A method for tension sensing and disturbance rejection control of a tethered underwater robot

Abstract

This invention discloses a tension-sensing and disturbance-resistant control method for a tethered underwater robot, belonging to the field of underwater robot automatic control technology. It is used for tension-sensing and disturbance-resistant control of tethered underwater robots, including acquiring the current pose and velocity of the underwater robot, calculating the six-degree-of-freedom nominal generalized force generated by the umbilical cable on the underwater robot, and constructing a high-fidelity six-degree-of-freedom dynamic model of the underwater robot; rewriting the control design model of the underwater robot into a state-space form of a second-order nonlinear system; constructing a fixed-time residual disturbance observer and an observation error system; constructing a vector expression for the final transformation error based on the underwater robot's pose tracking error; and designing the desired velocity output thruster control command. This invention achieves high-precision depth-keeping and trajectory tracking control of a tethered underwater robot under complex disturbances through cable force feedforward and disturbance observation compensation, tension adaptive performance boundary constraints, and fixed-time control.

Description

Technical Field

[0001] This invention discloses a tension sensing and disturbance rejection control method for a cabled underwater robot, belonging to the field of underwater robot automatic control technology. Background Technology

[0002] Existing research on cabled ROV systems mainly focuses on ROV dynamics modeling, umbilical cable dynamics modeling, tension analysis, motion response testing, and trajectory tracking control. Related methods typically employ mechanistic modeling, numerical calculation, robust control, sliding mode control, disturbance observer control, or specified performance control to improve the motion control capabilities of ROVs in complex environments. While these methods can improve system tracking performance and disturbance rejection under certain conditions, due to the characteristics of cabled ROV systems, such as rigid-flexible coupling, strong nonlinearity, parameter uncertainty, and significant environmental disturbances, traditional methods may still suffer from insufficient cable disturbance compensation, large control input fluctuations, increased tracking errors, and insufficiently smooth system response.

[0003] Furthermore, some existing methods typically treat umbilical cable forces, environmental disturbances, and model uncertainties as a unified unknown total disturbance for estimation, failing to fully utilize the physical information provided by the umbilical cable dynamics model and easily increasing the estimation burden on the observer. While other methods introduce cable model feedforward compensation, discrepancies may still exist between the model-calculated cable force and the actual cable force; relying solely on model feedforward is insufficient to guarantee high-precision and stable control under complex operating conditions. Therefore, there is an urgent need to provide a tension-sensing disturbance rejection control method for cabled ROV systems. This method should retain the cable dynamics physical information, rapidly estimate and compensate for residual disturbances, and adjust control performance constraints based on the umbilical cable tension level, thereby improving the ROV's trajectory tracking accuracy, depth stability, disturbance rejection capability, and operational safety. Summary of the Invention

[0004] The purpose of this invention is to provide a tension sensing and disturbance rejection control method for tethered underwater robots, in order to solve the problem in the prior art that it is difficult to simultaneously take into account the utilization of umbilical cable dynamic physical information, rapid estimation of residual disturbance, and adaptive adjustment of control performance under tension changes.

[0005] A tension-sensing disturbance rejection control method for a tethered underwater robot includes: S1. Collect the current pose and velocity of the underwater robot, solve the lumped mass model based on the boundary state of the umbilical cable, and obtain the six-degree-of-freedom nominal generalized force generated by the umbilical cable on the underwater robot. S2. Decompose the actual six-degree-of-freedom generalized force into six-degree-of-freedom nominal generalized force and umbilical cable model error. Combine external environmental disturbances, model uncertainties and unmodeled dynamic terms to establish a high-fidelity six-degree-of-freedom dynamic model of the underwater robot. Based on the high-fidelity six-degree-of-freedom dynamic model, define the nominal nonlinear term and residual disturbance of the underwater robot, and rewrite the control design model of the underwater robot into the state-space form of a second-order nonlinear system. S3. Construct a fixed-time residual perturbation observer, substitute the observer estimation error and the residual perturbation estimation error into the system of observation errors; S4. Define the underwater robot pose tracking error, set the specified performance boundary constraints, construct the smooth tension amplitude and normalized tension index based on the nominal generalized force, and construct the tension-sensing specified performance boundary; combine the tension-sensing specified performance boundary and pose tracking error to define the normalized error and construct the error transformation variable, construct the specified performance transformation matrix to convert the pose tracking error into the error transformation variable, and obtain the vector expression of the final transformation error. S5. Design the original virtual velocity and input it into a first-order command filter to obtain the filtered desired velocity. Based on the filtered desired velocity, the nominal cable generalized force, the disturbance estimate, and the error transformation variable, construct the tension sensing disturbance rejection control law, output the six-degree-of-freedom generalized control force, and apply it to the underwater robot system.

[0006] S2 includes, S2.1, decomposing the actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot into: ; In the formula, The actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot. This represents the error in the umbilical cable model. A high-fidelity six-DOF dynamic model of an underwater robot, based on external environmental disturbances, model uncertainties, and unmodeled dynamic terms: ; In the formula, Here is the inertial matrix of the underwater robot. Let be the velocity vector of the underwater robot in the volume coordinate system. Let be the acceleration vector of the underwater robot in body coordinates. The Coriolis force and centripetal force matrix of the underwater robot. The hydrodynamic damping matrix for the underwater robot. Let this be the restoring force vector of the underwater robot. For the generalized control force generated by the thruster, For external environmental disturbances, generalized force This represents model uncertainty and unmodeled dynamics.

[0007] S2 includes S2.2, which defines the nominal nonlinear term for the underwater robot. : ; The rewritten six-degree-of-freedom dynamics model of the underwater robot is rearranged as follows: ; Define the residual disturbance after feedforward compensation using the lumped mass method (LMM) for umbilical cables. for: ; The control design model of the underwater robot is rewritten as a second-order nonlinear system: ; ; In the formula, Let be the pose vector of the underwater robot in the inertial coordinate system. Let be the pose change rate vector of the underwater robot in the inertial coordinate system. Let be the Jacobian transformation matrix from the underwater robot's body coordinate system to its inertial coordinate system.

[0008] S3 includes, S3.1, constructing a fixed-time residual perturbation observer: ; ; In the formula, The rate of change of the observer's state estimate. For the known nonlinear function in the nominal part of the system, The rate of change of the disturbance estimate, Estimate the error for the observer. This is the estimated value of the disturbance; , To obtain a positive definite gain, take a diagonal positive definite matrix; , The nonlinear injection function is in vector form: ; ; In the formula, It is the transpose symbol; and For non-linear injection functions: ; ; In the formula, For channel index, , ; These are standard symbolic functions.

[0009] S3 includes, in S3.2, substituting the observer into the observer estimation error and residual perturbation estimation error to obtain the observation error system: ; ; In the formula, The rate of change of the state estimation error. This is the residual perturbation estimation error. The rate of change of the disturbance estimation error. The time rate of change of the true lumped residual perturbation; make , , , No. The error system for each channel is as follows: ; ; In the formula, For the first The state estimation error of each channel For the first Rate of change of the state estimation error of each channel For the first The perturbation estimation error for each channel, For the first Rate of change of channel perturbation estimation error For the first The time-varying rate of the actual disturbance in each channel; For the first The state estimation error of each channel For the first The residual perturbation estimation error for each channel For the first The true perturbation change rate of each channel.

