Under-actuated unmanned ship formation control method based on output redefinition

Abstract

The invention discloses an under-actuated unmanned ship formation control method based on output redefinition, and relates to the technical field of under-actuated unmanned ship formation control. In order to solve the technical defects of insufficient control input, model uncertainty and external interference of the existing under-actuated unmanned ship formation control technology and the differential explosion problem of the traditional control method in the prior art, the technical scheme provided by the invention is as follows: the under-actuated unmanned ship formation control method based on output redefinition. The method comprises the following steps: establishing kinematics and dynamics models of the underactuated unmanned ship, and decomposing the kinematics and dynamics models into an attitude subsystem and a position subsystem; respectively designing an attitude controller and a position controller through the attitude subsystem and the position subsystem, and approaching a nonlinear term of the system; repeated differentiation of the virtual control law in the model is avoided through a first-order filter; and combining a self-adaptive control law and an auxiliary self-adaptive law based on a minimum learning parameter method. The method is suitable for the formation control of the under-actuated unmanned surface vehicles.

Description

Technical Field

[0001] The invention relates to the technical field of underactuated unmanned boat formation control, and in particular to underactuated unmanned boat formation control based on output redefinition. Background Art

[0002] In recent years, with the rapid development of unmanned driving technology and marine engineering technology, the research on unmanned surface vehicles (USVs) has gradually become a focus, especially in the fields of military, search and rescue, environmental monitoring, etc., the importance of formation control technology has become increasingly prominent. Unmanned boat formations can achieve multi-target and multi-task coordination and cooperation. Compared with a single unmanned boat, they have higher flexibility, better mission adaptability and higher operating efficiency. In many scenarios such as marine search and rescue, environmental monitoring, resource exploration, navigation guidance, military escort, etc., the use of unmanned boat formations can significantly improve the coverage and reliability of mission execution.

[0003] Existing unmanned boat formation control methods include fuzzy control, backstepping control, sliding mode control, and graph theory-based control algorithms. These methods are widely used in fully-driven unmanned boat formations and are relatively mature. Fully-driven unmanned boats can achieve independent control of all degrees of freedom through control inputs, so their formation control problem is relatively simple. However, with the complexity of mission requirements, the use of underactuated unmanned surface vehicles (UUSVs) has gradually increased. Since the control input of underactuated unmanned surface vehicles is less than the system's degrees of freedom, they face the problem of insufficient control degrees of freedom during navigation, especially in complex environments, where their stability and accuracy are difficult to guarantee. Therefore, the formation control method for underactuated unmanned boats is the focus and difficulty of current research.

[0004] In existing research, some scholars have proposed a method of combining sliding mode control with neural networks to improve the robustness of the control system. However, when these methods are applied to underactuated unmanned boat formations, there are still problems such as insufficient control input, model uncertainty, and external interference, which makes it difficult to ensure the stability of the formation. In addition, although backstepping control can solve the problem of insufficient control freedom to a certain extent, due to the high complexity of the system, it often faces the problem of "differential explosion" in the differential calculation process, which greatly limits its feasibility and real-time performance in practical applications. On the other hand, radial basis function (RBF) is used to approximate the nonlinear terms in the system. However, due to its large number of learning parameters, the computational complexity in real-time control is still high, which affects the rapid response capability of the controller.

[0005] In addition, existing formation control methods generally lack effective interference suppression methods. Since unmanned boats sail in the ocean environment, they are affected by external interference such as waves and wind speed. How to effectively suppress the impact of these interferences on formation control has become a key challenge in achieving a stable formation. Although some methods have introduced adaptive control laws, they often require more learning parameters, which makes the controller design complex and difficult to achieve real-time adjustment.

[0006] In summary, the existing underactuated unmanned boat formation control technology has the following main problems: insufficient control input makes it difficult to achieve independent control of all degrees of freedom; model uncertainty and external interference affect the stability of the formation; traditional control methods have differential explosion problems when dealing with complex nonlinear systems, with high computational complexity, and are difficult to meet the needs of real-time control.

