Design method of a robust control system for an underwater robot and the underwater robot

Abstract

The present invention discloses a design method for a robust control system of an underwater robot and an underwater robot. The design method includes: S1, establishing a multi-degree-of-freedom nonlinear coupled motion model of the underwater robot with external disturbances; S2, quantifying the modeling uncertainty of the motion model; S3, establishing an extended state observer for external disturbances and modeling uncertainty; S4, establishing a robust controller for modeling uncertainty and coupling; S5, designing a control system for the underwater robot based on the extended state observer and the robust controller. It can effectively improve the robustness and anti-interference ability of the underwater robot's motion control, suppress the coupled motion, reduce the tracking error and response time, so as to obtain better control performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of underwater robot control, and particularly relates to a design method for a robust control system of an underwater robot and an underwater robot. Background Art

[0002] Underwater robots play an important role in ocean scientific research work. Underwater robots are indispensable in many scientific fields such as pipeline inspection, safety search and rescue, underwater archaeology, and ocean environment observation. However, not only does the underwater robot itself have problems of multiple degrees of freedom, modeling uncertainty, and coupling, but the underwater environment also brings non-linearity and external disturbance uncertainty.

[0003] Simultaneously dealing with the problems brought by the underwater robot itself and the external environment is the key to improving the accuracy and robustness of the motion control of the underwater robot. Existing technologies include methods such as proportional-integral-derivative control, active disturbance rejection control, sliding mode control based on an extended state observer, or model predictive control. These methods mainly address the problems of modeling uncertainty and external disturbance uncertainty. However, little consideration is given to the non-linearity, coupling, etc. of the multi-degree-of-freedom underwater robot. That is, these methods can only consider some of the problems in the motion control of the underwater robot. Therefore, the robustness of these control methods is lacking, resulting in poor motion control performance such as the control accuracy, response speed, and coupling motion suppression ability of the underwater robot.

[0004] In view of this, how to design a robust control system technology with high control accuracy, fast response speed, and good motion control performance is the technical problem to be solved by the present invention. Summary of the Invention

[0005] The present invention provides a design method for a robust control system of an underwater robot and an underwater robot, thereby improving the control accuracy, response speed, and motion control performance of the underwater robot.

[0006] To achieve the above technical objectives, the present invention is implemented by the following technical solutions:

[0007] In one aspect, the present invention provides a design method for a robust control system of an underwater robot, including the following steps:

[0008] S1, establishing a multi-degree-of-freedom non-linear coupling motion model of an underwater robot with external disturbances;

[0009] S2, quantifying the modeling uncertainty of the motion model;

[0010] S3, establishing an extended state observer for external disturbances and modeling uncertainty;

[0011] S4, establishing a robust controller for modeling uncertainty and coupling;

[0012] S5. Design the control system of the underwater robot based on the extended state observer and the robust controller.

[0013] For the design method of the robust control system of the underwater robot as described above, the steps for establishing the motion model of the underwater robot with multi-degree-of-freedom nonlinear coupling and external disturbances in step S1 are as follows: Establish the body coordinate system and the earth coordinate system of the underwater robot, and establish the motion model based on the body coordinate system and the earth coordinate system. The motion model is as follows:

[0014] ;

[0015] where, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the nonlinear damping matrix of the underwater robot; represents the thruster thrust and torque vector of the underwater robot; represents the external disturbance force and torque vector of the underwater robot.

[0016] For the design method of the robust control system of the underwater robot as described above, the formula for quantifying the modeling uncertainty of the motion model in step S2 is as follows:

[0017] ;

[0018] where, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot; represents the modeling uncertainty matrix of the assumed linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the input resultant force and resultant torque of the underwater robot motion model; represents the external disturbance force and torque vector; represents the output of the robust controller; represents the nonlinear compensation amount; represents the linear damping matrix of the underwater robot; represents the non - linear damping matrix of the underwater robot; represents the modeling uncertainty boundary of the yaw of the underwater robot motion model; represents the measured yaw linear damping coefficient of the underwater robot; represents the measured yaw non - linear damping coefficient of the underwater robot; represents the yaw linear damping coefficient of the underwater robot calculated by the hydrodynamic software; represents the yaw non - linear damping coefficient of the underwater robot calculated by the hydrodynamic software; represents the modeling uncertainty matrix of the assumed linear damping matrix the modeling uncertainty of yaw in; represents the identity matrix of order n, where n represents the degrees of freedom of the underwater robot.

