Waterjet propulsion thrust vectoring method based on feasible region

Abstract

A kind of water jet propulsion vector thrust distribution method based on feasible region, the feasible region model of double water jet propulsion vector thrust is established from control logic, according to the boundary condition of feasible region, introduce distance relaxation variable to deal with constraint condition, through the optimization algorithm with weight coefficient to deal with the thrust distribution problem under the condition of no solution, then the distribution result of each water jet is translated into control command and output.The water jet propulsion vector thrust distribution based on feasible region of the present application, significantly improve the degree of automation of water jet propulsion ship while the calculation speed is faster, can better cope with the situation of no solution, more universal, more fully play to the performance of water jet.

Description

Technical Field

[0001] This invention relates to a technology in the field of ship control, specifically a method for waterjet propulsion vector thrust distribution based on a feasible domain. Background Technology

[0002] Thrust distribution methods are fundamental to the vector motion control of multi-jet propulsion ships, and numerous studies have been conducted on thrust distribution methods in recent years. Most existing studies on thrust distribution in waterjet propulsion employ a technical approach of physical mechanism modeling followed by solving an optimization problem. They establish a mathematical model of the vector thrust of multi-jet propulsion based on physical phenomena, formulate an optimization problem with the objective of minimizing thrust distribution error, and establish constraints based on the hardware capabilities of the waterjet propulsion equipment (power limitations, nozzle angle limitations, and reverse bucket angle limitations). Relaxed variables are used to address situations where thrust distribution has no solution. Summary of the Invention

[0003] This invention addresses the problems of existing controllers being unable to handle unsolvable problems, which pose a risk of motion control failure and are unable to effectively handle thrust allocation in unsolvable situations, while also incurring large computational costs, long processing times, and performance waste in optimization problems. It proposes a waterjet propulsion vector thrust allocation method based on feasible regions. Starting from the control logic, a feasible region model of the vector thrust of dual waterjet propulsion units is established, and the vector thrust of the waterjet propulsion unit is allocated based on the characteristics of the feasible region. This significantly improves the automation level of waterjet propulsion vessels while offering faster computation speed, better handling of unsolvable situations, greater versatility, and more efficient utilization of the waterjet propulsion unit's performance.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a method for allocating vector thrust of water jet propulsion based on a feasible region. Starting from the control logic, a feasible region model of the vector thrust of dual water jet propulsion is established. Distance relaxation variables are introduced to deal with the constraints based on the boundary conditions of the feasible region. After dealing with the thrust allocation problem in the case of no solution through an optimization algorithm with weighted coefficients, the allocation result of each water jet propulsion is translated into control commands and output.

[0006] This invention relates to a waterjet propulsion vector thrust allocation system based on a feasible region, comprising six parts: a unit for determining the upper and lower limits of the control quantity, a unit for establishing the mathematical expression of the feasible region model, a unit for calculating the boundary surface of the feasible region, a unit for establishing the thrust allocation optimization problem, a unit for introducing the feasible region boundary constraints into the optimization problem, and a unit for iteratively optimizing and calculating the thrust allocation result. Specifically: the unit for determining the upper and lower limits of the control quantity obtains the upper and lower limits of the control quantity at the current moment through calculation and conversion based on the input states of the waterjet propellers at the previous time step and the performance constraints of the waterjet propellers; the unit for establishing the mathematical expression of the feasible region model obtains the mathematical model expression of the feasible region for the current control cycle through vector synthesis relationships based on the upper and lower limits of the control quantity obtained in the previous unit; the unit for calculating the feasible region... The boundary surface unit, based on the feasible region expression of the current control cycle obtained from the previous unit, obtains the expression of the surface patch constituting the outer surface of the feasible region; the thrust allocation optimization problem establishment unit defines the thrust allocation optimization problem through a weighted quadratic error function based on the input expected vector force and the upper and lower limit conditions of the control quantity at the current moment; the feasible region boundary constraint introduction optimization problem unit, based on the optimization problem established in the previous unit, rewrites the upper and lower limit constraints of the control quantity into feasible region boundary surface constraints through distance relaxation variables, and incorporates them into the optimization problem expression to obtain a computation-oriented optimization problem; finally, the iterative optimization calculation thrust allocation result unit performs iterative calculation on the previously established optimization problem to obtain the optimal thrust allocation result, translates it into control commands, and sends them to the lower-level machine actuator.

