Modeling and quantitative self-triggering control method and system of under-actuated underwater robot dragging system

Abstract

The invention relates to the field of automatic control of underwater robots, and discloses a modeling and quantitative self-triggering control method and system for an under-actuated underwater robot dragging system, and the method comprises the steps: building a load position subsystem model, a cable direction subsystem model and an underwater robot attitude subsystem model based on Newtonian mechanics; the control task of each subsystem is decomposed into a kinematics model and a dynamics model based on a backstepping method so as to describe the kinematics and dynamics characteristics of each subsystem when the underwater robot executes the dragging task; setting a load subsystem controller by adopting a quantitative self-triggering control method so as to enable the position response of a load subsystem to be constrained in a preset boundary function; a cable direction subsystem controller and an underwater robot attitude subsystem controller are arranged by adopting a backstepping self-triggering control method, and a control signal is updated and transmitted to an execution mechanism only when and only when a preset condition is met through self-triggering. According to the method, the blank of modeling of the underwater robot dragging system is filled.

Description

Technical Field

[0001] This invention relates to the field of automatic control of underwater robots, and in particular to a modeling method for an underactuated underwater robot towing system, as well as a quantitative self-triggering control method and system. Background Technology

[0002] Underactuated underwater robot towing systems are miniaturized, intelligent transport platforms capable of carrying various measuring instruments to perform seabed tasks such as wreckage recovery, resource exploration and transportation, and reconnaissance. Currently, underwater salvage and transportation methods mainly include salvage engineering vessel operations and saturation diving. Salvage engineering vessels, characterized by high power and wide operating range, are the core means of salvage operations. However, their large size and high energy consumption lead to high salvage costs. Furthermore, the high pressure and low transparency of the deep sea limit the use of saturation diving operations in the deep sea; in addition, saturation diving operations also have significant limitations on the weight and volume of the objects being salvaged / transported. Therefore, there is an urgent need to develop automated underwater robot towing systems; however, there is still a lack of kinematic and dynamic modeling results for underwater robot towing systems. Underwater robot towing systems are high-order nonlinear multi-input multi-output underactuated systems with strong coupling between state variables, making it impossible to directly use the classical backstepping method design framework for controller design. In addition, underwater robot towing systems are subject to system uncertainties and unknown environmental interference, which poses a great challenge to achieving automatic control of underwater robot towing systems.

[0003] Currently, the academic community has developed various control methods for underwater robots. Among them, the PID controller based on backstepping is simple, mature, and low-cost, and has been widely studied. However, the transient and steady-state responses of this control method depend on the upper bound of the predicted external disturbances, resulting in significant design conservatism and making it impossible to achieve prior quantitative design to meet the trajectory tracking requirements of fast convergence and small overshoot. Meanwhile, to reduce the consumption of onboard energy and communication resources while ensuring the trajectory tracking capability of underwater robots, event-triggered control strategies have been extensively studied. Currently, there are many general event-triggered control strategies, each with its own advantages and disadvantages, including fixed threshold event triggering, relative threshold event triggering, and hybrid threshold event triggering. However, these event-triggered control strategies still require high-bandwidth sensors to detect in real time whether the control signal meets the preset triggering conditions, which will increase additional research and development costs. Summary of the Invention

[0004] To address the aforementioned problems, the purpose of this invention is to provide a modeling method for an underactuated underwater robot towing system, as well as a quantitative self-triggering control method and system, filling the gap in underwater robot towing system modeling and solving the trajectory tracking problem of high-order multi-input multi-output systems.

[0005] To achieve the above objectives, in a first aspect, the technical solution adopted by the present invention is as follows: a modeling and quantitative self-triggering control method for an underactuated underwater robot towing system, comprising: establishing load position subsystem, cable direction subsystem, and underwater robot attitude subsystem models based on Newtonian mechanics, and decomposing the control task of each subsystem into a kinematic model and a dynamic model based on backstepping to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs the towing task; setting the load subsystem controller using a quantitative self-triggering control method to ensure that the position response of the load subsystem is constrained within a pre-set boundary function; setting the cable direction subsystem controller and the underwater robot attitude subsystem controller using a backstepping self-triggering control method, so that the control signal is updated and transmitted to the actuator only when the preset conditions are met through self-triggering.

