Method for unmanned surface vehicle to collaboratively surround unknown target in GPS denial environment

Abstract

The invention discloses a method for an unmanned ship to cooperatively surround an unknown target in a GPS denial environment, and relates to the technical field of unmanned ship cooperative control. In order to solve the problems that effective surrounding is difficult to complete in a GPS denial or unstable signal environment, the unmanned surface vehicle does not respond to target maneuvering in time and the surrounding precision of a dynamic complex water area is difficult to guarantee, the scheme is provided as follows: establishing an unmanned surface vehicle motion mathematical model, and describing the two-dimensional plane motion and dynamics of the unmanned surface vehicle; calculating a target speed estimator according to the distance and azimuth measurement between the adjacent unmanned ships; designing a first-order fixed time differentiator, and approaching a target speed and a derivative thereof within a preset time; on the basis of azimuth rigidity, the azimuth between the adjacent unmanned surface vehicle and the target is regarded as a rigid constraint, a rotation item is introduced to realize collaborative surrounding, and uncertain interference and model errors are compensated online. The scheme can be applied to cooperative surrounding operation of multiple unmanned ships on unknown targets in a GPS denial or signal limited environment.

Description

Technical Field

[0001] It relates to the technical field of unmanned boat cooperative control. Background Art

[0002] In the field of unmanned boat cooperative control, formation control and cooperative decision-making based on multiple unmanned boats jointly performing tasks have always been one of the research hotspots. In the prior art, in order to achieve the tracking and surrounding of dynamic targets, researchers usually rely on high-precision global positioning systems (GPS) or other satellite navigation means to obtain the position information of the unmanned boats and the targets, so as to accurately control the attitude and trajectory of the unmanned boats. For example, some research uses distributed consensus algorithms to maintain the relative distance and formation among multiple unmanned boats; there are also some methods that combine multi-sensor data fusion technology, by combining inertial navigation systems, vision sensors and GPS information, to improve the perception accuracy of the cluster for the target position and speed. These studies can achieve good results in an environment with normal GPS signals, and can effectively monitor and capture the target.

[0003] However, the above-mentioned surrounding control means that rely on high-precision positioning signals such as GPS will face severe challenges in complex or harsh environments. With the proposal and development of the area denial strategy, GPS signals are vulnerable to interference, occlusion or spoofing attacks; even in general waters, positioning may be unstable due to terrain, climate or other equipment interference. Once the unmanned boat cluster cannot obtain accurate position information, the existing methods will have large errors in target surrounding and dynamic formation maintenance, and even lose the effective tracking of the target. In addition, most control algorithms can only ensure consistent convergence or finite-time convergence during design, and cannot quickly and stably complete formation surrounding in case of emergencies; and the existing formation control process often lacks a fast estimation scheme for the situation where the target speed is unmeasurable or uncertain, resulting in a delay in the formation's response to target maneuvers when the target speed information is missing, reducing the completion degree and safety of the surrounding task.

[0004] In summary, the prior art mainly faces the following problems:

[0005] It has a strong dependence on positioning information such as high-precision GPS, and it is difficult to complete effective surrounding tasks in an environment with GPS denial or unstable signals.

[0006] There is a lack of a fast estimation and dynamic response mechanism for the situation where the target speed is unmeasurable or uncertain, resulting in untimely response of the unmanned boat to target maneuvers.

[0007] The convergence speed is insufficient to cope with sudden interference or high-speed escape of the target, and it is difficult to ensure the safety and accurate surrounding of the unmanned boat formation in dynamically complex waters. Summary of the Invention

[0008] To solve the technical problems existing in the prior art, namely, the prior art faces difficulties in completing effective surrounding tasks in GPS-denied or signal-unstable environments, the unmanned boat's response to target maneuvers is not timely, and it is difficult to ensure the safety and precise surrounding of an unmanned boat formation in dynamically complex waters, the technical solution provided by the present invention is as follows:

[0009] A method for an unmanned boat to cooperatively surround an unknown target in a GPS-denied environment, comprising:

[0010] Step 1: Establish a kinematic mathematical model of the unmanned boat:

[0011] Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane;

[0012] Step 2: Estimate the target speed using azimuth information:

[0013] Utilize the relative distance and azimuth measurements between adjacent unmanned boats to obtain an estimated quantity of the target speed;

[0014] Step 3: Design a first-order fixed-time differentiator:

[0015] For the target speed estimate and the unmanned boat state information obtained in Step 2, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism;

[0016] Step 4: Design of surrounding control based on azimuth rigidity:

[0017] Regard the azimuths between adjacent unmanned boats and between the unmanned boat and the target as rigid constraints, introduce a rotation term to achieve cooperative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

[0018] Furthermore, it further includes:

[0019] Step 5: Simulation or actual verification:

[0020] Combine the kinematic and dynamic models of the unmanned boat for verification, turn on the GPS-denied or signal-unstable scenario, and test the tracking and encirclement effects on the target.