[0010] S4 includes, S4.1, defining the underwater robot pose tracking error. for: ; In the formula, The desired pose trajectory; The specified performance boundary constraints are as follows: ; In the formula, For the first The pose tracking error for each degree of freedom For the first The tension sensing specification defines the performance boundary for each degree of freedom channel.

[0011] S4 includes, S4.2, according to Constructing smooth tension amplitude : ; In the formula, It is a positive semidefinite weight matrix. To prevent small positive numbers from being singular, for Moment ; Define the normalized tension index : ; In the formula, The tension scale constant is ; The performance boundary for tension sensing is: ; In the formula, As the initial performance boundary, For steady-state performance boundary, The boundary contraction rate, This is the tension adjustment coefficient. , , , .

[0012] S4 includes, S4.3, defining the normalization error: ; In the formula, For the first Normalization error of each degree of freedom channel , Define the error transformation variable: ; In the formula, For the first Error transformation variables for each degree of freedom channel. Define the performance transformation matrix : ; The vector expression for the final transformation error is: ; In the formula, The rate of change of the error transformation variable, The desired speed after filtering The expected rate of change of pose in an inertial frame. The time derivative of the desired trajectory itself. This is a compensation term generated by dynamic changes in the performance boundary. The time derivative of the performance boundary vector. For the normalized error vector, For speed tracking error Error correction term mapped to the inertial frame.

[0013] S5 includes S5.1, and the design of the original virtual speed. for: ; In the formula, The low-order fixed-time gain matrix is ​​the transformation error. The higher-order fixed-time gain matrix for the transformation error. For lower-order power parameters, For higher-order power parameters, It is a nonlinear power function sign function. , , , , ; Virtual speed Input first-order command filter: ; In the formula, The desired speed after filtering. The time derivative of the desired velocity after filtering. It is a positive definite diagonal matrix; Define command filtering error : .

[0014] S5 includes, S5.2, constructing a tension-sensing disturbance rejection control law: ; In the formula, For six degrees of freedom generalized control, The velocity error is a low-order fixed-time gain matrix. The velocity error is a high-order fixed-time gain matrix. Here is the linear damping gain matrix for velocity error; The tension sensing speed error feedback gain is: ; In the formula, For the first Tension-sensing speed error feedback gain matrix, For the first Fixed components of class gain, For the first The tension-sensitive component of the gain-like structure , .

[0015] Compared with existing technologies, this invention has the following advantages: Firstly, this invention introduces the nominal cable generalized force calculated from the lumped mass model of the umbilical cable into the ROV controller. This enables proactive compensation of the main force exerted by the umbilical cable on the ROV during the control input calculation stage, avoiding the treatment of all cable forces, ocean current disturbances, and model uncertainties as unknown total disturbances. This reduces the estimation burden on the disturbance observer and improves the targeting and physical interpretability of the cabled ROV trajectory tracking control. Secondly, this invention constructs residual disturbances based on nominal cable feedforward compensation and uses a fixed-time residual disturbance observer to assess umbilical cable model errors, environmental disturbances, and other factors. The invention enables rapid estimation and compensation of modeling dynamic errors, making the convergence time of residual disturbance estimation independent of the initial error magnitude, thereby improving the system's resilience under complex sea conditions, model parameter variations, and cable tension fluctuations. Furthermore, the invention constructs a tension-sensing performance boundary based on the tension level at the umbilical cable end, allowing tracking error constraints to adaptively adjust with cable tension changes, thus balancing control accuracy, control smoothness, and system safety. This improves the ROV's depth-holding stability under the influence of umbilical cable pulling, ocean current disturbances, and attitude coupling, reduces vertical drift, and enhances positioning accuracy and operational reliability during underwater operations. Attached Figure Description

[0016] Figure 1 This is a comparison chart of tracking errors in the x-direction; Figure 2 This is a comparison chart of tracking errors in the y-direction; Figure 3 This is a comparison chart of tracking errors in the z-direction; Figure 4 This is a comparison chart of tracking errors in the bow rocking channel; Figure 5 This is a schematic diagram comparing the tracking error in the x-direction of the method of the present invention with the specified performance boundary; Figure 6 This is a schematic diagram comparing the tracking error in the y-direction of the method of the present invention with the specified performance boundary; Figure 7 This is a schematic diagram comparing the tracking error in the z-direction of the method of the present invention with the specified performance boundary; Figure 8 This is a schematic diagram comparing the tracking error of the bow rocking channel in the method of the present invention with the specified performance boundary; Figure 9These are the residual perturbation dynamic observation results obtained using the method of this invention; Figure 10 These are the observation results of the disturbance amplitude using the method of this invention; Figure 11 These are the observation results of the Euclidean norm of the residual perturbation vector of the proposed method; Figure 12 It is the curve showing the variation of the nominal generalized force amplitude of the umbilical cable; Figure 13 It is the time history curve of the tension-sensing scheduling factor; Figure 14 It is an adaptive adjustment curve that senses the performance boundary of the tension. Figure 15 This is a schematic diagram illustrating the root mean square error of six methods for horizontal tracking; Figure 16 This is a schematic diagram of the root mean square error of vertical tracking for six methods; Figure 17 This is a schematic diagram showing the maximum normalization error ratio of the six methods; Figure 18 This is a diagram showing the energy comparison of six methods; Figure 19 This is a diagram illustrating the maximum control force of the six methods; Figure 20 This is a schematic diagram of the root mean square error of the observer for six methods. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0018] A tension-sensing disturbance rejection control method for a tethered underwater robot includes: S1. Collect the current pose and velocity of the underwater robot, solve the lumped mass model based on the boundary state of the umbilical cable, and obtain the six-degree-of-freedom nominal generalized force generated by the umbilical cable on the underwater robot. S2. Decompose the actual six-degree-of-freedom generalized force into six-degree-of-freedom nominal generalized force and umbilical cable model error. Combine external environmental disturbances, model uncertainties and unmodeled dynamic terms to establish a high-fidelity six-degree-of-freedom dynamic model of the underwater robot. Based on the high-fidelity six-degree-of-freedom dynamic model, define the nominal nonlinear term and residual disturbance of the underwater robot, and rewrite the control design model of the underwater robot into the state-space form of a second-order nonlinear system. S3. Construct a fixed-time residual perturbation observer, substitute the observer estimation error and the residual perturbation estimation error into the system of observation errors; S4. Define the underwater robot pose tracking error, set the specified performance boundary constraints, construct the smooth tension amplitude and normalized tension index based on the nominal generalized force, and construct the tension-sensing specified performance boundary; combine the tension-sensing specified performance boundary and pose tracking error to define the normalized error and construct the error transformation variable, construct the specified performance transformation matrix to convert the pose tracking error into the error transformation variable, and obtain the vector expression of the final transformation error. S5. Design the original virtual velocity and input it into a first-order command filter to obtain the filtered desired velocity. Based on the filtered desired velocity, the nominal cable generalized force, the disturbance estimate, and the error transformation variable, construct the tension sensing disturbance rejection control law, output the six-degree-of-freedom generalized control force, and apply it to the underwater robot system.

