Safe arrival-avoidance differential game controller for multiple unmanned ships

Abstract

The invention provides a multi-unmanned-ship safe arrival-avoidance differential game controller. The multi-unmanned-ship safe arrival-avoidance differential game controller comprises an unmanned ship kinematics mathematical model unit, a region protection design unit, an optimal interception point solving unit, an optimal interception point selection unit, an unmanned ship optimal differential game strategy design unit, an unmanned ship safety constraint unit and an unmanned ship input constraint unit. According to the invention, the defense unmanned surface vehicle can protect the target area and intercept the attack unmanned surface vehicle. Firstly, an optimal interception point is calculated by using a geometric method, and an optimal game strategy is designed for two groups of unmanned ships based on a differential game idea. And secondly, based on a fixed time control obstacle function and speed constraint, optimizing the designed control strategy by solving a quadratic programming problem so as to ensure the safety of the system. And finally, an optimal safe game guidance law is constructed by using an auxiliary variable method, so that the under-actuated unmanned ship can effectively complete a protection task on the target area.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned boat motion control, and in particular to a differential game controller for safe arrival and avoidance of multiple unmanned boats. Background Art

[0002] Unmanned boats (UDVs) boast advantages such as miniaturization, flexibility, low cost, and long endurance. They can navigate autonomously in a variety of marine environments and perform missions around the clock. They play a vital role in port defense, patrol surveillance, and maritime rescue, becoming key to enhancing comprehensive marine capabilities. Their technological development is crucial for ensuring safety and holds significant potential for application in strategic and competitive scenarios.

[0003] As a key research area in the field of swarm motion control for unmanned aerial vehicles (UAVs), the game-based confrontation problem of UAVs has attracted considerable attention and in-depth research in recent years. For the control of non-cooperative games between two groups, Sun Zhiyuan designed a self-organizing cooperative pursuit strategy based on a polynomial sliding fitting method to address the pursuit-escape confrontation game problem of UAVs in complex environments. Wang Yueying proposed a distributed attack-defense game control method for UAV systems based on threat potential fields. Lin Bin proposed an interception strategy based on backstepping technology for underactuated UAV systems subject to external interference and parameter uncertainty, enabling the UAV to intercept targets at a desired velocity within a finite time. Xing Ning proposed a control strategy based on a distributed prescribed time estimator for defenders, designed to capture attackers with a switching mechanism at a specified time. Li Fanbiao designed a distributed capture strategy optimization method based on deep reinforcement learning and multi-agent proximal policy optimization to address the attack-defense problem of UAVs. Notably, differential game theory can comprehensively consider the cooperative and conflicting relationships between multiple agents, as well as the impact of these relationships on the system state and evolution, providing a suitable framework for analyzing the possible outcomes of continuous game conflicts in continuous time. Yan Rui used a differential game-based approach to design optimal strategies for players in a reach-avoidance scenario with two escapees and one pursuer, and a matching-based capture strategy for a three-dimensional multi-player reach-avoidance differential game. Eloy Garcia constructed a reach-avoidance differential game problem involving multiple drones protecting a static target point in three-dimensional space. However, existing approaches to designing unmanned watercraft game strategies still have some shortcomings: First, existing UAV game strategy design methods mostly focus on the design and optimization of unilateral strategies to resolve conflicts between two groups of UAVs. However, when faced with non-cooperative game scenarios involving multiple UAVs, the strategic interactions and mutual influences between them may not be fully considered when dealing with non-cooperation between multiple UAVs.

[0004] Second, existing differential game control methods are only applicable to single-integrator or fully actuated models and have not yet been applied to underactuated unmanned vehicle systems. Furthermore, existing research on reach-avoid differential game problems uses static targets as protected points, whereas real-world applications are often more complex and diverse, potentially requiring protection of areas with specific ranges and boundaries.

[0005] Third, in addition, the existing unmanned boat game confrontation strategy design method ignores the potential collision problem. During the mission, the unmanned boat still faces the risk of collision with obstacles or adjacent unmanned boats, which will affect the navigation safety of the unmanned boat and the smooth completion of the mission. Summary of the Invention

[0006] In view of this, the purpose of the present invention is to propose a multi-unmanned boat safe arrival-avoidance differential game controller to solve the technical problem that the existing unmanned boat game confrontation strategy cannot be used for under-actuated unmanned boat systems.