[0021] Furthermore, Step 1 is specifically to define state variables such as position, speed, heading angle, etc., as well as external disturbances and model uncertainty terms.

[0022] Furthermore, Step 2 is specifically to obtain the distance between the unmanned boat and the target through geometric inference, and average the estimated values of the distances from multiple adjacent unmanned boats to the target to reduce the influence of noise; further, according to the azimuth vector projection, obtain the estimated quantity of the target speed.

[0023] Further, step 3 specifically involves introducing a non-linear observation equation, setting the observed quantity and its differential estimator, and approximating the true signal and its derivative within a preset time through a fixed-time convergence mechanism.

[0024] Further, step 4 specifically involves setting a virtual control signal, integrating the azimuth error with the desired safety distance, and combining with the differential estimator output in step 3 to perform online compensation for uncertain disturbances and model errors.

[0025] There is also provided a device for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment, including:

[0026] Module 1: Establish the mathematical model of the unmanned boat's motion:

[0027] Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane;

[0028] Module 2: Estimate the target speed using azimuth information:

[0029] Utilize the relative distance and azimuth measurements between adjacent unmanned boats to obtain the speed estimator of the target;

[0030] Module 3: Design a first-order fixed-time differentiator:

[0031] For the target speed estimation and unmanned boat state information obtained in step 2, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism;

[0032] Module 4: Design of surrounding control based on azimuth rigidity:

[0033] Regard the azimuth between adjacent unmanned boats and between the unmanned boat and the target as a rigid constraint, introduce a rotation term to achieve collaborative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

[0034] There is also provided a computer storage medium for storing a computer program, and when the computer program is read by a computer, the computer executes the described method.

[0035] There is also provided a computer, including a processor and a storage medium, and when the processor reads the computer program stored in the storage medium, the computer executes the described method.

[0036] There is also provided a computer program product, which, as a computer program, when executed, implements the described method.

[0037] The advantages of the technical solution provided by the present invention compared with the prior art are as follows:

[0038] This solution realizes the surrounding control of an unmanned boat for an unknown target by relying only on azimuth information in a GPS-denied environment. Compared with the existing research methods that rely on precise position information, it has stronger environmental adaptability. In the case where the target speed is unmeasurable, this solution uses a speed estimation module based on azimuth information to replace the high-precision positioning system, enabling the unmanned boat to still maintain effective detection and cooperation with the target in complex or interfering environments. This azimuth information estimation part enables the system to get rid of the strict dependence on GPS signals, providing higher flexibility and robustness for the unmanned boat cluster to perform cooperative surrounding tasks in an environment where satellite signals are blocked or unstable.

[0039] This solution specifically designs a first-order fixed-time differentiator for the problems of noise and signal distortion in differential calculation, and quickly converges to the accurate tracking of the target trajectory and its derivative within a fixed time. Compared with traditional finite-time differentiators or super-twisting differentiators, the fixed-time differentiator part can complete the convergence of differential signals within a pre-set time, significantly improving the response speed and accuracy when the target suddenly accelerates or the path changes. This improvement makes multiple unmanned boats more robust during the execution of cooperative surrounding, and effectively avoids the phenomenon of high-frequency chattering.

[0040] This solution uses the azimuth rigidity theory to ensure that the unmanned boat maintains a stable formation structure while surrounding, and through the constraint of only using azimuth information, the formation can complete safe surrounding in a local communication environment. Compared with traditional methods based on global coordinate systems or consensus algorithms, the azimuth rigidity part enables the azimuth to remain unchanged and not to disperse through local information even when the number of unmanned boats changes, improving the scalability of the system. Since it does not need to always rely on global positioning or other sensors for coordinate correction, this method can also ensure that there is no collision between unmanned boats and complete close surrounding in scenarios where the target escapes or there are dynamic interferences.