[0007] Technical effect

[0008] This invention describes a waterjet propulsion system from a control logic perspective, using the resultant thrust and thrust component coefficients to construct a feasible region mathematical model. Compared to existing technologies that use main engine power, nozzle angle, and inverted bucket angle as independent variables, this modeling approach better aligns with control logic and thrust distribution needs. The correlation between independent variables and motion control is closer, effectively reducing the number of independent variables and achieving decoupling between different independent variables. This also effectively reduces the complexity of boundary constraints and the difficulty of subsequent mathematical calculations. Furthermore, this invention solves for the mathematical expression of the outer surface of the feasible region and incorporates it into an optimization problem. For cases where the desired vector force falls outside the feasible region, the three-dimensional spatial search of the optimization problem is reduced to a two-dimensional distance search, lowering the difficulty of handling constraints and improving computational convergence speed. This invention redefines the concept of closest approximation by incorporating weight coefficients into the optimization problem and performing iterative optimization calculations. When the desired vector force falls outside the feasible region, this invention prioritizes motion control on the degrees of freedom with higher weights during the control process. After the errors on these degrees of freedom converge, the motion errors on the secondary degrees of freedom are then processed. This process is continuously repeated during the control process to realize the desired vector thrust on different degrees of freedom step by step, achieving the motion errors that converge in turn, thus achieving a feasible and relatively good control effect.

[0009] This invention provides a complete analytical method and modeling approach for describing the feasible region of vector thrust in waterjet propulsion. It addresses the problem that existing technologies cannot effectively handle thrust distribution when the desired vector force falls outside the feasible region, leading to force (or torque) in some degrees of freedom being opposite to the desired force (or torque), thus causing motion control failure. Compared to existing technologies that typically use main engine power, nozzle angle, and the deflection angle of the water flow by the inverted bucket as independent variables, the relationship between these three variables and vector thrust is not intuitive, and the influence of these three variables on vector thrust is coupled, resulting in a complex modeling structure. This invention achieves a clearer and more intuitive description of the feasible region and decoupling of independent variables through feasible region modeling based on control logic. Compared to existing technologies that typically use artificially added constraints to preserve the convexity of the optimal solution search space, essentially discarding some feasible solutions and wasting some of the waterjet propulsion's potential performance, this invention achieves iterative optimization calculations throughout the entire feasible region by processing the feasible region boundary, without discarding any solutions within the feasible region, thus enabling a more complete utilization of the waterjet propulsion's performance. Attached Figure Description

[0010] Figure 1 This is a flowchart of the present invention;

[0011] Figure 2 Axonometric drawing and three-view drawing of the feasible region for vector propulsion of dual waterjet propulsion;

[0012] Figure 3This is a schematic diagram of an experimental dual-waterjet propulsion unmanned surface vessel platform.

[0013] Figure 4 A schematic diagram of the two waterjet propulsion units mounted on the experimental dual-waterjet propulsion unmanned surface vessel;

[0014] Figure 5 This is a schematic diagram of the test site;

[0015] Figure 6 This is a schematic diagram of the trajectory for the comparative test of lateral movement;

[0016] Figure 7 A schematic diagram illustrating the change in the contribution of position error during lateral motion control;

[0017] Figure 8 This is a schematic diagram of the distribution and tracking curve of the desired vector force by a conventional thrust allocation algorithm;

[0018] Figure 9 A schematic diagram of the vector force position at different times for a conventional thrust allocation algorithm;

[0019] Figure 10 This is a schematic diagram of the tracking curve for the allocation of the desired vector force by the thrust allocation algorithm based on the feasible region.

[0020] Figure 11 This is a schematic diagram of the vector force position at different times for the thrust allocation algorithm based on the feasible region;

[0021] Figure 12 A schematic diagram of the control motion trajectory for thrust allocation with different weighting coefficients;

[0022] Figure 13 A schematic diagram comparing motion errors controlled by thrust allocation with different weighting coefficients. Detailed Implementation

[0023] like Figure 1 As shown, this embodiment relates to a waterjet propulsion vector thrust allocation method based on a feasible domain, including:

[0024] Step 1) Feasible domain modeling, specifically including:

[0025] 1.1) Determine the upper and lower limit conditions, specifically including:

[0026] 1.1.1) Based on the main engine power of the left and right water jet thrusters at the previous moment, the jet velocity of the left and right water jet thrusters at the previous moment is obtained, specifically: , ,in: This is the input power from the main engine to the left and right water jet propulsion units at the previous moment. It is the average velocity of the water flow at the nozzle around the previous moment. It is the density of water. It is gravitational acceleration. It is the nozzle cross-sectional area. It refers to the power absorption efficiency of the waterjet propulsion system. This is the nozzle loss coefficient. The loss coefficient, The kinetic energy influence coefficient is... The average inflow velocity before the inlet. The average lift height of the water flow from the inlet to the nozzle;

[0027] 1.1.2) Based on the jet velocities of the left and right water jet thrusters at the previous moment, combined with the nozzle angles and the angle of the reversing bucket at the previous moment, the thrust components of the left and right water jet thrusters at the previous moment are obtained, specifically: ,in: These are the nozzle angles of the left-side waterjet propulsion unit and the angle of the reversing bucket at the previous moment. These are the nozzle angles of the right-side waterjet propulsion unit and the angle of the reversing bucket at the previous moment. These are the longitudinal and lateral components of the thrust from the left-side waterjet propulsion unit at the previous moment. These are the longitudinal and lateral components of the thrust from the right-side waterjet propulsion unit at the previous moment. These are the ship's longitudinal and lateral speeds. It is the boundary layer momentum influence coefficient. and These are the longitudinal thrust and lateral thrust loss coefficients, respectively.