[0006] Furthermore, the kinematic and dynamic models of the load position subsystem are as follows:

[0007]

[0008] in, These are the position and velocity vectors of the load, respectively. The inertial matrix of the underwater robot is represented by m. L For the mass of the load; Represents the identity matrix; This represents the angular velocity vector of the load in the inertial frame. The unit direction vector of the cable; The mapping from a 3D vector to a 3D matrix satisfies S(x)y = x × y, where g represents the acceleration due to gravity; e3 = [0, 0, 1] T P q (F) represents the projection of vector F onto the direction of vector q, F = M -1 Rf, where Let be a rotation matrix. This indicates the control input provided by the underwater robot's propeller. This represents the term that cancels out the weight and buoyancy of the underwater robot. This refers to the lumped disturbance experienced by the load subsystem.

[0009] Furthermore, the kinematic and dynamic models of the cable direction subsystem are as follows:

[0010]

[0011] in, This represents lumped interference in the cable direction subsystem.

[0012] Furthermore, the kinematic and dynamic models of the underwater robot's attitude subsystem are as follows:

[0013]

[0014] in, These represent the Euler angles of the underwater robot and its angular velocity in the coordinate system of the underwater robot's towing system, respectively. Represents the transformation matrix; This is the moment of inertia matrix; Indicates control input; This represents the lumped disturbance in the underwater robot's attitude subsystem.

[0015] Furthermore, the underwater robot towing system is modeled as a high-order nonlinear multi-input multi-output underactuated system. The system states of the underwater robot towing system include the three-dimensional load position, three-dimensional load velocity, three-dimensional cable direction, three-dimensional load angular velocity, three-dimensional underwater robot Euler angles, and three-dimensional underwater robot angular velocity. The control inputs are...

[0016] Furthermore, the pre-defined boundary function is:

[0017]

[0018] In the formula, Let z be the upper boundary function, and b be the lower boundary function; pi (0) is the initial value of the tracking error; λ These are the scaling factors for the upper and lower boundary functions, respectively, where ρ is the smooth piecewise function, and ρ0, ρ ∞ r and T are design parameters of the boundary function.

[0019] Furthermore, the cable direction subsystem controller is configured using a backstepping self-triggering control method as follows:

[0020]

[0021] The underwater robot attitude subsystem controller is configured using a backstepping self-triggering control method as follows:

[0022]

[0023] In the formula, F d For control inputs within a continuous-time design framework; P q (F d ) is a vector F d Projection along the direction of vector q; Π q (F d ) is F d The projection onto a plane orthogonal to vector q; τ is a non-negative design parameter; τ is the control input; τ d It is a continuous-time control signal; These are non-negative design parameters.

[0024] Secondly, the technical solution adopted by this invention is as follows: a modeling and quantitative self-triggering control system for an underactuated underwater robot towing system, comprising: a subsystem establishment module, which establishes models of a load position subsystem, a cable direction subsystem, and an underwater robot attitude subsystem based on Newtonian mechanics, and decomposes the control task of each subsystem into a kinematic model and a dynamic model based on backstepping to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs the towing task; a load subsystem control module, which sets the load subsystem controller using a quantitative self-triggering control method to ensure that the position response of the load subsystem is constrained within a pre-set boundary function; and a cable direction and attitude control module, which sets the cable direction subsystem controller and the underwater robot attitude subsystem controller using a backstepping self-triggering control method, and through self-triggering, ensures that the control signal is updated and transmitted to the actuator only when the preset conditions are met.

[0025] Thirdly, the technical solution adopted by the present invention is as follows: the one or more programs include instructions, which, when executed by a computing device, cause the computing device to perform any of the methods described above.

[0026] Fourthly, the technical solution adopted by the present invention is: a computing device comprising: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing any of the methods described above.

[0027] The present invention has the following advantages due to the adoption of the above technical solutions:

[0028] 1. The modeling method for underwater robot towing systems provided by this invention models the underwater robot towing system as a high-order nonlinear multi-input multi-output underactuated system, divided into three parts: load position subsystem, cable orientation subsystem, and underwater robot attitude subsystem. This modeling method accurately characterizes the kinematic and dynamic characteristics of each part of the underwater robot when performing towing tasks, filling the gap in the modeling of underwater robot towing systems.