[0007] Therefore, there is an urgent need for an under-actuated unmanned boat formation control method that can reduce the computational complexity and enhance the system's anti-interference capability, so as to achieve more stable and efficient formation control. Summary of the invention

[0008] In order to solve the technical defects in the prior art, the existing underactuated unmanned boat formation control technology has insufficient control input, model uncertainty and external interference, and the traditional control method has the problem of differential explosion when dealing with complex nonlinear systems, the technical solution provided by the present invention is:

[0009] A method for controlling an underactuated unmanned boat formation based on output redefinition, the method comprising:

[0010] Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into the steps of attitude subsystem and position subsystem;

[0011] The step of designing a posture controller and a position controller through the posture subsystem and the position subsystem respectively to approximate the nonlinear terms of the system;

[0012] Avoiding repeated differentiation steps of the virtual control law in the model by means of a first-order filter;

[0013] The steps of combining the adaptive control law based on the minimum learning parameter method and the auxiliary adaptive law.

[0014] Furthermore, a preferred embodiment is provided, in which the kinematic and dynamic models of the underactuated unmanned vehicle are decomposed into an attitude subsystem and a position subsystem by redefining the output.

[0015] Furthermore, a preferred implementation is provided, which combines the minimum learning parameter method with the radial basis neural network to approximate the nonlinear terms of the system.

[0016] Furthermore, a preferred embodiment is provided, which is based on a dynamic surface control method and avoids repeated differentiation of the virtual control law in the model through a first-order filter.

[0017] Furthermore, a preferred embodiment is provided, which also includes the step of performing stability analysis on the attitude controller and the position controller in the control system of the underactuated unmanned boat by constructing a Lyapunov function.

[0018] Furthermore, a preferred embodiment is provided, which also includes the step of combining a fuzzy control strategy in the posture controller and the position controller.

[0019] Based on the same inventive concept, the present invention also provides an underactuated unmanned boat formation control device based on output redefinition, the device comprising:

[0020] Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into modules of attitude subsystem and position subsystem;

[0021] The attitude controller and the position controller are designed respectively through the attitude subsystem and the position subsystem to approximate the module of the nonlinear term of the system;

[0022] A module for avoiding repeated differentiation of a virtual control law in said model by means of a first order filter;

[0023] A module that combines an adaptive control law based on the minimum learning parameter method and an auxiliary adaptive law.

[0024] Based on the same inventive concept, the present invention also provides a computer storage medium for storing a computer program. When the computer reads the computer program, the computer executes the method described.

[0025] Based on the same inventive concept, the present invention also provides a computer, including a processor and a storage medium. When the processor reads a computer program stored in the storage medium, the computer executes the method described.

[0026] Based on the same inventive concept, the present invention also provides a computer program product, which is a computer program. When the computer program is executed, the method described above is implemented.

[0027] Compared with the prior art, the technical solution provided by the present invention is beneficial in that:

[0028] By redefining the output, the original model of the underactuated unmanned boat is decomposed into the attitude subsystem and the position subsystem, which greatly simplifies the complexity of the overall control problem and enables the controller design to achieve independent control of attitude and position in a more targeted manner. Compared with the existing technology, this method effectively solves the problem of insufficient control input, makes the degree of freedom control of the underactuated system more precise, and significantly improves the stability and robustness of the formation control.

[0029] The design of the attitude controller and position controller, combined with the minimum learning parameter method and radial basis neural network, significantly improves the nonlinear approximation ability and robustness of the system. Compared with the traditional single control method, this combination can show stronger adaptability in dealing with model uncertainty and external interference. At the same time, by reducing the learning parameters, the computational complexity of the system is reduced and the real-time performance is improved.

[0030] The introduction of dynamic surface control technology avoids the "differential explosion" problem in the control law design process, and greatly reduces the amount of calculation by using a first-order filter to replace repeated differential operations. This makes the present invention more suitable for real-time applications than traditional backstepping control, especially in complex marine environments, and can achieve faster and more accurate control response.

[0031] Combined with the adaptive control law based on the minimum learning parameter method, the system can dynamically adjust the control parameters during the mission execution, enhancing the system's anti-interference ability. Compared with the existing fixed parameter control method, this adaptability enables the unmanned boat to better maintain the stability and consistency of the formation when facing changes and interference in the external environment, significantly improving the control effect.

[0032] Through stability analysis and the construction of Lyapunov function, it is proved that the designed control law can make the system error converge to a small area near zero, and all signals satisfy the global eventually uniform boundedness (SGUUB). Compared with traditional methods, this process provides a rigorous mathematical proof, ensures the stability and effectiveness of the controller design, and further enhances the reliability of the system.