[0028] 1.1.3) Using the thrust components of the waterjet propulsion system obtained from the previous moment, the resultant thrust and thrust component coefficients of the waterjet propulsion system from the previous moment can be calculated, specifically as follows: ,in: These are the calculated resultant thrust and thrust component coefficients of the left waterjet propulsion unit from the previous moment. It is the calculated resultant thrust and thrust component coefficient of the right waterjet propulsion unit at the previous moment.

[0029] 1.1.4) Based on the operating performance of the waterjet propulsion unit to be deployed, input the performance constraints of the waterjet propulsion unit, including: the maximum positive thrust of the left waterjet propulsion unit. Maximum negative thrust Maximum nozzle angle Maximum thrust change within a single control cycle Maximum change in nozzle angle within a single control cycle and the maximum positive thrust of the right water jet propulsion unit Maximum negative thrust Maximum nozzle angle Maximum thrust change within a single control cycle and the maximum change in nozzle angle within a single control cycle .

[0030] 1.1.5) Obtain the upper and lower limit constraints of the control quantity at the current moment, including: ,in: The resultant thrust of the left waterjet propulsion unit is respectively The lower and upper limits, These are the thrust components of the left waterjet propulsion unit. The lower and upper limits, The resultant thrust of the right-side waterjet propulsion unit is respectively The lower and upper limits, These are the thrust component coefficients of the right-side waterjet propulsion unit. The lower and upper limits.

[0031] 1.2) Establishing the mathematical expression of the feasible region: Based on the upper and lower limit conditions of the control quantity at the current moment obtained in step 1.1, a mathematical model of the feasible region of the vector thrust of the dual waterjet propeller in the current control cycle is established, specifically as follows: , ,in: These are the longitudinal component, lateral component, and yaw torque of the vector thrust generated by the two waterjet propulsion units, respectively. For feasible regions, This is a vector composition function. It is the longitudinal distance of the thruster from the center of gravity. It is the lateral distance of the thruster from the center of gravity;

[0032] 1.3) Calculate the feasible region interface: For the feasible region of the current control cycle established in step 1.2, its outer boundary surface includes six major categories of surfaces. Each major category of surface includes four surface patches. For each fixed surface patch, of the four control quantities—the resultant thrust of the left and right water jet thrusters and the thrust component coefficient—two control quantities take the limit values, and the other two control quantities vary within the upper and lower limits. The feasible region of the dual-jet propulsion vector thrust is drawn in three-dimensional space, and its isometric view and three-view drawing are as follows: Figure 2 As shown.

[0033] The aforementioned major categories of curved surfaces include:

[0034] A) Take the limit value , The surface expression after eliminating the independent variable through algebraic transformation is: ,in: , , , Take the limit value , Freedom; Matrix: ;when hour: Substitute The expression for the surface is obtained by: ,in: , ,when At that time, the surface expression after algebraic transformation is: ,in: , .

[0035] B) Take the limit , Freedom; elimination of independent variables through algebraic transformation The subsequent surface expression is: ,in: , ;

[0036] C) Take the limit , Freedom; elimination of independent variables through algebraic transformation The subsequent surface expression is: ,in: , ;

[0037] D) Take the limit , Freedom; elimination of independent variables through algebraic transformation The subsequent surface expression is: ,in: , ;

[0038] E) Take the limit , Freedom; elimination of independent variables through algebraic transformation The subsequent surface expression is: ,in: , ;

[0039] In the aforementioned limit values: or , or , or , or .

[0040] Step 2) Solving the thrust distribution optimization problem, specifically including:

[0041] 2.1) Establish the thrust distribution optimization problem: , ,in: , , , , These are weighting coefficients; The desired vector thrust output by the controller; Indicates It is a function with the independent variable.

[0042] 2.2) Introducing feasible region boundary constraints into the optimization problem: The upper and lower limit constraints of the four control variables are rewritten as feasible region boundary surface constraints, and these are incorporated into the optimization problem through relaxation variables. The feasible region boundary constraints of the dual waterjet thruster vector thrust are rewritten as obstacle functions and introduced into the original optimization problem. The original problem is then rewritten as an equivalent optimization problem with obstacle functions. , ,in: , , These are the coefficients of the barrier function. These are introduced slack variables. It is the distance from the vector force point to the boundary of the feasible region. For the feasible region of vector thrust of dual waterjet propulsion, The outer boundary surface of the feasible region (consisting of the six major categories of surfaces given above) This is the implicit expression for the outer boundary surface of the feasible region after simplification. , , , ;

[0043] 2.3) Iterative optimization calculation of thrust allocation results, specifically including:

[0044] 2.3.1) Based on the optimization problem established in step 2.2, the optimization conditions are calculated iteratively. First, Lagrange multipliers are introduced into this problem. Construct the Lagrange function After KKT conditional expansion, we get: Among them: residual ; Perform a first-order expansion on the iteration point to obtain , , , The superscript k represents the k-th iteration point. Considering the continuity of the vector motion of the waterjet propulsion ship, it is recommended that the initial iteration point (i.e., step 0) is generally taken as the result of the previous round of thrust distribution.

