Under-actuated water surface unmanned ship trajectory planning method and system capable of reducing output redefinition error

Abstract

The invention discloses an under-actuated water surface unmanned ship trajectory planning method and system capable of reducing output redefinition errors. According to the method, aiming at the tracking error problem caused by changing a controlled object from a centroid to an offset point by using output redefinition, each point of an expected trajectory is translated, and sideslip angle compensation is introduced in the translation direction, so that a new compensation offset point expected trajectory is generated. When the deviation point of the unmanned ship tracks the new trajectory, the mass center of the unmanned ship can accurately move along the original expected trajectory. The system comprises a trajectory acquisition module, a kinematics parameter calculation module, a compensation trajectory generation module and a tracking control module which are used for implementing the method. According to the method, geometric tracking errors caused by output redefinition and a sideslip effect can be eliminated from the source, tracking error convergence of the mass center of the unmanned ship is ensured, and the precision and robustness of trajectory tracking are remarkably improved.

Description

Technical Field

[0001] This application belongs to the field of trajectory planning and motion control technology for underactuated unmanned surface vessels, specifically relating to an underactuated unmanned surface vessel trajectory planning method and system that reduces output redefinition error. Background Technology

[0002] In recent years, unmanned surface vehicles (USVs) have been increasingly widely used in marine environmental exploration, hydrographic mapping, fisheries production support, surface security patrols, and military applications due to their unique advantages such as low cost, high flexibility, long endurance, and ability to operate in dangerous or uninhabitable environments. In these complex tasks, motion control is the core and key to the autonomous navigation and operation of USVs, especially trajectory tracking control. This requires USVs not only to reach a designated location but also to arrive at a designated time, placing strict requirements on spatiotemporal synchronization.

[0003] However, most conventional unmanned surface vessels (USVs) are designed as typical underactuated systems. A key characteristic of these systems is that the number of independent control actuators (such as the main thruster and rudder) is less than the number of degrees of freedom they possess. Specifically, an USV moving on a two-dimensional water surface has three degrees of freedom: surge along the longitudinal axis, sway along the transverse axis, and yaw around its center of gravity. However, they typically only have a main thruster providing longitudinal thrust and rudders controlling the sway, lacking side thrusters that directly generate lateral forces, thus making it impossible to directly control sway motion. This inherent physical constraint poses a significant challenge to achieving high-precision trajectory tracking control. Furthermore, when subjected to external environmental disturbances such as wind, waves, and currents, or during large-angle turns, the hull inevitably sideslips, causing its actual direction of motion to deviate from the bow direction and thus from the preset trajectory.

[0004] To address this challenge, researchers in the field of control have proposed a series of control strategies, among which output redefinition is a widely adopted key method (L. Ye and Q. Zong, "Tracking control of an underactuated ship by modified dynamic inversion,"). ISA transactions(Vol. 83, pp. 100–106, 2018.). The core idea of ​​this strategy is to avoid underactuation by selecting specific variables as new control outputs, ensuring a definite relative relationship between the new output and the input parameters. This method no longer uses the ship's center of mass as the direct control object, but instead defines a new virtual "offset point" as the control target through coordinate transformation. This offset point is typically located on the ship's longitudinal axis at a distance δ from the center of mass (e.g., forward of the center of mass). With this setup, the controller can indirectly and effectively control the position of this offset point using the ship's surge and yaw motions. For this new "output" (i.e., the offset point) after coordinate transformation, the original underactuated system mathematically behaves as fully actuated, thus allowing the application of mature feedback control theory and effectively circumventing the control design challenges of underactuated systems.