[0007] The technical means adopted in the present invention are as follows: A differential game controller for safe arrival and avoidance of multiple unmanned boats, comprising: Defense unmanned boat kinematics mathematical model unit; the defense unmanned boat kinematics mathematical model unit sends a position signal and To the optimal differential game strategy design unit for the defense unmanned boat; the kinematic mathematical model unit of the defense unmanned boat sends a position signal and To the optimal interception point solution unit; Attack unmanned boat kinematics mathematical model unit; the attack unmanned boat kinematics mathematical model unit sends a position signal To the optimal differential game strategy design unit for attacking unmanned boats; the kinematic mathematical model unit for attacking unmanned boats sends a position signal To the regional protection design unit; the attack unmanned boat kinematic mathematical model unit sends a position signal To the optimal interception point solution unit; Regional protection design unit; the regional protection design unit sends an intrusion point location signal To the optimal interception point solution unit; Optimal interception point solving unit; the optimal interception point solving unit sends the optimal interception point position signal and Select the unit to the best interception point; Optimal interception point selection unit; the optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for defending unmanned boats; the optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for attacking unmanned boats; Optimal differential game strategy design unit for defending unmanned boats; the optimal differential game strategy design unit for defending unmanned boats sends an optimal speed signal To the unit for solving the optimal safety strategy for defending unmanned boats; Attacking unmanned boat optimal differential game strategy design unit; the attacking unmanned boat optimal differential game strategy design unit sends an optimal speed signal To the unit for solving the optimal safety strategy for attacking unmanned boats; Defense unmanned boat safety constraint unit; the defense unmanned boat safety constraint unit sends a safety constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat safety constraint unit; the attack unmanned boat safety constraint unit sends a safety constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Defense unmanned boat input constraint unit; the defense unmanned boat input constraint unit sends an input constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat input constraint unit; the attack unmanned boat input constraint unit sends an input constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Optimal safety strategy solving unit for defending unmanned boat; said optimal safety strategy solving unit for defending unmanned boat sends optimal safety speed signal To the optimal safety guidance design unit for defense unmanned boats; Attacking unmanned boat optimal safety strategy solving unit; the attacking unmanned boat optimal safety strategy solving unit sends the optimal safety speed signal To the optimal safety guidance design unit for attacking unmanned boats; Optimal safety guidance design unit for defending unmanned boats; the optimal safety guidance design unit for defending unmanned boats sends an optimal safety guidance signal and To the kinematic mathematical model unit of the defense unmanned boat; Attack unmanned boat optimal safety guidance design unit; the attack unmanned boat optimal safety guidance design unit sends the optimal safety guidance signal and To the kinematic mathematical model unit of attack unmanned boat.

[0008] Furthermore, the kinematic mathematical model of the defense unmanned boat is as follows: (1) in, i Indicates the number of defense unmanned boats; Represents the position coordinates of the defense unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the defense unmanned boat, where represents the forward velocity of the defense unmanned boat in the hull coordinate system, represents the lateral velocity of the defense unmanned boat in the hull coordinate system; Indicates the actual movement direction of the defense unmanned boat, represents the bow angle of the defense unmanned boat in the earth coordinate system; represents the bow angular velocity of the defense unmanned boat in the boat coordinate system; It represents the sideslip angle of the defense unmanned boat in the boat coordinate system; Introducing positive constants The first i The position information of the defense unmanned boat is converted into , where the rotation vector ; The time derivative of is as follows: (2) in, ; The kinematic mathematical model of the attack unmanned boat is as follows:

[0009] in, k Indicates the number of attacking unmanned boats; Represents the position coordinates of the attacking unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the attacking unmanned boat, where represents the forward speed of the attacking unmanned boat in the hull coordinate system, represents the lateral velocity of the attacking unmanned boat in the hull coordinate system; Indicates the actual movement direction of the unmanned boat. represents the bow angle of the attack unmanned boat in the earth coordinate system; It represents the bow angular velocity of the attack unmanned boat in the boat coordinate system; It represents the sideslip angle of the attacking unmanned boat in the boat coordinate system; Introducing positive constants The first k The position information of the attack unmanned boat is converted into , where the rotation vector ; The time derivative of is as follows: (2) in, ; definition , Indicates the kth attack unmanned boat The position of each two defense unmanned boats intercepts an attack unmanned boat. In the differential game, each group of states is defined as ,in , , Representation and defense of unmanned boats Collaborative capture of attack drones Defense Unmanned Boat ;definition Indicates the initial state of the system.

[0010] Furthermore, the regional protection design unit is as follows: When i The first defense unmanned boat and the k The distance between the attacking unmanned boats is less than the capture radius When the defending unmanned boat successfully intercepts the attacking unmanned boat, that is: (3) In the reach-avoid strategy design, the area is taken as the protected target; for the attacking unmanned boat, it is necessary to solve the point on the target area that the attacking unmanned boat can reach. , and continuously updated based on the corresponding game strategy, it can be explained as an equivalent optimization problem: .

[0011] Furthermore, the optimal interception point solving unit includes a 1v1 game strategy and a 2v1 game strategy, which are as follows: The 1v1 game strategy is that the attacking unmanned boat is intercepted by a single defensive unmanned boat; all unmanned boats have the same combined speed, and the line segment The orthogonal lines divide the winning areas of the defensive and attacking unmanned boats , defense unmanned boat , attack unmanned boats and target point The relationship between is defined as: (5) Divide the state space into The barrier function The expression is as follows: (6) With line segment Orthogonal lines are represented by: (7) Attack drone boat Aiming and Line Segments The point on the orthogonal line closest to the target area, thereby minimizing the distance to the target area, is represented as , that is, defense unmanned boats The best interception point; The two-point equation is: (8) Coordinates: (9) Where: ; The 2v1 game strategy is that the attacking unmanned boat is intercepted by the two defending unmanned boats in cooperation; the two defending unmanned boats cooperate to intercept the attacking unmanned boat at a location far away from the target area, thereby reducing the risk faced by the target area; Define the barrier function: (10) Where: , , ; definition A sub-area for two defending UAVs to simultaneously capture the attacking UAV; The expression is as follows: (11) when The best capture point as follows: (12) (13) Where: .