[0019] For the design method of the underwater robot robust control system as described above, the steps of establishing an extended state observer for external disturbances and modeling uncertainties in step S3 are as follows:

[0020] S31, establish a system model for solving the extended state observer;

[0021] S32, establish a state - space equation for solving the extended state observer according to the system model;

[0022] S33, establish an extended state observer for external disturbances and modeling uncertainties according to the state - space equation.

[0023] For the design method of the underwater robot robust control system as described above, the formula for establishing a system model for solving the extended state observer in step S31 is as follows:

[0024] ;

[0025] where, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot; represents the modeling uncertainty matrix of the assumed linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the external disturbance force and moment vector; represents the output of the robust controller; represents the non - linear compensation quantity; Denote the gain of the extended state observer system; Denote the gain of the extended state observer system; Denote the input of the extended state observer; Denote the lumped disturbance of the external disturbance and the modeling uncertainty of the damping matrix; Denote the disturbance function related to the velocity and angular velocity of the underwater robot, external disturbance and uncertainty.

[0026] For the design method of the robust control system of the underwater robot as described above, the formula for establishing the state space equation for solving the extended state observer according to the system model in step S32 is as follows:

[0027] ;

[0028] Wherein, Denote the position and angle of the underwater robot in the extended state observer system; Denote the velocity and angular velocity of the underwater robot in the extended state observer system; Denote the disturbance related to the velocity and angular velocity of the underwater robot, external disturbance and uncertainty in the extended state observer system; Denote the gain of the extended state observer system; Denote the input of the extended state observer; Denote the intermediate variable; Denote the velocity and angular velocity of each degree of freedom of the underwater robot in the body coordinate system; Denote the disturbance function related to the velocity and angular velocity of the underwater robot, external disturbance and uncertainty.

[0029] For the design method of the robust control system of the underwater robot as described above, the formula for establishing the extended state observer for external disturbance and modeling uncertainty according to the state space equation in step S33 is as follows:

[0030] ;

[0031] Wherein, Denote the observation error of the position and angle of the underwater robot by the extended state observer; Denote the position and angle of the underwater robot observed by the extended state observer; Denote the position and angle of the underwater robot measured by the sensor; Denote the nonlinear filtering function; Denote the nonlinear factor; Denote the sign function; Denote the filtering constant; and Both represent the output after the observation errors of the position and angle of the underwater robot by the extended state observer are non-linearly filtered, and ; represents the element in the i-th row and the 1st column of the vector; represents the velocity and angular velocity of the underwater robot observed by the extended state observer; represents the observer gain; represents the total disturbance observed by the extended state observer; represents the gain of the extended state observer system; represents the observer gain; represents the observer gain.

[0032] For the design method of the robust control system of the underwater robot as described above, the linear matrix inequality for establishing a robust controller for modeling uncertainty and coupling in step S4 is as follows:

[0033] ;

[0034] where, represents the robust controller; represents the performance weight function; represents the identity matrix; represents the nominal state space model of the multi-degree-of-freedom underwater robot with descriptions of modeling uncertainty and coupling characteristics; represents the error weight function; represents the control weight function; represents the performance index.

[0035] For the design method of the robust control system of the underwater robot as described above, the control system of the underwater robot designed based on the extended state observer and the robust controller in step S5 is as follows:

[0036] ;

[0037] where, represents the inertia mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the non-linear damping matrix of the underwater robot; represents the input resultant force and resultant moment of the underwater robot motion model; represents the external disturbance force and moment vector; represents the output of the robust controller; represents the non - linear compensation amount; represents the total disturbance observed by the extended state observer; represents the assumed linear damping matrix of the underwater vehicle; represents the velocity and acceleration of the underwater vehicle observed by the extended state observer; represents the sought - after multi - input multi - output robust controller for modeling uncertainties and couplings of the state variables; represents the robust controller of the system matrix in state - space form; represents the robust controller of the control matrix in state - space form; represents the robust controller of the input; represents the robust controller of the output; represents the robust controller of the output matrix in state - space form; represents the robust controller of the feed - forward matrix in state - space form; represents the reference input; represents the position and angle of the underwater vehicle observed by the extended state observer.

