Polar icebreaker formation cooperative navigation control method based on distributed model

Abstract

This invention provides a distributed model-based collaborative navigation control method for polar icebreaker convoys, comprising: Step S1, acquiring ship parameters of the icebreaker convoy, ice condition data of the navigation area, and the motion state of the lead ship to determine safety constraints; Step S2, establishing a longitudinal dynamic model, including a first resistance model based on ice resistance experienced by the lead ship and a second resistance model based on still water resistance experienced by the following ships; Step S3, constructing a safe distance model based on ship parameters, safety constraints, the first resistance model, and the second resistance model; Step S4, setting a distributed model predictive controller for each following ship, and generating control commands by continuously solving a local optimization problem based on the current state of the ship itself, the motion state of the lead ship, and the assumed trajectories of adjacent ships, while satisfying the safety constraints. The beneficial effect is that this invention can improve the autonomy, safety, and overall escort efficiency of icebreaker convoy navigation in ice-covered areas.

Description

Technical Field

[0001] This invention relates to the technical field of ship motion control, and more specifically, to a method for cooperative navigation control of polar icebreaker formations based on a distributed model. Background Technology

[0002] In polar ice-covered waterways, especially during winter navigation, merchant ships typically need to travel in convoys, led by icebreakers. However, this process faces significant challenges: as icebreakers break through the ice, the ice resistance dynamically changes with factors such as ice thickness and strength, causing significant and unpredictable fluctuations in their speed. If these fluctuations are not promptly and accurately transmitted to following vessels, it will directly lead to inaccurate control of convoy spacing—too short a spacing can easily cause collisions, while too long a spacing may cause the channel cleared by the icebreaker to be re-blocked or frozen by broken ice before the following vessels arrive, seriously threatening the navigation safety and efficiency of the entire convoy.

[0003] Currently, convoy navigation in ice-covered areas relies heavily on the individual experience of drivers for manual operation, lacking a systematic automated collaborative control strategy. While existing research has incorporated road vehicle following theory into ship following models, it often treats each ship as an independent response unit, neglecting the communication and collaborative capabilities required of the convoy as a whole. Model predictive control (MPC) can effectively handle multi-constraint optimization problems, but traditional centralized MPC schemes require aggregating the state information of all ships to a central processor for unified optimization. This exposes inherent flaws in convoy applications, such as a sharp increase in computational complexity with the number of ships, a heavy burden on communication networks, and poor system fault tolerance (a central node failure can lead to a complete system failure). Although distributed model predictive control (DMPC) has shown advantages in areas such as vehicle convoys, a navigation control method that balances accurate models, safety constraints, and distributed collaboration remains a technological gap in the high-risk, highly disruptive, and highly dynamic maritime scenario of icebreaker escort. Therefore, there is an urgent need for an intelligent collaborative control solution that can fundamentally improve the autonomy, safety, and overall escort efficiency of icebreaker convoy navigation in ice-covered areas. Summary of the Invention

[0004] The technical problem to be solved by this invention is how to improve the autonomy, safety and overall escort efficiency of icebreaker formations in ice-covered areas. In order to overcome the defects of the above-mentioned existing technologies (or related technologies), this invention provides a polar icebreaker formation cooperative navigation control method based on a distributed model.

[0005] This invention provides a method for cooperative navigation control of polar icebreaker formations based on a distributed model, comprising the following steps: Step S1: Obtain the ship parameters of the icebreaker formation, the ice condition data of the navigation waters, and the motion status of the lead ship; and determine the safety constraints for formation navigation based on the ship parameters and the ice condition data. Step S2: Establish a longitudinal dynamic model of the icebreaker formation. The longitudinal dynamic model includes a first resistance model based on the ice resistance experienced by the lead ship and a second resistance model based on the still water resistance experienced by the follower ships. Step S3: Construct a safe distance model for the icebreaker formation based on the ship parameters, the safety constraints, the first resistance model, and the second resistance model. The limiting factors of the safe distance model include the absolute braking distance between the lead ship and the first follower ship, and the relative braking distance between adjacent follower ships. Step S4: Assign a distributed model predictive controller to each of the following vessels. Each distributed model predictive controller, based on its own current state, the motion state of the lead vessel, and the assumed state trajectories of adjacent vessels, solves a local optimization problem in a rolling manner to generate control commands for the current moment, provided that the safety constraints are met. The control objectives of the local optimization problem include: making the speed of the following vessels track the speed of the lead vessel, and making the actual distance between adjacent vessels approach the absolute braking distance or the relative braking distance defined by the safety distance model.

