An AUV control method based on fixed-time extended state observer
By constructing a fixed-time extended state observer and an adaptive dual sliding surface controller, the model error and interference observation problems in AUV formation control were solved, and high-precision, fast and stable control of the AUV system in complex environments was achieved.
Patent Information
- Application Number
- CN202610340544.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-03-19
- Publication Date
- 2026-06-23
AI Technical Summary
AUV formation control suffers from problems such as model simplification errors, insufficient accuracy of interference observations, inadequate optimization of transient performance, and difficulty in suppressing chattering. In particular, it is difficult to achieve high-precision, fast, and stable control in complex underwater environments.
A control method for AUV based on a fixed-time extended state observer is constructed. By using an adaptive term and a nonlinear first-order filter, a dual sliding surface controller is designed to achieve real-time estimation and compensation of the total disturbance set, thereby reducing model complexity and improving observer accuracy and controller computational efficiency.
This technology enables fast and stable tracking of AUV systems within a fixed time frame, improving control accuracy and anti-interference capabilities, optimizing transient performance, reducing computational complexity, and making it suitable for large formations and dynamic environments.
Smart Images
Figure CN122261185A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of underwater vehicle technology, specifically relating to an AUV control method based on a fixed-time extended state observer. Background Technology
[0002] With the increasing demand for marine resource development and underwater operations, formation control technology for multiple autonomous underwater vehicles (AUVs) has attracted widespread attention due to its significant advantages in cooperative search, resource exploration, and rescue missions. However, AUV formation tracking control faces many challenges, mainly including model complexity, environmental disturbances, and the accuracy of state observation, specifically manifested in:
[0003] First, an AUV is a six-degree-of-freedom space mechanical system with a highly complex motion model, making accurate modeling and controller design extremely difficult. In practical applications, the model usually needs to be simplified, but this simplification process may introduce errors and affect control accuracy.
[0004] Secondly, the underwater environment is complex and variable, and the external and internal disturbances experienced by AUVs are difficult to accurately describe analytically. Existing technologies use fixed-time extended state observers for estimation; however, in dynamic underwater environments, the steady-state values obtained by existing extended state observers are prone to oscillations, leading to control signal jitter and affecting system stability. Furthermore, the convergence time of the observer typically depends on the initial state of the system, and in environments with frequent disturbances, it is prone to decreased convergence speed or control failure, making it difficult to meet real-time control requirements.
[0005] Currently, backstepping control and terminal sliding mode control are the mainstream methods for AUV formation control. However, backstepping control suffers from a "complexity explosion" problem in multi-AUV systems, leading to extremely complex controller design and an exponential increase in computational burden, severely limiting its application potential in large formations and dynamic environments. Existing methods are mostly based on semi-global fixed-time stability theory to design terminal sliding mode control laws. Although they can stably control AUVs to travel along the desired trajectory in a finite time, existing research focuses mainly on the steady-state performance of the system (referring to the performance table when the system finally reaches and stabilizes in the desired state after experiencing the initial dynamic process or external disturbances, used to measure the final accuracy and stability of the system, including position / attitude error, velocity error, and anti-interference capability, etc.), and does not adequately optimize transient performance (the performance of the system during the dynamic process of transitioning from the initial state to the desired steady state, used to measure the speed, smoothness, and anti-interference capability of the system to reach steady state, including convergence time, rise time, and overshoot, etc.), affecting the system response speed and overshoot, which may lead to overshoot or convergence delay in the dynamic adjustment phase.
[0006] The unique nature of the underwater environment makes it difficult to directly measure certain AUV states (such as velocity vectors, attitude angles, water flow disturbances, and thruster efficiency) using sensors. Furthermore, the high cost of high-precision sensors limits the accuracy of state feedback. In swarm control, communication latency further complicates formation maintenance. Summary of the Invention
[0007] The purpose of this invention is to address the shortcomings of existing AUV formation control technologies, such as model simplification errors, insufficient interference observation accuracy, lack of transient performance optimization, and difficulty in suppressing chattering. Instead, it provides an AUV control method based on a fixed-time extended quasi-solid-state observer. By introducing an adaptive term and a nonlinear first-order filter, the total set of interference received by the AUV and the difficult-to-measure velocity are estimated, effectively solving the chattering and the inherent "complexity explosion" problem of traditional backstepping controllers, thereby improving control accuracy.