[0041] This solution proposes a target speed estimator to accurately predict the movement of an unknown target, and uses an autonomous learning algorithm to online approximate and adaptively adjust external interferences and target speeds. Compared with traditional data-driven methods that require prior information or a large amount of offline modeling, the online learning part of this solution can make real-time corrections for model uncertainties and external disturbances during the execution process, making the control performance independent of an accurate prior model. Even when the target maneuvers in an unpredictable manner, this online estimation and learning mechanism can quickly adjust the virtual control quantity to ensure the effective capture and control of the target by the unmanned boat group.

[0042] It can be used for the cooperative surrounding operation of multiple unmanned boats for unknown targets in a GPS-denied or signal-limited environment. Description of the Drawings

[0043] Figure 1Schematic flow diagram of a method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment;

[0044] Figure 2 Curve graph of the change in the target surrounding trajectory;

[0045] Figure 3 Curve graph of the change in the surrounding distance error;

[0046] Figure 4 Curve graph of the change in the surrounding angle error;

[0047] Figure 5 Curve graph of the change in the target speed estimation. Detailed implementation method

[0048] To make the advantages and benefits of the technical solution provided by the present invention more clearly reflected, the technical solution provided by the present invention will now be further described in detail with reference to the accompanying drawings. Specifically:

[0049] Embodiment 1. This embodiment provides a method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment, including:

[0050] Step 1: Establish a kinematic mathematical model of the unmanned boat:

[0051] Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane;

[0052] Step 2: Estimate the target speed using azimuth information:

[0053] Utilize the relative distance and azimuth measurements between adjacent unmanned boats to obtain the speed estimation of the target;

[0054] Step 3: Design a first-order fixed-time differentiator:

[0055] For the target speed estimation and unmanned boat state information obtained in Step 2, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism;

[0056] Step 4: Surrounding control design based on azimuth rigidity:

[0057] Regard the azimuth between adjacent unmanned boats and between the unmanned boat and the target as a rigid constraint, introduce a rotation term to achieve collaborative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

[0058] It also includes:

[0059] Step 5: Simulation or actual verification:

[0060] Verify in combination with the kinematic and dynamic models of the unmanned boat, turn on the GPS-denied or signal-unstable scenario, and test the tracking and encirclement effects on the target.

[0061] Step 1 specifically defines state variables such as position, velocity, and heading angle, as well as external disturbances and model uncertainty terms.

[0062] Step 2 specifically obtains the distance between the unmanned boat and the target through geometric inference, and averages the estimated values of the distances of multiple adjacent unmanned boats to the target to reduce the influence of noise; further, according to the azimuth vector projection, the velocity estimator of the target is obtained.

[0063] Step 3 specifically introduces a non-linear observation equation, sets the observed quantity and its differential estimator, and approximates the true signal and its derivative within a preset time through a fixed-time convergence mechanism.

[0064] Step 4 specifically sets a virtual control signal, integrates the azimuth error and the desired safety distance, and combines the differential estimator output in Step 3 to perform online compensation for uncertain disturbances and model errors.

[0065] There is also provided a device for unmanned boats to cooperate and surround an unknown target in a GPS-denied environment, including:

[0066] Module 1: Establish a mathematical model for the motion of the unmanned boat:

[0067] Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane;

[0068] Module 2: Estimate the target velocity using azimuth information:

[0069] Utilize the relative distance and azimuth measurement between adjacent unmanned boats to obtain the velocity estimator of the target;

[0070] Module 3: Design a first-order fixed-time differentiator:

[0071] For the target velocity estimation and the unmanned boat state information obtained in Step 2, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism;

[0072] Module 4: Design of surrounding control based on azimuth rigidity:

[0073] Regard the azimuth between adjacent unmanned boats and between the unmanned boat and the target as a rigid constraint, introduce a rotation term to achieve cooperative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

[0074] Embodiment 2: This embodiment is a further description of the technical solution provided in Embodiment 1. Specifically:

[0075] (1) Establish a mathematical model for the motion of the unmanned boat

[0076] In this step, a kinematic and dynamic description of the unmanned boat in the two-dimensional plane is established. By defining the state variables of the unmanned boat (position, velocity, heading angle, etc.), it lays a foundation for subsequent target velocity estimation based on bearing information, fixed-time differentiator design, and the development of the surrounding controller.