[0006] Compared with existing technologies, the distributed model-based collaborative navigation control method for polar icebreaker formations of this invention has the following advantages: This invention acquires actual navigation data, including ship parameters, ice condition data, and motion status, and determines safety constraints to dynamically adapt to the complex polar navigation environment. It establishes a longitudinal dynamic model that distinguishes between ice resistance for the lead ship and water resistance for follower ships, significantly improving model accuracy and more realistically reflecting the physical characteristics of convoy navigation in ice-covered areas, laying the foundation for precise control. Furthermore, it constructs a safety distance model including absolute and relative braking distances, providing a quantified safety standard based on braking performance for icebreaker convoys, effectively preventing collisions. Simultaneously, it designs an independent distributed model predictive controller for each ship, enabling each follower ship to make optimization decisions with only local information, reducing communication bandwidth requirements and computational burden. Single-point failures do not affect the overall convoy operation, improving fault tolerance. By rolling the solution of local optimization problems, it can handle lead ship speed fluctuations and ice resistance changes in real time and proactively, achieving rapid tracking of the lead ship's speed and stable collaborative maintenance of convoy spacing. This, while ensuring safety, reduces following distance, improves channel utilization efficiency, and enhances overall escort efficiency.

[0007] In one possible implementation, the safety constraint determined in step S1 includes at least a maximum safe speed, and the process of determining the maximum safe speed includes: Step A1: Determine the ice class of each vessel based on the vessel parameters, and identify the ice type and density in the navigation area based on the ice condition data; Step A2: Based on the ice class, ice type, and ice density, calculate the risk index result of the current navigation waters using the polar operations limitation assessment risk index system; Step A3: Determine the recommended operating mode based on the risk index result, and set or adjust the maximum safe speed based on the recommended operating mode.

[0008] Compared with existing technologies, the above-mentioned technical solution can introduce a polar operation limitation assessment risk index system to quantify complex factors such as ship ice class and real-time ice conditions into a unified risk index result, and determine the recommended operating mode and maximum safe speed accordingly. This makes the safe speed constraint no longer a fixed value, but an intelligent variable that adaptively matches the dynamic navigation environment, which significantly improves the scientific nature and authority of the safe speed constraint setting, ensures that the control strategy is neither too conservative nor too aggressive, and achieves an intelligent balance between safety and navigation efficiency.

[0009] In one possible implementation, in step S2, the first resistance model is an ice resistance model based on the Lindqvist semi-empirical formula, which is as follows: in, Indicates ice resistance; This indicates the bending strength of ice; Indicates ice thickness; Indicates ship speed; Indicates the mass of the ship; Indicates the width of the ship.

[0010] In one possible implementation, in step S2, the second resistance model is a hydrostatic resistance model, and the calculation formula is as follows: in, Indicates hydrostatic resistance; Indicates the hydrostatic resistance coefficient; Indicates the ship's speed.

[0011] In one possible implementation, the safety constraints determined in step S1 include at least the minimum safe distance between adjacent vessels, and the absolute braking distance between the pilot vessel and the first following vessel is calculated in step S3 using the following formula: in, This indicates the absolute braking distance; Indicates the captain of the first ship to follow; This indicates the minimum safe distance.

[0012] In one possible implementation, the safety constraints determined in step S1 include at least the minimum safe distance between adjacent vessels, and the relative braking distance between adjacent following vessels is obtained in step S3 using the following formula: in, This indicates the relative braking distance; Indicates a ship The captain; Indicates a ship The captain; This indicates the minimum safe distance.

[0013] In one possible implementation, in step S4, the local optimization problem is solved by minimizing a local cost function, which includes at least one of a velocity tracking error term, a spacing tracking error term, and a control input penalty term.

[0014] Compared with existing technologies, the above-mentioned technical solution can design a local cost function that includes terms such as speed tracking error, spacing tracking error, and control input penalty. This allows the distributed model predictive controller to simultaneously balance and optimize multiple performance indicators such as tracking accuracy, control energy consumption, and smoothness under a unified optimization objective. This method is highly flexible. By adjusting the composition and weight of different terms in the local cost function, it can easily adapt to different task requirements or ship performance preferences. It is the key to achieving high-performance, customizable collaborative control.