[0008] To achieve the above objectives, the technical solution provided by this invention is:
[0009] An AUV control method based on a fixed-time extended state observer includes the following steps:
[0010] Step 1: Ignoring the roll motion of the AUV, based on the reasonable assumptions of ignoring high-order nonlinear water damping, the coincidence of the origin of the AUV's carrier coordinate system and the center of gravity of the AUV, the symmetry of the AUV body about the horizontal and vertical planes, and the AUV being in a state of equilibrium between buoyancy and gravity in the water, a five-degree-of-freedom motion model of the AUV is constructed.
[0011] Step 2: Introduce intermediate state variables to integrate external disturbances, AUV internal uncertainties, and unmeasurable velocities into a total disturbance set, thereby achieving a holistic representation of various disturbances;
[0012] Step 3: Based on the AUV five-degree-of-freedom motion model, construct an adaptive fixed-time extended state observer with an adaptive term. The adaptive term is used to suppress steady-state chattering. The adaptive fixed-time extended state observer is used to estimate and output the AUV's pose observation, velocity observation, and total disturbance observation in real time based on the input AUV pose information.
[0013] Step 4: Based on the pose observations, velocity observations, and total disturbance observations output by the adaptive fixed-time extended state observer, design a fixed-time convergent dynamic surface sliding mode controller; the design steps of the dynamic surface sliding mode controller include:
[0014] Step 4.1: Design a double sliding surface; wherein, the first sliding surface is used to ensure that the AUV position tracking error converges within a fixed time, and the second sliding surface is used to ensure that the AUV velocity tracking error converges within a fixed time.
[0015] Step 4.2: Design a virtual control law based on the backstepping method, and introduce a nonlinear first-order filter to filter the virtual control law according to the fixed-time convergence condition of the first sliding surface, so as to eliminate the complexity explosion in the backstepping method.
[0016] Step 4.3: Based on the fixed-time convergence condition of the second sliding surface, design a control input law that includes feedforward compensation of total disturbance observations to obtain the control torque of the AUV;
[0017] Step 5: Obtain the current actual pose and desired pose of the AUV, input them into the adaptive fixed-time extended state observer and the dynamic surface sliding mode controller, calculate and output the AUV control torque and input it into the AUV system to obtain the true pose of the AUV, and realize the fixed-time stable closed-loop control of the AUV.
[0018] Furthermore, in step 1, the expression for the constructed five-degree-of-freedom motion model of the AUV is as follows:
[0019]
[0020]
[0021] in: For the additional mass matrix; Here is the Coriolis centripetal force matrix; This is the hydrodynamic damping coefficient matrix; The restoring force matrix; This represents the actual velocity of the AUV in the carrier coordinate system. This represents the actual pose of the AUV in the ground coordinate system. The control torque of the AUV; This is the interference matrix, representing interference from complex underwater environments. This is the transformation matrix between the ground coordinate system and the vehicle coordinate system, determined by the pitch and heading angles of the AUV in the ground coordinate system.
[0022] Furthermore, in step 2, intermediate state variables are introduced. ,make ,Will Represented as:
[0023]
[0024] Set the total interference set for:
[0025]
[0026] In the formula, This represents the total set of disturbances, including the combined effects of external disturbances, internal uncertainties of the AUV, and unmeasurable velocities.
[0027] Furthermore, the expression for the adaptive fixed-time extended state observer constructed in step 3 is:
[0028]
[0029] In the formula, , as well as These are the AUV's pose observations, velocity observations, and total disturbance observations, respectively. , and This is the gain of the pre-observer, with a value range of [0, 1]. , and This is the gain of the post-observer, and all values are greater than 1; , , To assist the gain of the pre-observer, the value range is [0.1, 5]; , , The gain of the auxiliary post-observer is set to [0.1, 5]; the gain of the observer sign term is... and adaptive term update gain All are positive numbers; This is an adaptive term used to prevent oscillations in the steady-state value. For the adaptive term, the adaptive law; This represents the actual pose of the AUV in the ground coordinate system. The control torque of the AUV; It is a symbolic function.
[0030] Furthermore, in step 4.1, the first sliding surface Second sliding surface The expression is:
[0031] First sliding surface ,in ;
[0032] Second sliding surface ,in ;
[0033] In the formula, This refers to the AUV position tracking error. These are AUV pose observations; The desired pose of the AUV; For AUV speed tracking error; These are AUV velocity observations; This represents the expected speed of the AUV. and These are the auxiliary variables for the first and second sliding surfaces, respectively. and Both are the first sliding mode reaching rate gain, and , ; and Both are the weighting coefficients of the first and second sliding surfaces, and both are positive numbers; and The gain for fixed-time convergence with small error is a constant; , Both are parameters for suppressing large errors in sliding surfaces.