[0012] Furthermore, the optimal interception point selection unit is as follows: Given the initial position of the unmanned boat and assuming , there are three possibilities: the first possibility is Single interception is the optimal result; the second possibility is Single interception is the optimal result; the third possibility is and Cooperative Interception is the optimal result; by comparing various solutions of the 1v1 game, the problem of each unmanned boat determining the interception type and applying the best strategy is solved; Based on the orthogonal line expression that divides the winning areas of the defense unmanned boat and the attack unmanned boat, calculate which side of the line the optimal interception point is located on; let 、 They are and and and The best interception point in a 1v1 game is calculated as follows: (14) when and When , the cooperative interception of the defense unmanned boat is the optimal result, where the interception point is ;if and , based on the optimal strategy, Single interception , where the intercept point is ;if and , based on the optimal strategy, Single interception , where the intercept point is ;when and The best interception point is 、 Zhongwei Provide the minimum cost point, so Closest to the target area.

[0013] Furthermore, the optimal differential game strategy design unit is as follows: The optimal safety game guidance strategy for 1v1 game strategy is as follows: (15) Where: , ; The optimal safety game guidance strategy for the 2v1 game strategy is as follows: (16) Where: , , .

[0014] Furthermore, the attack unmanned boat safety constraint unit and the defense unmanned boat safety constraint unit are as follows: To ensure that there is no collision between two groups of UAVs in the area protection mission, the distance between the UAVs in each group and the distance between each UAV participating in the game and the obstacle must meet the following requirements:

[0015] in: Indicates the location of static obstacles; Indicates the position of dynamic obstacles; Indicates safe distance; Static obstacle avoidance; In order to prevent the collision between the defense unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; Dynamic obstacle avoidance; In order to prevent collisions between the defense unmanned boat and dynamic obstacles, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the dynamic obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; Collision avoidance between adjacent unmanned boats; In order to prevent collisions between the defense unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0016] Furthermore, the attack unmanned boat input constraint unit and the defense unmanned boat input constraint unit are as follows: The speed of the defense unmanned boat and the attack unmanned boat is limited by ,in, 、 、 and Represents a given boundary.

[0017] Furthermore, the optimal safety strategy solving unit for attacking unmanned boats and the optimal safety strategy solving unit for defending unmanned boats are as follows: In order to minimize the impact of collision avoidance design on the heading change of the defensive unmanned boat, quadratic programming is used to generate the optimal safe heading signal : (17) in, , , ; In order to minimize the impact of collision avoidance design on the heading change of the attacking unmanned boat, quadratic programming is used to generate the optimal safe heading signal ; (18) in, .

[0018] Furthermore, the optimal safety guidance design unit for attacking unmanned boats and the optimal safety guidance design unit for defending unmanned boats are as follows: Design the optimal safety guidance signal based on the kinematic model and optimal safety strategy: (19) Defense unmanned boat Attack unmanned boat and its cooperative unmanned boat Current status and Adjust defense strategies to make decisions based on the current situation; attack unmanned boats Consider defending against unmanned boats Current status , update the avoidance strategy in time.

[0019] Compared with the prior art, the present invention has the following advantages: First, compared to existing methods that rely solely on unilateral strategy design to resolve conflicts between two groups of UAVs, this invention incorporates differential game theory to address the area protection problem between two groups of UAVs. This method more fully considers conflict and cooperation between UAVs in a dynamic environment, enhancing the robustness of the control strategy. Furthermore, this strategy enables the defending UAVs to decide whether to cooperate based on orthogonal line conditions, thereby ensuring efficient mission completion.

[0020] Second, compared to existing differential game control methods that only consider single-integrator or fully actuated unmanned vehicle models, this paper investigates an underactuated unmanned vehicle with a speed constraint. By introducing auxiliary variables, the proposed optimal strategy is adapted to the proposed underactuated unmanned vehicle model. Furthermore, unlike static points, this paper considers circular regions as protected targets and uses an equivalent optimization method to update the point within the target region closest to the attacking unmanned vehicle.

[0021] Third, unlike existing unmanned vehicle game strategy design methods that ignore potential collisions, this invention employs a quadratic programming problem based on a fixed-time control obstacle function to ensure that collisions between the unmanned vehicle and obstacles, as well as between adjacent unmanned vehicles, do not occur during the game. When encountering collision risks, the fixed-time control obstacle function employed in this invention provides a faster response than traditional control obstacle functions. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0023] Figure 1 Schematic diagram of the controller of the present invention.