[0015] In one possible implementation, the local cost function is constructed using the following expression: in, Represents the local cost function; Indicates a ship The state vector, including position and velocity; Indicates a ship The control commands; The assumed trajectory representing the vessel's own state; The assumed state trajectory of the adjacent ships; Indicates the sampling time; Indicates the prediction time domain; Indicates the cost; This represents the speed weighting coefficient; This represents the speed tracking error term; Indicates a ship speed; This indicates the speed of the pilot vessel; This represents the spacing weighting coefficient; This represents the spacing tracking error term; Indicates a ship The position of the icebreaker formation; Indicates a ship The position of the icebreaker formation; Indicates the ideal distance between adjacent ships; This indicates the control input weighting coefficient; This indicates the control input penalty item; This represents the weighting coefficient for the rate of change of the control input; This indicates the rate of change of the control input.

[0016] In one possible implementation, in step S4, each of the distributed model prediction controllers performs the following steps within each control cycle: Step B1: Receive the motion state of the pilot ship and the assumed state trajectory of the adjacent ships. Based on the current state of the ship itself, the motion state of the pilot ship, the assumed state trajectory of the adjacent ships, and the safety constraints, solve the local optimization problem to obtain the optimal control sequence in the future prediction time domain. Step B2: Output the first control quantity in the optimal control sequence as the control command at the current moment to the actuator of the ship itself.

[0017] Compared with existing technologies, the above technical solution can demonstrate its model-based prediction and optimization nature through step B1, and plan control actions in advance to cope with future state changes; through step B2, it not only utilizes optimization information, but also eliminates model errors and disturbances through feedback correction. Attached Figure Description

[0018] Figure 1 This is a flowchart of the steps of the present invention; Figure 2 This is a flowchart illustrating the steps involved in determining the maximum safe speed according to the present invention. Figure 3 This is a schematic diagram of the formation cooperative control structure of the present invention; Figure 4 This is a schematic diagram illustrating the formation safety distance calculation of the present invention; Figure 5 This is a flowchart illustrating the execution steps of each of the distributed model prediction controllers within each control cycle of the present invention. Figure 6 This is a simulation result diagram based on AIS data from the present invention. Detailed Implementation

[0019] First, those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention. Those skilled in the art can make adjustments as needed to adapt to specific application scenarios.

[0020] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0021] See Figure 1 This invention discloses a method for cooperative navigation control of polar icebreaker formations based on a distributed model, comprising the following steps: Step S1: Obtain the ship parameters of the icebreaker formation, the ice condition data of the navigation waters, and the motion status of the lead ship; determine the safety constraints for formation navigation based on the ship parameters and ice condition data. Step S2: Establish a longitudinal dynamic model of the icebreaker formation. The longitudinal dynamic model includes a first resistance model based on the ice resistance experienced by the lead ship and a second resistance model based on the still water resistance experienced by the follower ships. Step S3: Construct a safe distance model for the icebreaker formation based on ship parameters, safety constraints, the first resistance model, and the second resistance model. The limiting factors of the safe distance model include the absolute braking distance between the lead ship and the first follower ship, and the relative braking distance between adjacent follower ships. Step S4: Set up a distributed model predictive controller for each following vessel. Each distributed model predictive controller, based on its own current state, the motion state of the lead vessel, and the assumed state trajectories of adjacent vessels, solves a local optimization problem in a rolling manner to generate control commands for the current moment, provided that safety constraints are met. The control objectives of the local optimization problem include: making the speed of the following vessel track the speed of the lead vessel, and making the actual distance between adjacent vessels approach the absolute braking distance or relative braking distance defined by the safety distance model.

[0022] In this embodiment of the invention, considering the complex and changeable ice conditions in the Arctic waters, the ice thickness, density, and distribution dynamically change with the seasons and meteorological conditions, causing significant speed changes in icebreakers due to ice resistance fluctuations during operations. If these fluctuations are not transmitted to following vessels in a timely and coordinated manner, they can easily lead to collision risks due to excessively close following distances or secondary freezing and blockage risks in the waterway due to excessively large following distances. Therefore, in icebreaker escort formations, achieving communication-based collaborative longitudinal control among multiple vessels is crucial to ensuring the safety and efficiency of navigation in the Arctic winter.

