensuring high-precision tracking and control of the AUVs along the desired formation trajectory. Current AUV cooperative formation control methods have the following problems: (1) The formation tracking control strategy of AUV focuses on pursuing the closed-loop asymptotic stability of the system. That is, when the convergence time approaches infinity, the error state asymptotically converges to the equilibrium point. However, infinite time control may cause the AUV to respond slowly or overshoot and cause an accident. (2) Uncertain dynamics and unknown ocean disturbances affect the high-precision formation control of AUVs, greatly increasing the design difficulty of underactuated AUV formation tracking controllers. To overcome these factors, existing technologies have designed observers such as unknown input observers, nonlinear disturbance observers, and extended state observers (ESOs) in terms of observer development. Among them, the ESO is a key component in Active Disturbance Rejection Control (ADRC) for estimating the total amount of uncertainty and unknown disturbances, which can reduce jitter. However, due to its large gain, the ESO has a large initial error, which can easily lead to inaccurate system results. Summary of the Invention

[0003] This invention provides a distributed preset time integral sliding mode control method based on an extended state observer to overcome the above-mentioned technical problems.

[0004] To achieve the above objectives, the technical solution of the present invention is as follows: A distributed preset time integral sliding mode control method based on an extended state observer, comprising the following steps: S1. Establish a pilot-follower formation and create an underactuated kinematic model for each follower in the pilot-follower formation; S2. The underactuated kinematic model is transformed by redefining to obtain a fully driven kinematic model. The fully driven kinematic model can transform the underactuated kinematic model into a control model with full drive characteristics, so that the follower's sway angle and heave displacement are in a stable state. S3. Design a preset time-expanded state observer based on the full-drive kinematic model, and derive a formation observation error system for observing the lumped disturbance of the pilot-follower formation based on the preset time-expanded state observer. S4. Define the error system of each follower based on the preset time-dilation state observer, and design the switching function of the error system of the follower; S5. Based on the switching function, design a distributed preset time integral sliding mode controller to enable the followers to form a formation and track within a preset time and to maintain the formation after the preset time. Based on the lumped disturbance of the lead-follow formation observed by the formation observation error system, design a distributed preset time integral sliding mode control law for the distributed preset time integral sliding mode controller to achieve control of the lead-follow formation.

[0005] Furthermore, in S1, the specific steps for establishing a pilot-follower formation and creating an underactuated kinematic model for each follower in the pilot-follower formation include: S11, Defined to represent the leader-follower formation N A directed graph of the communication structure among followers. , , Represents the set of vertices. , Describe the set of edges. ; Define adjacency matrix ,when hour, ,on the contrary, ; Define the Laplace matrix ,in ,and ; When a navigator exists in a leader-follower formation, the navigator is marked as node 0 and... This represents the communication link between the leader and the follower. When a communication link exists ,on the contrary ; S12, Establish the first i The underactuated kinematic model of a follower is represented as follows: , In the formula, , Represents the position vector. Represents the direction vector. , Represents a linear vector. Represents the angular velocity component. Represents a rotation matrix. Let represent the inertia matrix, and , Let the matrix represent the Coriolis and centrifugal forces, and , Denotes the damping matrix, and ; Represents the gravity vector, and ; Both represent the nominal inertia matrix. All of these represent uncertain dynamic information correction items; To control the input vector, , Unknown ocean disturbance, , , , , , They are represented as follows: , , , , , In the formula, Represents the inertial component; Indicates the damping component; Indicates the density of seawater. Indicates the amount of water discharged. The vertical center of the floating height.

[0006] Furthermore, in S2, the specific steps for transforming the underactuated kinematic model into a fully acted kinematic model using a redefinition approach include: Combine the original position vector With state variables Redefine the position vector of the underactuated kinematic model. , is represented as: , In the formula, The distance from the point of application of the control force to the follower's center of gravity; The fully driven kinematic model is obtained by combining the underactuated kinematic model, and is expressed as: , In the formula, , , , , , , .

[0007] Furthermore, in S3, the specific steps for designing a preset time-dilation state observer for obtaining formation observation errors based on the fully driven kinematic model include: definition , To re-engineer the full-drive kinematic model Defined as: , In the formula, For the first i The lumped perturbation of a follower system , This is a time-varying disturbance in the ocean, and , satisfy ,and and It is a positive real number; It is a positive number, and ; A preset time-dilation state observer is designed based on the redefined fully driven kinematic model. The preset time-dilation state observer is expressed as follows: , In the formula, , , , , , It is a time-varying scaling function. The observed value representing the position vector. The observation error is the position vector. The observed value representing the velocity vector. Observations representing disturbances; , , , and These are preset parameters. , and A constant that is greater than zero. and , , ,function , For switching functions, and ; Further derivation yields the formation observation error system for observing lumped disturbances in the pilot-follower formation, expressed as: , In the formula, , , , , and The first i The actual position, velocity, and lumped disturbance of each follower.