[0033] The simulation experiment verified the effectiveness of the designed method, showing that the six unmanned boats successfully achieved the transition from the initial state to the expected formation shape, and all control signals were continuous and without jitter. Compared with other methods, the controller designed by the present invention can better maintain the smoothness of the control signal and reduce the jitter phenomenon of the system, thereby improving the control quality of the formation and the reliability of task execution.

[0034] It is suitable for application in the control of under-actuated unmanned boat formations. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1is a schematic diagram of the formation trajectory on the plane;

[0036] Figure 2 Schematic diagram of model error variables for six ships;

[0037] Figure 3 is the control input signal τ of Vehicle X and τ σ Schematic diagram;

[0038] Figure 4 Schematic diagram of the virtual control laws α1 and α2 of Vehicle. DETAILED DESCRIPTION

[0039] In order 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 is now further described in detail with reference to the accompanying drawings, specifically:

[0040] Implementation method 1: This implementation method provides a method for controlling an underactuated unmanned boat formation based on output redefinition, the method comprising:

[0041] Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into the steps of attitude subsystem and position subsystem;

[0042] The step of designing a posture controller and a position controller through the posture subsystem and the position subsystem respectively to approximate the nonlinear terms of the system;

[0043] Avoiding repeated differentiation steps of the virtual control law in the model by means of a first-order filter;

[0044] The steps of combining the adaptive control law based on the minimum learning parameter method and the auxiliary adaptive law.

[0045] Specifically, they include:

[0046] 1. Establish kinematic and dynamic models and redefine output

[0047] First, the kinematic and dynamic models of the underactuated unmanned vehicle (UUSV) are established, and the outputs are redefined. Through output redefinition, the original model is decomposed into attitude subsystem and position subsystem. This transformation can simplify the overall control problem into more manageable parts, laying the foundation for the subsequent controller design.

[0048] 2. Design attitude controller and position controller

[0049] After the model is redefined, the attitude controller and position controller are designed. The attitude controller is mainly used to control the attitude of each unmanned boat to achieve the target direction and angle; the position controller is used to control the position of the unmanned boat to achieve the expected formation shape.

[0050] Specifically, through the attitude subsystem, the error variables are defined and the virtual control law is constructed, and then the minimum learning parameter method (MLP) is combined with the radial basis function neural network (RBF) to approximate the nonlinear terms in the system. Then, the control law of the position subsystem is designed to further ensure the precise control of the position.

[0051] 3.Introduction of Dynamic Surface Control (DSC) technology

[0052] In the process of designing the controller, the dynamic surface control (DSC) technology is introduced to solve the "differential explosion" problem in control design. The dynamic surface control technology avoids repeated differentiation of the virtual control law by introducing a first-order filter, greatly reduces the calculation complexity, and enhances the real-time performance of the control system.

[0053] 4. Combining adaptive control law with disturbance suppression

[0054] In order to enhance the anti-interference ability of the system, the present invention combines an adaptive control law based on the minimum learning parameter method. Through the adaptive law, the system can continuously adjust the control parameters during the execution of the task to cope with external environmental changes and model uncertainty. At the same time, the design of the auxiliary adaptive law also further improves the stability of the system.

[0055] 5. Stability analysis

[0056] After the controller design is completed, the stability analysis of the entire formation system is performed. First, the Lyapunov function is constructed for the attitude controller, and it is proved that the designed control law can make the attitude error converge to a small area near zero, and all signals in the system satisfy the global eventually uniform boundedness (SGUUB). Then, a similar stability analysis is performed on the position controller to ensure that the position error also converges to the expected range.

[0057] 6. Simulation Verification

[0058] Finally, the effectiveness of the present invention is verified through simulation experiments. The simulation results show that by using the designed control law and adaptive law, the six unmanned boats successfully achieve the desired formation shape from the initial state, and realize the transformation from wedge formation to column formation and then to horizontal formation. All control signals are continuous and without chattering, which verifies the superiority and practicality of the proposed method.

[0059] Implementation method 2: This implementation method further limits the underactuated unmanned boat formation control method based on output redefinition provided in implementation method 1, by redefining the output of the kinematic and dynamic models of the underactuated unmanned boat, and decomposing them into an attitude subsystem and a position subsystem.

