Heterogeneous aircraft anti-collision method and system based on Nash bargaining

Abstract

The invention relates to a heterogeneous aircraft anti-collision method and system based on Nash bargaining, and belongs to the technical field of aircraft control. In order to solve the problem of lack of heterogeneous aircraft anti-collision methods in the prior art, the invention provides the heterogeneous aircraft anti-collision method and system based on Nash bargaining, the Nash bargaining method is adopted, Pareto optimization is realized under the condition of considering the maneuverability of each aircraft, fair cooperation of the aircrafts in the formation can be realized, and the anti-collision performance of the aircrafts is improved. The method comprises the following steps: step 1, defining a utility function: taking the size of a speed output scalar of each aircraft as a utility function of the aircraft; 2, determining negotiation parameters according to the utility function in the step 1; step 3, determining a target function according to the utility function and the constraint condition; 4, solving the target function to obtain the speed of each aircraft; and 5, adjusting the speed of each aircraft to obtain a final result.

Description

Technical Field

[0001] The present invention relates to a heterogeneous aircraft collision avoidance method and system, in particular to a heterogeneous aircraft collision avoidance method and system based on Nash bargaining, belonging to the technical field of aircraft control. Background Art

[0002] In some mission scenarios, high-speed aircraft with different flight speeds need to cooperate to complete the task. When performing formation flying or collaborative tasks, collision avoidance between aircraft is the most basic issue involving flight safety. Currently, most existing technologies are aimed at homogeneous aircraft, while there is little research on the optimal collision avoidance control between heterogeneous aircraft with different flight speeds. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of lack of heterogeneous aircraft collision avoidance method in the prior art, and to provide a heterogeneous aircraft collision avoidance method and system based on Nash bargaining. The method adopts the Nash bargaining method to achieve Pareto optimality while considering the maneuverability of each aircraft, which helps to achieve fair cooperation among aircraft in the formation and improve the efficiency and stability of the overall mission execution.

[0004] In order to solve the above problems, the present application is implemented through the following technical solutions: A heterogeneous aircraft collision avoidance method based on Nash bargaining is special in that it includes the following steps: Step 1, define the utility function: take the size of the speed output scalar of each aircraft as a utility function of the aircraft; Step 2: Determine negotiation parameters based on the utility function in step 1; Step 3: Determine the objective function based on the utility function in step 1 and the constraints in step 2; Step 4: Solve the objective function in step 3 to obtain the speed of each aircraft; Step 5: Adjust the speed of each aircraft in step 4 to obtain the final result.

[0005] Furthermore, the utility function in step 1 is: , Where: is the utility function of the aircraft, describing the aircraft The speed reflects the consumption of the aircraft when adjusting its position. Change vector for the aircraft velocity; For aircraft In coordinates Axis direction and The actual speed in the axis direction.

[0006] Furthermore, the negotiation parameters in step 2 include the maximum speed of the aircraft Negotiation breakdown point And the range of feasible solutions that satisfy the constraints ; The negotiation result cannot exceed the maximum flight speed of the aircraft. The negotiation breaking point is defined as: .

[0007] Furthermore, the constraints in step 2 include the Lyapunov condition for flying to the destination and the Lyapunov barrier function condition. Among them, the Lyapunov condition for flying to the destination is: , Where: It is the Lyapunov candidate function, which is a non-negative scalar function that describes the energy or some cost of the system state; and for The derivative along the system dynamics describes rate of change under system dynamics; for About system status The time derivative of , which describes the influence of the natural evolution of the system given its current state; for About control input The derivative of , which describes the effect of the system response under a given control input; is the control input, which represents the control action applied to the system; is a non-negative constant, which is regarded as the decay rate or margin; is the threshold of system stability; The Lyapunov barrier function condition is: , Where: is the Lyapunov obstacle function, which is a non-negative scalar function. In the collision avoidance problem, it represents the rate of change of the distance between the aircraft. is a non-negative constant that is considered as a safety margin or the growth rate of the barrier function.