[0029] 2. To address the problem that the load position of an underwater robot towing system cannot be quantitatively adjusted a priori, this invention adopts a quantitative control design paradigm for nonlinear systems, which enables the position response of the load subsystem to be constrained within a pre-designed boundary function. This improves the trajectory tracking performance of the underwater robot towing system under given index constraints, thereby enhancing the efficiency and safety of underwater robot towing tasks.

[0030] 3. To address the energy and communication resource waste caused by traditional controller design methods within a continuous-time frame, this invention employs a self-triggering mechanism. This ensures that the control signal is updated and transmitted to the actuator only when preset conditions are met. This effectively reduces energy consumption and communication resource usage in the underwater robot towing system while maintaining system performance. Furthermore, the event-triggered controller design eliminates the need for high-bandwidth sensors to monitor the controller output in real time, reducing hardware design costs.

[0031] 4. This invention simultaneously solves the quantitative control problem and the self-triggering control problem of underwater robot towing systems, and also provides a solution for solving the same control problem for a class of high-order nonlinear multi-input multi-output underactuated systems. Attached Figure Description

[0032] Figure 1 This is a flowchart of the modeling method and quantitative self-triggering control method for the underactuated underwater robot towing system in this embodiment of the invention;

[0033] Figure 2 This is a diagram showing the position vector and force analysis of the underwater robot towing system in this embodiment of the invention.

[0034] Figure 3 This is a structural diagram of a quantitative self-triggering controller designed for the load position subsystem and cable direction subsystem in this embodiment of the invention;

[0035] Figure 4 This is a structural diagram of a self-triggering controller designed for the attitude subsystem of an underwater robot in an embodiment of the present invention;

[0036] Figure 5 This is a schematic diagram of the basic structure of an underactuated underwater robot towing system;

[0037] Explanation of reference numerals in the attached figures:

[0038] 1. Underwater robot (AUV), 2. Cable, 3. Payload;

[0039] {I}-x,y,z represents the inertial coordinate system, and {B}-x B ,y B ,z B This represents the coordinate system of the underwater robot's body, where T represents the cable tension, l represents the cable length, and p... A underwater robot position vector, p L Load position vector, q is the unit direction vector of the cable. Detailed Implementation

[0040] To achieve automated operation of underwater robot towing systems under low-energy conditions, this invention proposes a modeling method and a quantitative self-triggering control method and system for underactuated underwater robot towing systems, addressing control issues such as modeling, quantitative design, and energy reduction. The method includes: a modeling approach based on Newtonian mechanics and a hierarchical controller structure. The underwater robot towing system is modeled as three subsystems: a load position subsystem, a cable orientation subsystem, and an underwater robot attitude subsystem. The controller designed for each subsystem decomposes the control task into kinematic and dynamic levels. For the kinematic level of the load position subsystem, this invention, based on the concept of nonlinear quantitative control, solves the problem that traditional nonlinear control methods cannot perform prior quantitative adjustment of the load position response. For the dynamic level of the load position subsystem, a self-triggering controller is designed, solving the problem of unreasonable consumption of airborne communication resources and power caused by traditional continuous control strategies. For the cable orientation subsystem and the underwater robot attitude subsystem, unlike the traditional backstepping design framework, a self-triggering controller is constructed to solve the trajectory tracking problem of high-order multi-input multi-output systems. Compared with existing technologies, this invention establishes a low-energy underwater unmanned transportation technology with prior quantitative adjustment of trajectory tracking performance.

[0041] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention are within the scope of protection of the present invention.

[0042] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0043] like Figure 5As shown, the basic structure of the underwater robot towing system includes the underwater robot, cable, and load. Based on the spatial relationship between the cable direction vector, cable length, load position vector, and underwater robot position vector in the inertial frame, force analysis is performed on the load, cable, and underwater robot using Newton's second law. This yields the numerical relationships between the cable direction vector, cable length, load velocity vector, and the differential of the underwater robot velocity vector, which are then used for dynamic modeling of the load position subsystem and the cable direction subsystem. Combining the kinematic and dynamic models of the underwater robot's attitude, a model of an underactuated underwater robot towing system is finally obtained, comprising three subsystems: the load position subsystem, the cable direction subsystem, and the underwater robot attitude subsystem.