[0045] 2.3.2) Calculate the iteration step size: First, calculate the maximum feasible step size. Then, update the variables, determine the convergence of the step size, and define the criteria for judgment, including... , , , , When the new point satisfies Then update the barrier function coefficients. Proceed to the next calculation step; if the new point does not meet the requirements, the step size needs to be reduced. And then re-evaluate the convergence. It is a manually set reduction factor; finally, the termination condition is judged.

[0046] The termination conditions include:

[0047] I) Optimization calculation stops when the residual is less than the set value: ;

[0048] II) The change in the objective function satisfies the acceptable condition for several consecutive cycles: ;

[0049] III) The number of iterations exceeds the set maximum number of iterations: .

[0050] Step 3) Translate the optimization conditions into control instructions: Iterate through Step 2 to obtain the optimization conditions. Based on the thrust characteristic curves of the deployed waterjet propulsion units, the resultant thrust and thrust component coefficients of the left and right waterjet propulsion units are translated into main unit input power, nozzle angle, and reversing bucket angle control commands, which are then sent to the lower-level machine for execution.

[0051] Through specific experiments, a dual-waterjet propulsion unmanned surface vessel (USV) was used as the test platform. This USV is 3.5 meters long, 1.1 meters wide, and has a displacement of 150 kilograms. It is equipped with two asynchronously controlled small waterjet propulsion units, achieving a maximum speed of 16 knots. A photo of the USV is shown below. Figure 3 As shown, the two water jet propulsion units mounted on it are arranged as follows: Figure 4 As shown, the test site is located in Rizhao City, Shandong Province, China, and is directly connected to the actual sea area, effectively simulating the wind, wave, and current environmental disturbances under real sea conditions. A photograph of the test site is shown below. Figure 5 As shown.

[0052] To verify the performance advantages of the vector thrust allocation algorithm based on feasible region proposed in this invention compared with existing technologies, this experiment conducted a set of comparative experiments to compare the motion control effects achieved by different thrust allocation methods under the same motion and the same controller control, and to analyze the advantages of the algorithm proposed in this invention compared with conventional algorithms when the expected vector force falls outside the feasible region.

[0053] The conventional thrust allocation algorithm used as a control group is a thrust allocation method designed in our laboratory's early research for a single-handle vector control system of a manned, dual-waterjet propulsion vessel. Its optimization model uses a quadratic cost function with relaxed variables, and a quadratic programming method is used to solve the local optimization problem to obtain the thrust magnitude and direction. The thrust allocation optimization model is as follows: ,in: , , , , , , , , , subscript The variables used to label the control group algorithm definition are similar in symbol to some of the variables in this invention, but have different physical meanings. It is a vector of four thrust components. As slack variables, Here is the weight matrix for the slack variables. For the desired vector thrust, It is a vector composite matrix. To account for the thrust boundary vector under the nozzle rotation constraint, The coefficients are linear superposition coefficients for the boundary thrust vector. These are the longitudinal and lateral components of the thrust from the left-side waterjet propulsion unit. These are the longitudinal and lateral components of the thrust from the right-side waterjet propulsion unit. It is the longitudinal distance of the thruster from the center of gravity. It is the lateral distance of the thruster from the center of gravity. The desired vector force consists of three components (longitudinal component, lateral component, and turning moment). For nozzle angle, The left and right nozzle angles at the previous moment. The maximum value of the nozzle angle is the same as that in the equation. This represents the maximum change in nozzle angle within a control cycle. However, since the water jet propulsion used in this experiment is fully electric and has a fast response speed, the maximum change in nozzle angle is taken as the entire range of change.

[0054] The lateral motion exhibits a clear distinction between primary and secondary forces across different control degrees of freedom. Furthermore, during the motion, the desired vector force moves from within the feasible region to outside the feasible region as the heading angle error changes. This clearly demonstrates the difference between the conventional thrust allocation algorithm and the thrust allocation algorithm proposed in this invention.

[0055] This experiment used the same PID controller (without any output constraints) to control an unmanned surface vessel (USV) to move laterally in real water with environmental interference: maintaining the bow pointing due south (i.e., a bow angle of 180 degrees, corresponding to the negative X-axis in the diagram) while controlling the USV to move laterally due east (corresponding to the positive Y-axis in the diagram). The controller took the position error in each of the three degrees of freedom as input and output the desired vector control force. Thrust allocation was performed using both the control group's thrust allocation algorithm and the thrust allocation algorithm proposed in this invention. The motion trajectory and error of the USV were compared to verify the performance advantage of the thrust allocation algorithm proposed in this invention compared to the conventional algorithm. The control motion trajectories obtained by the two thrust allocation algorithms are shown below. Figure 6 As shown: Cases 1-3 use the conventional thrust allocation algorithm, while Cases 4-6 use the thrust allocation algorithm proposed in this invention. The red lines represent the desired trajectory, the blue dashed lines represent the actual trajectory of the unmanned surface vessel (USV), and the red dashed lines on either side of the desired trajectory represent the boundary where the position deviation relative to the desired trajectory is 0.3L, used to evaluate the performance of vector motion tracking. The green dashed lines represent the offset distance of the average position error relative to the desired trajectory throughout the entire motion process. To quantitatively describe the control effect throughout the entire control process, this experiment defines the dimensionless average motion error of the lateral motion. ,in: To control the number of steps during the movement, To control the first The positional error of the unmanned surface vessel (USV) to the desired trajectory during movement. The figure shows the average error of the six experimental trajectories. Table 1 shows the average error of each trajectories shown in the figure.