[0034] Furthermore, the virtual control law designed in step 4.2 is as follows:
[0035]
[0036] in, This is the virtual speed command, which is the output of the virtual control law; and These are the weighting coefficients for the first and second sliding surfaces, respectively, both of which are positive values. and All are normal values that adjust the pose convergence speed;
[0037] The virtual control law is filtered by a nonlinear first-order filter to obtain the filtered virtual control law as follows:
[0038]
[0039] In the formula, and All are first sliding mode approach rate gains; The filter time constant has a value ranging from 0.01 to 1. It is a virtual speed command after being filtered.
[0040] Furthermore, the control input law designed in step 4.3 is as follows:
[0041]
[0042] In the formula, and This is the first sliding mode approach rate gain; The control torque of the AUV; and The gain of the second sliding mode reaching law is a positive constant with a value range of 0.1 to 1. The transformation matrix between the ground coordinate system and the vehicle coordinate system is determined by the pitch angle and heading angle displacement in the AUV coordinate system. Represents the additional mass matrix; The total disturbance observation value output by the observer is used for feedforward compensation; It is the auxiliary variable of the second sliding surface; It is an introduced velocity dummy variable The first derivative of the filtered value after filtering; It is the first sliding surface; It is the second sliding surface.
[0043] Furthermore, the specific process for implementing AUV closed-loop control in step 5 is as follows:
[0044] Step 5.1: Obtain the current actual pose of the AUV using sensors;
[0045] Step 5.2, change the current actual pose and desired pose The input is an adaptive fixed-time extended state observer, which is based on the control torque output from the previous cycle. Based on the current pose information, calculate pose observations in real time. Velocity observations and total disturbance observations ;
[0046] Step 5.3, set the desired pose pose observations Velocity observations and total disturbance observations Input the dynamic surface sliding mode controller to calculate the first sliding surface sequentially. Second sliding surface Virtual speed command corresponding to virtual control law Filtered virtual speed command Finally, the control torque for the current cycle is calculated using the control input law. ;
[0047] Step 5.4, control torque The thrusters and control rudders applied to the AUV drive its movement;
[0048] Step 5.5, return to step 5.1, enter the next control cycle, and realize continuous closed-loop tracking control of AUV pose.
[0049] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor, when executing the program, implements the above-described AUV control method based on a fixed-time extended state observer.
[0050] The present invention also provides a computer-readable storage medium storing computer instructions, characterized in that the instructions, when executed by a processor, implement the above-described AUV control method based on a fixed-time extended state observer.
[0051] The advantages of this invention are:
[0052] 1. This invention addresses the problem of introducing errors during model simplification in traditional AUV control methods. By constructing a five-degree-of-freedom model that ignores the roll motion of the AUV, the complexity of the model is effectively reduced while ensuring control accuracy. This provides a simpler and more reliable controlled object for the subsequent design of the observer and controller, avoiding the problem of controller design difficulties caused by overly complex models.
[0053] 2. This invention introduces an adaptive term into the designed adaptive fixed-time extended state observer. By adjusting the observer gain, the steady-state jitter of the observer is effectively suppressed. The adaptive fixed-time extended state observer is used to accurately estimate the unmeasurable velocity. At the same time, external disturbances, internal uncertainties, and unmeasurable velocities are treated as a total disturbance set and estimated and compensated in real time. Without increasing hardware costs, the accuracy of the observer's state feedback to the AUV in complex underwater environments is improved, and the estimation accuracy and stability are enhanced, providing the controller with a more accurate basis for disturbance compensation.
[0054] 3. To address the complexity explosion problem of traditional backstepping control methods in multi-AUV systems, this invention introduces a nonlinear first-order filter to filter the designed virtual control law. This avoids the exponential increase in computational burden caused by directly differentiating the virtual control law, significantly reducing the computational complexity of the controller. This makes the method more suitable for real-time control applications in large formations and dynamic environments, enabling the position and pose of the AUV formation to converge stably and quickly to the desired value within a fixed time, thereby improving the accuracy of the AUV system.
[0055] 4. This invention employs fixed-time convergence theory to design a dual sliding surface. The first sliding surface ensures that the AUV position tracking error converges within a fixed time, while the second sliding surface ensures that the AUV velocity tracking error converges within a fixed time. Furthermore, through the designed virtual control law and AUV system control input law, the position and velocity tracking errors of the AUV system can converge to zero within a fixed time independent of the initial state. This not only ensures the steady-state accuracy of the AUV system but also optimizes its transient response speed, solving the problem of insufficient optimization of AUV system transient performance in traditional sliding mode control technology.