[0077] First, select the position coordinates and heading angle of the unmanned boat on the plane as the basic motion states, and at the same time introduce quantities such as longitudinal and lateral velocities and yaw angular velocity that characterize the dynamic characteristics of the unmanned boat to construct a complete motion model. This model includes various factors such as mass, moment of inertia, hydrodynamic damping, and external disturbances, and can be uniformly expressed as a set of equations describing the evolution of position over time and the evolution of velocity over time.

[0078] On this basis, according to the actual structural characteristics of the unmanned boat (for example, considering factors such as the length of the unmanned boat), the position and velocity variables can be appropriately corrected and calibrated so that the model can more accurately reflect the real motion of the unmanned boat. Finally, by unifying and summarizing the uncertainty terms and external disturbances in the model, the comprehensive kinematic and dynamic equations of the unmanned boat are obtained, providing the necessary state variables and constraint relationships for subsequent velocity estimation and the solution of the surrounding control law.

[0079] After completing this step, the system obtains key variables such as the position and velocity of the unmanned boat that can be updated over time, providing input data for subsequent target velocity estimation and fixed-time differentiator.

[0080] (2) Construct a target velocity estimation method based on bearing information

[0081] In an environment where GPS signals are limited or completely lost, it is difficult to obtain accurate global position information. This step uses local information such as the neighbor distance and bearing measurement between unmanned boats to design a target velocity estimation method, so as to infer the motion trend of the target even when the target velocity is unknown.

[0082] First, in order to utilize the relative position relationship between unmanned boats, define the relative edge vector and unit direction vector between each unmanned boat and its neighbors, and then rely on geometric relationships to calculate the distance between the unmanned boat and the target. Since in actual use, a single unmanned boat may simultaneously maintain perception with multiple neighbors, thus obtaining multiple sets of distance measurements; to reduce the influence of noise, these distance estimates can be averaged to obtain more accurate results.

[0083] After obtaining the distance between the unmanned boat and the target, the method of projection and geometric inference can be further applied to directly obtain the estimated value of the target speed from the only azimuth information. This method can obtain the heading speed of the target without an external GPS signal. When a part of the unmanned boats are temporarily unable to perceive the target, the azimuth measurements of their neighbors can be transmitted in local communication, enabling the overall system to still estimate the target speed.

[0084] After this step is completed, real-time estimation results of the target speed and the distance between the unmanned boat and the target can be obtained. Subsequently, the design of a fixed-time differentiator will be combined to achieve precise observation of these quantities and their rates of change, thereby providing the necessary prior information for the surrounding control.

[0085] (3) Design a first-order fixed-time differentiator

[0086] The unmanned boat usually encounters problems such as non-linearity, uncertainty, and measurement noise during the dynamic target surrounding. The traditional finite-time differentiator may not converge stably within the specified time. In this step, a first-order fixed-time differentiator is designed to quickly and accurately observe the signal and its rate of change within a fixed time and enhance the system's robustness to noise.

[0087] The core idea of this step is to set up two observed quantities, representing the system input signal and the differential value of this signal respectively. By introducing non-linear terms for the input signal and the observation error, the observer quickly converges to the actual signal and its differential within a fixed time. Compared with traditional methods, the fixed-time differentiator can complete the process of the observation error tending to zero or entering a very small neighborhood within a pre-set time interval without relying on the initial conditions. In the specific implementation, parameters such as the differentiator gain and non-linear exponent need to be reasonably selected according to the dynamic characteristics and noise level of the unmanned boat system to ensure that there is no high-frequency chattering in the face of noise and a sufficiently fast convergence speed can be achieved. The estimated value of the signal rate of change output by the differentiator will continue to support the subsequent backstepping design and formation surrounding control.

[0088] (4) Method for surrounding control of bearing-only information target based on bearing rigidity

[0089] After obtaining the speed estimates of the unmanned boat and the target and reliable differential observations, this step uses the bearing rigidity principle to design a distributed surrounding control law to achieve cooperative surrounding of unknown targets. This method only depends on the bearing information between adjacent unmanned boats and between the unmanned boat and the target, enabling the formation to maintain a stable surrounding posture when the GPS signal is blocked.