[0005] While the output redefinition method theoretically solves the design difficulties of the controller, it introduces a new and significant problem in practical applications: geometric tracking error. The root cause of this error lies in the fact that there is always a physical positional deviation between the offset point and the center of mass. When the controller successfully drives the offset point precisely along the desired trajectory, the trajectory of the center of mass, as part of the rigid body, will inevitably deviate from the desired trajectory. Furthermore, the sideslip angle generated by the hull during motion—the angle between the hull's longitudinal axis and the actual velocity direction—further exacerbates this deviation, making the relationship between the actual trajectory and the desired trajectory of the center of mass even more complex.

[0006] Therefore, how to effectively compensate for the tracking error caused by the combined effects of output redefinition and sideslip to improve the trajectory tracking accuracy of the unmanned vessel's center of mass has become a key technical problem that urgently needs to be solved in the field of underactuated unmanned vessel control. Summary of the Invention

[0007] The purpose of this application is to provide a trajectory planning method for underactuated surface unmanned vessels that reduces output redefinition error. It aims to solve the problem of centroid trajectory tracking error caused by the deviation between the offset point and the centroid position and the influence of the sideslip angle when using the output redefinition control method in the prior art. Ultimately, it aims to achieve accurate tracking of the centroid to the original desired trajectory and ensure that the tracking error converges.

[0008] To achieve the above objectives, the technical solution adopted in this application is as follows: The method includes the following steps: Step (1): Obtain the original desired trajectory that the underactuated unmanned surface vessel needs to track. ,in These represent the coordinates in the Earth's fixed coordinate system { E In}, the expected trajectory is shaft and axial direction with time A changing function, where each point on the trajectory is determined by the position coordinates at a specific moment; Step (2): Calculate the tangent direction vector at each point on the original desired trajectory. ; Step (3), based on the sway speed of the unmanned vessel and sway speed Calculate the sideslip angle ; Step (4) convert the tangent direction vector of each point. Sideslip angle around this point The offset direction after compensation is obtained. , obtained This indicates that in order to keep the center of mass on its original trajectory, the offset point should be positioned relative to the orientation of the center of mass; Step (5): Move each point on the original desired trajectory along the offset direction. Translation distance Generate the desired trajectory of the new offset point. This formula is the final step in generating the new trajectory. It will take each point on the original desired trajectory ( , ) Along the compensation direction calculated in step 4 The distance was translated (The distance between the offset point and the centroid) thus generates the desired trajectory of the new offset point. ; Step (6): Control the unmanned vessel's offset point to track the new offset point's desired trajectory, so that the unmanned vessel's center of mass moves along the original desired trajectory. This trajectory has been pre-considered and compensated for the geometric deviation between the offset point and the center of mass, as well as the effects of the sideslip angle, so that the unmanned vessel's center of mass can accurately follow the original desired trajectory. Movement, thereby eliminating tracking errors.

[0009] In some embodiments of this application, the offset point is the position of a point on the ship's axis, denoted as... .

[0010] In some embodiments of this application, the coordinates of the offset point are: ,in The location of the ship's center of mass. This represents the distance between the offset point and the ship's center of mass. This is the ship's yaw angle.

[0011] In some embodiments of this application, in step (2), the tangent direction vector The calculation formula is: ,in These are the original expected trajectories. The derivative with respect to time.

[0012] In some embodiments of this application, in step (3), the sideslip angle The calculation formula is ,in , These are the ship's pitching and swaying speeds, respectively.

[0013] In some embodiments of this application, in step (4), the offset direction It is obtained by calculation using the rotation matrix.

[0014] Preferably, in step (4), the rotation matrix is ,and The rotation matrix here serves as a precise mathematical tool, transforming a dynamic physical quantity (sideslip angle) into a deterministic geometric transformation (vector rotation).

[0015] In some embodiments of this application, in step (5), the new trajectory The calculation formula is .

[0016] In some embodiments of this application, the tracking error of the unmanned vessel's center of mass converges when the offset point tracks the new trajectory using a control algorithm.