[0008] Furthermore, in S4, the specific steps for defining the error system of each follower based on the preset time-dilation state observer and designing the switching function of the follower's error system include: S41, Define the first based on the preset time-dilation state observer. i The formation position and speed error of each follower are expressed as: , In the formula, ; Indicates the first i The expected relative positions between followers and leaders; Indicates the first j The expected relative positions between followers and leaders; Further obtain the first i The error system for each follower is: , definition , , Then we obtain the compact form of the error system, expressed as: , S42. Introducing a time-varying scaling function and Design a switching function to control the error system of the follower to reach the convergence phase and the sliding phase, including: design , as follows: , In the formula, and The time taken for the follower's error system to go through the convergence and sliding phases; calculate and The derivative of the function is obtained as follows: , In the formula, Represents a constant greater than or equal to 1; exist The right derivative at time t is , exist The right derivative at time t is Therefore, the switching function between the convergence phase and the sliding phase is defined as: , In the formula, It is a constant greater than 1, and .

[0009] Furthermore, the distributed preset time integral sliding mode controller designed based on the switching function is expressed as follows: , In the formula, , , ; set up Then, the compact form of the distributed preset time integral sliding membrane controller is obtained, expressed as: .

[0010] Furthermore, the specific steps for designing the distributed preset time integral sliding mode control law of the distributed preset time integral sliding mode controller based on the lumped disturbance of the lead-follow formation observed by the formation observation error system include: right Taking the derivative, we get: , Further design of a distributed preset time integral sliding mode control law, expressed as: , , , In the formula, It is a constant, and , This is an equivalent control law. For robust control laws, For the lumped perturbation of the follower system.

[0011] Beneficial Effects: This invention employs a redefinition approach to transform the underactuated kinematic model, enabling the underactuated AUV to directly perform stable swaying and heave motions. By designing a preset time-dilation state observer to acquire formation observation errors, it better addresses uncertain dynamics and unknown ocean disturbances, acquiring formation observation errors within a preset time frame. This avoids slow response or overshoot accidents caused by infinite-time control, allowing the AUV to respond more quickly and accurately within the preset time. Furthermore, by designing a distributed preset-time integral sliding mode controller and a distributed preset-time integral sliding mode control law to enable followers to form and maintain a formation within the preset time frame and continue to do so after the preset time, the follower can form and maintain a formation within the preset time, avoiding infinite-time control problems and thus improving the AUV's response speed and accuracy. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is a flowchart of a distributed preset time integral sliding mode control method based on an extended state observer according to the present invention; Figure 2 This is a schematic diagram of the topology of the leader-follower formation in an embodiment of the present invention; Figure 3 This is a schematic diagram of the follower model in an embodiment of the present invention; Figure 4 This is a three-dimensional schematic diagram of the leader-follower formation tracking control in an embodiment of the present invention; Figure 5 This is a simulation diagram of the leader-follower formation positions in an embodiment of the present invention; Figure 6 This is a simulation diagram of the follower's velocity parameters in an embodiment of the present invention; Figure 7 This is a simulation diagram of the control input corresponding to the follower in an embodiment of the present invention; Figure 8 This is a simulation diagram of the observation error of the preset time-dilation state observer in an embodiment of the present invention; Figure 9 This is a simulation diagram comparing the positional errors of the navigator-follower formation in an embodiment of the present invention; Figure 10 This is a simulation diagram comparing the control inputs of the navigator-follower formation in an embodiment of the present invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0015] This embodiment provides a distributed preset time integral sliding mode control method based on an extended state observer, such as... Figure 1 As shown, the specific steps include: S1. Establish a pilot-follower formation and create an underactuated kinematic model for each follower in the pilot-follower formation; Specifically, in this embodiment, the topology of the distributed preset time integral sliding mode based on the extended state observer is as follows: Figure 2 As shown. In Figure 2 The diagram illustrates the formation topology of this embodiment, dividing the entire formation control process into two parts. The first part defines the communication topology of the leader-follower formation, representing the communication relationships between the leader and followers, and between followers themselves. The second part establishes the cluster control model, describing the model structure of the leader-follower formation. The modeling of the followers is as follows... Figure 3 As shown. S2. The underactuated kinematic model is transformed by redefining to obtain a fully driven kinematic model. The fully driven kinematic model can transform the underactuated kinematic model into a control model with full drive characteristics, so that the follower's sway angle and heave displacement are in a stable state. S3. Design a preset time-expanded state observer based on the full-drive kinematic model, and derive a formation observation error system for observing the lumped disturbance of the pilot-follower formation based on the preset time-expanded state observer. S4. Define the error system of each follower based on the preset time-dilation state observer, and design the switching function of the error system of the follower; S5. Based on the switching function, design a distributed preset time integral sliding mode controller to enable the followers to form a formation and track within a preset time and to maintain the formation after the preset time. Based on the lumped disturbance of the lead-follow formation observed by the formation observation error system, design a distributed preset time integral sliding mode control law for the distributed preset time integral sliding mode controller to achieve control of the lead-follow formation.