[0023] In this embodiment of the invention, step S1 first obtains the ship parameters (such as ship length) of all ships in the icebreaker formation. , ship width ,quality Inertial time constant Ice condition data (such as ice thickness) for the Arctic shipping route. Ice bending strength (such as sea ice concentration) and the pilot vessel's movement status (position). With speed Based on the above data, and in conjunction with international shipping practices and safety regulations, the safety constraints for icebreaker convoy navigation were determined, including the minimum safe distance between vessels. (Usually set at 100 meters) and the maximum safe speed under current ice conditions. .

[0024] In this embodiment of the invention, in order to quantify the navigation risks in ice-covered areas and determine the safe speed threshold, the invention draws on the POLARIS risk assessment framework. POLARIS (Polar Operational Limit Assessment Risk Index System) was proposed by the International Maritime Organization (IMO). It can quantify the navigation risks of ice-class vessels navigating Arctic waters by combining historical or near-real-time ice condition data. The principle of POLARIS is to assess the navigation risks brought to vessels by various ice conditions by combining the ice class assigned to them for navigation in Arctic waters.

[0025] See Figure 2 In this embodiment of the invention, the safety constraints determined in step S1 include at least the maximum safe speed, and the process of determining the maximum safe speed includes: Step A1: Determine the ice class of each vessel based on the vessel parameters, and identify the type and density of ice in the navigation area based on the ice condition data; Step A2: Based on ice class, ice type, and concentration, calculate the risk index result for the current navigation waters using the Polar Operations Limitations Risk Assessment Index System; Step A3: Determine the recommended operating mode based on the risk index results, and set or adjust the maximum safe speed based on the recommended operating mode.

[0026] In this embodiment of the invention, by establishing a longitudinal dynamic model that accurately distinguishes the resistance experienced by the lead ship and the following ships, and incorporating a safety distance model based on braking performance, an accurate description of the controlled object is provided for the collaborative control of icebreaker formations. Furthermore, by designing an independent distributed model predictive controller for each following ship, it can solve the local optimization problem online using only its own state and limited information from the lead ship and forward neighboring ships. Thus, under the premise of strictly satisfying the safety distance and speed constraints, it can achieve rapid and smooth tracking of the speed fluctuations of the lead ship and maintain the stability of the icebreaker formation spacing. This method elevates formation navigation from the traditional independent following problem to a collaborative optimization problem, significantly improving the overall safety, efficiency, and robustness to dynamic environments of ice escort operations.

[0027] In this embodiment of the invention, after acquiring ship ice class and ice condition data, a risk assessment is performed based on the POLARIS principle. POLARIS assigns risk index values ​​(RIVs) to ships of different ice classes navigating in waters with different ice types. The risk index result RIO is calculated by summing the products of the concentration of each ice type within the statistical unit (expressed in decimal places) and its corresponding RIVs, as shown in the following formula: in, For the density of various ice types, The RIO value corresponds to the risk index value. The higher the RIO value, the lighter the ice conditions and the lower the navigation risk. Subsequently, based on the calculated RIO value and referring to the POLARIS operational restriction hierarchy table, the recommended operational mode for the formation in the current waters can be determined (e.g., "normal operation," "high-risk operation," or "operation requiring special consideration"). This determination directly guides the maximum safe speed. Setting: In "High-Risk Operation" or more stringent modes, the maximum safe cruising speed should be reduced. To ensure safety; in "normal operation" mode, a higher maximum safe speed can be set according to the ship's performance and mission requirements. By embedding the POLARIS risk assessment into the control framework, an adaptive match between safety constraints and dynamic ice conditions is achieved.

[0028] In this embodiment of the invention, in step S2, the first resistance model is an ice resistance model based on the Lindqvist semi-empirical formula, which is as follows: in, Indicates ice resistance; This indicates the flexural strength of ice (kPa). Indicates ice thickness (m); Indicates the ship's speed (m / s); Indicates the ship's mass (kg); Indicates the ship's width (m); The second resistance model is the still water resistance model. When a ship is sailing in an open channel, it is mainly affected by still water resistance, and the formula is as follows: in, Indicates hydrostatic resistance; Indicates the hydrostatic resistance coefficient; Indicates the ship's speed.

[0029] In this embodiment of the invention, each ship in the longitudinal dynamics model in step S2 The motion is described by the following model: Equations of state: , where the state vector Includes position and velocity, For control input (thrust / command); Considering the first-order inertial element with lag in the maneuvering of large ships: ; Discrete update equation: In the formula, The inertial time constant, For the delay steps, Sampling time.