[0056] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description
[0057] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:
[0058] Figure 1 This is a flowchart of the AUV control method based on a fixed-time extended state observer according to the present invention;
[0059] Figure 2 This is a schematic diagram of the control principle of the observer and controller for the AUV system in this invention;
[0060] Figure 3 This is a comparison diagram of the expected trajectory and the actual trajectory in the method of this invention;
[0061] Figure 4 AUV pitch angle obtained based on the method of this invention Tracking error curve;
[0062] Figure 5 AUV heading angle obtained based on the method of this invention Error plot; Detailed Implementation
[0063] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0064] Reference Figure 1 and Figure 2 This invention provides an AUV control method based on a fixed-time extended state observer, comprising the following steps:
[0065] Step 1: Construct a five-degree-of-freedom motion model for the AUV.
[0066] Considering that roll motion of underwater vehicles (AUVs) can usually be suppressed by mechanical structures, this embodiment ignores roll motion (roll angular velocity) to simplify controller design. Based on the reasonable assumptions of neglecting high-order nonlinear water damping, the coincidence of the origin of the AUV's carrier coordinate system and the AUV's center of gravity, the symmetry of the AUV body about the horizontal and vertical planes, and the AUV being in equilibrium between buoyancy and gravity in water, a five-degree-of-freedom motion model of the AUV is constructed. Its matrix expression is as follows:
[0067] (1)
[0068] (2)
[0069] in: This represents the actual pose of the AUV in the ground coordinate system, including its three-dimensional position coordinates. , , and pitch angle and yaw angle ; Represents the additional mass matrix. ; This represents the added mass of the AUV in the lateral velocity direction. This represents the additional mass of the AUV in the lateral velocity direction. This represents the added mass of the AUV in the vertical velocity direction. This represents the added mass of the AUV in the direction of pitch angular velocity. This indicates the added mass of the AUV in the yaw angle and angular velocity directions;
[0070] For Coriolis centripetal torque, , These represent the linear velocities of the AUV in the carrier coordinate system; This represents the hydrodynamic damping coefficient matrix. , This represents the parameters of the hydrodynamic damping parameter matrix of the AUV in the lateral velocity direction. This represents the hydrodynamic damping coefficient of the AUV in the lateral velocity direction. This represents the hydrodynamic damping coefficient of the AUV in the vertical velocity direction. This represents the hydrodynamic damping coefficient of the AUV in the direction of pitch angular velocity. This represents the hydrodynamic damping coefficient of the AUV in the direction of yaw angular velocity; To restore torque; To represent the actual speed of the AUV in the carrier coordinate system, The pitch angular velocity, Yaw angular velocity; The control torque of the AUV, where , This indicates the operating torque generated by the AUV propulsion system. This indicates the operating torque generated by the AUV elevator. This indicates the operating torque generated by the AUV's rudder; This is the interference matrix, representing the interference from complex underwater environments. , This represents the torque exerted by model uncertainties and external disturbances on the lateral velocity direction of the AUV. This represents the torque exerted by model uncertainties and external disturbances on the lateral velocity direction of the AUV. This represents the torque exerted by model uncertainties and external disturbances on the vertical velocity direction of the AUV. This represents the torque exerted by model uncertainties and external disturbances on the pitch angular velocity direction of the AUV. This represents the torque exerted by model uncertainties and external disturbances on the AUV's yaw rate.
[0071] This is the transformation matrix between the ground coordinate system and the vehicle coordinate system, derived from the pitch angle of the AUV in the ground coordinate system. and heading angle Uniquely certain;
[0072] (3)
[0073] Step 2: Introduce intermediate state variables to determine the total disturbance set. .
[0074] To achieve holistic estimation and compensation for various disturbances, this invention introduces intermediate state variables to integrate external disturbances, AUV internal uncertainties, and unmeasurable velocities into a total disturbance set, thereby achieving a holistic characterization of various disturbances. Specifically, the process includes the following:
[0075] First, based on the five-degree-of-freedom motion model of the AUV, intermediate state variables are introduced. ,make ,but This can be expressed as:
[0076] (4)
[0077] Then set the total interference direction set for:
[0078] (5)
[0079] in, This represents the set of total disturbances, including the combined effects of external disturbances, internal uncertainties of the AUV, and unmeasurable velocities. The purpose of determining this set of total disturbances is to unify all uncertainties and external disturbances in the AUV system into a single set, facilitating subsequent overall estimation and compensation by the observer.