[0024] Figure 2 This is a schematic diagram of a defensive unmanned boat intercepting an attacking unmanned boat according to the present invention.

[0025] Figure 3 It is a schematic diagram of two defense unmanned boats cooperating to intercept an attack unmanned boat according to the present invention.

[0026] Figure 4 is a schematic diagram of the trajectory of the defensive unmanned boat and the attacking unmanned boat under the optimal safety game guidance strategy of the present invention, where (a) is at t=20s; (b) is at t=40s; (c) is at t=60s; (d) is at t=80s; Figure 5 This is a schematic diagram of the final distance between the defense unmanned boat and the attack unmanned boat of the present invention.

[0027] Figure 6 This is a schematic diagram of the optimal safety guidance signal for attacking an unmanned boat according to the present invention.

[0028] Figure 7 This is a schematic diagram of the optimal safety guidance signal for defending against unmanned boats according to the present invention.

[0029] Figure 8 It is a schematic diagram of the safe collision avoidance of the unmanned boat of the present invention. DETAILED DESCRIPTION

[0030] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0031] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0032] like Figure 1 As shown, the present invention provides a multi-unmanned boat safe arrival-avoidance differential game controller, comprising: Defense unmanned boat kinematics mathematical model unit; the defense unmanned boat kinematics mathematical model unit sends a position signal and To the optimal differential game strategy design unit for the defense unmanned boat; the kinematic mathematical model unit of the defense unmanned boat sends a position signal and To the optimal interception point solution unit; Attack unmanned boat kinematics mathematical model unit; the attack unmanned boat kinematics mathematical model unit sends a position signal To the optimal differential game strategy design unit for attacking unmanned boats; the kinematic mathematical model unit for attacking unmanned boats sends a position signal To the regional protection design unit; the attack unmanned boat kinematic mathematical model unit sends a position signal To the optimal interception point solution unit; Area protection design unit; the area protection design unit sends an intrusion point location signal (the location of the nearest point on the protected area that the attacker can reach) To the optimal interception point solution unit; Optimal interception point solving unit; the optimal interception point solving unit sends the optimal interception point position signal and Select the unit to the best interception point; Optimal interception point selection unit; the optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for defending unmanned boats; the optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for attacking unmanned boats; Optimal differential game strategy design unit for defending unmanned boats; the optimal differential game strategy design unit for defending unmanned boats sends an optimal speed signal To the unit for solving the optimal safety strategy for defending unmanned boats; Attacking unmanned boat optimal differential game strategy design unit; the attacking unmanned boat optimal differential game strategy design unit sends an optimal speed signal To the unit for solving the optimal safety strategy for attacking unmanned boats; Defense unmanned boat safety constraint unit; the defense unmanned boat safety constraint unit sends a safety constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat safety constraint unit; the attack unmanned boat safety constraint unit sends a safety constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Defense unmanned boat input constraint unit; the defense unmanned boat input constraint unit sends an input constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat input constraint unit; the attack unmanned boat input constraint unit sends an input constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Optimal safety strategy solving unit for defending unmanned boat; said optimal safety strategy solving unit for defending unmanned boat sends optimal safety speed signal To the optimal safety guidance design unit for defense unmanned boats; Attacking unmanned boat optimal safety strategy solving unit; the attacking unmanned boat optimal safety strategy solving unit sends the optimal safety speed signal To the optimal safety guidance design unit for attacking unmanned boats; Optimal safety guidance design unit for defending unmanned boats; the optimal safety guidance design unit for defending unmanned boats sends an optimal safety guidance signal and To the kinematic mathematical model unit of the defense unmanned boat; Attack unmanned boat optimal safety guidance design unit; the attack unmanned boat optimal safety guidance design unit sends the optimal safety guidance signal and To the kinematic mathematical model unit of attack unmanned boat.

[0033] The output end of the kinematic mathematical model unit of the defense unmanned boat is respectively connected to the input end of the optimal differential game strategy design unit of the defense unmanned boat and the optimal interception point solution unit; the output end of the kinematic mathematical model unit of the attack unmanned boat is respectively connected to the input end of the optimal differential game strategy design unit of the attack unmanned boat, the area protection design unit and the optimal interception point solution unit; the input end of the kinematic mathematical model unit of the defense unmanned boat is connected to the output end of the optimal safety guidance design unit of the defense unmanned boat; the input end of the kinematic mathematical model unit of the attack unmanned boat is connected to the output end of the optimal safety guidance design unit of the attack unmanned boat; the input end of the optimal safety guidance design unit of the defense unmanned boat is connected to the output end of the optimal safety strategy solution unit of the defense unmanned boat; the input end of the optimal safety guidance design unit of the attack unmanned boat is connected to the output end of the optimal safety strategy solution unit of the attack unmanned boat The output end of the safety strategy solving unit is connected; the input end of the defense unmanned boat optimal safety strategy solving unit is respectively connected to the output ends of the defense unmanned boat safety constraint unit, the defense unmanned boat input constraint unit and the defense unmanned boat optimal differential game strategy design unit; the input end of the attack unmanned boat optimal safety strategy solving unit is respectively connected to the output ends of the attack unmanned boat safety constraint unit, the attack unmanned boat input constraint unit and the attack unmanned boat optimal differential game strategy design unit; the output end of the area protection design unit is connected to the input end of the optimal interception point solving unit; the output end of the optimal interception point solving unit is connected to the input end of the optimal interception point selection unit; the output end of the optimal interception point selection unit is respectively connected to the input ends of the defense unmanned boat optimal differential game strategy design unit and the attack unmanned boat optimal differential game strategy design unit.