[0060] Implementation method three: This implementation method is a further limitation of the underactuated unmanned boat formation control method based on output redefinition provided in implementation method one, combining the minimum learning parameter method with the radial basis neural network to approximate the nonlinear terms of the system.

[0061] Implementation method 4: This implementation method further limits the underactuated unmanned boat formation control method based on output redefinition provided in implementation method 1. Based on the dynamic surface control method, a first-order filter is used to avoid repeated differentiation of the virtual control law in the model.

[0062] Implementation method five: This implementation method is a further limitation of the underactuated unmanned boat formation control method based on output redefinition provided in implementation method one, and also includes the step of performing stability analysis on the attitude controller and position controller in the control system of the underactuated unmanned boat by constructing a Lyapunov function.

[0063] Implementation method six: This implementation method further limits the underactuated unmanned boat formation control method based on output redefinition provided in implementation method one, and also includes the step of combining fuzzy control strategy in the attitude controller and the position controller.

[0064] Embodiment 7: This embodiment provides an underactuated unmanned boat formation control device based on output redefinition, the device comprising:

[0065] Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into modules of attitude subsystem and position subsystem;

[0066] The attitude controller and the position controller are designed respectively through the attitude subsystem and the position subsystem to approximate the module of the nonlinear term of the system;

[0067] A module for avoiding repeated differentiation of a virtual control law in said model by means of a first order filter;

[0068] A module that combines an adaptive control law based on the minimum learning parameter method and an auxiliary adaptive law.

[0069] Embodiment 8: This embodiment provides a computer storage medium for storing a computer program. When the computer reads the computer program, the computer executes the method provided in embodiment 1.

[0070] Embodiment 9: This embodiment provides a computer, including a processor and a storage medium. When the processor reads a computer program stored in the storage medium, the computer executes the method provided in embodiment 1.

[0071] Embodiment 10: This embodiment provides a computer program product, which is a computer program. When the computer program is executed, the method provided in embodiment 1 is implemented.

[0072] Implementation Method XI: Combination Figure 1-4 This embodiment is described in detail by using specific examples to further describe the technical solution provided above. Specifically:

[0073] include:

[0074] (1) The kinematic and dynamic models of the UUSV are redefined and decomposed into attitude subsystem and position subsystem;

[0075] (2) Design attitude controller and position controller;

[0076] (3) Stability analysis;

[0077] 1. In step 1, the kinematics and dynamics of the UUSV are transformed and redefined, decomposing them into the attitude subsystem and the position subsystem, as shown below:

[0078] Considering a cluster of N UUSVs, the kinematic and dynamic equations of UUSVi are described as

[0079]

[0080]

[0081] Where i = 1, 2, ..., N represents the number of UUSV, P i =[x i ,y i ] T is the position vector of UUSV in the geodetic coordinate system, (x i ,y i ) is the position coordinate; is the rotation matrix related to the yaw angle, θ i is the bow pitch angle; Q i =[u i ,v i ] T is the velocity vector in the ship coordinate system, u i and v i Represents forward and horizontal drift speeds, r i Indicates the UUSV's bow angular velocity. i (x i ,y i )=[f i (x i ),f i (y i )]T and f i (σ i ) is the unknown model unmodeled dynamics; as well as For external interference during the navigation of UUSV, as well as is the thrust output of UUSV.

[0082] Since the above model is an underactuated model, for the convenience of further research, the UUSV model can be converted into an attitude subsystem and a position subsystem as shown below:

[0083]

[0084] in and represents the state-dependent nonlinear term that includes the dynamics not modeled in the model as well as external disturbances.

[0085] 2. In step 2, design the attitude controller and position controller as follows:

[0086] The design of the distributed controller for the UUSVs formation is divided into two parts. First, the control law for controlling the attitude of each UUSV is designed through the attitude subsystem. Then, the position subsystem is used to design the control law that can control the position of each UUSV. The specific design process is as follows.

[0087] (1) For the attitude subsystem, define the error variable z i1 ,z i2 ,z i3 as follows

[0088]

[0089] where α i1 is the virtual control law, is the filtering control law, Each element in is α i1 Obtained through a first-order filter, the time constant of the filter is γ i is given by the corresponding diagonal elements and is a diagonally positive definite matrix.