[0044] In this invention, the following assumptions are made regarding the constant load, the cable, and the underwater robot:

[0045] (1) The load is treated as a point mass, and the effect of volume on the modeling is ignored;

[0046] (2) The rope connecting the load and the underwater robot is a rigid body with a fixed length and no elasticity;

[0047] (3) The external disturbances experienced by the underwater robot have a known upper bound;

[0048] (4) The absolute value of the pitch angle of the underwater robot is less than Π / 2 during operation;

[0049] (5) The underwater robot towing system is a slow system. Therefore, the Coriolis force, centripetal force and hydrodynamic damping related to the speed of the underwater robot are considered as bounded disturbance terms with fixed amplitude changes.

[0050] In one embodiment of the present invention, a modeling method and a quantitative self-triggering control method for an underactuated underwater robot towing system are provided. The aim is to overcome the modeling and control problems in the autonomous load transport process of an underwater robot. This includes establishing a kinematic and dynamic model of the underwater robot towing system to accurately characterize the motion of the load, the swaying of the cable, and the motion characteristics of the underwater robot during transport. Based on this, a quantitative self-triggering control strategy for the underwater robot towing system under low energy consumption conditions is proposed. In this embodiment, as shown... Figure 1 As shown, the method includes the following steps:

[0051] 1) Based on Newtonian mechanics, establish models of the load position subsystem, cable direction subsystem, and underwater robot attitude subsystem to achieve simultaneous control of load movement, cable swing, and underwater robot attitude; and based on the backstepping method, decompose the control task of each subsystem into two levels: kinematics and dynamics, so as to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs the towing task.

[0052] 2) The load subsystem controller is set using a quantitative self-triggering control method so that the position response constraint of the load subsystem is within the pre-designed boundary function;

[0053] 3) The cable direction subsystem controller and the underwater robot attitude subsystem controller are set up using a backstepping self-triggering control method. The control signal is updated and transmitted to the actuator only when the preset conditions are met through self-triggering.

[0054] In this embodiment, an underwater robot towing system model is first established. The underwater robot towing system mainly consists of a six-degree-of-freedom underwater robot 1 and a two-degree-of-freedom point mass (load 3), connected by a fixed-length, taut cable 2, as shown below. Figure 2 and Figure 5 As shown.

[0055] In step 1) above, based on Figure 2 The mechanical analysis of the underwater robot towing system is presented, and mathematical modeling is performed based on Newton's second law. The towing process requires the rope to be taut, and the underwater robot uses the rope to transport the towed object.

[0056] The kinematic and dynamic models of the load position subsystem in the mathematical model of the underwater robot towing system are as follows:

[0057]

[0058] in, These are the position vector and velocity vector of the load, respectively. These are the derivatives of the position vector of the dragged object with respect to time and the derivatives of the velocity vector of the dragged object with respect to time, respectively. The inertial matrix of the underwater robot is represented by m. L For the mass of the load; Represents the identity matrix; The unit direction vector of the cable; This represents the angular velocity vector of the load as it moves in a circular motion around the underwater robot; it's important to note that ω and q are orthogonal. Let S(x)y be a mapping from a 3D vector to a 3D matrix, satisfying S(x)y = x × y; g represents the acceleration due to gravity; e3 = [0, 0, 1] T ;P q (F) represents the projection of vector F onto the direction of vector q, F = M -1 Rf, where Let be a rotation matrix. This indicates the control input provided by the underwater robot's propeller; This represents the term that cancels out the weight and buoyancy of the underwater robot. The lumped disturbances experienced by the load subsystem are treated as known in the following controller design because this invention does not emphasize the contribution of estimating the lumped disturbances.

[0059] In step 1) above, the kinematic and dynamic models of the cable direction subsystem are shown below:

[0060]

[0061] in, This refers to the lumped interference in the cable direction subsystem, which is treated as a known item in this invention. Let be the derivative of the unit direction vector along the cable direction with respect to time; Let l be the derivative of the angular velocity vector of the loaded object with respect to time; l is the length of the cable.