[0034] A. Kinematic mathematical model unit for defense unmanned boat and attack unmanned boat; The kinematic mathematical model of the defense unmanned boat is as follows: (1) in,i Indicates the number of defense unmanned boats, the value is ; Represents the position coordinates of the defense unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the defense unmanned boat, where represents the forward velocity of the defense unmanned boat in the hull coordinate system, represents the lateral velocity of the defense unmanned boat in the hull coordinate system; Indicates the actual movement direction of the defense unmanned boat, represents the bow angle of the defense unmanned boat in the earth coordinate system; represents the bow angular velocity of the defense unmanned boat in the boat coordinate system; It represents the sideslip angle of the defense unmanned boat in the boat coordinate system; In order to facilitate the design of underactuated unmanned boats, a normal function is introduced. The first i The position information of the defense unmanned boat is converted into , where the rotation vector ; Based on the kinematic mathematical model formula (1) of the defense unmanned boat, The time derivative of is as follows: (2) in, ; The kinematic mathematical model of the attack unmanned boat is as follows:

[0035] in, k Indicates the number of attacking unmanned boats; Represents the position coordinates of the attacking unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the attacking unmanned boat, where represents the forward speed of the attacking unmanned boat in the hull coordinate system, represents the lateral velocity of the attacking unmanned boat in the hull coordinate system; Indicates the actual movement direction of the unmanned boat. represents the bow angle of the attack unmanned boat in the earth coordinate system; It represents the bow angular velocity of the attack unmanned boat in the boat coordinate system; It represents the sideslip angle of the attacking unmanned boat in the boat coordinate system; Introducing positive constants The first k The position information of the attack unmanned boat is converted into , where the rotation vector ; The time derivative of is as follows: (2) in, ; definition , Indicates the kth attack unmanned boat The position of each two defense unmanned boats intercepts an attack unmanned boat. In the differential game, each group of states is defined as ,in , , Representation and defense of unmanned boats Collaborative capture of attack drones Defense unmanned boat ;definition Indicates the initial state of the system. 、 and The control inputs are described as , , .

[0036] B. Design of arrival-avoidance strategies for defending against and attacking unmanned boats; B1. Regional protection design unit; When i The first defense unmanned boat and the k The distance between the attacking unmanned boats is less than the capture radius When the defending unmanned boat successfully intercepts the attacking unmanned boat, that is: (3) In the design of the reach-avoid strategy, the area is used as the protected target. For the attacking unmanned boat, it is necessary to find the point closest to the target area that it can reach. , and continuously updated based on the corresponding game strategy, can be formulated as an equivalent optimization problem: (4) B2, optimal interception point solution unit; In a game involving two defending UAVs and one attacking UAV, the attacking UAV can be intercepted by either a single defending UAV or by the cooperation of two defending UAVs. This paper designs game strategies for these two scenarios, referred to as 1v1 and 2v1.

[0037] (1) 1v1 1v1 situation Figure 2 As shown, all unmanned boats have the same total speed, and the line segment The orthogonal lines divide the winning areas of the defensive and attacking unmanned boats , unmanned boat 、 and target point The relationship between is defined as: (5) Divide the state space into The barrier function The expression is as follows: (6) With line segment Orthogonal lines are represented by: (7) Attack drone boat The point on (7) that is closest to the target area should be aimed at to minimize the distance to the target area, which is represented as , and also a defense against unmanned boats The best interception point. By passing point And it is determined by the line perpendicular to (7), and its two-point equation is: (8) Based on equations (7) and (8), we can determine Coordinates: (9) Where: .

[0038] (2) 2v1 2v1 situation Figure 3 As shown in the figure, the two defense UAVs can cooperate to intercept the attacking UAV from a distance from the target area, reducing the risk to the target area. If the defense UAVs intercept alone, it will be difficult to achieve the optimal interception effect. To improve interception efficiency, the defense UAVs need to determine the best way to cooperate and maximize the distance between the attacking UAV and the target area.

[0039] Define the barrier function: (10) Where: , , .

[0040] In a 2v1 mission scenario, the attacking UAV can be intercepted by one of the two defending UAVs, or by both defending UAVs at the same time, and the latter has a greater team benefit. The sub-area where two defending unmanned boats simultaneously capture the attacking unmanned boat.

[0041] Two orthogonal lines 、 The expressions of are shown in formula (7) and formula (11): (11) when The best capture point as follows: (12) (13) Where: .

