Non-cooperative game collaborative control method for air-floating microgravity experimental platform

Abstract

The present invention relates to a non-cooperative game collaborative control method for an air-floating microgravity test platform. A planar motor and a servo platform are defined as two participants in a non-cooperative game when the air-floating microgravity test platform is working. The core goal of the game strategy is to ensure that the resultant force acting on the air-floating microgravity test platform is close to zero, that is, the resultant force is minimized. The optimization problem of the game strategy is determined. When the game forms a situation, a profit function is introduced as an evaluation criterion for the participants to select strategies, and two profit functions are constructed: the resultant force profit and the speed profit of the air-floating microgravity test platform. The final result of the game is a Nash equilibrium solution.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace microgravity simulation platform control, and in particular relates to a cooperative control method of an air-floating microgravity test platform based on non-cooperative game. Background Art

[0002] With the rapid development of space technology, large deployable structures such as solar panels and satellite antennas, as important components of spacecraft, have a significant impact on the success of the entire space mission due to their stable and accurate performance. Because it is difficult to fully simulate the microgravity operating conditions of these structures in space on the ground, building an efficient and reliable microgravity simulation system is crucial.

[0003] Traditional air-floating microgravity test platforms simulate microgravity environments through the collaborative operation of planar motors and servo platforms. Cooperative game theory has been applied to the coordinated control of the servo platform and planar motor, aiming to achieve optimal control through close cooperation and information sharing between the two parties. However, this approach faces a number of challenges in practical applications: First, the cooperative game requires extensive information exchange between the servo platform and the planar motor, which not only increases the system's communication burden but can also lead to information transmission delays and errors. Second, the complex information processing mechanism increases system complexity and cost, reducing the overall system efficiency and reliability. Finally, under extreme operating conditions or sudden failures, the cooperative game-based collaborative control may fail due to information interruptions or processing delays, affecting the accuracy and stability of microgravity simulations. Given these challenges, a new non-cooperative game-based collaborative control strategy is urgently needed to replace or optimize existing cooperative game control methods. Summary of the Invention

[0004] In order to solve the existing problems, the purpose of the present invention is to propose a non-cooperative game collaborative control model for an air-floating microgravity test platform. On a limited air-floating microgravity test platform, the non-cooperative goal of minimizing the combined force is achieved by selecting strategies for each leveling output. The core idea of ​​the non-cooperative game collaborative control strategy is to enable the servo platform and the planar motor to achieve autonomous and efficient collaborative work without relying on a large amount of information exchange through an intelligent control algorithm. This control strategy not only reduces the complexity and cost of the system, but also improves the robustness and adaptability of the system, and can maintain stable control performance under various working conditions. The technical solution is as follows:

[0005] A non-cooperative game collaborative control method for an air-floating microgravity test platform is disclosed. The air-floating microgravity test platform includes an upper support structure, a measurement baseplate, and an air-floating bearing. A planar motor and a servo platform are defined as two participants in a non-cooperative game when the air-floating microgravity test platform is operating. In the non-cooperative task, the participants aim to achieve leveling as quickly as possible. The motion mode of the planar motor is simplified to uniformly accelerated linear motion. Each participant knows each other's current state information. The non-cooperative game collaborative control method is as follows:

[0006] In the game process, the set of the participant's currently available movement strategies is called the participant's strategy set, and Indicates that the subscript i represents the i-th step strategy to be executed, represents the strategy of the servo-following system at step i, is the angle (°) that the servo platform will move in step i, represents the strategy of the planar motor in step i, is the electromagnetic force required to be output by the planar motor in step i (N);

[0007] The core goal of the game strategy is to keep the net force on the air-floating microgravity test platform close to zero, that is, to minimize the net force, while ensuring that the following two constraints are met:

[0008] Planar motor displacement distance constraint: Ensures that after each strategy step, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from detaching from the servo platform;

[0009] Planar motor static state constraint: requires the moving speed of the planar motor to be strictly 0;

[0010] Determine the optimization problem of the game strategy for step i (i = 1, 2, ..., n);

[0011] When the game forms a situation, the profit function is introduced as a participant The evaluation criteria for strategy selection are constructed by constructing two benefit functions: one is the combined benefit of the air-floating microgravity test platform The resultant force threshold is preset. At each step of control, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, when the difference between the resultant force generated by each participant and the target is within the resultant force threshold, the smaller the value, the greater the benefit the participant obtains. Otherwise, the resultant force sub-item benefit value is set to zero. The other is the speed benefit of the air-floating microgravity test platform. A speed threshold is preset. When the planar motor speed value is less than the speed threshold, the smaller the planar motor speed value, the greater the benefit the participant obtains. Otherwise, the speed sub-item benefit value is set to zero.