[0080] Step 3: Construct an adaptive fixed-time extended state observer.
[0081] This step constructs an adaptive fixed-time extended state observer with an adaptive term, used to determine the actual pose information of the AUV measured by the sensors. and control torque The system estimates and outputs the pose, velocity, and total disturbance observations of the AUV in real time. This embodiment designs the observer based on fixed-time convergence theory and introduces an adaptive term to suppress steady-state chattering.
[0082] The expression for the adaptive fixed-time extended state observer is:
[0083] (6)
[0084] In the formula, , as well as These are the AUV's pose observations, velocity observations, and total disturbance observations, respectively. The current actual pose of the AUV can be obtained by sensor measurement; , and is the gain of the pre-observer (power parameter), with a value range of [0, 1]; , and The gain of the post-observer can be determined by those skilled in the art through simulation and debugging based on the system characteristics, and is usually taken as 10~20; , , To assist the gain of the pre-observer, the value range is [0.1, 5]; , , The gain of the auxiliary post-observer is set to [0.1, 5]; the gain of the observer sign term is... and adaptive term update gain All are positive numbers; This is an adaptive term used to prevent oscillations in the steady-state value. For the adaptive term, the adaptive law can be selected by those skilled in the art based on the balance requirements of convergence speed and adaptive gain. Typically... The value range is 1~10, used to adjust the adaptive rate; The control torque of the AUV; It is a symbolic function.
[0085] In the observer equations designed above, the pre-observer parameters and post-observer parameters are used to ensure fast convergence of the observer when it is far from the equilibrium point and close to the equilibrium point, respectively; the adaptive term... It is used to dynamically compensate for unknown interference estimation errors and avoid steady-state chattering caused by fixed high gain.
[0086] In this embodiment, the gain of the pre-observer , and The values are 0.6, 0.8, and 0.7 respectively; Post-observer gain , and The values are 12, 16, and 14 respectively; Auxiliary pre-observer gain , , The values are 0.3, 0.7, and 2.1 respectively; auxiliary post-observer gain. , , The values are 0.3, 0.5, and 0.7 respectively; the observer sign term gain. and adaptive term update gain The values are 3 and 10 respectively;
[0087] It should be noted that the observer equation includes control inputs. (Control torque of AUV), therefore the observer needs to obtain the control torque information output by the controller in real time in order to accurately update the state estimate and realize the coupling relationship between the observer and the controller.
[0088] Step 4: Design a dynamic surface sliding mode controller based on fixed-time convergence.
[0089] This step is based on the pose observations output from step 3. Velocity observations and total disturbance observations Design a sliding mode controller. The goal of this sliding mode controller is to achieve the actual pose of the AUV. It can quickly and accurately track the desired pose, and the tracking error converges to zero within a fixed time. The specific design steps include:
[0090] Step 4.1: To ensure kinematic and dynamic stability, a double sliding surface is designed, namely the first sliding surface. Second sliding surface .
[0091] First, define ,in The AUV pose observation values output by the observer. For the desired pose of the AUV, This represents the position tracking error. To ensure the fixed-time convergence of the position tracking error, a first sliding surface is designed. for:
[0092] (7)
[0093] To achieve speed control, speed tracking error is introduced. Definition ,in The velocity observation value output by the observer. To achieve the desired speed for the AUV, a second sliding surface is designed to ensure fixed-time convergence of the speed tracking error. for:
[0094] (8)
[0095] In the formula, and These are the auxiliary variables for the first and second sliding surfaces, respectively. and The introduction of this can achieve dimensionality reduction and decoupling on the one hand, and alleviate observer chattering on the other. and Both are the first sliding mode reaching rate gain, and , ; and These are the weighting coefficients for the first and second sliding surfaces, respectively, both of which are positive values. and For fixed-time convergence with small error gain; , Both are parameters for suppressing large errors in the sliding surface, and those skilled in the art can select them according to the system response position and speed requirements.
[0096] In this embodiment, the first sliding mode approach rate gain and The values are 0.7 and 11 respectively; and The values are set to 5 and 5 respectively; fixed-time convergence small error gain , The values are 5 and 5 respectively; large error suppression parameters for sliding surfaces. and The values are 5 and 5 respectively.
[0097] Step 4.2: Design the virtual control law and filter the virtual speed command.