[0019] S2 includes, S2.1, decomposing the actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot into: ; In the formula, The actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot. This represents the error in the umbilical cable model. A high-fidelity six-DOF dynamic model of an underwater robot, based on external environmental disturbances, model uncertainties, and unmodeled dynamic terms: ; In the formula, Here is the inertial matrix of the underwater robot. Let be the velocity vector of the underwater robot in the volume coordinate system. Let be the acceleration vector of the underwater robot in body coordinates. The Coriolis force and centripetal force matrix of the underwater robot. The hydrodynamic damping matrix for the underwater robot. Let this be the restoring force vector of the underwater robot. For the generalized control force generated by the thruster, For external environmental disturbances, generalized force This represents model uncertainty and unmodeled dynamics.

[0020] S2 includes S2.2, which defines the nominal nonlinear term for the underwater robot. : ; The rewritten six-degree-of-freedom dynamics model of the underwater robot is rearranged as follows: ; Define the residual disturbance after feedforward compensation using the lumped mass method (LMM) for umbilical cables. for: ; The control design model of the underwater robot is rewritten as a second-order nonlinear system: ; ; In the formula, Let be the pose vector of the underwater robot in the inertial coordinate system. Let be the pose change rate vector of the underwater robot in the inertial coordinate system. Let be the Jacobian transformation matrix from the underwater robot's body coordinate system to its inertial coordinate system.

[0021] S3 includes, S3.1, constructing a fixed-time residual perturbation observer: ; ; In the formula, The rate of change of the observer's state estimate. For the known nonlinear function in the nominal part of the system, The rate of change of the disturbance estimate, Estimate the error for the observer. This is the estimated value of the disturbance; , To obtain a positive definite gain, take a diagonal positive definite matrix; , The nonlinear injection function is in vector form: ; ; In the formula, It is the transpose symbol; and For non-linear injection functions: ; ; In the formula, For channel index, , ; These are standard symbolic functions.

[0022] S3 includes, in S3.2, substituting the observer into the observer estimation error and residual perturbation estimation error to obtain the observation error system: ; ; In the formula, The rate of change of the state estimation error. This is the residual perturbation estimation error. The rate of change of the disturbance estimation error. The time rate of change of the true lumped residual perturbation; make , , , No. The error system for each channel is as follows: ; ; In the formula, For the first The state estimation error of each channel For the first Rate of change of the state estimation error of each channel For the first The perturbation estimation error for each channel, For the first Rate of change of channel perturbation estimation error For the first The time-varying rate of the actual disturbance in each channel; For the first The state estimation error of each channel For the first The residual perturbation estimation error for each channel For the first The true perturbation change rate of each channel.

[0023] S4 includes, S4.1, defining the underwater robot pose tracking error. for: ; In the formula, The desired pose trajectory; The specified performance boundary constraints are as follows: ; In the formula, For the first The pose tracking error for each degree of freedom For the first The tension sensing specification defines the performance boundary for each degree of freedom channel.

[0024] S4 includes, S4.2, according to Constructing smooth tension amplitude : ; In the formula, It is a positive semidefinite weight matrix. To prevent small positive numbers from being singular, for Moment ; Define the normalized tension index : ; In the formula, The tension scale constant is ; The performance boundary for tension sensing is: ; In the formula, As the initial performance boundary, For steady-state performance boundary, The boundary contraction rate, This is the tension adjustment coefficient. , , , .

[0025] S4 includes, S4.3, defining the normalization error: ; In the formula, For the first Normalization error of each degree of freedom channel , Define the error transformation variable: ; In the formula, For the first Error transformation variables for each degree of freedom channel. Define the performance transformation matrix : ; The vector expression for the final transformation error is: ; In the formula, The rate of change of the error transformation variable, The desired speed after filtering The expected rate of change of pose in an inertial frame. The time derivative of the desired trajectory itself. This is a compensation term generated by dynamic changes in the performance boundary. The time derivative of the performance boundary vector. For the normalized error vector, For speed tracking error Error correction term mapped to the inertial frame.

[0026] S5 includes S5.1, and the design of the original virtual speed. for: ; In the formula, The low-order fixed-time gain matrix is ​​the transformation error. The higher-order fixed-time gain matrix for the transformation error. For lower-order power parameters, For higher-order power parameters, It is a nonlinear power function sign function. , , , , ; Virtual speed Input first-order command filter: ; In the formula, The desired speed after filtering. The time derivative of the desired velocity after filtering. It is a positive definite diagonal matrix; Define command filtering error : .

[0027] S5 includes, S5.2, constructing a tension-sensing disturbance rejection control law: ; In the formula, For six degrees of freedom generalized control, The velocity error is a low-order fixed-time gain matrix. The velocity error is a high-order fixed-time gain matrix. Here is the linear damping gain matrix for velocity error; The tension sensing speed error feedback gain is: ; In the formula, For the first Tension-sensing speed error feedback gain matrix, For the first Fixed components of class gain, For the first The tension-sensitive component of the gain-like structure , .

[0028] The technical solution of the present invention will be further explained below with reference to specific steps and calculation formulas.

[0029] Step one is to establish a dynamic model of the ROV system with cables. The first step is to establish a coordinate system. To uniformly describe the motion of the ROV body, the motion of the umbilical cable nodes, and the forces acting on the umbilical cable ends, this invention uses three coordinate systems: an inertial coordinate system {n}, an ROV body coordinate system {b}, and an umbilical cable local coordinate system {c}. The inertial coordinate system {n} adopts the NED coordinate system, with the x-axis pointing north, the y-axis pointing east, and the z-axis vertically downward. The position and attitude of the ROV, the position of the umbilical cable nodes, the ocean current velocity, and the position of the ship's end or fixed lifting point boundary are all described in this coordinate system. The ROV body coordinate system {b} is fixed to the ROV body, with its origin located at the ROV's center of mass. The axis points in the direction of ROV movement. The axis points to the starboard side. The axes are in a right-handed coordinate system and consistent with the NED definition. A local coordinate system {c} for the umbilical cable is attached to each discrete cable segment, used to describe the tangential direction, normal direction, axial tension, and fluid resistance decomposition of the segment. For the ... The local tangential direction of a segment of umbilical cable is determined by the nodes at both ends of the segment.

[0030] The second step is to establish a six-degree-of-freedom dynamic model of the ROV. The pose vector of the ROV in the inertial coordinate system is defined as: Where x, y, and z are the positions of the ROV in the inertial coordinate system {n}, and φ, θ, and ψ are the roll, pitch, and bow angles, respectively. The ROV position vector is denoted as: The velocity vector of a ROV in volume coordinates is defined as follows: Where u, v, and w are the longitudinal, lateral, and vertical linear velocities of the ROV in the body coordinate system, and p, q, and r are the angular velocities of the ROV around the three axes of the body coordinate system.

[0031] The kinematic model of ROV is as follows: ,in, , The rotation matrix from the ROV body coordinate system {b} to the inertial coordinate system {n} can be written as: ;

[0032] The angular velocity rotation matrix from the ROV body coordinate system {b} to the inertial coordinate system {n} can be written as: ; The six-degree-of-freedom dynamic model of the ROV is as follows: ; The third step is to establish a lumped mass dynamic model of the umbilical cable. Assume the umbilical cable is discretized into N segments and N+1 nodes, with node numbers as follows: .in, To fix the lifting point end, This is the ROV connection end. (Number) Each node in the inertial coordinate system The position and velocity of the following are: , ; For the i-th segment of the umbilical cable, i.e., the segment between node i-1 and node i, its length and unit direction vector are: ; ; The axial tension of the i-th segment of the umbilical cable is: ; Where E is Young's modulus. The cross-sectional area of ​​the umbilical cable. This refers to the unstretched length of a single segment of the umbilical cable. The axial damping coefficient, Let the velocity of node i be... This is to ensure that the umbilical cable can only withstand tensile force and not compressive force.