[0008] Furthermore, the objective function of the aircraft in step 3 is:  * ( N , S , d ) = a r g m a x [ ∏ i = 1 N ( U i − d i ) ] , Where: is the set of feasible solutions, that is, the set of solutions that satisfy all constraints; The number of aircraft calculated for the purpose of participating in the negotiations; is the state space, i.e., the set of possible states of all aircraft; is the distance threshold, i.e., the minimum allowed distance between aircraft; For the The utility function value under the constraints describes the utility or performance of the aircraft under the given constraints; For the The distance threshold under each constraint is specific to each constraint; To find feasible solution set The combination of parameters that maximizes a given function; is a set of optimal control inputs, which are the control outputs of each aircraft The vector formed; .

[0009] Furthermore, the step 4 uses Sequential Quadratic Programming to solve the objective function in step 3, and the specific steps are as follows: Step 4.1, initialize the currently estimated optimal solution, x0; Step 4.2, evaluate the objective function in step 3 and the constraint conditions in step 2 at x0; Step 4.3, by using quadratic functions to approximate the objective function and constraints, a QP subproblem is formed; Step 4.4, solve the QP subproblem to obtain a new optimal solution estimate, x1; Step 4.5, use x1 to update the currently estimated optimal solution; Step 4.6: Repeat steps 4.2 to 4.5 until the solution meets the constraints.

[0010] Furthermore, the step 5 is adjusted using an iterative method.

[0011] A Nash bargaining-based heterogeneous aircraft collision avoidance system is characterized in that: it includes a main controller for solving an optimal control input that satisfies constraints and a safety distance, and transmits the optimal control input to each aircraft, and simultaneously receives speed information of each aircraft; A communication module, used to transmit information between the main controller and each aircraft; An aircraft comprises an aircraft communication module and a flight control cross-linking interface, wherein the aircraft communication module is used to transmit information between the communication module and the flight control cross-linking structure, and the flight control cross-linking interface is used to collect speed information of the aircraft and transmit information of the aircraft communication module.

[0012] The present invention determines the constraint requirements of the aircraft by defining the Lyapunov condition, determines the range of feasible solutions by using the Lyapunov function and the Lyapunov barrier function, and uses the Nash bargaining method to solve the problem. The optimal control instructions of the overall task can be achieved while considering the maneuverability of each aircraft, thereby achieving Pareto optimality. The maximum speed instruction limit of each aircraft is set by negotiating a breaking point, and the speed output instruction is optimized based on the breaking point setting value, which is suitable for heterogeneous aircraft clusters with obvious speed differences. The method helps to achieve fair cooperation among the aircraft in the formation and improve the efficiency and stability of the overall task execution. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of the present invention; Figure 2 It is a structural schematic diagram of the present invention. DETAILED DESCRIPTION

[0014] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0015] Example 1. A heterogeneous aircraft collision avoidance method based on Nash bargaining, the specific process is as follows Figure 1 As shown, the following steps are included: Step 1, define the utility function: take the size of the speed output scalar of each aircraft as a utility function of the aircraft; Step 2, determine the negotiation parameters according to the utility function in step 1; Step 3: Determine the objective function based on the utility function in step 1 and the constraints in step 2; Step 4: Solve the objective function in step 3 to obtain the speed of each aircraft; Step 5: Adjust the speed of each aircraft in step 4 to obtain the final result.

[0016] Furthermore, the utility function in step 1 is: , Where: is the utility function of the aircraft, describing the aircraft The speed reflects the consumption of the aircraft when adjusting its position. Change vector for the aircraft velocity; For aircraft In coordinates Axis direction and The actual speed in the axis direction.

[0017] Furthermore, the negotiation parameters in step 2 include the maximum speed of the aircraft Negotiation breakdown point And the range of feasible solutions that satisfy the constraints ; The negotiation result cannot exceed the maximum flight speed of the aircraft. The negotiation breaking point is defined as: .