[0038] In another aspect, the present invention provides an underwater vehicle, including an underwater vehicle body, and the underwater vehicle body applies the design method of the underwater vehicle robust control system as described above.

[0039] Compared with the prior art, the advantages and positive effects of the present invention are: by quantifying the uncertainties of the multi - degree - of - freedom non - linear coupled motion model of the underwater vehicle with external disturbances, it is beneficial to design an extended state observer and a robust controller for the problems of modeling uncertainties, couplings, external disturbances, and non - linearities of the multi - degree - of - freedom underwater vehicle; improving the control effect of the entire system and the robustness against external disturbances and modeling uncertainties, and being able to effectively improve the robustness and anti - interference ability of the underwater vehicle motion control, suppressing the coupled motion, reducing the tracking error and response time, so as to obtain better control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0041] Figure 1 It is a flowchart of an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0042] Figure 2(a) is a schematic diagram of the earth coordinate system of an underwater robot in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0043] Figure 2(b) is a schematic diagram of the body coordinate system of an underwater robot in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0044] Figure 3 It is a block diagram of the robust control system for an underwater robot based on an extended state observer in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0045] Figure 4 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0046] Figure 5 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves provided by the active disturbance rejection control of the comparative method in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0047] Figure 6 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves provided by the proportional-integral-derivative control of the comparative method in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0048] Figure 7 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves of the motion model perturbation in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0049] Figure 8 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves of the motion model perturbation provided by the active disturbance rejection control of the comparative method in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0050] Figure 9 It is a tracking diagram of the heave and coupled maximum degrees of freedom curves of the motion model perturbation provided by the proportional-integral-derivative control of the comparative method in an embodiment of the design method of the robust control system for an underwater robot of the present invention;

[0051] Figure 10 This is the tracking diagram of the heave and coupled maximum degree of freedom curves under ocean current disturbance in an embodiment of the design method of the robust control system for the underwater robot of the present invention;

[0052] Figure 11 This is the tracking diagram of the heave and coupled maximum degree of freedom curves under ocean current disturbance provided by the active disturbance rejection control of the comparative method in an embodiment of the design method of the robust control system for the underwater robot of the present invention;

[0053] Figure 12 This is the tracking diagram of the heave and coupled maximum degree of freedom curves under ocean current disturbance provided by the proportional-integral-derivative control of the comparative method in an embodiment of the design method of the robust control system for the underwater robot of the present invention. Detailed implementation manners

[0054] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0055] It should be noted that in the description of the present invention, the terms indicating directions or positional relationships such as "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings. This is only for convenience of description and does not indicate or imply that the device or element must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation of the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0056] In the present invention, unless otherwise clearly defined and limited, the terms such as "installation", "connection", "connection" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0057] In the present invention, unless otherwise clearly specified and defined, the first feature being "on" or "under" the second feature may include direct contact between the first and second features, or may include the situation where the first and second features are not in direct contact but are in contact through additional features therebetween. Moreover, the first feature being "above", "over" and "on top of" the second feature includes that the first feature is directly above and obliquely above the second feature, or merely means that the horizontal height of the first feature is higher than that of the second feature. The first feature being "under", "beneath" and "underneath" the second feature includes that the first feature is directly below and obliquely below the second feature, or merely means that the horizontal height of the first feature is lower than that of the second feature.

[0058] The following disclosure provides many different embodiments or examples for implementing different structures of the present invention. To simplify the disclosure of the present invention, components and settings of specific examples are described below. Of course, they are merely examples and are not intended to limit the present invention. In addition, the present invention may repeat reference numerals and / or reference letters in different examples. Such repetition is for the purpose of simplification and clarity, and does not itself indicate the relationship between various embodiments and / or settings discussed. In addition, the present invention provides examples of various specific processes and materials, but those of ordinary skill in the art can be aware of the application of other processes and / or the use of other materials.