[0090] First, introduce the concept of azimuth constraint: consider the relative azimuth between adjacent unmanned boats and the azimuth between the unmanned boat - target as important constraints. By transmitting these constraints in the local communication network, maintain the overall surrounding structure of the formation relative to the target. If it is necessary to achieve counterclockwise or clockwise surrounding, corresponding rotation terms can be embedded in the azimuth constraint to control the formation to move in the corresponding direction around the target.

[0091] On this basis, introduce virtual control signals, integrate various azimuth errors and requirements such as safety distance into an adjustable control quantity, and then combine the auxiliary information output by the aforementioned differentiator and an online learner (such as a neural network) to compensate for uncertain disturbances, and construct a hierarchical backstepping control law. By adjusting key parameters such as control gain and rotation speed, the unmanned boats can be distributed at the desired surrounding radius within a fixed time and move evenly around the target. During this process, due to azimuth rigidity, the relative azimuth relationship between adjacent unmanned boats can be guaranteed not to be damaged. Even if some unmanned boats cannot detect the target, they can still rely on the azimuth relationship with their neighbors to achieve the overall surrounding of the target.

[0092] Through this design, when multiple unmanned boats perform tasks together, they only need local azimuth information to complete tight surrounding without relying on a global positioning system. Even if the target speed has large uncertainties or sudden maneuvers occur, this control scheme can quickly make corrections and maintain the stability of the formation structure with the help of the aforementioned fixed-time differentiator and online compensation mechanism.

[0093] (5) Verification based on simulation experiments or actual deployment

[0094] After completing the design of the control law, test the effectiveness of this scheme through simulation experiments or actual deployment, and verify its performance and stability in performing target surrounding only relying on azimuth information in a GPS-denied environment.

[0095] In the simulation environment, set several unmanned boats and a maneuverable target, and add random external disturbances to simulate harsh water areas or signal interference scenarios. At the same time, artificially make the GPS signal invalid, and observe whether the unmanned boat system can complete the detection and capture of the target only by using neighbor and azimuth information.

[0096] The experimental process usually includes:

[0097] Drive the simulated movement of the unmanned boats by the previously established motion model, and provide the sensor output data to the target speed estimation module.

[0098] Based on the azimuth and distance information of adjacent unmanned boats, the target speed estimation module obtains the speed estimation of the target and the distance between the unmanned boat - target.

[0099] The first-order fixed-time differentiator completes the observation of the relevant control signal and its rate of change within a set time, ensuring the rapid response of the control algorithm to the target's sudden movements.

[0100] Based on the azimuth rigidity principle, the distributed surrounding controller calculates the desired motion commands for each unmanned boat, guiding the unmanned boats to maintain a safe distance and evenly surround the target within a fixed time.

[0101] Finally, by observing whether the unmanned boats enter the established surrounding formation within the expected time and verifying their robustness performance under external disturbances or the high-speed movement of the target, it can be proved that this solution can still successfully achieve the cooperative surrounding of unknown targets in the case of complete loss or severe limitation of GPS.

[0102] Through the implementation of the above five steps, the solution of "cooperative surrounding of unknown targets by unmanned boats in a GPS-denied environment" can be fully realized. This solution is based on target speed estimation, fixed-time differential observation, and a distributed surrounding control strategy that only relies on azimuth information. It uses the backstepping method combined with an online learner to compensate for external disturbances and model uncertainties, ensuring that multiple unmanned boats are distributed around the target collectively and maintain a safe interval within a pre-set fixed time. Compared with the traditional GPS-dependent method, this solution significantly improves the task completion rate and the control ability of the target in harsh environments, providing an important reference for the cooperative operation of multiple unmanned boat formations in complex waters.

[0103] Embodiment 3. Combination Figures 1-5 To illustrate this embodiment, this embodiment further describes the above-provided technical solution in detail through specific examples. Specifically:

[0104] (1) Establish the mathematical model of the unmanned boat's motion. Define p i = [x i , y i T to represent the position coordinates of the unmanned boat, to represent the heading angle of the unmanned boat, q i = [u i , v i T to represent the longitudinal speed and lateral speed of the unmanned boat, and r i to represent the yaw angular velocity of the unmanned boat. Define a new variable where, are design parameters. Then the kinematic and dynamic systems of the unmanned boat can be expressed as:

[0105]

[0106] In the formula, Δ iThe uncertainty term caused by the model observation errors of the mass inertia matrix, the Coriolis centripetal matrix, and the hydrodynamic damping matrix. Denotes the external disturbance term. f u,i and f r,i Denotes the non - linear coupling term, and its specific form is:

[0107]

[0108] τ i Denotes the control input. X * ,Y * and N * Denotes the hydrodynamic coefficients. m denotes the mass of the unmanned boat. I = denotes the inertia matrix.