[0062] In step 1) above, the kinematic and dynamic models of the underwater robot's attitude subsystem are shown below:

[0063]

[0064] in, These represent the Euler angles of the underwater robot and its angular velocity in the coordinate system of the underwater robot's towing system, respectively. Let represent the Euler angles and the derivative of the angular velocity with respect to time for the underwater robot, respectively. Represents the transformation matrix; This is the moment of inertia matrix; Indicates control input; This represents the lumped disturbance in the underwater robot's attitude subsystem.

[0065] In this embodiment, the system state of the underwater robot towing system includes 18 state variables: three-dimensional load position, three-dimensional load velocity, three-dimensional cable direction, three-dimensional load angular velocity, three-dimensional underwater robot Euler angles, and three-dimensional underwater robot angular velocity. However, the control input is only... Therefore, the underwater robot towing system is modeled as a high-order nonlinear multi-input multi-output underactuated system.

[0066] In step 2) above, a quantitative self-triggering control method is used to configure the load subsystem controller, as detailed below:

[0067] 2.1) Define the original load position tracking error z p for:

[0068] z p =p L -p Ld (1)

[0069] Where, p LdThis is a reference instruction for the load position.

[0070] 2.2) To achieve quantitative design of the system response at load position, the following coordinate transformation function is introduced:

[0071]

[0072] Where, σ i For the converted load position tracking error, b i These are the pre-designed upper and lower boundary functions; z pi For the load position tracking error z p Components in the x, y, z directions.

[0073] 2.3) Differentiating equation (2), we get:

[0074]

[0075] in:

[0076]

[0077]

[0078] In equation (4), λ i , For design parameters; For z respectively pi The time derivatives of the upper and lower boundary functions of the design; z pi (0) is the initial value of the tracking error; Let be the time derivative of the smooth piecewise function. Then the boundary function is designed as follows:

[0079]

[0080] In equation (5), ρ0,ρ ∞ r and T are the design parameters of the boundary function; Let be the upper boundary function. b It is the lower boundary function; λ ρ and ρ are the scaling factors for the upper and lower boundary functions, respectively, and ρ is the smooth piecewise function.

[0081] 2.4) To design the control signal in the q direction, the following error definition is introduced:

[0082]

[0083] The relevant symbol q d Defined as:

[0084]

[0085] in, z is a diagonal positive definite matrix; v Tracking error designed for load velocity vector; v L The velocity vector of the load; Let ξ be the time derivative of the reference trajectory of the load; P i Z is the algebraic term defined by formula (4); σ is the transformed load position tracking error defined by formula (3); z q Tracking error designed for the unit direction vector of the cable; Let be the second derivative of the reference trajectory of the load with respect to time.

[0086] Combining the above equation (7), the final control input along the q direction is:

[0087] P q (F d ) = P q (F q )-‖ω‖ 2 q (8)

[0088] With the above control signals, the following equation will hold:

[0089]

[0090] Due to boundary function b i If the pre-designed quantitative indicators are met, as shown in Table 1, then the position response of the load position subsystem will also meet the pre-designed quantitative indicators.

[0091] Table 1 Quantitative Indicators

[0092]

[0093] In this embodiment, as Figure 3 As shown, the transportation of the towed object is controlled by the aforementioned controller time limit.

[0094] In step 3) above, if Figure 3 As shown, the cable direction control employs a backstepping self-triggering control method to configure the cable direction subsystem controller, as detailed below:

[0095] 3.1.1) Design the reference command ω for the load angular velocity. d for:

[0096]

[0097] in, S(q) is a diagonal positive definite matrix; S(q) represents the mapping from a three-dimensional vector to a three-dimensional matrix, satisfying S(q)q d =q×q d ; express In F = F q Values ​​under given conditions; This represents the transpose of the load velocity vector.

[0098] 3.1.2) Design load angular velocity tracking error z ω for:

[0099] z ω =S(q)(ω-ω d (11) Based on equations (10) and (11), the control signal component Π in the plane orthogonal to q is designed. q (F d ):

[0100]

[0101] in, z is a diagonal positive definite matrix; ω This represents the tracking error designed for the load angular velocity vector.