[0098] The virtual control law is designed based on the backstepping method. The only output of this virtual control law is the introduced virtual speed command. The fixed-time convergence condition of the first sliding surface is achieved through the design of a virtual control law. The specific design process is as follows:
[0099] When the AUV control system converges to the corresponding slip surface within a fixed time, that is... Then we have: (9)
[0100] According to Lyapunov's second method, , All of them can converge within a fixed time, that is, satisfy the condition that they meet the condition. This allows the AUV system to converge within a fixed time. Utilizing the backstepping method, the first sliding surface is first ensured... Convergence. (Regarding) Differentiation yields:
[0101] (10)
[0102] In order to make Fixed-time convergence, introducing virtual velocity commands This parameter is an intermediate control variable designed to achieve pose tracking. It is used to transform the control objective of the upper sliding surface into the desired command for the AUV velocity loop. The virtual control law obtained using the backstepping method is:
[0103] (11)
[0104] in, This is the virtual speed command, which is the output of the virtual control law; and These are the weighting coefficients for the first and second sliding surfaces, respectively, both of which are positive values. and These are all normal values used to adjust the pose convergence speed. Those skilled in the art can select them according to the convergence speed requirements, and the values are usually in the range of 1-10. In this embodiment, the values are 5 and 7, respectively.
[0105] In subsequent steps, the virtual control law needs to be differentiated. Directly differentiating the introduced virtual variables (i.e., the virtual velocity command) would involve complex calculations of parameters such as the first and second sliding surfaces, leading to a complexity explosion problem. Therefore, a nonlinear first-order filter is introduced to filter the virtual control law, allowing the virtual variables to pass through the filter and obtain new state variables. (Right now The filtered value (after filtering) is used to eliminate the complexity explosion in the backstepping method. In this embodiment, the expression for the nonlinear first-order filter is:
[0106] (12)
[0107] In the formula, This is the input to the filter, i.e., the introduced virtual velocity command. ; The output of the filter is the virtual speed command after filtering. . is the time constant of the nonlinear first-order filter, which determines the filter's response speed. Its value typically ranges from 0.01 to 1; in this embodiment, it is set to 0.05. After filtering with the introduced nonlinear filter, the following is obtained:
[0108] (13)
[0109] In the formula, and The approach rate gain of the first sliding mode controller; The time constant of the filter, with a value ranging from 0.01 to 1; It is a virtual speed command after being filtered, used to utilize its derivative. Approximate replacement of the originally introduced virtual velocity command derivative This avoids complex differentiation operations.
[0110] Step 4.3: Design the final control input law.
[0111] The purpose of this step is to design the control input law to obtain the actual control torque of the AUV, ensuring the second sliding surface... It converges within a fixed time. Differentiating with respect to the second sliding surface yields:
[0112] (14)
[0113] Combining the designed observer and the five-degree-of-freedom motion model of the AUV, and using the total disturbance observations provided by the observer for feedforward compensation, the control input law of the AUV system is designed as follows:
[0114] (15)
[0115] In the formula, The control torque of the AUV; and All are first sliding mode approach rate gains; and All are the second sliding mode reaching law gains, all are positive numbers and their values range from 0.1 to 1. Those skilled in the art can select them according to the convergence speed requirements. The transformation matrix between the ground coordinate system and the vehicle coordinate system is determined by the pitch angle and heading angle displacement in the AUV coordinate system. Represents the additional mass matrix; The total interference observation value output by the observer is used for feedforward compensation to enhance the anti-interference capability of the AUV system. It is the auxiliary variable of the second sliding surface; It is the first derivative of the virtual speed command after being filtered by the filter; Expected value used to represent AUV speed ; It is the first sliding surface; It is the second sliding surface; and These are the weighting coefficients for the first and second sliding surfaces, respectively, both of which are positive values.
[0116] Step 5: Use the designed observer, controller, and control input law to perform closed-loop control of the AUV system.
[0117] After completing the above design, the AUV control system can be put into closed-loop operation. The current pose information and the desired pose of the AUV are input into the adaptive fixed-time extended state observer and the dynamic surface sliding mode controller to calculate the control torque of the AUV, which is then input into the AUV system to achieve fixed-time stable control of the AUV. Within each control cycle, the following operations are performed:
[0118] Step S5.1: Obtain the current actual pose of the AUV through sensors (such as attitude sensors, depth sensors, etc.). ;
[0119] Step S5.2, change the current actual pose and desired pose Input an adaptive fixed-time extended state observer, the observer adjusts according to the current control torque. (Previous cycle output) and pose information, to calculate pose observations in real time. Velocity observations and total disturbance observations ;
[0120] Step S5.3, set the desired pose pose observations Velocity observations Interference observations Input the sliding mode controller and calculate the first sliding surface according to the formula. Second sliding surface Calculate the initial virtual speed command according to the virtual control law calculation formula. and the filtered virtual speed command Finally, the control torque for the current cycle is calculated based on the control input law formula. .