[0016] In a specific embodiment, S1, the specific steps of establishing a lead-follow formation and creating an underactuated kinematic model for each follower in the lead-follow formation include: S11, Defined to represent the leader-follower formation N A directed graph of the communication structure among followers. , , Represents the set of vertices. , Describe the set of edges. ; Define adjacency matrix ,when hour, ,on the contrary, ; Define the Laplace matrix ,in ,and ; When a navigator exists in a leader-follower formation, the navigator is marked as node 0 and... This represents the communication link between the leader and the follower. When a communication link exists ,on the contrary ; S12, Establish the first i The underactuated kinematic model of a follower is represented as follows: , In the formula, , Represents the position vector. Represents the direction vector. , Represents a linear vector. Represents the angular velocity component. Represents a rotation matrix. Let represent the inertia matrix, and , Let the matrix represent the Coriolis and centrifugal forces, and , Denotes the damping matrix, and ; Represents the gravity vector, and ; Both represent the nominal inertia matrix. All of these represent uncertain dynamic information correction items; To control the input vector, , Unknown ocean disturbance, , , , , , They are represented as follows: , , , , , In the formula, Represents the inertial component; Indicates the damping component; Indicates the density of seawater. Indicates the amount of water discharged. The vertical center of the floating height.

[0017] In a specific embodiment, S2, the specific steps of transforming the underactuated kinematic model to obtain the fully actuated kinematic model by redefining it include: Combine the original position vector With state variables Redefine the position vector of the underactuated kinematic model. , is represented as: , In the formula, The distance from the point of application of the control force to the follower's center of gravity; The fully driven kinematic model is obtained by combining the underactuated kinematic model, and is expressed as: , In the formula, , , , , , , .

[0018] Specifically, for underactuated AUVs, this embodiment adopts a redefinition approach to convert the underactuated model into a fully actuated model, which solves the difficulties brought about by the underactuated characteristics to the controller design, such as the AUV's control input dimension being lower than the system's degrees of freedom, which makes it unable to directly compensate for dynamic coupling terms and amplify strong coupling disturbances. In a specific embodiment, S3, the specific steps of designing a preset time-dilation state observer for obtaining formation observation errors based on the full-drive kinematic model include: definition , To re-engineer the full-drive kinematic model Defined as: , In the formula, For the first i The lumped perturbation of a follower system , This is a time-varying disturbance in the ocean, and , satisfy ,and and It is a positive real number; It is a positive number, and ; A preset time-dilation state observer is designed based on the redefined fully driven kinematic model. The preset time-dilation state observer is expressed as follows: , In the formula, , , , , , It is a time-varying scaling function. The observed value representing the position vector. The observation error is the position vector. The observed value representing the velocity vector. Observations representing disturbances; , , , and These are preset parameters. , and A constant that is greater than zero. and , , ,function , For switching functions, and ; For ease of writing, the time variable has been omitted in the following text. ; Further derivation yields the formation observation error system for observing lumped disturbances in the pilot-follower formation, expressed as: , In the formula, , , , , and The first i The actual position, velocity, and lumped disturbance of each follower.

[0019] Specifically, this embodiment employs a preset time-dilation state observer to handle the uncertain dynamics and unknown ocean disturbances of AUVs, effectively mitigating the jitter problem caused by the inability to adjust the scale function due to its rapid change rate. Furthermore, the preset time-dilation state observer uses a time-varying scale function with adjustable parameters as the gain, ensuring that the observation error converges to the origin within a specified time. Compared to ordinary ESO observers, this avoids peak phenomena caused by applying large gains.