[0030] See Figure 3 and Figure 4 In this embodiment of the invention, the safety constraints determined in step S1 include at least the minimum safe distance between adjacent vessels. In step S3, the absolute braking distance between the pilot vessel and the first following vessel is calculated using the following formula: in, Indicates the absolute braking distance; Indicates the captain of the first ship to follow; Indicates the minimum safe distance; The relative braking distance between adjacent following vessels can be obtained using the following formula: in, Indicates relative braking distance; Indicates a ship The captain; Indicates a ship The captain; This represents the minimum safe distance. The model is based on experimental data of ship reversing braking performance and ensures that there is enough distance to avoid collisions in emergency situations.

[0031] In this embodiment of the invention, step S4, designing and implementing the distributed model prediction controller, specifically includes: Local optimization problem definition: Ship The distributed model predictive controller is based on its own model and current state. Neighbor Assumed Trajectory In the prediction time domain Inner rolling solves the following local optimization problem: Control objective: Maintain spacing: Speed ​​tracking: in, The desired following distance can be set as a safety distance. ; Local cost function: Minimize the cost function : Instant cost Usually: in, Represents the local cost function; Indicates a ship The state vector, including position and velocity; Indicates a ship Control commands; It represents the assumed trajectory of the vessel itself. Represents the assumed trajectory of adjacent ships; Indicates the sampling time; Indicates the prediction time domain; Indicates the cost; This represents the speed weighting coefficient; This indicates the speed tracking error term; Indicates a ship speed; Indicates the speed of the pilot ship; This represents the spacing weighting coefficient; This indicates the spacing tracking error term; Indicates a ship Its position within the icebreaker formation; Indicates a ship Its position within the icebreaker formation; Indicates the ideal distance between adjacent ships; This indicates the control input weighting coefficient; This indicates the input penalty item; This represents the weighting coefficient for the rate of change of the control input; This indicates the rate of change of the control input.

[0032] See Figure 5 In this embodiment of the invention, in step S4, within each control cycle, each distributed model prediction controller performs the following steps: Step B1: Receive the motion state of the pilot ship and the assumed state trajectories of adjacent ships. Based on the current state of the ship itself, the motion state of the pilot ship, the assumed state trajectories of adjacent ships, and safety constraints, solve the local optimization problem to obtain the optimal control sequence in the future prediction time domain. Step B2: Output the first control variable in the optimal control sequence as the control command at the current moment to the actuators of the ship itself.

[0033] In this embodiment of the invention, the optimal control sequence is obtained by solving the above-mentioned local optimization problem, and its first element is taken. As the actual control command output at the current moment, it also sends its own future trajectory, predicted based on the current optimal solution, to its neighboring ships (vessels). This process, which serves as the "assumed trajectory" for the next optimization cycle, is repeated in each control cycle. Through local coordination, it achieves global stability and coordination of the formation.

[0034] In this embodiment of the invention, AIS (Automatic Identification System) is a system for communication and information exchange between ships. Its main functions include: automatically identifying ship identities (such as ship name, position, speed, and heading); improving navigation safety and helping to avoid collisions; supporting real-time voice and data communication between ships; and displaying the dynamics of surrounding ships on electronic charts to support navigation. AIS follows international standards and achieves information exchange through specific radio frequencies.

[0035] See Figure 6 In this embodiment of the invention, simulation verification based on AIS data specifically includes: Step C1, Data Preparation: Extract real navigation data of icebreaker formations from the historical AIS database, and select a segment of data with significant speed fluctuations of the lead ship and dense AIS points as the reference speed trajectory for simulation testing. ; Step C2, Simulation Setup: Set up the icebreaker formation to include one lead icebreaker and two follower ships. Match or set the dynamic parameters of each ship based on AIS data. etc.), set ice condition parameters ( To simulate typical winter ice conditions, configure DMPC controller parameters (prediction time domain). (weighting coefficients, etc.) Step C3, Performance Evaluation: Run the simulation, record the changes in the position, speed, spacing, and control input of each ship over time, and calculate the following key performance indicators: Root mean square error of spacing tracking: Root mean square error in speed tracking: .