[0033] For internal node i, the resultant force generated by the tension of the two adjacent umbilical cable segments is: ; Let the ocean current velocity at node i be... The relative velocity between the node and the water body is: ; The relative velocity along the local tangential and normal directions of the umbilical cable is decomposed into: , ; in, The relative tangential velocity, The normal relative velocity, Let i be the local tangential direction of the umbilical cable at node i.

[0034] The tangential and normal resistance forces acting on umbilical cable node i are as follows: ; ; in, Where d is the fluid density and d is the diameter of the umbilical cable. The tangential drag coefficient, Normal drag coefficient, subscript Represents the physical properties between nodes i+1 and i, such as This represents the length between nodes i+1 and i.

[0035] The gravitational and buoyant forces acting on node i are as follows: ; ; in, Let g be the inertial mass of node i, and g be the acceleration due to gravity. For fluid density, It represents the cross-sectional area.

[0036] If we consider additional mass, the mass matrix of node i is... for: ; in, For nodal inertial mass, Let I be the additional mass of the object in water, and let I be the third-order identity matrix.

[0037] Finally, the dynamic equation of node i is: .

[0038] The fourth step is to set the boundary conditions for the umbilical cable and calculate the cable tension at the ROV end. The upper boundary of the umbilical cable is a fixed suspension point, and its position and velocity in the inertial coordinate system {n} are as follows: ; ; in, To fix the position of the lifting point, To fix the speed of the lifting point.

[0039] The lower end of the umbilical cable is connected to the ROV body. Let the position vector of the umbilical cable connection point in the ROV body coordinate system {b} be: Then the location of the ROV end boundary node is: ; in, This is the location of the lower end of the umbilical cord. This refers to the location of the ROV. The velocity of the ROV end boundary node is: .

[0040] The cable tension at the ROV end is the tension of the last segment of the umbilical cable, which can be represented in an inertial coordinate system as follows: ; in, For the tension of the last segment of the umbilical cord, Let N be the unit tangent vector of the last segment of the umbilical cable from node N−1 to node N.

[0041] Since the generalized force in the ROV dynamic equations is expressed in the volume coordinate system {b}, it is necessary to transform the force to the ROV volume coordinate system, and consider the lever arm of the connection point relative to the ROV's center of mass. The six-degree-of-freedom nominal generalized force exerted by the umbilical cable on the ROV can be obtained: ; Should This is the nominal cable generalized force calculated by the lumped mass model, which is also the basis for subsequent tension sensing boundary, residual disturbance modeling, and control feedforward compensation.

[0042] Step two involves constructing a residual disturbance model based on umbilical cable feedforward compensation. The actual cable forces acting on an ROV are often difficult to obtain accurately; therefore, the actual umbilical cable forces are decomposed into: ; in, The nominal generalized force of the cable is obtained from online calculation using the lumped mass model. The errors in the umbilical cable model include model parameter errors, numerical discretization errors, boundary condition variations, and cable slack-tension conversion errors.

[0043] Considering external environmental disturbances, model uncertainties, and unmodeled dynamic terms, the ROV six-degree-of-freedom dynamic equations can be written as: ; in, External environmental disturbances. This represents model uncertainty and unmodeled dynamics.

[0044] To facilitate subsequent controller design, the nominal nonlinear term of the ROV is defined as follows: ; The ROV dynamics can then be written as: .

[0045] Define the residual disturbance after feedforward compensation using the lumped mass method (LMM) for umbilical cables as: ; The system can then be rewritten in the form of residual disturbances: ; ; The characteristic of this form lies in: the main physical function of the umbilical cord. Instead of being treated as an unknown disturbance as a whole, it directly participates in control as a calculable feedforward term; model errors and external disturbance errors that LMM cannot accurately describe are attributed to residual disturbances. The residual observer estimates and compensates for the disturbance, thereby reducing the burden on the disturbance observer and improving the accuracy of the compensation.

[0046] Step three involves designing a fixed-time residual disturbance observer. The original virtual velocity generated by the tension-sensing specified performance controller is denoted as... A first-order command filter is used to generate a filtered virtual velocity. , in, In the formula, This is the gain matrix of the command filter. For the first The filtering time constant of each degree of freedom channel. Original virtual speed The filtered desired velocity, obtained after smoothing by a first-order command filter, is used as the reference input for the underwater robot's inner velocity loop and provides a continuous and directly calculable input for the control law. The derivative of . Because It is composed of the desired trajectory, time-varying performance boundary, error transformation variables, the inverse matrix of the underwater robot's kinematic Jacobian matrix, and a nonlinear fixed-time error feedback term. If directly applied... Analytical differentiation introduces higher-order derivatives of the desired trajectory, performance boundaries, the Jacobian matrix, and nonlinear error terms. This not only increases the complexity of control law derivation and online calculation but also amplifies noise in pose, velocity, and other measurement signals, leading to control command jitter and hindering the smooth and stable operation of the underwater robot. Therefore, a first-order command filter is used to generate... and its derivative, to avoid direct interaction with Differentiation improves the real-time implementability of the control method and the smoothness of control commands. The initial value of the command filter is set to... ,in The initial virtual velocity is calculated by substituting the desired trajectory at the initial moment, the initial pose of the underwater robot, and the specified performance error variables into the original virtual velocity expression, ensuring that the initial command filtering error satisfies... This avoids additional jumps in control commands at startup due to inconsistencies between the filter's initial state and the original virtual speed.

[0047] Define the filtered velocity tracking error of the underwater robot as: ; Differentiating with respect to s, we get: ; Multiplying both sides by M on the left and substituting into the residual form of dynamics, we get: ; Define computable terms: ; Then we have: ; To avoid using acceleration measurements, an auxiliary variable is introduced: ; but: .

[0048] To estimate the residual perturbation without directly measuring the ROV acceleration, an auxiliary state estimate is constructed. and residual disturbance estimates And define the observation error: ; Define residual perturbation estimation error: ; in, for Get the estimated value, This is the residual disturbance.

[0049] The fixed-time residual perturbation observer designed in this invention is as follows: ; ; in, , It is a positive definite gain, that is Typically, a diagonal positive definite matrix is ​​chosen. , ; It is a nonlinear injection function in vector form; and ; .

[0050] Substituting the observer into the observation error and the residual perturbation estimation error, we can obtain the observation error system as follows: ; ; because Taking a diagonal positive definite matrix allows for channel-by-channel analysis. Let , , , No. The error system for each channel is as follows: ; ; Assuming residual disturbance It is locally absolutely continuous, and its first-order time derivative exists almost everywhere and is bounded, meaning that a known constant exists for each degree of freedom channel. ,satisfy: For each degree of freedom channel, the observer gain satisfies either of the following two sets of conditions, the first set of conditions being: , Second set of conditions: , .