[0102] 3.1.3) Combining the control input in the q direction (Equation (8)) and the control input in the q orthogonal plane (Equation (12)), the control input F under the continuous-time design framework can be calculated. d :

[0103] F d =P q (F d )+Π q (F d (13)

[0104] It should be noted that this invention emphasizes quantitative control of the underwater robot towing system under low energy consumption conditions, therefore further processing is required based on formula (13). Unlike traditional event-triggered mechanisms that require real-time detection of whether the triggering conditions are met, this invention proposes a self-triggered mechanism to achieve non-periodic sampling of the control signal, as shown below:

[0105]

[0106] In the above formula All are positive numbers; F di (t s ) indicates that F occurs at time t = t s The value at time; Indicates the previous trigger time; express The derivative of time at the previous triggering moment.

[0107] It can be seen from formula (14) that the control signal F i (t) will be in [t] s ,t s+1 Keep the same value F within the interval di (t s ), and in t s+1 Updated to F in real time di (t s The next triggering time t is determined by design parameters or the control signal from the previous moment. s+1 It is not necessary to sample the control signal at every moment.

[0108] Furthermore, in order to compensate for the triggering error caused by non-equal interval sampling and improve the robustness of the closed-loop control system, formula (13) is redesigned as follows:

[0109]

[0110] In step 3) above, if Figure 4 As shown, the underwater robot's attitude control employs a backstepping self-triggering control method to configure the underwater robot's attitude subsystem controller, as detailed below:

[0111] 3.2.1) The following tracking errors are defined for the attitude angle and attitude angular velocity of the underwater robot:

[0112]

[0113] Among them, z θ This represents the tracking error designed for the attitude angle of an underwater robot; z Ω This indicates the tracking error designed for the attitude angular velocity of an underwater robot; θ d This serves as a reference signal for the underwater robot's attitude angle. It is a diagonal positive definite matrix.

[0114] 3.2.2) Based on the tracking error, design the following continuous-time control signal τ d :

[0115]

[0116] in, S is a diagonal positive definite matrix; S(Ω) represents the mapping from a three-dimensional vector to a three-dimensional matrix.

[0117] 3.2.3) Similar to the design concept of the self-triggered system controller for the cable direction subsystem, design a self-triggered mechanism:

[0118]

[0119] In the above formula All are positive integers. Based on equations (17) to (18), the following controller is designed:

[0120]

[0121] In summary, regarding the kinematics of the load position subsystem, this invention, based on the concept of nonlinear quantitative control, solves the problem that traditional nonlinear control methods cannot perform prior quantitative control of the load position in a high-order underactuated multi-input multi-output (MIMO) underwater robot towing system. This enables the controller to a priori adjust the convergence time, maximum deviation, overshoot, and steady-state accuracy performance indicators of the load position in a high-order underactuated MIMO underwater robot towing system. For the dynamics of the load position subsystem, a self-triggering controller is designed, resolving the unreasonable consumption of airborne communication resources and power caused by traditional continuous control strategies. For the cable orientation subsystem and the underwater robot attitude subsystem, unlike the traditional backstepping design framework, a self-triggering controller is designed, solving the trajectory tracking problem of the high-order nonlinear MIMO underactuated system.

[0122] In one embodiment of the present invention, a modeling and quantitative self-triggering control system for an underactuated underwater robot towing system is provided, comprising:

[0123] The subsystem establishment module establishes models of the load position subsystem, cable direction subsystem, and underwater robot attitude subsystem based on Newtonian mechanics. Based on the backstepping method, the control task of each subsystem is decomposed into kinematic and dynamic models to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs the towing task.

[0124] The load subsystem control module uses a quantitative self-triggering control method to set the load subsystem controller so that the position response constraint of the load subsystem is within a pre-set boundary function.

[0125] The cable direction and attitude control module adopts a backstepping self-triggering control method to set the cable direction subsystem controller and the underwater robot attitude subsystem controller. Through self-triggering, the control signal will be updated and transmitted to the actuator only when the preset conditions are met.