[0121] Step S5.4, calculate the control torque The thrusters applied to the AUV drive the movement of the AUV's thrusters and rudders, changing the AUV's attitude and speed.
[0122] Step S5.5, return to step S5.1, and enter the next control cycle.
[0123] Through the above closed-loop control, the actual pose of the AUV is determined. Will quickly track the desired pose Furthermore, the tracking error converges to zero within a fixed time.
[0124] This embodiment verifies the effectiveness of the technical solution of the present invention through simulation experiments. Figure 3 As shown, the actual trajectory of the AUV controlled by the method in this embodiment is highly consistent with the expected trajectory, with no significant deviation. Figure 4 Demonstrated AUV pitch angle The tracking error curve Figure 5 Demonstrated AUV heading angle The tracking error curve is shown in the figure. It can be seen that the tracking error can quickly converge to zero within a fixed time of 230s, and the steady-state accuracy is high, the chattering is small, and the transient overshoot is less than 0.03 degrees. This verifies the effectiveness and superiority of the fixed-time convergence characteristics, control accuracy and anti-interference of the proposed method.
[0125] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned AUV control method based on a fixed-time extended state observer. The computer-readable storage medium can be any medium with program storage capabilities, such as ROM, RAM, magnetic disk, optical disk, USB flash drive, or portable hard drive.
[0126] This invention also provides an electronic device, which includes a memory and a processor. The memory stores a computer program that, when executed by the processor, implements the aforementioned AUV control method based on a fixed-time extended state observer.
[0127] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.
Claims
1. An AUV control method based on a fixed-time extended state observer, characterized in that, Includes the following steps: Step 1: Ignoring the roll motion of the AUV, based on the reasonable assumptions of ignoring high-order nonlinear water damping, the coincidence of the origin of the AUV's carrier coordinate system and the center of gravity of the AUV, the symmetry of the AUV body about the horizontal and vertical planes, and the AUV being in a state of equilibrium between buoyancy and gravity in the water, a five-degree-of-freedom motion model of the AUV is constructed. Step 2: Introduce intermediate state variables to integrate external disturbances, AUV internal uncertainties, and unmeasurable velocities into a total disturbance set, thereby achieving a holistic representation of various disturbances; Step 3: Based on the AUV five-degree-of-freedom motion model, construct an adaptive fixed-time extended state observer with an adaptive term. The adaptive term is used to suppress steady-state chattering. The adaptive fixed-time extended state observer is used to estimate and output the AUV's pose observation, velocity observation, and total disturbance observation in real time based on the input AUV pose information. Step 4: Based on the pose observations, velocity observations, and total disturbance observations output by the adaptive fixed-time extended state observer, design a dynamic surface sliding mode controller with fixed-time convergence. The design steps for the dynamic surface sliding mode controller include: Step 4.1: Design a double sliding surface; wherein, the first sliding surface is used to ensure that the AUV position tracking error converges within a fixed time, and the second sliding surface is used to ensure that the AUV velocity tracking error converges within a fixed time. Step 4.2: Design a virtual control law based on the backstepping method, and introduce a nonlinear first-order filter to filter the virtual control law according to the fixed-time convergence condition of the first sliding surface, so as to eliminate the complexity explosion in the backstepping method. Step 4.3: Based on the fixed-time convergence condition of the second sliding surface, design a control input law that includes feedforward compensation of total disturbance observations to obtain the control torque of the AUV; Step 5: Obtain the current actual pose and desired pose of the AUV, input them into the adaptive fixed-time extended state observer and the dynamic surface sliding mode controller, calculate and output the AUV control torque and input it into the AUV system to obtain the true pose of the AUV, and realize the fixed-time stable closed-loop control of the AUV.
2. The AUV control method based on a fixed-time extended state observer according to claim 1, characterized in that, In step 1, the expression for the constructed AUV five-degree-of-freedom motion model is: in: For the additional mass matrix; Here is the Coriolis centripetal force matrix; This is the hydrodynamic damping coefficient matrix; The restoring force matrix; This represents the actual velocity of the AUV in the carrier coordinate system. This represents the actual pose of the AUV in the ground coordinate system. The control torque of the AUV; This is the interference matrix, representing interference from complex underwater environments. This is the transformation matrix between the ground coordinate system and the vehicle coordinate system, determined by the pitch and heading angles of the AUV in the ground coordinate system.