[0059] As Figures 1 to 12 shown, the present application provides a design method for a robust control system of an underwater robot, specifically including the following steps:

[0060] S1, establish a motion model of a multi-degree-of-freedom non-linear coupling of an underwater robot with external disturbances. Specifically:

[0061] First, establish a body coordinate system and a geodetic coordinate system of the underwater robot, and establish the conversion relationship between the geodetic coordinate system and the body coordinate system. In the present application, a six-degree-of-freedom underwater robot is taken as an example for description. The body coordinate system is: , and the geodetic coordinate system is: , and the conversion relationship between the geodetic coordinate system and the body coordinate system is as follows:

[0062] ;

[0063] wherein, represents the coordinates and attitude vectors of six degrees of freedom of the underwater robot in the geodetic coordinate system. The six degrees of freedom are surge, sway, heave, roll, pitch and yaw in sequence; represents the velocity or angular velocity vectors of six degrees of freedom of the underwater robot in the body coordinate system. The six degrees of freedom are surge, sway, heave, roll, pitch and yaw in sequence; Represents the velocity or angular velocity vector of the six degrees of freedom of the underwater robot in the geodetic coordinate system, that is The derivative of; Represents the velocity transformation; Represents a third-order zero matrix; Represents the angular velocity transformation.

[0064] Then, based on the body coordinate system and the geodetic coordinate system of the underwater robot, a six-degree-of-freedom nonlinear coupled motion model of the underwater robot with external disturbances is established. The motion model is as follows:

[0065] ;

[0066] Among them, Represents the inertial mass matrix of the underwater robot; Represents the added mass matrix of the underwater robot; Represents the acceleration or angular velocity of each degree of freedom of the underwater robot in the body coordinate system, that is The derivative of; Represents the damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; Represents the restoring force and moment vector of the underwater robot; Represents the Coriolis force and moment matrix of the underwater robot; Represents the added mass matrix of the Coriolis force and moment of the underwater robot; Represents the external disturbance force and moment vector of the underwater robot; Represents the thruster thrust and moment vector of the underwater robot.

[0067] Since most underwater robots have a slow speed, it is possible to generally omit and And the distance between the center of mass and the center of buoyancy is also relatively close, so that Can also be omitted. Therefore, a simplified six-degree-of-freedom nonlinear coupled motion model of the underwater robot with external disturbances is established as follows:

[0068] ;

[0069] Among them, Represents the inertial mass matrix of the underwater robot; Represents the added mass matrix of the underwater robot; Represents the acceleration or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; Represents the linear damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the non - linear damping matrix of the underwater robot; represents the thruster thrust and torque vector of the underwater robot; represents the external disturbance force and torque vector of the underwater robot. , , and There are non - zero coupling elements in the non - diagonal of

[0070] In the motion model, , , and The parameters of , , and are obtained by computational fluid dynamics software (such as ANSYS software, etc.) and 3D design software (such as Solidworks software, etc.). The process of calculating by computational fluid dynamics and 3D design software

[0071] ;

[0072] S2 quantifies the modeling uncertainty of the motion model, and the specific steps are as follows:

[0073] S21, processes the non - linearity and modeling uncertainty in the motion model through non - linear compensation, and its formula is as follows:

[0074] ;

[0075] Among them, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot, The specific parameters are selected according to , and the set reference speed and angular velocity. In this application, the working speed of the underwater robot provided is set to 1 m / s, and the angular velocity is set to 1 rad / s. Therefore ; represents the modeling uncertainty matrix of the assumed linear damping matrix of the underwater robot; represents the speed or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the input resultant force and resultant torque of the underwater robot motion model; Denote the external disturbance force and moment vector of the underwater robot; Denote the output of the robust controller; Denote the nonlinear compensation amount; Denote the linear damping matrix of the underwater robot; Denote the nonlinear damping matrix of the underwater robot.

[0076] S22. Establish the yaw damping fitting relationship of the underwater robot through physical experiments. The yaw damping fitting relationship of the underwater robot is as follows:

[0077] ;

[0078] Among them, Denote the measured yaw damping of the underwater robot; Denote the measured yaw constant term damping coefficient of the underwater robot, which is generally small and can be ignored; Denote the measured yaw linear damping coefficient of the underwater robot; Denote the measured yaw nonlinear damping coefficient of the underwater robot; Denote the yaw angular velocity. Through actual measurement, the = 5.351, = 12.797.

[0079] The yaw linear damping coefficient of the underwater robot is calculated by computational fluid dynamics software (specifically refers to in the six-degree-of-freedom underwater robot) and the nonlinear damping coefficient ((specifically refers to in the six-degree-of-freedom underwater robot) have the largest difference from the actual situation among the six degrees of freedom. Therefore, by comparing the measured yaw linear damping coefficient and the nonlinear damping coefficient with the data obtained by computational fluid dynamics software, the modeling uncertainty boundary of the underwater robot can be obtained.