[0017] On the other hand, this application also provides an underactuated unmanned surface vessel trajectory planning system to reduce output redefinition error, comprising: The trajectory acquisition module is used to acquire the original desired trajectory that the underactuated unmanned surface vessel needs to track. ,in These represent the coordinates in the Earth's fixed coordinate system { E In}, the expected trajectory is shaft and axial direction with time A changing function, where each point on the trajectory is determined by the position coordinates at a specific moment; The kinematic parameter calculation module is used to calculate the original desired trajectory output by the kinematic parameter calculation module. Obtain the oscillation speed of the unmanned ship and sway speed According to the oscillation speed and sway speed Calculate the sideslip angle And calculate the tangent direction vector at each point on the original desired trajectory. ; The compensation trajectory generation module is used to generate the tangent direction vector output by the kinematic parameter calculation module. Sideslip angle around the trajectory point The offset direction after compensation And each point on the original desired trajectory is moved along this offset direction. Translate by preset distance To generate a new desired trajectory at the offset point. ; The tracking control module is used to control the unmanned surface vessel's offset point tracking to follow the new trajectory generated by the compensation trajectory generation module. This allows the center of mass of the unmanned vessel to move precisely along the original desired trajectory; The system works in concert with the aforementioned modules to achieve trajectory planning and tracking control using the methods described above.

[0018] Compared with existing technologies, the trajectory planning method and system constructed in this application have the following significant advantages: 1. Fundamentally Eliminate Geometric Errors: This method and system solve the geometric deviation problem caused by the output redefinition method at its root by actively planning a new compensatory trajectory. It ensures that when the offset point tracking task is completed, the centroid tracking task is also completed simultaneously, theoretically reducing the steady-state tracking error to zero.

[0019] 2. Precise Compensation for Sideslip Influence: This method and system introduce the sideslip angle β as a key variable into trajectory planning, dynamically compensating for the offset direction. This allows the unmanned vessel to maintain the accuracy of its center-of-gravity trajectory even when turning or experiencing significant sideslip due to lateral disturbances, significantly improving control robustness in complex dynamic environments.

[0020] 3. Strong compatibility and easy implementation: This method and system adopt a front-end trajectory planning strategy that can be combined with various mature back-end trajectory tracking controllers without fundamentally modifying existing control algorithms. It has good compatibility and engineering practice value. Attached Figure Description

[0021] Figure 1 The flowchart illustrates the underactuated surface unmanned vessel trajectory planning method for reducing output redefinition error provided in this application.

[0022] Figure 2 The diagram shows the unmanned vessel model and the location of the offset point, illustrating the geometric relationships between the Earth fixed coordinate system {E}, the ship coordinate system {b}, the center of mass, the offset point, and related kinematic variables.

[0023] Figure 3 This is a trajectory comparison diagram of circular trajectory tracking using the method of this application in Example 1.

[0024] Figure 4 The graph shows the position tracking error curve of the center of mass of the unmanned vessel when performing circular trajectory tracking using the method of this application in Example 1.

[0025] Figure 5 The image shown in Comparative Example 1 is a comparison of the trajectories when using the traditional output redefinition method for circular trajectory tracking, clearly demonstrating the steady-state error between the centroid trajectory and the desired trajectory.

[0026] Figure 6 As shown in Comparative Example 1, when using the traditional output redefinition method for circular trajectory tracking, the position tracking error curve of the unmanned vessel's center of mass shows that the error cannot converge.

[0027] Figure 7 This is a trajectory comparison diagram of sine curve trajectory tracking using the method of this application in Example 2.

[0028] Figure 8 This is a graph showing the position tracking error of the unmanned vessel's center of mass when using the method of this application to track a sinusoidal trajectory in Example 2.

[0029] Figure 9 The image shows a comparison of sine curve trajectories when using the traditional output redefinition method for tracking, as shown in Comparative Example 2. It reveals a significant tracking deviation.