[0109] (2) Establish the azimuth rigid relationship. The edge vector from unmanned boat i to unmanned boat j is denoted by ξ ij and the unit direction vector from unmanned boat j to unmanned boat i is denoted by g ij and their specific definitions are as follows:

[0110]

[0111] And, it satisfies the relational expressions ξ ij =-ξ ji and g ij =-g ji . For any given azimuth vector g ij , the orthogonal projection operator is defined as:

[0112]

[0113] Its function is to project any given vector onto the orthogonal complement space of g ij . The edge vector from unmanned boat i to the target is denoted by ξ it and the unit direction vector from unmanned boat j to unmanned boat i is denoted by g it and their specific definitions are as follows:

[0114]

[0115] To better achieve the surrounding mission and minimize the escape probability of the target, the rotation matrix J(ωt) is introduced, where ω represents the desired rotational angular velocity. When ω > 0, the surrounding formation rotates counter - clockwise, and when ω < 0, the surrounding formation rotates clockwise. The time - varying azimuth constraint is controlled by the rotation matrix, and its specific form is where and denote the initial azimuth constraints.

[0116] Considering the translation and scaling coefficients, a framework with infinitesimal azimuthal stiffness is uniquely determined. In practical application scenarios, the unmanned surface vehicle (USV) cluster system can effectively complete various surrounding tasks, including cooperative obstacle avoidance and navigation in irregular waters, by adjusting the formation's telescopic maneuver. Importantly, during the scaling process, the relative azimuthal information between adjacent USVs remains unchanged, ensuring the integrity and stability of the system throughout the rigid surrounding process.

[0117] (3) Construct a target velocity estimation method based on azimuthal information. Define the distance between USV i and USV j as d ij , and the distance between USV i and the target as d it . The distance d it between USV i and the target can be obtained as follows:

[0118] where ψ ti represents the angle between the side (USV j - target) and the side (USV j - USV i). Similarly, ψ ij represents the angle between the side (target - USV i) and the side (target - USV j).

[0119] Considering that USV i may be adjacent to multiple other USVs simultaneously, to reduce the impact of Gaussian noise on the estimation error in practical applications, USV i can cooperate with |N i | adjacent USVs to estimate its distance to the target, and then the average of the N i distance estimation values can be taken as the final estimation value. Based on the above analysis, the distance estimation value of USV i to the target can be expressed as:

[0120]

[0121] When the matrix is a non-singular matrix, the target velocity can be estimated as:

[0122]

[0123] where I2 represents the second-order identity matrix.

[0124] (4) Design a first-order fixed-time differentiator.

[0125] First, define the function v(t) in the interval [0, ∞). Generally, the function v(t) consists of an n-times differentiable basic signal v0(t) and a uniformly bounded noise signal v d (t), i.e., v(t) = v0(t) + v d (t). The purpose of the differentiator is to approximate the derivative of the function v0(t) with respect to time as accurately as possible. To estimate the differential signal the first-order fixed-time differentiator is designed as follows:

[0126]

[0127] Wherein, v0 represents the input signal, and y1 and y2 respectively represent the estimated values of v0 and .

[0128] represents the nonlinear term function, and the exponents c1 and c2 satisfy the following relational expressions: c1 = c and c2 = 2c - 1, where c belongs to the interval (1 - σ1, 1), σ1 > 0; the exponents h1 and h2 satisfy the following relational expressions: h1 = h and h2 = 2h - 1, where h belongs to the interval (1, 1 + σ2), σ2 > 0; the observer parameters ζ1, ζ2, h1, h2, H1, and H2 need to be designed such that the error dynamics matrices and are Hurwitz matrices.