[0080] S23. Quantify the modeling uncertainty of the motion model according to the yaw damping fitting relationship. The formula is as follows:

[0081] ;

[0082] Among them, Denote the modeling uncertainty boundary of the yaw of the underwater robot motion model; Denote the measured yaw linear damping coefficient of the underwater robot; Denote the measured yaw nonlinear damping coefficient of the underwater robot; represents the yaw linear damping coefficient of the underwater robot calculated by hydrodynamic software; represents the yaw nonlinear damping coefficient of the underwater robot calculated by hydrodynamic software; represents the modeling uncertainty matrix assuming the linear damping matrix the modeling uncertainty of yaw in; represents the identity matrix of order n, where n represents the degrees of freedom of the underwater robot.

[0083] For a six-degree-of-freedom underwater robot, the above formula can be specifically as follows:

[0084] ;

[0085] where, represents the yaw linear damping coefficient of the underwater robot calculated by hydrodynamic software, that is the sixth row and sixth column of the matrix; represents the yaw nonlinear damping coefficient of the underwater robot calculated by hydrodynamic software, that is the sixth row and sixth column of the matrix; represents the sixth row and sixth column of the matrix, that is, the modeling uncertainty of yaw; represents the identity matrix of order six.

[0086] S3. Establish an extended state observer for external disturbances and modeling uncertainties. The specific steps are as follows:

[0087] S31. Establish a system model for solving the extended state observer, which is as follows:

[0088] ;

[0089] where, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot; represents the modeling uncertainty matrix of the assumed linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the external disturbance force and moment vector of the underwater robot; represents the output of the robust controller; represents the nonlinear compensation amount; represents the gain of the extended state observer system; Denote the gain of the extended state observer system; Denote the input of the extended state observer; Denote the lumped disturbance of the external disturbance and the modeling uncertainty of the damping matrix; Denote the disturbance function related to the velocity and angular velocity of the underwater vehicle, external disturbance and uncertainty.

[0090] S32. Establish the state space equation for solving the extended state observer. The state space equation of the extended state observer is as follows:

[0091] ;

[0092] Among them, Denote the position and angle of the underwater vehicle in the extended state observer system; Denote The first derivative of; Denote the velocity and angular velocity of the underwater vehicle in the extended state observer system; Denote The first derivative of; Denote the disturbance related to the velocity and angular velocity of the underwater vehicle, external disturbance and uncertainty in the extended state observer system; Denote The first derivative of; Denote the gain of the extended state observer system; Denote the input of the extended state observer; Denote the intermediate variable; Denote the velocity or angular velocity of each degree of freedom of the underwater vehicle in the body coordinate system; Denote the disturbance function related to the velocity and angular velocity of the underwater vehicle, external disturbance and uncertainty.

[0093] S33. Establish a six-degree-of-freedom extended state observer for external disturbance and modeling uncertainty. The six-degree-of-freedom extended state observer is as follows:

[0094] ;

[0095] Among them, Denote the observation error of the position and angle of the underwater vehicle by the extended state observer; Denote the position and angle of the underwater vehicle observed by the extended state observer; Denote the position and angle of the underwater vehicle measured by the sensor; Denote the nonlinear filtering function; Denote the nonlinear factor; Denote the sign function; Denote the filtering constant; It represents the output after the observation error of the position and angle of the underwater robot by the extended state observer passes through a non-linear filtering function with a non-linear factor of 0.5 and a filtering constant of 0.01; It represents the output after the observation error of the position and angle of the underwater robot by the extended state observer passes through a non-linear filtering function with a non-linear factor of 0.25 and a filtering constant of 0.01, and , It represents the degrees of freedom of the underwater robot; It represents the element in the first column of the i-th row of the vector; It represents the velocity and angular velocity of the underwater robot observed by the extended state observer; It represents the observer gain; It represents the total disturbance observed by the extended state observer, which is used for disturbance compensation; It represents the gain of the extended state observer system; It represents the observer gain; It represents the observer gain.

[0096] For the six-degree-of-freedom underwater robot, the above formula can be specifically as follows:

[0097] .