[0056] Table 1

[0057] Observing Cases 1-3 reveals that using conventional thrust distribution methods to control the unmanned surface vessel (USV) fails to produce stable lateral movement in real-world waters with environmental disturbances. Although the trajectories of the three movements are not identical, a common pattern emerges from the three failed lateral movement trajectories: when the bow angle is less than 180 degrees, the USV can complete a relatively good lateral movement, with the bow angle slowly increasing towards 180 degrees, but the longitudinal position error of the USV cannot be effectively converged; when the bow angle exceeds 180 degrees, the bow angle not only fails to converge effectively to 180 degrees, but further increases and rapidly becomes uncontrollable, leading to overall motion control failure. This phenomenon is most prominent in Cases 1 and 3. In Case 2, because the initial bow angle is closer to 180 degrees, the section of the trajectory with a bow angle less than 180 degrees is relatively short, but it still contrasts with the significantly increased error in the latter half.

[0058] Cases 4-6 present the control results using the thrust allocation algorithm based on the feasible region proposed in this invention. The weight coefficients for the optimization problem are set to Q1=Q2=100 and Q3=1. Their physical meaning is that during thrust allocation, priority is given to the allocation of the longitudinal vector component XT and the lateral vector component YT. That is, in motion control, more attention is paid to the control of position error. After the position error converges, the bow angle of the unmanned surface vessel (USV) is adjusted. Based on the above thrust allocation logic, it is observed that in the three sets of experimental trajectories, the position error and bow angle error of the USV converge alternately. A relatively good lateral movement motion control effect is achieved through step-by-step control.

[0059] To better describe this change in the control phase, the contribution of the position error in each control cycle to the overall motion position error is defined. The contribution curve of motion position error is as follows: Figure 7 As shown, the horizontal axis represents the percentage of the total distance traveled by the unmanned surface vessel (USV) during its lateral movement. Since the lateral movement distance varies for each group, normalization is applied. It can be seen that there is a significant increase in speed in the middle of the three curves in Cases 1-3, which aligns with the analysis above. Meanwhile, the three curves in Cases 4-6 all exhibit significant oscillations, confirming the analysis result above regarding the convergence of position error periodic control.

[0060] The loss of control in Cases 1-3 occurred because the conventional thrust distribution algorithm failed. When the unmanned surface vessel (USV) moves laterally to port, the waterjet propulsion system needs to generate a vector component pointing towards port. However, since the USV's waterjet propulsion system is located at the stern (behind the center of gravity), this vector component naturally generates a clockwise turning moment. When the bow angle is less than 180 degrees, this naturally generated clockwise turning moment coincides with the convergence direction of the bow angle error. Therefore, the USV... It can complete a relatively stable lateral movement, but when the bow angle is greater than 180 degrees, the naturally generated clockwise bow turning torque is opposite to the convergence direction of the bow angle error. At this time, the unmanned surface vessel (USV) needs a counterclockwise bow turning torque. In other words, when the bow angle is greater than 180 degrees, the control of the USV to maintain lateral movement to port and the control of the bow angle are contradictory. That is, the vector force expected by the controller falls outside the feasible region. At this time, the conventional thrust distribution algorithm fails, resulting in loss of motion control.

[0061] To better illustrate the process, we selected the expected vector force output by the controller and the vector force achieved after conventional thrust distribution during the control process corresponding to Case 1, where the phenomenon was most pronounced. Figure 8 As shown, the desired vector force output by the controller and the vector force achieved after conventional thrust distribution are shown in the corresponding control process. It can be seen that when the heading angle is less than 180 degrees, the distribution and tracking performance of the lateral force YT and the turning torque NT are good, so the unmanned surface vessel can be controlled to make a relatively stable lateral movement. However, when the heading angle is greater than 180 degrees (i.e. after t=60s), the desired vector force falls outside the feasible region, and the tracking performance of the lateral force YT and the turning torque NT deteriorates. The direction of the turning torque NT is opposite to the direction required by the motion control, which further expands the heading angle error and ultimately leads to the failure of motion control. Figure 9 This is a visual representation of the landing points of the expected vector force output by the controller and the actual vector force before and after the heading angle exceeds 180 degrees. As can be seen from the figure, when the heading angle is less than 180° (i.e., before t=60s), the expected vector force output by the controller is within the feasible region, and the actual vector force implemented by the conventional thrust allocation algorithm has a relatively good tracking effect. However, when the heading angle is greater than 180° (i.e., after t=60s), the expected vector force output by the controller gradually approaches the edge of the feasible region and eventually exceeds the feasible region. At this time, the conventional thrust allocation algorithm cannot cope with it, and the actual vector force hovers near the surface of the feasible region.