[0012] The final result of the game is the Nash equilibrium solution. It is necessary to determine the strategy of the initial control period servo platform and the planar motor; perform iterative solution to obtain the strategy set T consisting of the Nash equilibrium solution. i , T i It represents the strategy that the servo platform and planar motor can use to achieve the optimal performance at step i.

[0013] Further,

[0014] The optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows:

[0015]

[0016] Among them, the angle θ between the servo platform and the horizontal plane under the i-th step game strategy is i As the decision vector, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in step i, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set; F em,i represents the actual output electromagnetic force of the planar motor under the strategy of step i, which is obtained from the electromagnetic characteristics of the planar motor, G i Represents the gravity acting on the planar motor; x i represents the displacement of the planar motor under the game strategy in step i, and its absolute value |x i |, h is the maximum allowable displacement of the planar motor; for the movement speed of the planar motor, assuming that its movement direction is in the same direction as the force, its movement speed is expressed as where v i-1 That is, the speed of the i-1th step (mm / s). In the initial state, v0=0, m is the weight of the planar motor, and t is the movement time.

[0017] Furthermore, the combined benefits of the air-floating microgravity test platform The definition is as follows:

[0018] Assume that the difference between the current total force generated by each participant and the expected target is F i,goal (θ i ,F em,i ),

[0019] F i,goal (θ i ,F em,i )=F i (θ i,F em,i )-R (1)

[0020] Where, F i (θ i ,F em,i ) is the current resultant force generated by each participant, and the desired target is the minimum value R that the resultant force approaches;

[0021] Preset resultant force threshold F safe,i , the combined benefits of the air-floating microgravity test platform Expressed as:

[0022]

[0023] When the difference between the total force generated by each participant and the target is F i,goal (θ i ,F em,i ) is within the combined force threshold, the smaller its value is, the greater the benefits the participants will gain. i,goal (θ i ,F em,i ) is greater than F safe,i When , let the resultant component benefit be zero.

[0024] In each further control step, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, the resultant force threshold F is adjusted by dichotomy. safe,i .

[0025] Furthermore, the speed gain of the air-floating microgravity test platform The definition is as follows:

[0026] Let v i (θ i ) is the current speed value of the planar motor, which is calculated by the planar motor moving speed solution model; the preset speed threshold v safe,i ;

[0027] Speed ​​Gains of Air-Floating Microgravity Experimental Platform Expressed as:

[0028]

[0029] When the planar motor speed is less than the speed threshold v safe,i When v i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i When , let the speed sub-item benefit value be zero.

[0030] Furthermore, at each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the speed threshold v is adjusted by dichotomy. safe,i .

[0031] Furthermore, the strategy for the initial control period servo platform and planar motor is as follows: θ0 takes the angle of the servo platform in the initial state, and F0 takes the electromagnetic force required to be output when the planar motor starts.

[0032] Furthermore, the strategy set is solved by the Nash equilibrium solution of the game model constitute, is the angle that the servo platform will move in step i, is the displacement of the planar motor in the i-th step, is the speed at which the planar motor will move in the i-th step, satisfy

[0033]

[0034] Where, the subscript i represents the i-th step, j = 1, 2 represents two types of profit functions, namely, formula (2) and formula (3), θ i ,x i ,v i They are the platform tilt angle value, plane motor displacement distance value and speed value measured in the i-th step, collectively referred to as the measured state value.

[0035] Furthermore, the method of iteratively solving and obtaining a strategy set consisting of Nash equilibrium solutions is as follows:

[0036] The number of iterations is preset. At each step of control, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the combined force gain and speed gain of both participants; when the first iteration is performed, substitute the currently measured platform tilt angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (4), if the expected value of the platform inclination angle can be obtained Expected displacement distance of the planar motor Planar motor speed expectation The minimum value of is used as the strategy for the next step. The iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the strategy for the next step, and the iteration ends. If the minimum value of all expected values ​​cannot be solved after reaching the number of iterations, the expected value used in the last iteration is taken, and the current strategy combination is considered to be the Nash equilibrium solution, which is used as the strategy for the next step. The executable strategy of each participant in step i is obtained. Then, the first two steps strategy is and Re-substitute the combined force benefit and speed benefit, take the strategy with the largest benefit, and form the strategy set T i .