[0090] First, construct the virtual control law as

[0091]

[0092] Where K i1 ,K i0 ∈R 3×3 They are all diagonal matrices with positive diagonal elements and the remaining elements are 0, and ε is a variable positive constant.

[0093] Next, design the attitude control law for each UUSV

[0094]

[0095] exist Middle K i2 is a diagonal matrix where the diagonal elements are positive constants and the other elements are 0.

[0096] Adaptive control law based on MLP and auxiliary adaptive law as follows

[0097]

[0098] in φ i >0, represents the estimate of φ, The initial value is is the estimation error. Γ>0 is the adaptive gain, is the feedback gain. Yes di =ε N +b d The estimate, is the estimation error, Γ b is the positive adaptation gain, is the positive feedback gain.

[0099] (2) For the position subsystem, define the error variable z i4 ,z i5 ,z i6 as follows

[0100]

[0101] where α i4 is the virtual control law, is the filtering control law, Each element in is α i4 Obtained through a first-order filter, the time constant of the filter is i is given by the corresponding diagonal elements and is a diagonally positive definite matrix.

[0102] The virtual control law is constructed as

[0103]

[0104] Among them, M i1 ,M i0 ∈R 3×3They are all diagonal matrices with positive diagonal elements and the remaining elements are 0, and δ is a variable positive constant.

[0105] Next, we design the position control law for each UUSV

[0106]

[0107] exist Medium i2 is a diagonal matrix where the diagonal elements are positive constants and the other elements are 0.

[0108] Adaptive control law based on MLP and auxiliary adaptive law as follows

[0109]

[0110] in Represents φ X The estimate, The initial value is is the estimation error. X >0 is adaptive gain, is the feedback gain. Yes The estimate, is the estimation error, is the positive adaptation gain, is the positive feedback gain.

[0111] 3. Perform stability analysis in step 3 as follows:

[0112] (1) For the attitude control law, first define the Lyapunov function V1:

[0113]

[0114] It can be concluded that:

[0115]

[0116] Next, define the Lyapunov function V2:

[0117]

[0118] It can be concluded that:

[0119]

[0120] Further define the Lyapunov function V3:

[0121]

[0122] Finally, we can get:

[0123]

[0124] in:

[0125]

[0126] Therefore, the designed control law and adaptive law can make the attitude error of each UUSV in the formation converge to a small area near zero, and all signals in the system satisfy the global eventually consistent boundedness.

[0127] (2) For the position control law, first define the Lyapunov function V4:

[0128]

[0129] It can be concluded that:

[0130]

[0131] Next, define the Lyapunov function V5:

[0132]

[0133] It can be concluded that:

[0134]

[0135] Further define the Lyapunov function V6:

[0136]

[0137] Finally, we can get:

[0138]

[0139] in:

[0140]

[0141] Therefore, the designed control law and adaptive law can make the position error of each UUSV in the formation converge to a small area near zero, and all signals in the system satisfy the global eventually consistent boundedness.

[0142] Compared with the prior art, the beneficial effects of this embodiment are: the dynamic and kinematic models of the under-actuated unmanned boat are converted into an attitude subsystem and a position subsystem through output redefinition, thereby overcoming the problem of insufficient control input of the under-actuated unmanned boat, and using the MLP-based RBF neural network for online approximation to effectively solve the parameter uncertainty and external interference problems of the under-actuated unmanned boat formation, while using the dynamic surface control method to solve the problem of complex differential explosion generated in the calculation process, significantly reducing the amount of calculation and further improving the robustness of the system.

[0143] The effectiveness of this implementation is verified through data simulation:

[0144] The model ship parameters used in this section are shown in Table 1. Consider a formation consisting of 6 UUSVs, numbered 1-6, and the initial state settings of the formation are shown in Table 2.

[0145] Table 1. Main model parameters of UUSV.

[0146]

[0147] Table 2. Initial status of the UUSV formation.