[0036] In the description of this invention, the references to "one embodiment," "some embodiments," "in this embodiment," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0037] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for cooperative navigation control of polar icebreaker formations based on a distributed model, characterized in that, Includes the following steps: Step S1: Obtain the ship parameters of the icebreaker formation, the ice condition data of the navigation waters, and the motion status of the lead ship; and determine the safety constraints for formation navigation based on the ship parameters and the ice condition data. Step S2: Establish a longitudinal dynamic model of the icebreaker formation. The longitudinal dynamic model includes a first resistance model based on the ice resistance experienced by the lead ship and a second resistance model based on the still water resistance experienced by the follower ships. Step S3: Construct a safe distance model for the icebreaker formation based on the ship parameters, the safety constraints, the first resistance model, and the second resistance model. The limiting factors of the safe distance model include the absolute braking distance between the lead ship and the first follower ship, and the relative braking distance between adjacent follower ships. Step S4: Assign a distributed model predictive controller to each of the following vessels. Each distributed model predictive controller, based on its own current state, the motion state of the lead vessel, and the assumed state trajectories of adjacent vessels, solves a local optimization problem in a rolling manner to generate control commands for the current moment, provided that the safety constraints are met. The control objectives of the local optimization problem include: making the speed of the following vessels track the speed of the lead vessel, and making the actual distance between adjacent vessels approach the absolute braking distance or the relative braking distance defined by the safety distance model.

2. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, The safety constraints determined in step S1 include at least the maximum safe speed, and the process of determining the maximum safe speed includes: Step A1: Determine the ice class of each vessel based on the vessel parameters, and identify the ice type and density in the navigation area based on the ice condition data; Step A2: Based on the ice class, ice type, and ice density, calculate the risk index result of the current navigation waters using the polar operations limitation assessment risk index system; Step A3: Determine the recommended operating mode based on the risk index result, and set or adjust the maximum safe speed based on the recommended operating mode.

3. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, In step S2, the first resistance model is an ice resistance model based on the Lindqvist semi-empirical formula, which is as follows: in, Indicates ice resistance; This indicates the bending strength of ice; Indicates ice thickness; Indicates ship speed; Indicates the mass of the ship; Indicates the width of the ship.

4. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, In step S2, the second resistance model is a hydrostatic resistance model, and the calculation formula is as follows: in, Indicates hydrostatic resistance; Indicates the hydrostatic resistance coefficient; Indicates ship speed.

5. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, The safety constraints determined in step S1 include at least the minimum safe distance between adjacent vessels, and the absolute braking distance between the pilot vessel and the first following vessel is obtained in step S3 using the following formula: in, This indicates the absolute braking distance; Indicates the captain of the first ship to follow; This indicates the minimum safe distance.

6. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, The safety constraints determined in step S1 include at least the minimum safe distance between adjacent vessels, and the relative braking distance between adjacent following vessels is obtained in step S3 using the following formula: in, This indicates the relative braking distance; Indicates a ship The captain; Indicates a ship The captain; This indicates the minimum safe distance.

7. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, In step S4, the local optimization problem is solved by minimizing a local cost function, which includes at least one of the following: velocity tracking error term, spacing tracking error term, and control input penalty term.

8. The method for coordinated navigation control of polar icebreaker formations according to claim 7, characterized in that, The local cost function is constructed using the following expression: in, Represents the local cost function; Indicates a ship The state vector, including position and velocity; Indicates a ship The control commands; The assumed trajectory representing the vessel's own state; The assumed state trajectory of the adjacent ships; Indicates the sampling time; Indicates the prediction time domain; Indicates the cost; This represents the speed weighting coefficient; This represents the speed tracking error term; Indicates a ship speed; This indicates the speed of the pilot vessel; This represents the spacing weighting coefficient; This represents the spacing tracking error term; Indicates a ship The position of the icebreaker formation; Indicates a ship The position of the icebreaker formation; Indicates the ideal distance between adjacent ships; This indicates the control input weighting coefficient; This indicates the control input penalty item; This represents the weighting coefficient for the rate of change of the control input; This indicates the rate of change of the control input.

9. The method for coordinated navigation control of polar icebreaker formations according to claim 1, characterized in that, In step S4, within each control cycle, each of the distributed model prediction controllers performs the following steps: Step B1: Receive the motion state of the pilot ship and the assumed state trajectory of the adjacent ships. Based on the current state of the ship itself, the motion state of the pilot ship, the assumed state trajectory of the adjacent ships, and the safety constraints, solve the local optimization problem to obtain the optimal control sequence in the future prediction time domain. Step B2: Output the first control quantity in the optimal control sequence as the control command at the current moment to the actuator of the ship itself.

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