[0062] The vector thrust allocation method based on feasible region proposed in this invention can effectively solve the problem of conventional algorithm failure by relying on step-by-step control generated by weight coefficients. Taking Case 6 as an example, its motion trajectory corresponds to the control result using the thrust allocation algorithm based on feasible region proposed in this invention. The weight coefficients of the optimization problem are Q1=Q2=100 and Q3=1. Their physical meaning is: when allocating thrust, priority is given to the allocation of longitudinal vector component XT and lateral vector component YT. That is, in motion control, more attention is paid to the control of position error. After the position error is converged, the bow angle of the unmanned surface vessel is adjusted. Based on the above thrust allocation logic, the position error and bow angle error of the unmanned surface vessel are alternately controlled and converged during the motion process. A relatively good lateral movement motion control effect of the unmanned surface vessel is achieved through distributed control. The average motion error of the entire motion process is 0.23 times the length of the vessel.

[0063] like Figure 10 As shown, the desired vector force output by the controller during the corresponding control process and the vector force realized after conventional thrust distribution are shown. It can be seen that the tracking performance of the longitudinal vector component XT and the lateral vector component YT is very good throughout the entire control process. However, the tracking of the bow torque NT is selective. When the desired vector force falls outside the feasible region, the distribution and tracking of XT and YT are prioritized, and NT is appropriately abandoned. After the position error converges, NT is then distributed and tracked, and the bow angle error caused by the previous abandonment of NT is compensated. Therefore, the bow angle of the unmanned surface vessel oscillates continuously around 180 degrees. Figure 11 This is a visual representation of the landing points of the desired vector force output by the controller and the actual vector force during motion. It shows that when the desired vector force falls within the feasible region, the vector force achieved through thrust allocation based on the feasible region can track the desired vector force very well (i.e., the green dot and the yellow triangle in the diagram coincide). When the desired vector force falls outside the feasible region, the allocated vector force lands on the boundary of the feasible region, as close as possible to the desired vector force (e.g., the red dot cloud in region 1 corresponds to the purple triangle cloud on the feasible region boundary in region 2). Furthermore, this closest thrust allocation is not simply the closest geometrically, but based on different weights (e.g., the purple triangle on the red dot cloud above the NT=0 plane in region 3 does not land on the nearest lower feasible region boundary, but rather on the boundary in region 4, which is farther away). Figure 10 The NT achieved in this invention significantly exceeds the peak portion of the expected NT. By using weighting coefficients, the thrust allocation algorithm based on feasible region proposed in this invention can effectively cope with situations where the expected vector force falls outside the feasible region, and will not experience control failures like conventional thrust allocation algorithms.

[0064] During the fan-shaped motion of the vessel, all three degrees of freedom are constantly changing without a clear distinction between primary and secondary elements, allowing for a direct demonstration of the impact of changing the weighting coefficients on the control effect. This experiment uses a classic PID controller (without any output constraints) to control the unmanned surface vessel (USV) in a fan-shaped motion: while keeping the bow pointing towards the center of the circle, the USV is controlled to move clockwise along an arc with a radius of 10 meters. Different optimization problem weighting coefficients are used to distribute the thrust of the expected vector force output by the PID controller. The motion trajectory and error of the USV are compared to verify the impact of the weighting coefficients introduced in the thrust distribution algorithm proposed in this invention on the control effect, and to provide a reference for adjusting the weighting coefficients in practical applications. Case 1: Q1=Q2=100, Q3=1; Case 2: Q1=100, Q2=10, Q3=100. The motion control trajectories obtained from the thrust distribution experiments under the two cases are as follows: Figure 12 As shown:

[0065] Figure 13 As shown, Figure 12 The motion error of the two sets of experiments is represented by the horizontal axis β, which is the angle swept by the line connecting the position of the unmanned surface vessel to the center of the fan-shaped motion trajectory, with clockwise as positive.

[0066] observe Figure 12 and Figure 13 The study found that the weighting coefficients affect the control effect in three aspects:

[0067] Increasing the weighting coefficients in a specific degree of freedom can effectively improve the motion control performance in that degree of freedom. Compared to Case 1, Case 2 reduces the focus on the lateral vector component YT while increasing the focus on the bow torque NT. Therefore, the position error of Case 1 is relatively small and stable, while the position error of Case 2 is significantly larger than that of Case 1, and there are more violent oscillations in the range of β between 80 and 140 degrees. Conversely, the oscillation of the heading angle error in Case 1 is more violent than that in Case 2, specifically in terms of longer oscillation duration and higher frequency.

[0068] Motion performance on degrees of freedom with larger weighting coefficients is generally better than that on degrees of freedom with smaller weighting coefficients. For example, in Case 1, the thrust distribution algorithm prioritizes the allocation of longitudinal vector component XT and lateral vector component YT during operation, thus exhibiting smaller position errors in the control effect. However, the bow angle error oscillates more violently during the control process, requiring frequent corrections to the bow angle.