[0148] UUSV parameter Vehicle 1 <![CDATA[[-20m,30m,Orad,0.1m / s,0.1m / s,0.1rad / s] T ]]> Vehicle 2 <![CDATA[[-10m,20m,-π / 4rad,0.1m / s,0.1m / s,0.1rad / s] T ]]> Vehicle 3 <![CDATA[[-15m,5m,Orad,0.11m / s,0.1m / s,0.1rad / s] T ]]> Vehicle 4 <![CDATA[[-25m,10m,Orad,0.1m / s,0.1m / s,0.1rad / s] T ]]> Vehicle 5 <![CDATA[[-10m,5m,Orad,0.1m / s,0.1m / s,0.1rad / s] T ]]> Vehicle 6 <![CDATA[[-5m,5m,0rad,0.1m / s,0.1m / s,0.1rad / s] T ]]>

[0149] The control law and adaptive law designed above are used for simulation verification. Figure 1 The motion trajectories of the six vehicles on the plane are shown. It is obvious that the desired formation shape is finally obtained, and the transformation from the initial state to the wedge formation-column-horizontal formation is realized, which is in line with Theorems 1 and 2.

[0150] According to Theorem 1 and Theorem 2, using the designed controller, all signals in the closed-loop system should be SGUUB. Figure 2 Shows the error variable z of each vehicle control model i1 ,z i2 ,z i3 ,z i4 ,z i5 ,z i6 It can be clearly seen that the curve has less chattering and is smoother, and the error variables of the model are all SGUUB.

[0151] In addition, the control input signal τ of each vehicle X and τ σ like Figure 3 As shown, in this embodiment, τ σThe simulation curve is relatively smooth and free of chattering. All control signals of the position subsystem and attitude subsystem are continuous and consistent. The virtual control laws α1 and α2 of each vehicle are as follows: Figure 4 As shown, it can be observed that in this embodiment, all control signals of the attitude subsystem and the position subsystem are continuous and SGUUB.

[0152] The simulation results mentioned above are all consistent with Theorem 1 and Theorem 2.

[0153] The technical solution provided by the present invention is further described in detail above through several specific implementation modes in order to highlight the advantages and benefits of the technical solution provided by the present invention. However, the several specific implementation modes described above are not intended to be used as limitations on the present invention. Any reasonable modification and improvement of the present invention, combination of implementation modes and equivalent substitution within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for controlling an underactuated unmanned boat formation based on output redefinition, characterized in that: include: Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into the steps of attitude subsystem and position subsystem; The step of designing a posture controller and a position controller through the posture subsystem and the position subsystem respectively to approximate the nonlinear terms of the system; Avoiding repeated differentiation steps of the virtual control law in the model by means of a first-order filter; The steps of combining the adaptive control law based on the minimum learning parameter method and the auxiliary adaptive law.

2. The underactuated unmanned boat formation control method based on output redefinition according to claim 1 is characterized in that: The kinematic and dynamic models of the underactuated unmanned vehicle are decomposed into an attitude subsystem and a position subsystem by redefining the output.

3. The underactuated unmanned boat formation control method based on output redefinition according to claim 1 is characterized in that: The minimum learning parameter method is combined with radial basis neural network to approximate the nonlinear terms of the system.

4. The underactuated unmanned boat formation control method based on output redefinition according to claim 1, characterized in that: Based on the dynamic surface control method, a first-order filter is used to avoid repeated differentiation of the virtual control law in the model.

5. The underactuated unmanned boat formation control method based on output redefinition according to claim 1, characterized in that: It also includes the steps of conducting stability analysis on the attitude controller and position controller in the control system of the underactuated unmanned boat by constructing a Lyapunov function.

6. The underactuated unmanned boat formation control method based on output redefinition according to claim 1, characterized in that: Also included is the step of combining fuzzy control strategies in the attitude controller and the position controller.

7. An underactuated unmanned boat formation control device based on output redefinition, characterized in that: The device includes: Establish the kinematic and dynamic models of the underactuated unmanned vehicle and decompose them into modules of attitude subsystem and position subsystem; The attitude controller and the position controller are designed respectively through the attitude subsystem and the position subsystem to approximate the module of the nonlinear term of the system; A module for avoiding repeated differentiation of a virtual control law in said model by means of a first order filter; A module that combines an adaptive control law based on the minimum learning parameter method and an auxiliary adaptive law.

8. A computer storage medium for storing a computer program, characterized in that: When the computer reads the computer program, the computer executes the method of claim 1.

9. A computer, comprising a processor and a storage medium, characterized in that: When the processor reads the computer program stored in the storage medium, the computer executes the method of claim 1 .

10. A computer program product, being a computer program, characterized in that When the computer program is executed, the method of claim 1 is implemented.

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