[0051] Under the above conditions, the first Auxiliary state observation error of each degree of freedom channel and residual perturbation estimation error All converge to zero within a fixed time independent of the initial observation error. The upper bound for the fixed-time convergence of each degree of freedom channel is defined as follows: The upper bound for the fixed-time convergence of the system's overall observer is: For ,have .

[0052] Step four involves constructing the performance function for tension sensing. The ROV pose tracking error is defined as: ; in, The desired pose trajectory.

[0053] The specified performance boundary constraints are as follows ,Right now To incorporate umbilical cable tension information into the performance boundary, a smooth tension amplitude is first constructed based on the nominal cable generalized force calculated by LMM: ; in, It is a positive definite weight matrix. To prevent odd small positive numbers.

[0054] Further define the normalized tension index: ; in, , is the tension scale constant, because ,therefore, .

[0055] The tension sensing performance boundary design of this invention is as follows: ; in, As the initial performance boundary, For steady-state performance boundary, The boundary contraction rate, Let be the tension adjustment coefficient, and satisfy: Therefore, we can obtain .therefore, It is always positive and bounded. When the tension in the umbilical cord is low... The performance boundary is relatively small, and it mainly contracts according to a preset exponential law; when the umbilical cable tension increases, Increase the size and moderately relax the performance boundary to avoid the controller becoming overly aggressive under high tension conditions.

[0056] To perform a specified performance error transformation, a normalized error is defined as follows: ; As long as it meets the requirements This will guarantee: .

[0057] Further define the error transformation variables: ; Its inverse transformation is Therefore, for any finite There will always be This ensures that the original tracking error meets the specified performance constraints.

[0058] Depend on ,right Differentiate: ; therefore, .

[0059] Depend on Differentiating, we get: ; Substitution have to: .

[0060] Define matrix: ; definition Then the vector form of the transformation error is: .

[0061] ROV pose tracking error Differentiation yields: ; Substituting the ROV kinematic equations, we get: ; Will Substitute : ; Substitution have to: .

[0062] Step five involves designing a tension-sensing disturbance rejection control law. This is to minimize the transformation error. With a fixed-time convergence structure, design virtual velocity for: ; in, , , , .

[0063] Virtual speed Input first-order command filter and define the command filtering error. Substitute it into ,have to: ; The tension sensing disturbance rejection control law designed in this invention is as follows: ; in, Used to compensate for the nominal cable generalized force calculated by LMM. This is used to compensate for the residual perturbation estimated by the fixed-time observer. These two terms cannot be combined into a single ordinary perturbation compensation term, otherwise it would weaken the feedforward effect of the umbilical cable physical model. To specify the performance error feedback coupling term, It is a low-order fixed-time term, ensuring fast convergence near the origin. This is a higher-order fixed-time term, ensuring that the convergence time is independent of the initial value when far from the origin. It is a linear damping term that enhances noise robustness and provides absorption capability when the observation error is not zero.

[0064] The tension sensing speed error feedback gain is designed as follows: ; in, , ,therefore, .

[0065] When the tension in the umbilical cable increases By increasing the speed, the controller can appropriately enhance the speed error feedback function to improve its anti-interference capability; when the umbilical cable tension is low, The input is relatively small, and the control input remains relatively smooth.

[0066] Substituting the control law into the velocity error dynamics, we obtain the closed-loop velocity error equation: ; Combination From the equation, we can see that, Coupling terms in the channel Coupling terms in the S-channel In Lyapunov function analysis, they cancel each other out, thus forming a stable closed-loop error system.

[0067] Step six involves executing the closed-loop control process. In each control cycle... The method of the present invention is performed in the following order: Collect ROV current pose and velocity , ; Solving the lumped mass model based on the boundary state of the umbilical cable yields the following results: , , .

[0068] Calculate the tracking error based on the reference trajectory. ; Calculated based on the performance function specified by tension sensing. , , ; Calculate virtual speed ; The residual perturbation estimate is updated using a fixed-time residual observer. In a discrete implementation, this can be written as: ; ; in, , , .

[0069] Calculate the tension-sensing disturbance rejection control law: ; The control input is applied to the ROV system, and the above process is repeated in the next sampling period.

[0070] Step seven guarantees closed-loop stability and specified performance. The Lyapunov function of the controller is selected: ; Since M is positive definite, we have .

[0071] right Differentiating, we get: .

[0072] Substitution and We can obtain: ; in, ,so: ; when At that time, that is, after the fixed-time residual observer converges, Therefore: ; Remove negative terms There are still: ; Let the equivalent filtering error after the command filtering error undergoes the specified performance transformation and underwater robot kinematic mapping be: ; Assume there exist finite positive constants. , so that: .

[0073] Depend on We can obtain: ; ; ; ; in, Gain matrix The minimum eigenvalue, Gain matrix The minimum eigenvalue, Gain matrix The minimum eigenvalue, Gain matrix The smallest eigenvalue; therefore: .

[0074] According to the fixed-time stability theory, there exists a positive number. , , , so that: ; because , Therefore, the closed-loop error system is uniformly bounded over a fixed time, and its convergence time satisfies: .

[0075] Combined with the observer convergence time The overall system error convergence time does not exceed: ; At the same time, due to Bounded, and , can be obtained , combined , can be obtained Therefore, the ROV pose tracking error remains within the specified performance boundaries of tension sensing. Thus, this invention enables high-precision trajectory tracking, stable depth control, and disturbance-resistant motion control for cabled ROVs even under conditions of umbilical cable tension fluctuations, environmental disturbances, and model uncertainties.

[0076] The following is a further explanation with reference to the embodiments. This embodiment of the invention establishes a test model of the ROV-umbilical cable-fixed suspension point system based on the circular trajectory of a cabled ROV with a fixed suspension point. The system is uniformly described using an inertial coordinate system {n}, an ROV body coordinate system {b}, and an umbilical cable local coordinate system {c}. Specifically, the inertial coordinate system {n} adopts the NED coordinate system, with the x-axis pointing north, the y-axis pointing east, and the z-axis vertically downward; the ROV body coordinate system {b} is fixed to the ROV body; and the umbilical cable local coordinate system {c} is used to describe the tangential direction, normal direction, axial tension, and fluid resistance decomposition of the cable segment.

[0077] The ROV is described using a six-degree-of-freedom dynamic model. The ROV inertia matrix M consists of the rigid body inertia matrix and the added mass matrix. In this embodiment, the ROV mass is taken as... External dimensions The rigid body inertia matrix is ​​taken as follows: Additional mass matrix taken Therefore, M is obtained by adding the two matrices mentioned above. The linear damping coefficient in the hydrodynamic damping matrix D(|ν|) is taken as... The secondary damping coefficient is taken as The centroid involved in the restoring force matrix g(η) is taken as... Floating Heart Take Fluid density Pick gravitational acceleration Pick .

[0078] The umbilical cable is described using a lumped mass dynamics model. The number of discrete segments in the umbilical cable is... Pick The total unstretched length is Therefore, the unstretched length of a single segment is The Young's modulus E in the axial tension calculation formula is taken as... Pa, umbilical cord diameter Pick Cross-sectional area according to Calculate the axial damping coefficient. Additional mass matrix The tangential additional mass coefficient is taken as The normal additional mass coefficient is taken as Tangential drag coefficient Normal drag coefficient The umbilical cable is only considered under tensile stress, not compressive stress.