[0042] B3, optimal interception point selection unit; Given the initial position of the unmanned boat and assuming , there are three possibilities: (a) Single interception is the optimal result; (b) Single interception is the optimal result; (c) and Cooperative Interception By comparing various solutions of the 1v1 game, the problem of each unmanned boat determining the interception type and applying the best strategy is solved as follows.

[0043] Based on the orthogonal line expressions (7) and (11) that divide the winning areas of the defense unmanned boat and the attack unmanned boat, we can calculate which side of the line the optimal interception point is located on. 、 They are and and and The optimal interception point in the 1v1 game is further calculated as follows: (14) by For example, if , On the orthogonal line side; if , On the orthogonal line side, Therefore, when and When , the cooperative interception of the defense unmanned boat is the optimal result, where the interception point is , as shown in formula (12). If and , based on the optimal strategy, Single interception , where the intercept point is , as shown in formula (8). Similarly, if and , based on the optimal strategy, Single interception , where the intercept point is , as shown in formula (8). and The best interception point is 、 Zhongwei Provide the minimum cost point, so Closest to the target area.

[0044] B4, Optimal Differential Game Strategy Design Unit; (1) 1v1 Based on the above analysis, the optimal security game guidance strategy is further designed as follows: (15) Where: , .

[0045] (2) 2v1 Similarly, the optimal security game guidance strategy is designed as follows: (16) Where: , , .

[0046] C. Optimize the arrival-avoidance safety of defense and attack drone boats; C1, safety restraint unit; In order to ensure that there is no collision between two groups of unmanned boats in the area protection mission, it is necessary to ensure that the distance between the unmanned boats in each group and the distance between each unmanned boat participating in the game and the obstacle meet the requirements.

[0047] in: , Represent the positions of static obstacles and dynamic obstacles respectively; Indicates a safe distance.

[0048] The optimal game strategy aims to achieve the respective goals of defending and attacking unmanned boats. On this basis, a safety optimization method is proposed for both parties to ensure that no collision occurs during the game.

[0049] (1) Static obstacle avoidance In order to prevent the collision between the defense unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0050] Similar to the above analysis, in order to prevent the collision between the attacking unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0051] (2) Dynamic obstacle avoidance In order to prevent collisions between the defense unmanned boat and dynamic obstacles, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0052] Similar to the above analysis, in order to prevent the collision between the attacking unmanned boat and the dynamic obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0053] (3) Collision avoidance between adjacent unmanned boats In order to prevent the collision between the defense unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0054] Similar to the above analysis, in order to prevent the collision between the attacking unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

[0055] C2, input constraint unit; The speed of the defense unmanned boat and the attack unmanned boat is limited by ,in, 、 、 and Represents a given boundary.

[0056] C3, optimal security strategy solving unit; In order to minimize the impact of collision avoidance design on the heading change of the defensive unmanned boat, quadratic programming (QP) is used to generate the optimal safe heading signal.

[0057] (17) in, , , .

[0058] Similar to the above analysis, in order to minimize the impact of collision avoidance design on the heading change of the attacking unmanned boat, quadratic programming (QP) is used to generate the optimal safe heading signal

[0059] (18) in, .

[0060] D. Optimal safety guidance design unit for defense and attack unmanned boats; Design the optimal safety guidance signal based on the kinematic model and optimal safety strategy: (19) Defense unmanned boat Can be based on attack unmanned boats and its cooperative unmanned boat Current status and To adjust the defense strategy, so as to make decisions according to the current situation. You can also consider defending against unmanned boats Current status , update the avoidance strategy in time.

[0061] Example Consider a simulation scenario of area protection consisting of 5 attacking unmanned boats, 10 defending unmanned boats, 1 dynamic obstacle and 2 static obstacles. The protected target is a radius of A circular area of ​​15m, with the center point The initial state of the attacking unmanned boat is defined as , , ; Define the initial state of the defense unmanned boat as , , , , , . Capture radius of defensive drone boats μ To 4, set , the positions of the two static obstacles are , ; The initial position of the dynamic obstacle is The parameters related to safety optimization are designed as , , , , , , , , , , , , .

[0062] The simulation results are shown in Figures 4 to Figure 8 As shown in Figure 4, the trajectories of two groups of unmanned boats at different times are shown in Figure 4. Figure 3 The attacking unmanned boats were eventually captured before reaching the target area, and the defending unmanned boats successfully completed the regional protection mission. Figure 5 The final distance between the attacking unmanned boat and the defending unmanned boat is shown. It can be seen that the final distance between the defender and the attacker is The outside is equal to the capture radius, which proves that the defender successfully intercepts all attackers, including A 1 and A 3 was captured by the cooperation of two defense unmanned boats, A 2 were captured individually. Figure 6 and Figure 7 The combined speed and bow angular velocity of the attacking unmanned boat and the defending unmanned boat are displayed respectively. The results show that the combined speed and bow angular velocity of all unmanned boats meet the speed constraint conditions. Figure 8 Represents the distances between the two groups of UAVs and static and dynamic obstacles, as well as the distances between adjacent UAVs in the group. Figure 8 In , all distances are greater than the given minimum safety distance.