[0030] Figure 10 As shown in Comparative Example 2, when using the traditional output redefinition method for sine curve trajectory tracking, the position tracking error curve of the unmanned vessel's center of mass shows that the error continues to oscillate and cannot converge. Detailed Implementation

[0031] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0032] Example 1: Circular trajectory tracking This embodiment aims to verify the effectiveness of the trajectory planning method proposed in this application in typical curved trajectory tracking scenarios.

[0033] This embodiment provides an underactuated unmanned surface vessel trajectory planning method to reduce tracking errors caused by the use of output redefinition control methods. The embodiment of this planning method follows the following... Figure 1 The steps are as follows: Step 1: Establish a mathematical model for the motion of the unmanned vessel: , This indicates the ship's position in a fixed Earth coordinate system. Indicates the ship's yaw angle. Indicates the velocity in the direction of the ship's sway. Indicates the speed in the direction of the ship's sway. This represents the angular velocity of the ship's turn. Indicates the ship's inertial mass. Represents the hydrodynamic damping constant. This represents the ship's controllable pitch thrust and yaw moment. These are the environmental disturbance forces and moments in the sway, roll, and yaw directions. The examples selected are: .

[0034] Step 2: Define the position of the offset point as follows: , It is the distance between the offset point and the center of mass along the ship's axis, as selected in the embodiment. The positional relationship between the offset point and the centroid is as follows: Figure 2 As shown, the coordinates of the centroid are ( , The coordinates of the offset point are ( , ).

[0035] Step 3: Represent the relationship between the desired trajectory and time in two-dimensional Euclidean space as follows: The desired trajectory selected in this embodiment is: .

[0036] Step 4: For each point on the desired trajectory, calculate its tangent direction vector. The formula is: .

[0037] Step 5: Obtain the velocity of the unmanned vessel in the sway direction using the inertial measurement unit. and velocity in the sway direction Through formula Calculate the sideslip angle .

[0038] Step 6: Convert the tangent direction vector at each point on the desired trajectory. Sideslip angle around this point The offset direction after compensation for sideslip is obtained. Rotation matrix for: Offset direction .

[0039] Step 7: Move each point on the desired trajectory along the offset direction Translation distance This allows us to obtain the expected trajectory of the new offset point, using the following formula: .

[0040] Step 8: By using the output redefinition control algorithm, the unmanned vessel's offset point tracks the desired trajectory of the new offset point. At this time, the center of mass of the unmanned vessel will move along the original desired trajectory.

[0041] The implementation example was verified in the Simulink simulation platform, with the ship's initial position set as follows. The simulation results are as follows Figures 3 to 4 As shown.

[0042] Figure 3 This is a comparison diagram of the expected offset point trajectory, expected centroid trajectory, and offset point and centroid tracking in Example 1. The diagram shows four trajectories when using the method of this application: expected centroid trajectory (red dashed line), actual centroid trajectory (blue solid line), expected offset point trajectory (yellow dashed line), and actual offset point trajectory (green solid line). It can be clearly observed that when the offset point accurately tracks the newly generated expected trajectory (yellow dashed line), the centroid of the unmanned vessel (blue solid line), after a brief initial adjustment, can almost completely coincide with the original expected centroid trajectory (red dashed line).

[0043] Figure 4 This is a graph showing the position tracking error curve of the unmanned surface vessel's center of mass in Example 1. It can be seen that after approximately 20 seconds, the tracking errors in both the X and Y directions quickly converge to near zero and remain stable, quantitatively demonstrating that this method can effectively eliminate steady-state errors and achieve high-precision trajectory tracking.

[0044] Comparative Example 1: Circular trajectory tracking using traditional methods This comparative example is intended to be compared with Example 1 to demonstrate the technical defects of the traditional output redefinition method when the technical solution of this application is not adopted.

[0045] 1. Simulation Settings All simulation parameters, including the unmanned vessel model, offset distance δ, original desired trajectory, and initial state, are exactly the same as in Example 1.