3. The AUV control method based on a fixed-time extended state observer according to claim 2, characterized in that, In step 2, intermediate state variables are introduced. ,make ,Will Represented as: Set the total interference set for: In the formula, This represents the total set of disturbances, including the combined effects of external disturbances, internal uncertainties of the AUV, and unmeasurable velocities.
4. The AUV control method based on a fixed-time extended state observer according to claim 3, characterized in that, The expression for the adaptive fixed-time extended state observer constructed in step 3 is: In the formula, , as well as These are the AUV's pose observations, velocity observations, and total disturbance observations, respectively. , and This is the gain of the pre-observer, with a value range of [0, 1]. , and This is the gain of the post-observer, and all values are greater than 1; , , To assist the gain of the pre-observer, the value range is [0.1, 5]; , , The gain of the auxiliary post-observer is set to [0.1, 5]; the gain of the observer sign term is... and adaptive term update gain All are positive numbers; This is an adaptive term used to prevent oscillations in the steady-state value. For the adaptive term, the adaptive law; This represents the actual pose of the AUV in the ground coordinate system. The control torque of the AUV; It is a symbolic function.
5. The AUV control method based on a fixed-time extended state observer according to claim 1, characterized in that, In step 4.1, the first sliding surface Second sliding surface The expression is: First sliding surface ,in ; Second sliding surface ,in ; In the formula, This refers to the AUV position tracking error. These are AUV pose observations; The desired pose of the AUV; For AUV speed tracking error; These are AUV velocity observations; This represents the expected speed of the AUV. and These are the auxiliary variables for the first and second sliding surfaces, respectively. and Both are the first sliding mode reaching rate gain, and , ; and Both are the weighting coefficients of the first and second sliding surfaces, and both are positive numbers; and The gain for fixed-time convergence with small error is a constant; , Both are parameters for suppressing large errors in sliding surfaces.
6. The AUV control method based on a fixed-time extended state observer according to claim 5, characterized in that, The virtual control law designed in step 4.2 is as follows: in, This is the virtual speed command, which is the output of the virtual control law; and These are the weighting coefficients for the first and second sliding surfaces, respectively, both of which are positive values. and All are normal values that adjust the pose convergence speed; The virtual control law is filtered by a nonlinear first-order filter to obtain the filtered virtual control law as follows: In the formula, and All are first sliding mode approach rate gains; The filter time constant has a value ranging from 0.01 to 1. It is a virtual speed command after being filtered.
7. The AUV control method based on a fixed-time extended state observer according to claim 6, characterized in that, The control input law designed in step 4.3 is as follows: In the formula, and This is the first sliding mode approach rate gain; The control torque of the AUV; and The gain of the second sliding mode reaching law is a positive constant with a value range of 0.1-1. The transformation matrix between the ground coordinate system and the vehicle coordinate system is determined by the pitch angle and heading angle displacement in the AUV coordinate system. Represents the additional mass matrix; The total disturbance observation value output by the observer is used for feedforward compensation; It is the auxiliary variable of the second sliding surface; It is an introduced velocity dummy variable The first derivative of the filtered value after filtering; It is the first sliding surface; It is the second sliding surface.
8. The AUV control method based on a fixed-time extended state observer according to claim 1, characterized in that, The specific process for implementing AUV closed-loop control in step 5 is as follows: Step 5.1: Obtain the current actual pose of the AUV using sensors; Step 5.2, change the current actual pose and desired pose The input is an adaptive fixed-time extended state observer, which is based on the control torque output from the previous cycle. Based on the current pose information, calculate pose observations in real time. Velocity observations and total disturbance observations ; Step 5.3, set the desired pose pose observations Velocity observations and total disturbance observations Input the dynamic surface sliding mode controller to calculate the first sliding surface sequentially. Second sliding surface Virtual speed command corresponding to virtual control law Filtered virtual speed command Finally, the control torque for the current cycle is calculated using the control input law. ; Step 5.4, control torque The thrusters and control rudders applied to the AUV drive its movement; Step 5.5, return to step 5.1, enter the next control cycle, and realize continuous closed-loop tracking control of AUV pose.
9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the AUV control method based on a fixed-time extended state observer as described in any one of claims 1-8.
10. A computer-readable storage medium storing computer instructions, characterized in that, When the instructions are executed by the processor, they implement the AUV control method based on a fixed-time extended state observer as described in any one of claims 1-8.