[0129] When the second derivative of the function v0 is zero and there is no noise v d = 0, the fixed-time differentiator ensures that the differential estimation error converges to zero within a fixed time

[0130]

[0131] When the second derivative of the function v0 and the noise are bounded, the differential estimation error converges to a small region Δ1 near the origin within a fixed time T1, where ρ1 = λ min (P1) / λ max (Y), ρ2 = λ min (P2) / λ max (Y). The matrices P1, P2, and Y are symmetric positive definite matrices and satisfy the following relational expressions:

[0132] F1 T Y + YF1 + P1 = 0

[0133]

[0134] (5) Design an azimuth information target surrounding control method based on azimuth rigidity.

[0135] First, define the azimuth error of unmanned boat i relative to unmanned boat j and the azimuth error of unmanned boat i relative to the target respectively as:

[0136]

[0137] Let E t represent the stack form of the edge connecting the unmanned boat to the target, and E s represent the stack form of the remaining edges. Therefore, H can be utilizeds and H t represents their respective incidence matrices. Before continuing, define the following variables in stack form: g t = {g it}、 g s = {g ij}、 and The distance tracking error is defined as make d1 = diag{l it},

[0138]

[0139] Based on the above definition, combined with the first-order fixed time differentiator, through the backstepping control theory, the virtual control law θ of the unmanned boat is f Can be designed as:

[0140]

[0141] In the formula,

[0142]

[0143] and represents a positive design parameter. in

[0144] In the formula, θ represents the detection radius of the unmanned boat. f Indicates virtual control signal The stack form

[0145] The above formula shows that when the unmanned boat i can successfully detect the target, the dynamic target surround task can be completed by using the position of the unmanned boat i and the target, and the position of the unmanned boat i and the unmanned boat j. However, if the individual unmanned boat i cannot detect the target, it can also complete the dynamic target surround task by relying only on the position of the unmanned boat i and the unmanned boat j. The virtual control method consists of four parts: θ sf ,θ tf ,θ rf and where θ sf Used to minimize the azimuth error relative to adjacent unmanned boats; θ tf Used to reduce the azimuth error relative to the target; θ rf Used to keep a safe distance from the target; Used to prevent collisions during target orbit.

[0146] Combined with the design of the above first-order fixed-time differentiator, the following differentiator is designed:

[0147]

[0148] where represents the input signal, and represent the output of the fixed-time differentiator. Define the differential velocity tracking error of the unmanned boat as Define the stack form Using the above first-order fixed-time differentiator, the differential value of the virtual control law can be obtained without explicit derivation and calculation.

[0149] In practical engineering applications, the lumped disturbance term is an unknown term, resulting in a reduction in the robust performance of the control method. Therefore, using the online approximation characteristics of the radial basis neural network for any continuous function, the unknown model parameters and external disturbances can be approximated as:

[0150]

[0151] where W i * represents the ideal weight, H i (x) represents the output based on the Gaussian function, and ε i represents the estimation error.

[0152] Combined with the minimum parameter learning method, an online learning algorithm for unknown models is proposed, which can effectively weaken problems such as time-consuming and complex online learning:

[0153]

[0154] where ι i = ||W i * ||, ψ i = ||H i (x)||, D i = ||ε i ||.

[0155] Define the velocity error as To achieve an accurate estimate of the lumped disturbance term, design the adaptive law as:

[0156]

[0157] where γ1 and c1 represent positive design parameters.

[0158] Define the adaptive estimation error as For the convenience of the next control method design, the following variables are further expressed in a compact form as: and ψ = diag[ψ1, ψ2,..., ψ n T . The control input of the unmanned boat can be obtained according to the virtual control law, and the specific form is as follows:

[0159]

[0160] where λ i , i = 10, 11, 12, and represent the positive design control parameters.

[0161] The above control method realizes the surrounding of the target in an evenly distributed manner within a fixed time T1, satisfying and where d r > 0 represents the desired surrounding radius, and ψ ij represents the interval angle between the i-th unmanned boat and the j-th unmanned boat. The target surrounding formation is a formation with an infinitesimal azimuth rigid frame. The unmanned boat formation surrounds the dynamic target with a consistent angular velocity ω, thereby minimizing the escape probability of the dynamic target. The control method ensures that no collision events occur during the surrounding process of the unmanned boat, that is, at all times where R represents an unknown positive constant, and d ij represents the distance between the i-th unmanned boat and the j-th unmanned boat.

[0162] Technical effects

[0163] (1) The present invention designs a fixed-time differentiator, which can quickly extract the tracking signal and the differential signal, reduces the computational complexity and solves the potential signal distortion problem. In addition, it is robust to signal errors and noises and can ensure global fixed-time convergence.