[0069] When the desired vector force falls outside the feasible region, gradual motion control through weighting coefficients can achieve a relatively ideal motion effect. This phenomenon is... Figure 6 This is also reflected in the text.

[0070] In this experiment, the IPOPT algorithm is used to solve the vector thrust allocation nonlinear programming problem, as shown in the formula. As shown, the weighting coefficients are implicitly included in the original objective function. In the solution process, the weighting coefficients directly appear in the Lagrangian function and influence the equations in the KKT conditions. Therefore, the weighting coefficients not only determine the relative penalty intensity of different degrees of freedom in the objective function, but also affect the direction of Newton iterations and the local optimum. To further illustrate the influence of the weighting coefficients on thrust distribution, let's take the partial derivative of the distribution error with respect to the Lagrangian function. Under the KKT conditions, we can obtain: , , As can be seen from the above equation, when the feasible region condition remains unchanged (i.e., the distance function...), (Unchanged), the error in each degree of freedom is inversely proportional to the weighting coefficient; that is, the larger the weighting coefficient, the smaller the error allocated to that degree of freedom. This theoretically explains why increasing the weight coefficients in a specific degree of freedom can effectively improve the motion control effect in that degree of freedom.

[0071] When multiple degrees of freedom cannot be simultaneously and precisely satisfied within the current feasible region, the IPOPT solver will distribute the error by minimizing the cost under the constraints according to the weight coefficients: The distance function constructed in this experiment The spatial Euclidean distance is used, which is of the same order for the three degrees of freedom. Therefore, the error sharing relationship can be further simplified to: The relationship implies that when allocation cannot be simultaneously satisfied, the degree of freedom with a larger weight is assigned a smaller error, while the degree of freedom with a smaller weight is more likely to be sacrificed to satisfy the feasible region constraint. This theoretically explains the phenomenon in vector motion control where the motion performance of the degree of freedom with a larger weight coefficient is often inferior to that of the degree of freedom with a smaller weight coefficient.

[0072] However, this prioritization of high-weight degrees of freedom is not permanent. In closed-loop vector motion control systems, the IPOPT solver re-solves the problem based on the current state at each time step. High-weight degrees of freedom receive priority error compression during conflict phases; once their errors are reduced to a smaller order of magnitude, the penalty for these terms in the objective function decreases, and subsequent iterations prioritize correcting errors on the remaining degrees of freedom. During the IPOPT solver's solution of the optimization problem, the instantaneous driving effect of each degree of freedom on the solver can be represented by the gradient of the objective function, specifically: ,in: , , , Therefore, after several motion control cycles, the motion error of a high-weighted degree of freedom gradually converges to 0. The expected control force / torque for that degree of freedom decreases, making it easier to achieve through allocation within the feasible region. Thus, the allocation error on that degree of freedom will gradually converge to 0. Its corresponding gradient term will also gradually converge to 0, that is... At this point, even if the weighting coefficient is large, its influence on the optimization solver is still weak. When performing thrust allocation iterative calculations at this time, the solver will pay more attention to the degrees of freedom that still have large allocation errors. This theoretically explains the phenomenon that when the desired vector force falls outside the feasible region, the gradual motion control achieved through the weighting coefficient can achieve a more ideal motion effect.

[0073] Compared with existing technologies, the invention can effectively deal with situations where the desired vector force falls outside the feasible region by using weighting coefficients, and will not experience control failures like conventional thrust distribution algorithms.

[0074] The specific implementations described herein may be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of this invention. The scope of protection of this invention is defined by the claims and is not limited by the specific implementations described herein. All implementation schemes within the scope thereof are subject to the constraints of this invention.

Claims

1. A method for allocating vector thrust in waterjet propulsion based on a feasible domain, characterized in that, Starting from the control logic, a feasible region model of the vector thrust of the dual waterjet propulsion is established. Distance relaxation variables are introduced to deal with the constraints based on the boundary conditions of the feasible region. After dealing with the thrust allocation problem in the case of no solution through an optimization algorithm with weighted coefficients, the allocation result of each waterjet propulsion is translated into control commands and output.

2. The waterjet propulsion vector thrust distribution method based on feasible domain according to claim 1, characterized in that, Specifically, it includes: Step 1) Feasible domain modeling, specifically including: 1.1) The conditions for determining the upper and lower limits include: ,in: The resultant thrust of the left waterjet propulsion unit is respectively The lower and upper limits, These are the thrust components of the left waterjet propulsion unit. The lower and upper limits, The resultant thrust of the right-side waterjet propulsion unit is respectively The lower and upper limits, These are the thrust component coefficients of the right-side waterjet propulsion unit. The lower and upper limits; 1.2) Establish the mathematical expression for the feasible region, specifically: , ,in: These are the longitudinal component, lateral component, and yaw torque of the vector thrust generated by the two waterjet propulsion units, respectively. For feasible regions, This is a vector composition function. It is the longitudinal distance of the thruster from the center of gravity. It is the lateral distance of the thruster from the center of gravity; 1.3) Calculate the feasible region interface: For the feasible region of the current control cycle established in step 1.2, its outer boundary surface includes six major categories of surfaces. Each major category of surface includes four surface patches. For each fixed surface patch, of the four control quantities, two control quantities take the limit values ​​and the other two control quantities vary within the upper and lower limits. Step 2) Solve the thrust distribution optimization problem; Step 3) Translate the obtained optimization conditions into control commands.