[0079] In this embodiment, the upper end of the umbilical cord cable is a fixed suspension point, and the position of the fixed suspension point is... Fixed lifting point speed The lower end of the umbilical cable connects to the ROV body; the connection point in the ROV body coordinate system... This connection point is used to calculate the ROV end boundary node position, ROV end boundary node velocity, and the tension of the last cable segment. and unit tangent vector The generalized force of the nominal cable at the ROV end is obtained. .

[0080] This embodiment uses a fixed-point circular trajectory tracking operation. The ROV reference trajectory is a horizontal circular trajectory, with the center taken as... radius taken Periodicity The bow roll angle varies tangentially along the circumference. The total duration is... Integral step size To verify the initial error convergence capability, the ROV initial position was adjusted relative to the reference initial position. Deviation, initial attitude added The deviation, the initial velocity is taken .

[0081] In this embodiment, the nominal cable generalized force at the ROV end is first calculated. This force is then incorporated into the controller as a feedforward compensation term for the umbilical cable. The actual umbilical cable force is decomposed into a nominal cable generalized force. Errors in the umbilical cable model In this embodiment, it is for simulation The model parameter errors, numerical discretization errors, boundary condition variations, and cable slack-tension transition errors are all considered. LMM model mismatch is set within a range of 6 to 28 seconds. Specifically, The six-degree-of-freedom scaling mismatch coefficient is taken as Bias term take The first three units are in N, and the last three units are in N·m; the time-varying fluctuation amplitude is taken as... The fluctuation frequency is taken as The scaling, bias, and time-varying fluctuation terms mentioned above are all categorized under the umbilical cable model error defined in Part 5. .

[0082] Regarding external environmental disturbances, the ocean current velocity involved in the calculation of nodal relative velocities... Set to a moderate lateral current. The main current duration is 6 to 28 seconds, applied through a smoothed time window. The x-direction current includes... Basic flow rate, The slowly varying sinusoidal component, and its amplitude is and Additional low-frequency disturbance components; ocean currents in the y-direction include Basic flow rate, The slowly varying cosine component, and its amplitude. and The additional low-frequency disturbance component; the ocean current in the z-direction is set to 0. This ocean current velocity is used to calculate the relative velocity between the node and the water body, and further affects the tangential and normal drag of the node.

[0083] To further simulate the effects of non-uniform flow fields and local hydrodynamic forces on the umbilical cable, this embodiment applies distributed nodal perturbations along the cable's length. These perturbations affect the external load component of the umbilical cable's nodal dynamics equations and ultimately influence the ROV end cable tension. and The amplitude of the distributed disturbance is taken as 2.6N / node, and the proportion of the disturbance direction is taken as... This means that the disturbance is mainly lateral, while also including smaller longitudinal and vertical disturbances.

[0084] Between 14.4 s and 18.2 s, a localized contact disturbance was further applied to the middle of the umbilical cable to simulate short-term contact, snagging, or localized pulling of the cable. The center of the contact disturbance was located at the normalized cable length. At this location, the spatial width parameter is taken as 0.13, and the peak value of the lateral contact disturbance is taken as... The peak value of the vertical contact disturbance is taken as This contact disturbance also acts as an external load on the umbilical cable node dynamics model and is transmitted to the ROV end through the umbilical cable tension.

[0085] In this embodiment, the external environmental disturbance at the ROV end... It is incorporated as a six-degree-of-freedom generalized force. In the translational direction, the x-direction perturbation is... As the principal components and superimposed The low-frequency changes, the y-direction perturbation As the principal components and superimposed The low-frequency variation, the z-axis perturbation is from and It consists of low-frequency components. In the direction of rotation, the amplitudes of the rolling, pitching, and yaw disturbance moments are respectively... , and The aforementioned six-degree-of-freedom perturbation is used to simulate ocean current residuals, minor external effects, and hydrodynamic influences not accurately described by the cable model.

[0086] Meanwhile, in this embodiment, the thruster efficiency coefficient is set to... The thruster is biased to The low-frequency ripple amplitude of the thruster is Ripple frequency is taken Therefore, the residual disturbance after LMM feedforward compensation Depend on , and Together, they form a system used for subsequent fixed-time residual perturbation observer estimation.

[0087] In this embodiment, the residual disturbance constructed in step two of the fifth part is... A fixed-time residual perturbation observer was designed. This observer does not directly estimate the total cable force, but rather... Based on the fact that it has already participated in the control as a feedforward term, only the remaining term is estimated. This reduces the estimation burden on the observer.

[0088] Part 5: Exponential Parameter Selection in Fixed-Time Observers =0.75, =1.35, which satisfies the condition. , Requirements. Observer gain. , All are diagonal positive definite matrices, with their six diagonal elements set as follows: ; ; The first three channels correspond to the translational direction of the ROV, and the last three channels correspond to the rotational direction of the ROV. The residual disturbance estimation compensation weights are taken as follows: Compensation limit The first three units are The units for the last three items are After the above processing, the observer output is used as the residual disturbance estimation term in the control law for compensation.

[0089] In this embodiment, the nominal cable generalized force is first calculated by the LMM. Constructing smooth tension amplitude Furthermore, a normalized tension index was constructed. . weight matrix That is, mainly utilizing The first three force components reflect the tension level of the ROV end cable; preventing odd small positive values. The tension scale constant in the normalized tension index. To avoid Affected by instantaneous tension fluctuations, this embodiment... A first-order filter is used with a filter time constant of 0.28s. When the tension rises rapidly, a tension rise advance coefficient of 0.45 is used for appropriate correction.

[0090] Specify performance boundaries In the middle, the initial performance boundary: ; Steady-state performance boundary: ; Boundary contraction rate: ; Tension adjustment coefficient: ; The first three components correspond to the x, y, and z position error constraints, while the last three components correspond to the roll, pitch, and yaw angle error constraints.

[0091] During the control process, the tracking error is first calculated based on the ROV's current pose and the desired pose. Then use Calculate normalized error And obtained through error transformation To avoid the normalization error approaching the singular boundary in the numerical implementation, this embodiment limits the absolute value of the normalization error to within 0.98. With the above settings, when the umbilical cable tension is low, It mainly contracts according to a preset exponential pattern to ensure trajectory tracking accuracy; when the umbilical cable tension increases, This allows for a moderate relaxation of the performance boundaries, thereby preventing the controller from becoming overly aggressive under high tension conditions.

[0092] In this embodiment, the tension sensing disturbance rejection control law is designed according to step five. The control law includes a nominal dynamic compensation term, an LMM cable feedforward compensation term, a fixed-time residual disturbance compensation term, a specified performance error feedback coupling term, a low-order fixed-time term, a high-order fixed-time term, and a linear damping term.

[0093] Virtual speed The specified performance transformation error feedback gain , Take a diagonal positive definite matrix, whose six diagonal elements are as follows: ; .

[0094] The fixed-time exponent in virtual velocity and disturbance rejection control law is taken , Because the control law contains To avoid sudden changes in virtual speed commands, this embodiment... Command filtering is used, and the filtering time constant is taken as follows: .

[0095] In the speed error feedback control law , , All are diagonal positive definite matrices, with the following six diagonal elements: ; ; ; Tension adjustment gain in tension sensing speed error feedback gain Pick In actual implementation, the feedback gain of each speed error is adjusted based on the base gain. The appropriate increase in size allows the ROV to have stronger disturbance recovery capabilities when the umbilical cable tension is high, and to maintain smoother control input when the tension is low.