[0018] Furthermore, the constraints in step 2 include the Lyapunov condition for flying to the destination and the Lyapunov barrier function condition. Among them, the Lyapunov condition for flying to the destination is: , Where: It is the Lyapunov candidate function, which is a non-negative scalar function that describes the energy or some cost of the system state; and for The derivative along the system dynamics describes rate of change under system dynamics; for About System Status The time derivative of , which describes the influence of the natural evolution of the system given its current state; for About control input The derivative of , which describes the effect of the system response under a given control input; is the control input, which represents the control action applied to the system; is a non-negative constant, which is regarded as the decay rate or margin; is the threshold of system stability; Lyapunov conditions for flight to destination means that, through appropriate control input , ensuring that the Lyapunov candidate function decay at an appropriate rate, thereby ensuring that the system converges stably to the target state, i.e., flies to the destination. This condition ensures that the system dynamics and control input can make the candidate function Stay in the stable zone; The Lyapunov barrier function condition is: , Where: is the Lyapunov obstacle function, which is a non-negative scalar function. In the collision avoidance problem, it represents the rate of change of the distance between the aircraft. is a non-negative constant, which is regarded as the growth rate of the safety margin or barrier function; Lyapunov barrier function conditions It means that the control input It can ensure that the Lyapunov barrier function It is non-negative and grows at an appropriate rate, thus ensuring that the system state remains outside a safe distance, i.e., collision avoidance. This condition ensures that the distance between the aircraft is always greater than or equal to zero, thus avoiding collisions.

[0019] Furthermore, the objective function of the aircraft in step 3 is:  * ( N , S , d ) = a r g m a x [ ∏ i = 1 N ( U i − d i ) ] , Where: is the set of feasible solutions, that is, the set of solutions that satisfy all constraints. The number of aircraft calculated for negotiation, is the state space, that is, the set of possible states of all aircraft, is the distance threshold, i.e. the minimum allowed distance between aircrafts, For the The utility function value under the constraints describes the utility or performance of the aircraft under the given constraints. For the The distance threshold under each constraint is specific to each constraint; To find feasible solution set The combination of parameters that maximizes a given function; is a set of optimal control inputs, which are the control outputs of each aircraft The vector formed by , The whole equation  * ( N , S , d ) = a r g m i n [ ∏ i = 1 N ( U i − d i ) ] It means: find a set of control inputs , so that all aircraft simultaneously meet all constraints and maximize the difference between the utility function value under each constraint and the distance threshold, which means finding a set of control inputs that enables the aircraft to complete the task in the most efficient way while ensuring that all constraints and safety distance requirements are met.

[0020] Furthermore, the step 4 uses Sequential Quadratic Programming to solve the objective function in step 3, and the specific steps are as follows: Step 4.1, initialize the currently estimated optimal solution, x0; Step 4.2, evaluate the objective function in step 3 and the constraint conditions in step 2 at x0; Step 4.3, by using quadratic functions to approximate the objective function and constraints, a QP subproblem is formed; Step 4.4, solve the QP subproblem to obtain a new optimal solution estimate, x1; Step 4.5, use x1 to update the currently estimated optimal solution; Step 4.6: Repeat steps 4.2 to 4.5 until the solution meets the constraints.

[0021] Furthermore, the step 5 is adjusted by an iterative method, and the specific iterative solution adopts mature QP solver software, which can be automatically executed by a computer.

[0022] Embodiment 2. A Nash bargaining-based heterogeneous aircraft collision avoidance system using the Nash bargaining-based heterogeneous aircraft collision avoidance method described in Embodiment 1, such as Figure 2 As shown, it includes a main controller for solving the optimal control input that satisfies the constraint conditions and the safety distance, and transmitting the optimal control input to each aircraft, while receiving the speed information of each aircraft; A communication module, used to transmit information between the main controller and each aircraft; An aircraft comprises an aircraft communication module and a flight control cross-linking interface, wherein the aircraft communication module is used to transmit information between the communication module and the flight control cross-linking structure, and the flight control cross-linking interface is used to collect speed information of the aircraft and transmit information of the aircraft communication module.

[0023] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the defined scope.

Claims

1. A heterogeneous aircraft collision avoidance method based on Nash bargaining, characterized by: The following steps are involved: Step 1, define the utility function: take the size of the speed output scalar of each aircraft as a utility function of the aircraft; Step 2: Determine negotiation parameters based on the utility function in step 1; Step 3: Determine the objective function based on the utility function in step 1 and the constraints in step 2; Step 4: Solve the objective function in step 3 to obtain the speed of each aircraft; Step 5: Adjust the speed of each aircraft in step 4 to obtain the final result.