[0098] S4. Establish a robust controller for modeling uncertainty and coupling. The specific process is as follows:

[0099] S41. Describe the modeling uncertainty and coupling characteristics in the motion model of the underwater robot, and establish and :

[0100] ;

[0101] Among them, It represents the inertia matrix, and ; It represents the nominal inertia matrix; It represents the sixth-order identity matrix; It represents the perturbation range of; , It represents a random number with a value between -1 and 1; It represents the assumed linear damping matrix; It represents the nominal assumed linear damping matrix; It represents the perturbation range of; It represents the inertia matrix the uncertain boundary coefficient of, and =0.3; It represents uncertainty boundary coefficient, and = 0.4; represents the yaw modeling uncertainty boundary of the underwater robot motion model. Since the calculation of the inertia mass matrix and the added mass matrix is more accurate than that of the linear and nonlinear damping matrices, the uncertainty of the latter is greater. Therefore, without loss of generality, let have 30% uncertainty and have 40% uncertainty, so as to describe the modeling uncertainty and coupling characteristics in the underwater robot motion model.

[0102] S42. Establish the multi-degree-of-freedom nominal state model P of the underwater robot with descriptions of modeling uncertainty and coupling characteristics, as follows:

[0103] ;

[0104] Among them, represents the multi-degree-of-freedom nominal state model of the underwater robot; represents an n-order zero matrix. For a six-degree-of-freedom underwater robot, it can be expressed as ; represents an n-order identity matrix. For a six-degree-of-freedom underwater robot, it can be expressed as ; represents the nominal assumed linear damping matrix; represents the nominal inertia matrix; represents the perturbation range of M; represents the perturbation range of.

[0105] S43. Establish the linear matrix inequality for the robust controller against modeling uncertainty and coupling, as follows:

[0106] ;

[0107] Among them, represents the robust controller; represents the performance weight function; represents the identity matrix; represents the multi-degree-of-freedom nominal state space model of the underwater robot with descriptions of modeling uncertainty and coupling characteristics; represents the error weight function; represents the control weight function; represents the performance index. After multiple MATLAB simulation tests, the three sixth-order weight functions used in this application, that is, the three weight functions for six degrees of freedom are respectively: , , ;

[0108] Among them, represents the performance weight function for six degrees of freedom, represents the error weight function for six degrees of freedom, and represents the control weight function for six degrees of freedom; represents a complex variable in the complex number field, that is, the three weight functions are transfer functions in the complex number field.

[0109] S5. Design the control system of the underwater robot based on the extended state observer and the robust controller. Its structural block diagram is as Figure 3 shown. The control system is as follows:

[0110] ;

[0111] Among them, represents the inertial mass matrix of the underwater robot; represents the added mass matrix of the underwater robot; represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the linear damping matrix of the underwater robot; represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the nonlinear damping matrix of the underwater robot; represents the input resultant force and resultant moment of the underwater robot motion model; represents the external disturbance force and moment vector; represents the output of the robust controller; represents the nonlinear compensation amount; represents the total disturbance observed by the extended state observer; represents the assumed linear damping matrix of the underwater robot; represents the extended state observer observing the velocity and acceleration of the underwater robot; represents the sought multi-input multi-output robust controller for modeling uncertainty and coupling after the derivative of the state variables of the; represents the sought multi-input multi-output robust controller for modeling uncertainty and coupling of the state variables; represents the robust controller of the system matrix in state space form; represents the robust controller of the control matrix in state space form; represents the input of the robust controller ; represents the output of the robust controller ; represents the robust controller The output matrix in state space form; represents the robust controller The feedforward matrix in state space form; represents the reference input; Represents the position and angle of the underwater robot observed by the extended state observer.

[0112] Nonlinear compensation The unmeasured underwater robot speed and angular velocity observed by the extended state observer are calculated in real time, reducing the use of sensors.

[0113] In order to verify the robustness of this application to external interference of the underwater robot, the sea current interference is set as the external interference. As shown below:

[0114] ;

[0115] in, It indicates the current disturbance added when the underwater robot moves vertically; It represents the current disturbance added when the underwater robot is swinging; Indicates the current disturbance added when the underwater robot is swinging; It represents the current disturbance added when the underwater robot rolls; Indicates the current disturbance added when the underwater robot pitches; It indicates the current disturbance added when the underwater robot is in bow-rolling motion.

[0116] Then the extended state observer and multi-input multi-output robust controller are tuned:

[0117] The maximum performance index of K is 0.986154, which is less than 1, indicating that K has good robust stability; the observer gain of the extended state observer is obtained through multiple simulations (using simulation software such as MATLAB), which are:

[0118] .