[0046] 2. Control methods The traditional output redefinition method is adopted, that is: the original desired trajectory is directly used as the tracking target of the offset point, and the controller drives the actual offset point ( , To track the coordinates of the original desired trajectory. ).

[0047] 3. Simulation Results and Analysis Figure 5 This is a comparison chart of the expected trajectory, offset point, and centroid tracking in Example 1. The chart shows the trajectory tracking performance under the traditional method. As can be seen, although the offset point (green solid line) tracks the expected centroid trajectory (red dashed line) well, the actual trajectory of the centroid (blue solid line) always runs inside the expected trajectory, forming a concentric circle with a smaller radius. There is a significant and continuous geometric deviation between the two.

[0048] Figure 6 The centroid position tracking error curve for Comparative Example 1 is shown. (Compared to...) Figure 4 In stark contrast, the tracking error here did not converge to zero after the initial stage, but instead exhibited continuous oscillations in the X and Y directions with an amplitude of approximately 0.5 meters (equal to the offset distance δ). This clearly demonstrates that traditional methods cannot eliminate the geometric errors introduced by output redefinition.

[0049] By comparing Example 1 and Comparative Example 1, in Regarding the positional error, Example 1 has a 45.43% smaller error than Comparative Example 1. Furthermore, while the error of Comparative Example 1 oscillates continuously, the error of Example 1 converges at a rate of 0.234, ultimately converging in 21.269 seconds. Within; in Regarding the positional error, Example 1 has a 97.43% smaller error than Comparative Example 1. Furthermore, while the error of Comparative Example 1 oscillates continuously, the error of Example 1 converges at a rate of 0.006, ultimately converging in 40.183 seconds. Within this range, it is demonstrated that this application can fundamentally solve the steady-state error problem of traditional output redefinition methods by actively planning compensatory trajectories.

[0050] Example 2: Sine Curve Tracking This embodiment aims to verify the performance and universality of the present application under more complex trajectories with non-uniform velocity and non-constant curvature.

[0051] Except for the desired trajectory, other simulation parameters, such as the unmanned vessel model, offset distance δ, and initial state, are the same as in Example 1. Specifically: This embodiment provides an underactuated unmanned surface vessel trajectory planning method to reduce tracking errors caused by the use of output redefinition control methods. The embodiment of this planning method follows the following... Figure 1 The steps are as follows: Step 1: Establish a mathematical model for the motion of the unmanned vessel: , This indicates the ship's position in a fixed Earth coordinate system. Indicates the ship's yaw angle. Indicates the velocity in the direction of the ship's sway. Indicates the speed in the direction of the ship's sway. This represents the angular velocity of the ship's turn. Indicates the ship's inertial mass. Represents the hydrodynamic damping constant. This represents the ship's controllable pitch thrust and yaw moment. These are the environmental disturbance forces and moments in the sway, roll, and yaw directions. The examples selected are: .

[0052] Step 2: Define the position of the offset point as follows: , It is the distance between the offset point and the center of mass along the ship's axis, as selected in the embodiment. The positional relationship between the offset point and the centroid is as follows: Figure 2 As shown, the coordinates of the centroid are ( , The coordinates of the offset point are ( , ).

[0053] Step 3: Represent the relationship between the desired trajectory and time in two-dimensional Euclidean space as follows: The desired trajectory selected in this embodiment is: .

[0054] Step 4: For each point on the desired trajectory, calculate its tangent direction vector. The formula is: .

[0055] Step 5: Obtain the velocity of the unmanned vessel in the sway direction using the inertial measurement unit. and velocity in the sway direction Through formula Calculate the sideslip angle .

[0056] Step 6: Convert the tangent direction vector at each point on the desired trajectory. Sideslip angle around this point The offset direction after compensation for sideslip is obtained. Rotation matrix for: Offset direction .

[0057] Step 7: Move each point on the desired trajectory along the offset direction Translation distance This allows us to obtain the expected trajectory of the new offset point, using the following formula: .