[0063] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A differential game controller for safe arrival and avoidance of multiple unmanned boats, characterized by: include: Defense unmanned boat kinematics mathematical model unit; the defense unmanned boat kinematics mathematical model unit sends a position signal and To the optimal differential game strategy design unit for the defense unmanned boat; the kinematic mathematical model unit of the defense unmanned boat sends a position signal and To the optimal interception point solution unit; Attack unmanned boat kinematics mathematical model unit; the attack unmanned boat kinematics mathematical model unit sends a position signal To the optimal differential game strategy design unit for attacking unmanned boats; the kinematic mathematical model unit for attacking unmanned boats sends a position signal To the regional protection design unit; the attack unmanned boat kinematic mathematical model unit sends a position signal To the optimal interception point solution unit; Regional Protection Design Unit; The area protection design unit sends an intrusion point location signal To the optimal interception point solution unit; Optimal interception point solving unit; the optimal interception point solving unit sends the optimal interception point position signal and Select the unit to the best interception point; Optimal interception point selection unit; The optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for defending unmanned boats; The optimal interception point selection unit sends the selected optimal interception point position signal , or To the optimal differential game strategy design unit for attacking unmanned boats; Optimal differential game strategy design unit for defending unmanned boats; the optimal differential game strategy design unit for defending unmanned boats sends an optimal speed signal To the unit for solving the optimal safety strategy for defending unmanned boats; Attacking unmanned boat optimal differential game strategy design unit; the attacking unmanned boat optimal differential game strategy design unit sends an optimal speed signal To the unit for solving the optimal safety strategy for attacking unmanned boats; Defense unmanned boat safety constraint unit; the defense unmanned boat safety constraint unit sends a safety constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat safety constraint unit; the attack unmanned boat safety constraint unit sends a safety constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Defense unmanned boat input constraint unit; the defense unmanned boat input constraint unit sends an input constraint condition signal to the defense unmanned boat optimal safety strategy solving unit; An attack unmanned boat input constraint unit; the attack unmanned boat input constraint unit sends an input constraint condition signal to the attack unmanned boat optimal safety strategy solving unit; Optimal safety strategy solving unit for defending unmanned boat; said optimal safety strategy solving unit for defending unmanned boat sends optimal safety speed signal To the optimal safety guidance design unit for defense unmanned boats; Attacking unmanned boat optimal safety strategy solving unit; the attacking unmanned boat optimal safety strategy solving unit sends the optimal safety speed signal To the optimal safety guidance design unit for attacking unmanned boats; Optimal safety guidance design unit for defending unmanned boats; the optimal safety guidance design unit for defending unmanned boats sends an optimal safety guidance signal and To the kinematic mathematical model unit of the defense unmanned boat; Attack unmanned boat optimal safety guidance design unit; the attack unmanned boat optimal safety guidance design unit sends the optimal safety guidance signal and To the kinematic mathematical model unit of attack unmanned boat.

2. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The kinematic mathematical model of the defense unmanned boat is as follows: （1） in, i Indicates the number of defense unmanned boats; Represents the position coordinates of the defense unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the defense unmanned boat, where represents the forward velocity of the defense unmanned boat in the hull coordinate system, represents the lateral velocity of the defense unmanned boat in the hull coordinate system; Indicates the actual movement direction of the defense unmanned boat, represents the bow angle of the defense unmanned boat in the earth coordinate system; represents the bow angular velocity of the defense unmanned boat in the boat coordinate system; It represents the sideslip angle of the defense unmanned boat in the boat coordinate system; Introducing positive constants The first i The position information of the defense unmanned boat is converted into , where the rotation vector ; The time derivative of is as follows: （2） in, ； The kinematic mathematical model of the attack unmanned boat is as follows: in, k Indicates the number of attacking unmanned boats; Represents the position coordinates of the attacking unmanned boat in the two-dimensional plane, which is used to describe the position of the unmanned boat in the earth coordinate system; Indicates the actual movement speed of the attacking unmanned boat, where represents the forward speed of the attacking unmanned boat in the hull coordinate system, represents the lateral velocity of the attacking unmanned boat in the hull coordinate system; Indicates the actual movement direction of the unmanned boat. represents the bow angle of the attack unmanned boat in the earth coordinate system; represents the bow angular velocity of the attack unmanned boat in the boat coordinate system; It represents the sideslip angle of the attacking unmanned boat in the boat coordinate system; Introducing positive constants The first k The position information of the attack unmanned boat is converted into , where the rotation vector ; The time derivative of is as follows: （2） in, ； definition , Indicates the kth attack unmanned boat The position of each two defense unmanned boats intercepts an attack unmanned boat. In the differential game, each group of states is defined as ,in , , Representation and defense of unmanned boats Collaborative capture of attack drones Defense Unmanned Boat ;definition Indicates the initial state of the system.

3. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 2, characterized in that: The regional protection design units are as follows: When i The first defense unmanned boat and the k The distance between the attacking unmanned boats is less than the capture radius When the defending unmanned boat successfully intercepts the attacking unmanned boat, that is: （3） In the reach-avoid strategy design, the area is used as the protected target; for the attacking unmanned boat, it is necessary to solve the point on the target area that the attacking unmanned boat can reach. , and continuously updated based on the corresponding game strategy, it can be explained as an equivalent optimization problem: 。 4. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 3, characterized in that: The optimal interception point solving unit includes a 1v1 game strategy and a 2v1 game strategy, which are as follows: The 1v1 game strategy is that the attacking unmanned boat is intercepted by a single defensive unmanned boat; all unmanned boats have the same combined speed, and the line segment The orthogonal lines divide the winning areas of the defensive and attacking unmanned boats , defense unmanned boat , attack unmanned boats and target point The relationship between is defined as: （5） Divide the state space into The barrier function The expression is as follows: （6） With line segment Orthogonal lines are represented by: （7） Attack drone boat Aiming and Line Segments The point on the orthogonal line closest to the target area, thereby minimizing the distance to the target area, is represented as , that is, defense unmanned boats The best interception point; The two-point equation is: （8） Coordinates: （9） Where: ; The 2v1 game strategy is that the attacking unmanned boat is intercepted by the two defending unmanned boats in cooperation; the two defending unmanned boats cooperate to intercept the attacking unmanned boat at a location far away from the target area, thereby reducing the risk faced by the target area; Define the barrier function: （10） Where: , , ; definition A sub-area for two defending UAVs to simultaneously capture the attacking UAV; The expression is as follows: （11） when The best capture point as follows: （12） （13） Where: .

5. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 4, characterized in that: The optimal interception point selection unit is as follows: Given the initial position of the unmanned boat and assuming , there are three possibilities: the first possibility is Single interception is the optimal result; the second possibility is Single interception is the optimal result; the third possibility is and Cooperative Interception is the optimal result; by comparing various solutions of the 1v1 game, the problem of each unmanned boat determining the interception type and applying the best strategy is solved; Based on the orthogonal line expression that divides the winning areas of the defense unmanned boat and the attack unmanned boat, calculate which side of the line the optimal interception point is located on; let 、 They are and and and The best interception point in a 1v1 game is calculated as follows: （14） when and When , the cooperative interception of the defense unmanned boat is the optimal result, where the interception point is ;if and , based on the optimal strategy, Single interception , where the intercept point is ;if and , based on the optimal strategy, Single interception , where the intercept point is ;when and The best interception point is 、 Zhongwei Provide the minimum cost point, so Closest to the target area.

6. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The optimal differential game strategy design unit is as follows: The optimal safety game guidance strategy for 1v1 game strategy is as follows: （15） Where: , ; The optimal safety game guidance strategy for the 2v1 game strategy is as follows: （16） Where: , , .

7. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The attack unmanned boat safety restraint unit and the defense unmanned boat safety restraint unit are as follows: To ensure that there is no collision between the two groups of UAVs in the area protection mission, the distance between the UAVs in each group and the distance between each UAV participating in the game and the obstacle must meet the following requirements: in: , represents the position of the static obstacle; Indicates the position of dynamic obstacles; Indicates safe distance; Static obstacle avoidance; In order to prevent the collision between the defense unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the static obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; Dynamic obstacle avoidance; In order to prevent collisions between the defense unmanned boat and dynamic obstacles, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the dynamic obstacle, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; Collision avoidance between adjacent unmanned boats; In order to prevent collisions between the defense unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , ; In order to prevent the collision between the attacking unmanned boat and the adjacent unmanned boat, a fixed time control obstacle function is selected. , and meet the safety constraints ,in, , , , .

8. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The attack unmanned boat input constraint unit and the defense unmanned boat input constraint unit are as follows: The speed of the defense unmanned boat and the attack unmanned boat is limited by ,in, 、 、 and Represents a given boundary.

9. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The optimal safety strategy solving unit for attacking unmanned boats and the optimal safety strategy solving unit for defending unmanned boats are as follows: In order to minimize the impact of collision avoidance design on the heading change of the defensive unmanned boat, quadratic programming is used to generate the optimal safe heading signal : （17） in, , , ; In order to minimize the impact of collision avoidance design on the heading change of the attacking unmanned boat, quadratic programming is used to generate the optimal safe heading signal ; （18） in, .

10. The multi-unmanned boat safe arrival-avoidance differential game controller according to claim 1, characterized in that: The optimal safety guidance design unit for attacking unmanned boats and the optimal safety guidance design unit for defending unmanned boats are as follows: Design the optimal safety guidance signal based on the kinematic model and optimal safety strategy: （19） Defense unmanned boat Attack unmanned boat and its cooperative unmanned boat Current status and Adjust defense strategies to make decisions based on the current situation; Attack drone boat Consider defending against unmanned boats Current status , update the avoidance strategy in time.

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