[0126] In the above embodiments, the kinematic and dynamic models of the load position subsystem are as follows:

[0127]

[0128] in, These are the position and velocity vectors of the load, respectively. The inertial matrix of the underwater robot is represented by m. L For the mass of the load; Represents the identity matrix; This represents the angular velocity vector of the load in the inertial frame. The unit direction vector of the cable; The mapping from a 3D vector to a 3D matrix satisfies S(x)y = x × y, where g represents the acceleration due to gravity; e3 = [0, 0, 1] T P q (F) represents the projection of vector F onto the direction of vector q, F = M -1 Rf, where Let be a rotation matrix. This indicates the control input provided by the underwater robot's propeller. This represents the term that cancels out the weight and buoyancy of the underwater robot. This refers to the lumped disturbance experienced by the load subsystem.

[0129] In the above embodiments, the kinematic and dynamic models of the cable direction subsystem are as follows:

[0130]

[0131] in, This represents lumped interference in the cable direction subsystem.

[0132] In the above embodiments, the kinematic and dynamic models of the underwater robot attitude subsystem are as follows:

[0133]

[0134]

[0135] in, These represent the Euler angles of the underwater robot and its angular velocity in the coordinate system of the underwater robot's towing system, respectively. Represents the transformation matrix; This is the moment of inertia matrix; Indicates control input; This represents the lumped disturbance in the underwater robot's attitude subsystem.

[0136] In the above embodiments, the underwater robot towing system is modeled as a high-order nonlinear multi-input multi-output underactuated system; the system state of the underwater robot towing system includes the three-dimensional load position, three-dimensional load velocity, three-dimensional cable direction, three-dimensional load angular velocity, three-dimensional underwater robot Euler angles, and three-dimensional underwater robot angular velocity, and the control input is...

[0137] In the above embodiments, the pre-set boundary function is:

[0138]

[0139] In the formula, Let z be the upper boundary function, and b be the lower boundary function; pi (0) represents the initial value of the tracking error; λ These are the scaling factors for the upper and lower boundary functions, respectively, where ρ is the smooth piecewise function, and ρ0, ρ ∞ r and T are design parameters of the boundary function.

[0140] In the above embodiments, the cable direction subsystem controller is configured using a backstepping self-triggering control method as follows:

[0141]

[0142] The underwater robot attitude subsystem controller is configured using a backstepping self-triggering control method as follows:

[0143]

[0144] In the formula, F d For control inputs within a continuous-time design framework; P q (F d ) is a vector F d Projection along the direction of vector q; Π q (F d ) is F d The projection onto a plane orthogonal to vector q; τ is a non-negative design parameter; τ is the control input; τ d It is a continuous-time control signal; It is a positive number.

[0145] The system provided in this embodiment is used to execute the above-described method embodiments. For specific processes and details, please refer to the above embodiments, which will not be repeated here.

[0146] In one embodiment of the present invention, a computing device is provided. This computing device can be a terminal and may include a processor, a communication interface, memory, a display screen, and an input device. The processor, communication interface, and memory communicate with each other via a communication bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and computer programs. When the computer programs are executed by the processor, they implement the methods described in the above embodiments. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The communication interface is used for wired or wireless communication with external terminals. Wireless communication can be achieved through Wi-Fi, a management network, NFC (Near Field Communication), or other technologies. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input device can be a touch layer covering the display screen, or buttons, a trackball, or a touchpad mounted on the casing of the computing device, or an external keyboard, touchpad, or mouse. The processor can call logical instructions stored in the memory.

[0147] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0148] In one embodiment of the present invention, a computer program product is provided, the computer program product including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, and when the program instructions are executed by a computer, the computer is able to perform the methods provided in the above-described method embodiments.

[0149] In one embodiment of the present invention, a non-transitory computer-readable storage medium is provided, which stores server instructions that cause a computer to perform the methods provided in the above embodiments.

[0150] The computer-readable storage medium provided in the above embodiments has a similar implementation principle and technical effect to the above method embodiments, and will not be described again here.