[0058] Step 8: By using the output redefinition control algorithm, the unmanned vessel's offset point tracks the desired trajectory of the new offset point. At this time, the center of mass of the unmanned vessel will move along the original desired trajectory.

[0059] The implementation example was verified in the Simulink simulation platform, with the ship's initial position set as follows. The simulation results are as follows Figures 7 to 8 As shown.

[0060] Figure 7 This is a comparison diagram of the expected offset point trajectory, expected centroid trajectory, and tracking of the offset point and centroid in Example 2. The diagram shows four trajectories when using the method of this application: expected centroid trajectory (red dashed line), actual centroid trajectory (blue solid line), expected offset point trajectory (yellow dashed line), and actual offset point trajectory (green solid line). It can be clearly observed that when the offset point accurately tracks the newly generated expected trajectory (yellow dashed line), the centroid of the unmanned vessel (blue solid line), after a brief initial adjustment, can almost completely coincide with the original expected centroid trajectory (red dashed line).

[0061] Figure 8 This is a graph showing the position tracking error curve of the unmanned surface vessel's center of mass in Example 2. The graph illustrates the position tracking error of the center of mass. It can be seen that the position tracking error of the center of mass converges rapidly to zero after a brief initial adjustment. The results demonstrate that even under complex conditions with constantly changing trajectory curvature and desired velocity, the method of this application still exhibits excellent accuracy and robustness.

[0062] Comparative Example 2: Sine Curve Trajectory Tracking Using Traditional Methods This comparative example corresponds to Example 2, demonstrating the technical defects of the traditional output redefinition method when the technical solution of this application is not adopted.

[0063] 1. Simulation Settings All simulation parameters, including the unmanned vessel model, offset distance δ, original desired trajectory, and initial state, are exactly the same as in Example 2.

[0064] 2. Control methods The traditional output redefinition method is adopted, that is: the original desired trajectory is directly used as the tracking target of the offset point, and the controller drives the actual offset point ( , To track the coordinates of the original desired trajectory. ).

[0065] 3. Simulation Results and Analysis Figure 9 This is a comparison chart of the expected trajectory, offset points, and centroid tracking in Scale 2. The chart shows a significant and dynamically changing deviation between the actual trajectory of the centroid (solid blue line) and the expected sinusoidal trajectory (dashed red line). The deviation is particularly noticeable at the peaks and troughs due to the greater curvature.

[0066] Figure 10 The figure shows the position tracking error curve of the unmanned surface vessel's center of mass, as illustrated in Comparative Figure 2. It reveals that the position tracking error oscillates continuously throughout the process and fails to converge; its oscillation pattern is closely related to the shape of the sinusoidal trajectory.

[0067] By comparing Example 2 and Comparative Example 2, in Regarding the positional error, Example 2 has a 100.53% smaller error than Comparative Example 2, and the error of Comparative Example 2 does not converge at all, while the error of Example 2 converges at a rate of 0.010, finally converging in 4.136 seconds. Within; in Regarding the positional error, Example 2 has a 97.67% smaller error than Comparative Example 2, and the error of Comparative Example 2 does not converge at all, while the error of Example 2 converges at a rate of 0.031, finally converging in 4.14 seconds. Within this range. This indicates that the performance of traditional methods deteriorates further when faced with complex trajectories, while the method in this application maintains a relatively stable error convergence rate.

[0068] Through thorough comparison and verification of the above embodiments and comparative examples, the trajectory planning method for reducing output redefinition error proposed in this application can effectively and accurately compensate for the geometric tracking error caused by both output redefinition and sideslip angle. Whether under simple circular trajectories or complex curved trajectories, this application can ensure high-precision and stable tracking of the unmanned surface vessel's center of gravity. Its technical performance is far superior to traditional output redefinition control methods, and it has high engineering application value.