[0164] (2) The present invention designs a dynamic target rigid surrounding control method for an unmanned boat cluster system that only depends on azimuth information, eliminates the dependence of the unmanned boat cluster system on global positioning information, ensures that the system realizes the surrounding of the dynamic target within a fixed time, and avoids collisions between unmanned boats. In addition, a target speed estimator is designed to solve the problem of unmeasurable target speed.

[0165] ​(3) The control method proposed by the present invention is based on the concept of evenly distributed surrounding design. According to the azimuth rigidity theory, the azimuth constraints between adjacent unmanned boats and between the unmanned boat and the target are designed. The addition of azimuth constraints increases the flexibility of the dynamic target surrounding strategy. During the surrounding process, unmanned boat nodes may leave the system due to reasons such as out of control, damage, and loss, or may be added to the system due to the increase in target complexity. The number of unmanned boats is not fixed. Therefore, local communication can be used to determine the number of the unmanned boat system, that is, there is no need to specify the initial value of the number of unmanned boats in advance.

Claims

1. A method for unmanned boats to collaboratively surround an unknown target in a GPS-denied environment, characterized in that Including: Step 1: Establish a mathematical model for the motion of the unmanned boat: Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane; Step 2: Estimate the target speed using azimuth information: Utilize the relative distance and azimuth measurements between adjacent unmanned boats to obtain the speed estimation of the target; Step 3: Design a first-order fixed-time differentiator: For the target speed estimation obtained in Step 2 and the unmanned boat state information, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism; Step 4: Design of surrounding control based on azimuth rigidity: Regard the azimuths between adjacent unmanned boats and between the unmanned boat and the target as rigid constraints, introduce a rotation term to achieve cooperative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

2. A method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment according to claim 1, characterized in that, Also including: Step 5: Simulation or actual verification: Verify in combination with the kinematic and dynamic models of the unmanned boat, turn on the GPS denial or signal instability scenario, and test the tracking and encirclement effects on the target.

3. A method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment according to claim 1, characterized in that, Specifically, in Step 1, define state variables such as position, speed, heading angle, etc., as well as external disturbances and model uncertainty terms.

4. A method for unmanned boats to collaboratively surround an unknown target in a GPS-denied environment according to claim 1, characterized in that, Specifically, in Step 2, obtain the distance between the unmanned boat and the target through geometric inference, and average the estimated values of the distances of multiple adjacent unmanned boats to the target to reduce the influence of noise; further, according to the azimuth vector projection, obtain the speed estimation of the target.

5. A method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment according to claim 1, characterized in that Specifically, in Step 3, introduce a nonlinear observation equation, set the observed quantity and its differential estimation quantity, and approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism.

6. A method for collaborative surrounding of an unknown target by unmanned boats in a GPS-denied environment according to claim 1, characterized in that, Specifically, in Step 4, set a virtual control signal, integrate the azimuth error and the desired safety distance, and combine with the differential estimation quantity output in Step 3 to perform online compensation for uncertain disturbances and model errors.

7. A device for an unmanned boat to cooperatively surround an unknown target in a GPS denial environment, including: Module 1: Establish a mathematical model for the motion of the unmanned boat: Describe the kinematics and dynamics of the unmanned boat in a two-dimensional plane; Module 2: Estimate the target speed using azimuth information: Utilize the relative distance and azimuth measurements between adjacent unmanned boats to obtain the speed estimation of the target; Module 3: Design a first-order fixed-time differentiator: For the target speed estimation obtained in Step 2 and the unmanned boat state information, approximate the true signal and its derivative within a preset time through a fixed-time convergence mechanism; Module 4: Design of surrounding control based on azimuth rigidity: Regard the azimuths between adjacent unmanned boats and between the unmanned boat and the target as rigid constraints, introduce a rotation term to achieve cooperative surrounding of the target; perform online compensation for uncertain disturbances and model errors.

8. A computer storage medium for storing a computer program, when the computer program is read by a computer, the computer executes the method described in claim 1.

9. A computer, including a processor and a storage medium, when the processor reads the computer program stored in the storage medium, the computer executes the method described in claim 1.

10. A computer program product, as a computer program, when the computer program is executed, implements the method described in claim 1.

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