3. The waterjet propulsion vector thrust distribution method based on feasible domain according to claim 1, characterized in that, Step 2 specifically includes: 2.1) Establish the thrust distribution optimization problem: , ,in: , , , , These are weighting coefficients; The desired vector thrust output by the controller; Indicated by A function of the independent variable; 2.2) Introducing feasible region boundary constraints into the optimization problem: The upper and lower limit constraints of the four control variables are rewritten as feasible region boundary surface constraints, and these are incorporated into the optimization problem through relaxation variables. The feasible region boundary constraints of the dual waterjet thruster vector thrust are rewritten as obstacle functions and introduced into the original optimization problem. The original problem is then rewritten as an equivalent optimization problem with obstacle functions. , ,in: , , These are the coefficients of the barrier function. These are introduced slack variables. It is the distance from the vector force point to the boundary of the feasible region. For the feasible region of vector thrust of dual waterjet propulsion, The outer boundary surface of the feasible region. This is the implicit expression for the outer boundary surface of the feasible region after simplification. , , , ; 2.3) Iterative optimization calculation of thrust allocation results.

4. The waterjet propulsion vector thrust distribution method based on feasible domain according to claim 3, characterized in that, Step 2.3 specifically includes: 2.3.1) Based on the optimization problem established in step 2.2, the optimization conditions are calculated iteratively, specifically as follows: Among them: residual ; Perform a first-order expansion on the iteration point to obtain , , , The superscript k represents the k-th iteration point; 2.3.2) Calculate the iteration step size: First, calculate the maximum feasible step size. Then, update the variables, determine the convergence of the step size, and define the criteria for judgment, including... , , , , When the new point satisfies Then update the barrier function coefficients. Proceed to the next calculation step; if the new point does not meet the requirements, the step size needs to be reduced. And re-perform the convergence check, where It is a manually set reduction factor; finally, the termination condition is judged.

5. The waterjet propulsion vector thrust distribution method based on feasible domain according to claim 4, characterized in that, The termination conditions include: I) Optimization calculation stops when the residual is less than the set value: ; II) The change in the objective function satisfies the acceptable condition for several consecutive cycles: ; III) The number of iterations exceeds the set maximum number of iterations: .

6. The waterjet propulsion vector thrust distribution method based on feasible domain according to claim 1, characterized in that, Step 3 specifically involves iteratively optimizing step 2 to obtain the optimal conditions. Based on the thrust characteristic curves of the deployed waterjet propulsion units, the resultant thrust and thrust component coefficients of the left and right waterjet propulsion units are translated into main unit input power, nozzle angle, and reversing bucket angle control commands, which are then sent to the lower-level machine for execution.

7. A waterjet propulsion vector thrust distribution system based on a feasible domain for implementing the method of any one of claims 1-6, characterized in that, include: The system consists of six parts: a unit for determining the upper and lower limits of the control quantity, a unit for establishing the mathematical expression of the feasible region model, a unit for calculating the boundary surface of the feasible region, a unit for establishing the thrust allocation optimization problem, a unit for introducing the boundary constraints of the feasible region into the optimization problem, and a unit for iteratively optimizing and calculating the thrust allocation result. Among them, the unit for determining the upper and lower limits of the control quantity obtains the upper and lower limits of the control quantity at the current moment by calculating and converting the state of the water jet propulsion unit and the performance constraints of the water jet propulsion unit at the previous moment. The feasible region model mathematical expression unit, based on the upper and lower limit conditions of the control quantity at the current moment obtained from the previous unit, obtains the mathematical model expression of the feasible region for the current control cycle through vector composition relationships. The feasible region boundary surface calculation unit, based on the feasible region expression for the current control cycle obtained from the previous unit, obtains the expression of the surface patches constituting the outer surface of the feasible region. The thrust allocation optimization problem establishment unit, based on the input expected vector force and the upper and lower limit conditions of the control quantity at the current moment, defines the thrust allocation optimization problem through a weighted quadratic error function. The feasible region boundary constraint introduction optimization problem unit, based on the optimization problem established in the previous unit, rewrites the upper and lower limit constraints of the control quantity into feasible region boundary surface constraints through distance relaxation variables and incorporates them into the optimization problem expression, resulting in a computation-oriented optimization problem. Finally, the iterative optimization calculation thrust allocation result unit performs iterative calculation on the previously established optimization problem to obtain the optimal thrust allocation result, translates it into control commands, and sends them to the lower-level machine execution mechanism.

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