[0096] In each control cycle Inside, the current pose of the ROV is first acquired. ,speed The following steps are taken: First, determine the location and velocity of the umbilical cable nodes, and the boundary conditions of the fixed suspension points. Second, solve the lumped mass model based on the boundary conditions of the umbilical cable, calculating the length of each cable segment, unit tangent vector, axial tension, node fluid resistance, node gravity, and buoyancy. Finally, determine the tension of the last cable segment. and unit tangent vector Obtain the generalized force of the nominal cable at the ROV end .

[0097] Then, the ROV pose tracking error is calculated based on the reference trajectory. and according to Calculate tension amplitude Normalized tension index and tension sensing specified performance boundaries Based on this, the normalized error is calculated. Error transformation variables and virtual speed .

[0098] Subsequently, the auxiliary state estimate and residual perturbation estimate are updated using a fixed-time residual perturbation observer, resulting in... The controller calculates the six-degree-of-freedom generalized control force based on the tension-sensing disturbance rejection control law, integrating nominal dynamic compensation, LMM cable feedforward compensation, residual disturbance observation compensation, and specified performance error feedback. .

[0099] Finally, for After smoothing and limiting, the data is applied to the ROV dynamics model. After the system runs for one control cycle, the measurement state is updated and the above process is repeated, thereby achieving closed-loop trajectory tracking control of the cabled ROV under the combined effects of complex ocean currents, distributed disturbances of the umbilical cable, local contact disturbances, and model mismatch errors.

[0100] In this embodiment, since the ROV inertia matrix M is a positive definite matrix, the fixed-time residual perturbation observer can monitor the ROV within a fixed time upper bound. The estimation is performed, and the control law contains low-order fixed-time terms, high-order fixed-time terms, and linear damping terms, so the closed-loop error system can obtain fixed-time convergence characteristics.

[0101] Meanwhile, because the controller uses tension sensing to define performance boundaries By constraining the pose tracking error and transforming the constrained error control problem into an unconstrained error stability problem through error transformation, the pose tracking error can be effectively controlled. When bounded, the original tracking error Always maintain within the specified performance limits. When the umbilical cable tension is high, Increase the size of the cable, appropriately relax the performance boundaries, and improve the control safety margin; when the umbilical cable tension is low, The performance boundary shrinks according to a preset rule, ensuring tracking accuracy. Therefore, this invention can achieve stable, disturbance-resistant trajectory tracking and depth control of cabled ROVs even under conditions of umbilical cable tension fluctuations, external environmental disturbances, and model uncertainty errors.

[0102] Six control methods were compared. M1 was the method of this invention, in which LMM feedforward compensation, fixed-time residual disturbance observer, and tension-sensing specified performance control were all enabled. M2 removed the residual disturbance observer to verify the effect of fixed-time residual disturbance estimation compensation. M3 removed LMM feedforward compensation to verify the effect of umbilical cable lumped mass model feedforward. M4 used conventional specified performance control without enabling tension-sensing boundary adjustment. M5 used total disturbance observer specified performance control without distinguishing between LMM nominal cable force and residual disturbance. M6 used super-helical sliding mode control as a robust baseline method without enabling LMM feedforward, residual disturbance observer, and tension-sensing specified performance boundary.

[0103] The above six methods use the same ROV parameters, umbilical cable parameters, reference trajectory, initial conditions, ocean current disturbances, umbilical cable distributed disturbances, local contact disturbances, ROV end residual disturbances, and LMM model mismatch errors, changing only the key modules in the control structure. This comparison method allows for the verification of... The contributions of feedforward compensation, fixed-time residual disturbance observer, tension-sensing performance boundary specification, and overall disturbance rejection control structure to system performance.

[0104] The output includes the ROV's 3D trajectory, horizontal trajectory error, depth error, bow angle error, compliance with specified performance boundaries, ROV-end umbilical cable tension, thruster generalized control force, control energy, residual disturbance estimation error, and umbilical cable morphology changes. Regarding trajectory tracking performance, the focus is on comparing the horizontal trajectory error and depth error of different methods throughout the entire process from 0s to 30s. For disturbance recovery performance, the focus is on comparing the error recovery speed of each method after a local contact disturbance from 14.4s to 18.2s. Regarding tension sensing performance, the focus is on comparing the ROV-end cable tension changes, specified performance boundary changes, and the maximum normalized error ratio. Regarding control costs, the focus is on comparing the peak thruster control force and control energy of each method.

[0105] To visually illustrate the control effect of the method of the present invention, the test results of the present invention are as follows: Figures 1 to 5 As shown.

[0106] like Figures 1 to 4 As shown, all six methods exhibit varying degrees of pose tracking error during the initial transition phase and the local contact disturbance phase. Compared to the comparative methods, the method M1 of this invention has smaller error amplitudes in the x, y, z, and yaw channels, and recovers faster after the disturbance disappears, demonstrating better trajectory tracking, depth determination, and disturbance recovery capabilities.

[0107] like Figures 5 to 8 As shown, the tracking error of method M1 in the x, y, z and yaw channels of this invention remains between the corresponding upper and lower specified performance boundaries. Even during the local contact disturbance phase from 14.4 s to 18.2 s, the normalized error does not cross the performance boundary, indicating that the constructed specified performance constraints remain effective throughout the entire process.

[0108] like Figures 9 to 11 As shown, the fixed-time residual disturbance observer can track changes in residual disturbances caused by model mismatch, external environmental disturbances, and cable contact. When a contact disturbance occurs, the observation error increases briefly but then quickly decreases, indicating that the observer can provide effective residual disturbance estimation and compensation information for the control law.

[0109] like Figures 12 to 14As shown, local contact disturbances significantly increase the nominal cable generalized load calculated by LMM, leading to a corresponding increase in the normalized tension index and a moderate relaxation of the specified performance boundaries for each channel. As the cable load decreases, the tension index and performance boundaries correspondingly decline, thereby achieving online coordination between tracking accuracy and control safety margin under high tension conditions.

[0110] like Figures 15 to 20 As shown, the horizontal tracking root mean square error of method M1 in this invention is 0.003 m, the vertical tracking root mean square error is 0.0066 m, the maximum normalized error ratio is 0.81, and the observer error root mean square value is 11.25 N. Considering both the maximum control force and control energy indicators, it can be seen that M1 achieves superior tracking accuracy, performance constraint satisfaction, and disturbance observation accuracy while maintaining a moderate control cost.

[0111] The above results verify that the method of the present invention can utilize the main physical effects of the umbilical cable in advance, compensate for the residual disturbance using a fixed-time residual disturbance observer, and utilize tension sensing to define performance boundaries to improve the safety margin when the tension is large and maintain high control accuracy when the tension is small. Therefore, compared with methods such as observer removal, LMM feedforward removal, conventional defined performance control, total disturbance observer control, and ST-SMC, the present invention can better balance trajectory tracking accuracy, depth stability, disturbance recovery capability, tension constraint adaptability, and control input smoothness.