[0119] In order to verify the effectiveness and advancement of the robust control system proposed in this application, a tracking control comparison simulation experiment was carried out using the anti-disturbance control and proportional integral differential control methods. In the six-degree-of-freedom motion control simulation experiment, the heave swing is highly coupled with the remaining five degrees of freedom. Therefore, for the convenience of demonstration, the heave swing tracking trajectory and the coupled maximum degree-of-freedom trajectory are selected in the six-degree-of-freedom simulation experiment. The simulation results are shown in Figure 2. Figures 4 to 12 As shown, Figures 7 to 9The modeling uncertainty is considered, so the inertia matrix of the non-linear coupling model of the underwater robot is enlarged by 30% during simulation, Figures 10 to 12 and external ocean current disturbances are added .

[0120] From each simulation diagram, it can be seen that under the premise that the motion control performance of this application has the advantages of being faster, more accurate and more stable, the corresponding peaks and adjustment times of the coupling degrees of freedom of the trajectory tracking degrees of freedom are also greatly reduced. Figures 4 to 6 It shows that the response scores and adjustment times of the coupling degrees of freedom of the heave degree of freedom are reduced by 4 / 5 and 1 / 3 respectively, and it has good robustness to model uncertainty (as Figures 7 to 9 shown) and anti-interference ability (as Figures 10 to 12 shown).

[0121] Through the above experimental examples, the control effect of this application can be fully demonstrated. Compared with the active disturbance rejection control and the proportional-integral-derivative control, it shows faster, smoother and more accurate control advantages in tracking performance; it shows better and faster control advantages in the suppression and adjustment of coupled motion, and has better robustness to external disturbances and model perturbations; in addition, the unmeasured velocity and angular velocity are also obtained, reducing the use of sensors.

[0122] In another aspect, this application also provides an underwater robot, including an underwater robot body, and the underwater robot body applies the design method of the underwater robot robust control system as described above.

[0123] In the description of this specification, the description with reference to terms such as "one embodiment", "some embodiments", "illustrative embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic descriptions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.

[0124] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, for those of ordinary skill in the art, it is still possible to modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions required to be protected by the present invention.

[0125] Whenever possible, the various aspects and features described and illustrated in the specification may be applied separately, and these separate aspects may be the subject of divisional applications.

Claims

1. A design method for a robust control system of an underwater robot, characterized in that: The following steps are involved: S1, establish a multi-degree-of-freedom nonlinear coupling motion model of underwater robots with external disturbances; S2, quantifying the modeling uncertainty of the motion model; S3, establish an extended state observer for external disturbances and modeling uncertainties; the steps for establishing an extended state observer for external disturbances and modeling uncertainties are as follows: S31, establish a system model for solving the extended state observer; the formula for establishing the system model for solving the extended state observer is as follows: ； in, represents the inertial mass matrix of the underwater robot; represents the additional mass matrix of the underwater robot; Represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot; a modeling uncertainty matrix representing the assumed linear damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the external disturbance force and torque vector; represents the output of the robust controller; Indicates the amount of nonlinear compensation; represents the gain of the extended state observer system; represents the gain of the extended state observer system; represents the input of the extended state observer; Lumped perturbations representing the modeling uncertainty of the external disturbance and the damping matrix; represents the disturbance function related to the underwater robot's velocity and angular velocity, external disturbance and uncertainty; S32, establishing a state space equation for solving the extended state observer according to the system model; the formula for establishing a state space equation for solving the extended state observer according to the system model is as follows: ； in, represents the position and angle of the underwater robot in the extended state observer system; represents the velocity and angular velocity of the underwater robot in the extended state observer system; Represents the disturbances of the underwater robot's velocity and angular velocity, external disturbances and uncertainties in the extended state observer system; represents the gain of the extended state observer system; represents the input of the extended state observer; represents an intermediate variable; Represents the velocity and angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the disturbance function related to the underwater robot's velocity and angular velocity, external disturbance and uncertainty; S33, establishing an extended state observer for external interference and modeling uncertainty according to the state space equation; the formula for establishing an extended state observer for external interference and modeling uncertainty according to the state space equation is as follows: ； in, represents the observation error of the extended state observer on the position and angle of the underwater robot; represents the position and angle of the underwater robot observed by the extended state observer; Represents the position and angle of the underwater robot measured by the sensor; represents a nonlinear filter function; represents the nonlinear factor; represents a symbolic function; represents the filtering constant; and Both represent the output of the extended state observer after nonlinear filtering of the observation error of the underwater robot position and angle, and ; express The i-th row and 1st column of the vector; It indicates that the extended state observer observes the speed and angular velocity of the underwater robot; represents the observer gain; represents the total disturbance observed by the extended state observer; represents the gain of the extended state observer system; represents the observer gain; represents the observer gain; S4, building robust controllers for modeling uncertainties and coupling; S5, designing a control system of an underwater robot based on the extended state observer and the robust controller; the control system of the underwater robot designed based on the extended state observer and the robust controller is as follows: ； in, represents the inertial mass matrix of the underwater robot; represents the additional mass matrix of the underwater robot; Represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the linear damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the nonlinear damping matrix of the underwater robot; Represents the input resultant force and torque of the underwater robot motion model; represents the external disturbance force and torque vector; represents the output of the robust controller; Indicates the amount of nonlinear compensation; represents the total disturbance observed by the extended state observer; represents the assumed linear damping matrix of the underwater robot; It indicates that the extended state observer observes the speed and acceleration of the underwater robot; Denotes the desired MIMO robust controller for modeling uncertainty and coupling state variables; represents the robust controller The system matrix in state space form; represents the robust controller The control matrix in state space form; represents the robust controller Input; represents the robust controller Output: represents the robust controller The output matrix in state space form; represents the robust controller The feedforward matrix in state space form; represents the reference input; Represents the position and angle of the underwater robot observed by the extended state observer.