[0020] In a specific embodiment, S4, the specific steps of defining the error system of each follower based on the preset time-dilation state observer and designing the switching function of the follower's error system include: S41, Define the first based on the preset time-dilation state observer. i The formation position and speed error of each follower are expressed as: , In the formula, ; Indicates the first i The expected relative positions between followers and leaders; Indicates the first j The expected relative positions between followers and leaders; Further obtain the first i The error system for each follower is: , definition , , Then we obtain the compact form of the error system, expressed as: , S42. Introducing a time-varying scaling function and Design a switching function to control the error system of the follower to reach the convergence phase and the sliding phase, including: design , as follows: , In the formula, Represents a constant; and The time taken for the follower's error system to go through the convergence and sliding phases; calculate and The derivative of the function is obtained as follows: , In the formula, Represents a constant greater than or equal to 1; exist The right derivative at time t is , exist The right derivative at time t is Therefore, the switching function between the convergence phase and the sliding phase is defined as: , In the formula, It is a constant greater than 1, and .

[0021] In a specific embodiment, the distributed preset time integral sliding mode controller designed based on the switching function is represented as follows: , In the formula, , , ; set up Then, the compact form of the distributed preset time integral sliding membrane controller is obtained, expressed as: .

[0022] In a specific embodiment, the specific steps for designing the distributed preset time integral sliding mode control law of the distributed preset time integral sliding mode controller based on the lumped disturbance of the lead-follow formation observed by the formation observation error system include: right Taking the derivative, we get: , Further design of a distributed preset time integral sliding mode control law, expressed as: , , , In the formula, It is a constant, and , This is an equivalent control law. For robust control laws, For navigation - follow the formation to gather disturbances.

[0023] Specifically, this embodiment designs a distributed preset time integral sliding mode control law based on a preset time-extended state observer, enabling underactuated AUV formations to converge within a specified time, regardless of the initial values ​​and design parameters of the AUVs. Simultaneously, it effectively reduces the cost required to suppress steady-state errors and solves problems such as parameter inaccuracies and disturbances in AUV formation control.

[0024] To verify the effectiveness of the method proposed in this embodiment, a leader-follower formation system comprising one leader AUV and three follower AUVs was simulated for testing. The simulation results are as follows: Figure 4-10 As shown, where: Figure 5 The 3D tracking position of the navigator-follower formation is shown, and it can be seen that the follower successfully tracks the navigator within the preset time and with high accuracy; Figure 6 The velocity parameters of each follower during the actual tracking process are shown. The fluctuation process is smooth and the fluctuation amplitude is extremely small, which fully demonstrates the good tracking performance of the proposed control strategy. Figure 7 It demonstrates that the control inputs of each follower can reach a stable state within a preset time.

[0025] Figure 8 The observation error curves of different observers during the tracking process are shown. In comparison, the oscillation degree generated by the preset time-dilation state observer given in this embodiment is smaller. Figure 9 The figure shows a comparison of positional errors during the AUV formation following the target. As can be seen from the figure, the tracking accuracy of the method proposed in this embodiment is better than that of other methods. Figure 10 The control inputs for AUV formations are compared. As can be seen from the figure, the control strategy proposed in this embodiment produces less jitter and provides better control performance.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A distributed preset time integral sliding mode control method based on an extended state observer, characterized in that, The specific steps include: S1. Establish a pilot-follower formation and create an underactuated kinematic model for each follower in the pilot-follower formation; S2. The underactuated kinematic model is transformed by redefining to obtain a fully driven kinematic model. The fully driven kinematic model can transform the underactuated kinematic model into a control model with full drive characteristics, so that the follower's sway angle and heave displacement are in a stable state. S3. Design a preset time-expanded state observer based on the full-drive kinematic model, and derive a formation observation error system for observing the lumped disturbance of the pilot-follower formation based on the preset time-expanded state observer. S4. Define the error system of each follower based on the preset time-dilation state observer, and design the switching function of the error system of the follower; S5. Based on the switching function, design a distributed preset time integral sliding mode controller to enable the followers to form a formation and track within a preset time and to maintain the formation after the preset time. Based on the lumped disturbance of the lead-follow formation observed by the formation observation error system, design a distributed preset time integral sliding mode control law for the distributed preset time integral sliding mode controller to achieve control of the lead-follow formation.

2. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 1, characterized in that, In S1, the specific steps for establishing a pilot-follower formation and creating an underactuated kinematic model for each follower in the pilot-follower formation include: S11, Defined to represent the leader-follower formation N A directed graph of the communication structure among followers. , , Represents the set of vertices. , Describe the set of edges. ; Define adjacency matrix ,when hour, ,on the contrary, ; Define the Laplace matrix ,in ,and ; When a navigator exists in a leader-follower formation, the navigator is marked as node 0 and... This represents the communication link between the leader and the follower. When a communication link exists ,on the contrary ; S12, Establish the first i The underactuated kinematic model of a follower is represented as follows: ， In the formula, , Represents the position vector. Represents the direction vector. , Represents a linear vector. Represents the angular velocity component. Represents a rotation matrix. Let represent the inertia matrix, and , Let the matrix represent the Coriolis and centrifugal force matrices, and , Denotes the damping matrix, and ; Represents the gravity vector, and ; Both represent the nominal inertia matrix. All of these represent uncertain dynamic information correction items; To control the input vector, , Unknown ocean disturbance, , , , , , They are represented as follows: ， ， ， ， ， In the formula, Represents the inertial component; Indicates the damping component; Indicates the density of seawater. Indicates the amount of water discharged. The vertical center of the floating height.

3. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 2, characterized in that, In S2, the specific steps for transforming the underactuated kinematic model into a fully acted kinematic model using a redefinition approach include: Combine the original position vector With state variables Redefine the position vector of the underactuated kinematic model. , is represented as: ， In the formula, The distance from the point of application of the control force to the follower's center of gravity; The fully driven kinematic model is obtained by combining the underactuated kinematic model, and is expressed as: ， In the formula, , , , , , , 。 4. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 3, characterized in that, In S3, the specific steps for designing a preset time-dilation state observer for obtaining formation observation errors based on the fully driven kinematic model include: definition , To re-engineer the full-drive kinematic model Defined as: ， In the formula, For the first i The lumped perturbation of a follower system , This is a time-varying disturbance in the ocean, and , satisfy ,and and It is a positive real number; It is a positive number, and ; A preset time-dilation state observer is designed based on the redefined fully driven kinematic model. The preset time-dilation state observer is expressed as follows: ， In the formula, , , , , , It is a time-varying scaling function. The observed value representing the position vector. The observation error is the position vector. The observed value representing the velocity vector. Observations representing disturbances; , , , and These are preset parameters. , and A constant that is greater than zero. and , , ,function , For switching functions, and ; Further derivation yields the formation observation error system for observing lumped disturbances in the pilot-follower formation, expressed as: ， In the formula, , , , , and The first i The actual position, velocity, and lumped disturbance of each follower.

5. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 4, characterized in that, In S4, the specific steps for defining the error system of each follower based on the preset time-dilation state observer and designing the switching function of the follower's error system include: S41, Define the first based on the preset time-dilation state observer. i The formation position and speed error of each follower are expressed as: ， In the formula, ; Indicates the first i The expected relative positions between followers and leaders; Indicates the first j The expected relative positions between followers and leaders; Further obtain the first i The error system for each follower is: ， definition , , Then we obtain the compact form of the error system, expressed as: ， S42. Introducing a time-varying scaling function and Design a switching function to control the error system of the follower to reach the convergence phase and the sliding phase, including: design , as follows: ， In the formula, and The time taken for the follower's error system to go through the convergence and sliding phases; calculate and The derivative of the function is obtained as follows: ， In the formula, Represents a constant greater than or equal to 1; exist The right derivative at time t is , exist The right derivative at time t is Therefore, the switching function between the convergence phase and the sliding phase is defined as: ， In the formula, It is a constant greater than 1, and .

6. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 5, characterized in that, The distributed preset time integral sliding mode controller designed based on the switching function is expressed as follows: ， In the formula, , , ; set up Then, the compact form of the distributed preset time integral sliding membrane controller is obtained, expressed as: 。 7. The distributed preset time integral sliding mode control method based on an extended state observer according to claim 6, characterized in that, The specific steps for designing the distributed preset time integral sliding mode control law of the distributed preset time integral sliding mode controller based on the lumped disturbance of the pilot-follower formation observed by the formation observation error system include: right Taking the derivative, we get: ， Further design of a distributed preset time integral sliding mode control law, expressed as: ， ， ， In the formula, It is a constant, and , This is an equivalent control law. For robust control laws, For the lumped perturbation of the follower system.

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