[0112] The above results verify that the method of the present invention can utilize... The primary physical function of the umbilical cable is compensated in advance using a fixed-time residual disturbance observer. , and The residual disturbance is generated, and the performance boundary is specified by tension sensing to improve the safety margin when the tension is large and maintain high control accuracy when the tension is small. Therefore, compared with comparative methods such as observer removal, LMM feedforward removal, conventional specified performance control, total disturbance observer control, and ST-SMC, this invention can better balance trajectory tracking accuracy, depth stability, disturbance recovery capability, tension constraint adaptability, and control input smoothness.

[0113] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. 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 or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A tension sensing and disturbance rejection control method for a tethered underwater robot, characterized in that, include: S1. Collect the current pose and velocity of the underwater robot, solve the lumped mass model based on the boundary state of the umbilical cable, and obtain the six-degree-of-freedom nominal generalized force generated by the umbilical cable on the underwater robot. S2. Decompose the actual six-degree-of-freedom generalized force into six-degree-of-freedom nominal generalized force and umbilical cable model error. Combine external environmental disturbances, model uncertainties and unmodeled dynamic terms to establish a high-fidelity six-degree-of-freedom dynamic model of the underwater robot. Based on the high-fidelity six-degree-of-freedom dynamic model, define the nominal nonlinear term and residual disturbance of the underwater robot, and rewrite the control design model of the underwater robot into the state-space form of a second-order nonlinear system. S3. Construct a fixed-time residual perturbation observer, substitute the observer estimation error and the residual perturbation estimation error into the system of observation errors; S4. Define the underwater robot pose tracking error, set the specified performance boundary constraints, construct the smooth tension amplitude and normalized tension index based on the nominal generalized force, and construct the tension-sensing specified performance boundary; combine the tension-sensing specified performance boundary and pose tracking error to define the normalized error and construct the error transformation variable, construct the specified performance transformation matrix to convert the pose tracking error into the error transformation variable, and obtain the vector expression of the final transformation error. S5. Design the original virtual velocity and input it into a first-order command filter to obtain the filtered desired velocity. Based on the filtered desired velocity, the nominal cable generalized force, the disturbance estimate, and the error transformation variable, construct the tension sensing disturbance rejection control law, output the six-degree-of-freedom generalized control force, and apply it to the underwater robot system.

2. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 1, characterized in that, S2 includes, S2.1, decomposing the actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot into: ； In the formula, The actual six-degree-of-freedom generalized force generated by the umbilical cable on the underwater robot. This represents the error in the umbilical cable model. A high-fidelity six-DOF dynamic model of an underwater robot, based on external environmental disturbances, model uncertainties, and unmodeled dynamic terms: ； In the formula, Here is the inertial matrix of the underwater robot. Let be the velocity vector of the underwater robot in the volume coordinate system. Let be the acceleration vector of the underwater robot in body coordinates. The Coriolis force and centripetal force matrix of the underwater robot. The hydrodynamic damping matrix for the underwater robot. Let this be the restoring force vector of the underwater robot. For the generalized control force generated by the thruster, For external environmental disturbances, generalized force This represents model uncertainty and unmodeled dynamics.

3. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 2, characterized in that, S2 includes S2.2, which defines the nominal nonlinear term for the underwater robot. : ； The rewritten six-degree-of-freedom dynamics model of the underwater robot is rearranged as follows: ； Define the residual disturbance after feedforward compensation using the lumped mass method (LMM) for umbilical cables. for: ； The control design model of the underwater robot is rewritten as a second-order nonlinear system: ； ； In the formula, Let be the pose vector of the underwater robot in the inertial coordinate system. Let be the pose change rate vector of the underwater robot in the inertial coordinate system. Let be the Jacobian transformation matrix from the underwater robot's body coordinate system to its inertial coordinate system.

4. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 3, characterized in that, S3 includes, S3.1, constructing a fixed-time residual perturbation observer: ； ； In the formula, The rate of change of the observer's state estimate. For the known nonlinear function in the nominal part of the system, The rate of change of the disturbance estimate, Estimate the error for the observer. This is the estimated value of the disturbance; , To obtain a positive definite gain, take a diagonal positive definite matrix; , The nonlinear injection function is in vector form: ； ； In the formula, It is the transpose symbol; and For non-linear injection functions: ； ； In the formula, For channel index, , ; These are standard symbolic functions.

5. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 4, characterized in that, S3 includes, in S3.2, substituting the observer into the observer estimation error and residual perturbation estimation error to obtain the observation error system: ； ； In the formula, The rate of change of the state estimation error. This is the residual perturbation estimation error. The rate of change of the disturbance estimation error. The time rate of change of the true lumped residual perturbation; make , , , No. The error system for each channel is as follows: ； ； In the formula, For the first The state estimation error of each channel For the first Rate of change of the state estimation error of each channel For the first The perturbation estimation error for each channel, For the first Rate of change of channel perturbation estimation error For the first The time-varying rate of the actual disturbance in each channel; For the first The state estimation error of each channel For the first The residual perturbation estimation error for each channel For the first The true perturbation change rate of each channel.

6. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 5, characterized in that, S4 includes, S4.1, defining the underwater robot pose tracking error. for: ； In the formula, The desired pose trajectory; The specified performance boundary constraints are as follows: ； In the formula, For the first The pose tracking error for each degree of freedom For the first The tension sensing specification defines the performance boundary for each degree of freedom channel.

7. The tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 6, characterized in that, S4 includes, S4.2, according to Constructing smooth tension amplitude : ； In the formula, It is a positive semidefinite weight matrix. To prevent small positive numbers from being singular, for Moment ; Define the normalized tension index : ； In the formula, The tension scale constant is ; The performance boundary for tension sensing is: ； In the formula, As the initial performance boundary, For steady-state performance boundary, The boundary contraction rate, This is the tension adjustment coefficient. , , , .

8. A tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 7, characterized in that, S4 includes, S4.3, defining the normalization error: ； In the formula, For the first Normalization error of each degree of freedom channel , Define the error transformation variable: ； In the formula, For the first Error transformation variables for each degree of freedom channel. Define the performance transformation matrix : ； The vector expression for the final transformation error is: ； In the formula, The rate of change of the error transformation variable, The desired speed after filtering The expected rate of change of pose in an inertial frame. The time derivative of the desired trajectory itself. This is a compensation term generated by dynamic changes in the performance boundary. The time derivative of the performance boundary vector. For the normalized error vector, For speed tracking error Error correction term mapped to the inertial frame.

9. A tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 8, characterized in that, S5 includes S5.1, and the design of the original virtual speed. for: ； In the formula, The low-order fixed-time gain matrix is ​​the transformation error. The higher-order fixed-time gain matrix for the transformation error. For lower-order power parameters, For higher-order power parameters, It is a nonlinear power function sign function. , , , , ; Virtual speed Input first-order command filter: ； In the formula, The desired speed after filtering. The time derivative of the desired velocity after filtering. It is a positive definite diagonal matrix; Define command filtering error : 。 10. A tension sensing and disturbance rejection control method for a cabled underwater robot according to claim 9, characterized in that, S5 includes, S5.2, constructing a tension-sensing disturbance rejection control law: ； In the formula, For six degrees of freedom generalized control, The velocity error is a low-order fixed-time gain matrix. The velocity error is a high-order fixed-time gain matrix. The linear damping gain matrix for velocity error; The tension sensing speed error feedback gain is: ； In the formula, For the first Tension-sensing speed error feedback gain matrix, For the first Fixed components of class gain, For the first The tension-sensitive component of the gain-like structure , .

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