2. The design method of the underwater robot robust control system according to claim 1 is characterized in that: The step of establishing the multi-degree-of-freedom nonlinear coupling motion model of the underwater robot with external interference in step S1 is: establishing the body coordinate system and the earth coordinate system of the underwater robot, and establishing the motion model according to the body coordinate system and the earth coordinate system. The motion model is as follows: ； in, represents the inertial mass matrix of the underwater robot; represents the additional mass matrix of the underwater robot; Represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the linear damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; represents the nonlinear damping matrix of the underwater robot; represents the thrust and torque vector of the underwater robot's propeller; Represents the external disturbance force and torque vector of the underwater robot.

3. The design method of the underwater robot robust control system according to claim 2 is characterized in that: The formula for quantifying the modeling uncertainty of the motion model in step S2 is as follows: ； in, represents the inertial mass matrix of the underwater robot; represents the additional mass matrix of the underwater robot; Represents the acceleration or angular acceleration of each degree of freedom of the underwater robot in the body coordinate system; represents the assumed linear damping matrix of the underwater robot; a modeling uncertainty matrix representing the assumed linear damping matrix of the underwater robot; Represents the velocity or angular velocity of each degree of freedom of the underwater robot in the body coordinate system; Represents the input resultant force and torque of the underwater robot motion model; represents the external disturbance force and torque vector; represents the output of the robust controller; Indicates the amount of nonlinear compensation; represents the linear damping matrix of the underwater robot; represents the nonlinear damping matrix of the underwater robot; Represent the modeling uncertainty bounds of the bow roll of the underwater robot motion model; represents the measured linear damping coefficient of the bow roll of the underwater robot; represents the measured nonlinear damping coefficient of the bow roll of the underwater robot; represents the linear damping coefficient of the bow roll of the underwater robot calculated by fluid dynamics software; represents the nonlinear damping coefficient of the bow roll of the underwater robot calculated by fluid dynamics software; Represents the modeling uncertainty matrix assuming a linear damping matrix Modeling uncertainty of mid-sail pitch; represents the n-order identity matrix, and n represents the degree of freedom of the underwater robot.

4. The design method of the underwater robot robust control system according to claim 1 is characterized in that: The linear matrix inequality for establishing a robust controller for modeling uncertainty and coupling in step S4 is as follows: ； in, represents the robust controller; represents the performance weight function; represents the identity matrix; Represents a multi-DOF nominal state space model of an underwater robot with modeling uncertainty and coupling characteristics description; represents the error weight function; represents the control weight function; Indicates performance indicators.

5. An underwater robot, characterized in that: It comprises an underwater robot body, and the underwater robot body applies the design method of the underwater robot robust control system according to any one of claims 1 to 4.

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