[0151] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0152] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0153] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0154] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for modeling and quantitative self-triggering control of an underactuated underwater robot towing system, characterized in that, include: Based on Newtonian mechanics, models of the load position subsystem, cable direction subsystem, and underwater robot attitude subsystem are established. Based on the backstepping method, the control task of each subsystem is decomposed into kinematic and dynamic models to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs towing tasks. A quantitative self-triggering control method is used to configure the load subsystem controller so that the position response constraint of the load subsystem is within a pre-set boundary function. The cable direction subsystem controller and the underwater robot attitude subsystem controller are set up using a backstepping self-triggering control method. The control signal is updated and transmitted to the actuator only when the preset conditions are met through self-triggering.

2. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 1, characterized in that, The kinematic and dynamic models of the load position subsystem are as follows: in, These are the position and velocity vectors of the load, respectively. The inertial matrix of the underwater robot is represented by m. L For the mass of the load; Represents the identity matrix; This represents the angular velocity vector of the load in the inertial frame. The unit direction vector of the cable; The mapping from a 3D vector to a 3D matrix satisfies S(x)y = x × y, where g represents the acceleration due to gravity; e3 = [0, 0, 1] T P q (F) represents the projection of vector F onto the direction of vector q, F = M -1 Rf, where For rotation matrix, This indicates the control input provided by the underwater robot's propeller. This represents the term that cancels out the weight and buoyancy of the underwater robot. This refers to the lumped disturbance experienced by the load subsystem.

3. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 2, characterized in that, The kinematic and dynamic model of the cable direction subsystem is as follows: in, This represents lumped interference in the cable direction subsystem.

4. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 1, characterized in that, The kinematic and dynamic models of the underwater robot's attitude subsystem are as follows: in, These represent the Euler angles of the underwater robot and its angular velocity in the coordinate system of the underwater robot's towing system, respectively. Represents the transformation matrix; This is the moment of inertia matrix; Indicates control input; This represents the lumped disturbance in the underwater robot's attitude subsystem.

5. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 1, characterized in that, The underwater robot towing system is modeled as a high-order nonlinear multi-input multi-output underactuated system. The system states of the underwater robot towing system include the three-dimensional load position, three-dimensional load velocity, three-dimensional cable direction, three-dimensional load angular velocity, three-dimensional underwater robot Euler angles, and three-dimensional underwater robot angular velocity. The control inputs are...

6. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 1, characterized in that, The pre-defined boundary function is: In the formula, Let z be the upper boundary function, and b be the lower boundary function; pi (0) is the initial value of the tracking error; λ These are the scaling factors for the upper and lower boundary functions, respectively, where ρ is the smooth piecewise function, and ρ0, ρ ∞ r and T are design parameters of the boundary function.

7. The modeling and quantitative self-triggering control method for an underactuated underwater robot towing system as described in claim 1, characterized in that, The cable direction subsystem controller is configured using a backstepping self-triggering control method as follows: The underwater robot attitude subsystem controller is configured using a backstepping self-triggering control method as follows: In the formula, F d For control inputs within a continuous-time design framework; P q (F d ) is a vector F d Projection along the direction of vector q; Π q (F d ) is F d The projection onto a plane orthogonal to vector q; τ is a non-negative design parameter; τ is the control input; τ d It is a continuous-time control signal; These are non-negative design parameters.

8. A modeling and quantitative self-triggering control system for an underactuated underwater robot towing system, characterized in that, include: The subsystem establishment module establishes models of the load position subsystem, cable direction subsystem, and underwater robot attitude subsystem based on Newtonian mechanics. Based on the backstepping method, the control task of each subsystem is decomposed into kinematic and dynamic models to characterize the kinematic and dynamic characteristics of each subsystem when the underwater robot performs the towing task. The load subsystem control module uses a quantitative self-triggering control method to set the load subsystem controller so that the position response constraint of the load subsystem is within a pre-set boundary function. The cable direction and attitude control module adopts a backstepping self-triggering control method to set the cable direction subsystem controller and the underwater robot attitude subsystem controller. Through self-triggering, the control signal will be updated and transmitted to the actuator only when the preset conditions are met.

9. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform any of the methods described in claims 1 to 7.

10. A computing device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including instructions for performing any of the methods described in claims 1 to 7.

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