2. The Nash bargaining-based heterogeneous aircraft collision avoidance method according to claim 1 is characterized in that: The utility function in step 1 is: , Where: is the utility function of the aircraft, describing the aircraft The speed reflects the consumption of the aircraft when adjusting its position. Change vector for the aircraft velocity; For aircraft In coordinates Axis direction and The actual speed in the axis direction.

3. A heterogeneous aircraft collision avoidance method based on Nash bargaining according to claim 1 or 2, characterized in that: The negotiation parameters in step 2 include the maximum speed of the aircraft Negotiation breakdown point And the range of feasible solutions that satisfy the constraints ; The negotiation result cannot exceed the maximum flight speed of the aircraft. The negotiation breaking point is defined as: .

4. The Nash bargaining-based heterogeneous aircraft collision avoidance method according to claim 3 is characterized by: The constraints in step 2 include the Lyapunov condition for flying to the destination and the Lyapunov barrier function condition. Among them, the Lyapunov condition for flying to the destination is: , Where: It is the Lyapunov candidate function, which is a non-negative scalar function that describes the energy or some cost of the system state; and for The derivative along the system dynamics describes rate of change under system dynamics; for About System Status The time derivative of , which describes the influence of the natural evolution of the system given its current state; for About control input The derivative of , which describes the effect of the system response under a given control input; is the control input, which represents the control action applied to the system; is a non-negative constant, which is regarded as the decay rate or margin; is the threshold of system stability; The Lyapunov barrier function condition is: , Where: is the Lyapunov obstacle function, which is a non-negative scalar function. In the collision avoidance problem, it represents the rate of change of the distance between the aircraft. is a non-negative constant that is considered as a safety margin or the growth rate of the barrier function.

5. The Nash bargaining-based heterogeneous aircraft collision avoidance method according to claim 3 is characterized by: The objective function of the aircraft in step 3 is: , Where: is the set of feasible solutions, that is, the set of solutions that satisfy all constraints; The number of aircraft calculated for the purpose of participating in the negotiations; is the state space, i.e., the set of possible states of all aircraft; is the distance threshold, i.e., the minimum allowed distance between aircraft; For the The utility function value under the constraints describes the utility or performance of the aircraft under the given constraints; For the The distance threshold under each constraint is specific to each constraint; To find feasible solution set The combination of parameters that maximizes a given function; is a set of optimal control inputs, which are the control outputs of each aircraft The vector formed; .

6. The Nash bargaining-based heterogeneous aircraft collision avoidance method according to claim 3 is characterized by: The step 4 uses Sequential Quadratic Programming to solve the objective function in step 3, and the specific steps are as follows: Step 4.1, initialize the currently estimated optimal solution, x0; Step 4.2, evaluate the objective function in step 3 and the constraint conditions in step 2 at x0; Step 4.3, by using quadratic functions to approximate the objective function and constraints, a QP subproblem is formed; Step 4.4, solve the QP subproblem to obtain a new optimal solution estimate, x1; Step 4.5, use x1 to update the currently estimated optimal solution; Step 4.6: Repeat steps 4.2 to 4.5 until the solution meets the constraints.

7. The Nash bargaining-based heterogeneous aircraft collision avoidance method according to claim 3 is characterized by: The step 5 is adjusted by an iterative method.

8. A heterogeneous aircraft collision avoidance system using a heterogeneous aircraft collision avoidance method based on Nash bargaining as described in any one of claims 1 to 7, characterized in that: It includes a main controller for solving the optimal control input that satisfies the constraints and the safety distance, and transmitting the optimal control input to each aircraft, and receiving the speed information of each aircraft; A communication module, used to transmit information between the main controller and each aircraft; An aircraft includes an aircraft communication module and a flight control cross-linking interface, wherein: the aircraft communication module is used to transmit information between the communication module and the flight control cross-linking structure, and the flight control cross-linking interface is used to collect speed information of the aircraft and transmit information of the aircraft communication module.

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