[0069] The present invention and its embodiments have been described above. This description is not restrictive, and the accompanying drawings are only one embodiment of the present invention; the actual structure is not limited thereto. In conclusion, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A trajectory planning method for underactuated unmanned surface vessels to reduce output redefinition error, characterized in that, Includes the following steps: Step (1): Obtain the original desired trajectory that the underactuated unmanned surface vessel needs to track. ,in These respectively represent the coordinates in the Earth's fixed coordinate system { E In}, the expected trajectory is shaft and axial direction with time A changing function, where each point on the trajectory is determined by the position coordinates at a specific moment; Step (2): Calculate the tangent direction vector at each point on the original desired trajectory. ; Step (3), based on the sway speed of the unmanned vessel and sway speed Calculate the sideslip angle ; Step (4) convert the tangent direction vector of each point. Sideslip angle around this point The offset direction after compensation is obtained. , obtained This indicates that in order to keep the center of mass on its original trajectory, the offset point should be positioned relative to the orientation of the center of mass; Step (5): Move each point on the original desired trajectory along the offset direction. Translation distance Generate the desired trajectory of the new offset point. ; Step (6): Control the unmanned surface vessel's offset point to track the new offset point's desired trajectory, so that the unmanned surface vessel's center of mass moves along the original desired trajectory. This trajectory has been pre-considered and compensated for the geometric deviation between the offset point and the center of mass, as well as the effects of the sideslip angle, so that the unmanned surface vessel's center of mass can accurately follow the original desired trajectory. Movement, thereby eliminating tracking errors.

2. The offset point according to claim 1, characterized in that, The offset point is the position of a point on the ship's axis, denoted as... .

3. The offset point according to claim 2, characterized in that, The coordinates of the offset point are ,in The location of the ship's center of mass. The distance between the offset point and the ship's center of mass. This is the ship's yaw angle.

4. The method according to claim 1, characterized in that, In step (2), the tangent direction vector The calculation formula is: ,in These are the original expected trajectories. The derivative with respect to time.

5. The method according to claim 1, characterized in that, In step (3), the sideslip angle The calculation formula is ,in , These are the ship's pitching and swaying speeds, respectively.

6. The method according to claim 1, characterized in that, In step (4), the offset direction It is obtained by calculation using the rotation matrix.

7. The method according to claim 6, characterized in that, In step (4), the rotation matrix is ,and .

8. The method according to claim 1, characterized in that, In step (5), the new trajectory The calculation formula is .

9. The method according to claim 1, characterized in that, By controlling the algorithm to make the offset point track the new trajectory, the tracking error of the unmanned vessel's center of mass converges.

10. A trajectory planning system for an underactuated unmanned surface vessel to reduce output redefinition error, characterized in that, include: The trajectory acquisition module is used to acquire the original desired trajectory that the underactuated unmanned surface vessel needs to track. ,in These respectively represent the coordinates in the Earth's fixed coordinate system { E In}, the expected trajectory is shaft and axial direction with time A changing function, where each point on the trajectory is determined by the position coordinates at a specific moment; The kinematic parameter calculation module is used to calculate the original desired trajectory output by the kinematic parameter calculation module. Obtain the oscillation speed of the unmanned ship and sway speed According to the oscillation speed and sway speed Calculate the sideslip angle And calculate the tangent direction vector at each point on the original desired trajectory. ; The compensation trajectory generation module is used to generate the tangent direction vector output by the kinematic parameter calculation module. Sideslip angle around the trajectory point The offset direction after compensation And each point on the original desired trajectory is moved along this offset direction. Translate by preset distance To generate a new desired trajectory at the offset point. ; The tracking control module is used to control the unmanned surface vessel's offset point tracking to follow the new trajectory generated by the compensation trajectory generation module. This allows the center of mass of the unmanned vessel to move precisely along the original desired trajectory; The system works in concert with the modules described above to achieve trajectory planning and tracking control using the method described in any one of claims 1-9.

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