[0037] The technical effects of the present invention are as follows:

[0038] 1. By constructing a non-cooperative game-based collaborative control model, the servo platform and planar motor intelligently select a leveling output strategy based on the principle of maximizing their respective interests. This strategy selection mechanism ensures that when working together, the two effectively reduce the net force, achieving the goal of minimizing the net force. Simulations have verified that the model can maintain stable leveling capabilities even with frequent sinusoidal net force changes, effectively addressing complex and changing operating conditions.

[0039] 2. During the design process, constraint functions were specifically introduced for the planar motor's speed and displacement control. These constraints effectively limit the motor's range of motion, preventing it from sliding off the limited cast iron platform due to excessive movement, thereby ensuring safe and stable system operation. This design not only improves system reliability but also reduces maintenance costs caused by unexpected failures.

[0040] 3. Strict maximum constraints are imposed on the number of iterations and the number of steps for strategy changes. This measure significantly reduces the amount of computation, allowing the system to complete the strategy selection and optimization process in a shorter time. As a result, the system's response speed is greatly improved, enabling faster adaptation to changes in the external environment and improving overall control efficiency. Furthermore, due to the reduced computational effort, the application scenarios of this invention are also widely expanded, making it applicable to more industrial control fields with high real-time requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 :Force conditions when the servo platform is working

[0042] Figure 2 : Air-floating workbench, in the figure: 1—servo drive; 2—upper support structure; 3—measurement substrate; 4—air-floating bearing.

[0043] Figure 3 : Planar motor force output response curve when the system initial force is given as a 100Hz sinusoidal change

[0044] Figure 4: Servo platform force output response curve when the system initial force is given as a 100Hz sine change

[0045] Figure 5 : Resultant force output response curve of the air-floating microgravity test platform when the system's initial resultant force is given as a 100Hz sinusoidal change

[0046] Figure 6 : Planar motor force output response curve when the system initial force is given as a 10Hz sinusoidal change

[0047] Figure 7 : Servo platform force output response curve when the system's initial force is given as a 10Hz sinusoidal change

[0048] Figure 8 : Resultant force output response curve of the air-floating microgravity test platform when the system's initial resultant force is given by a 10Hz sinusoidal change;

[0049] Figure 9 The process of solving the collaborative control game strategy of the air-floating microgravity experimental platform. DETAILED DESCRIPTION

[0050] The present invention proposes a non-cooperative game model for cooperative control of an air-floating microgravity test platform. The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0051] Based on the concept of non-cooperative game theory, this study investigates how each participant makes decisions to maximize their own interests. The basic research approach is to establish a non-cooperative game collaborative control model for an air-floating microgravity test platform, using the planar motor and servo platform as game participants, their respective leveling outputs as the strategy set, and the resulting horizontal force as the payoff function.

[0052] A non-cooperative game approach focuses on the strategy selection that maximizes the individual interests of the participants. The set of all possible motion strategies for the servo platform and the planar motor in the current environment is defined as the strategy set of each participant. Payoff functions are defined for the air-floating microgravity test platform. These functions evaluate the performance or benefits of each strategy based on the current strategy combination and solve for a Nash equilibrium to ensure that the coordinated control of the air-floating microgravity test platform achieves the minimum resultant force.

[0053] In order to describe the motion status of the participants, the leveling time is discretized and a scenario model is constructed. The working status of each participant is analyzed separately below.

[0054] Figure 2The figure shows the overall structure of the air bearing worktable. It consists of an upper support structure 2, a measuring baseplate 3, and an air bearing 4. The air bearing is positioned centrally above the worktable and coaxially with the measuring baseplate. An air bearing is a sliding bearing lubricated with gas. It supports loads by forming a pressurized air film between the sliding surfaces of the bearing. During operation, the sliding surfaces are completely separated by the air film, allowing it to simulate the zero-gravity state of supporting exhibition panels.

[0055] The planar motor structure consists of a porous aerostatic bearing, a rotor core and windings, and a fixed backplate housing. The porous aerostatic bearing is constructed from a bearing housing and porous graphite. The bearing housing serves as the air supply and support structure, with air holes on its exterior that connect to an annular groove on the bearing end face. The porous graphite material, filled with uniformly small pores, acts as a throttling element and is embedded in the annular groove of the bearing housing. High-pressure gas is introduced into the bearing through the air supply channel, entering the bearing gap through the countless capillaries in the porous graphite, forming a pressure film. Due to the properties of the porous material, the pressure distribution on the bearing surface is uniform, giving the bearing excellent load-bearing capacity and rigidity, and providing a stable air repulsive force to balance the gravity of large deployment mechanisms.

[0056] The force conditions of the air-floating microgravity test platform during operation are as follows: Figure 1 As shown, the forces acting on the two participants in the horizontal and vertical directions can be defined to represent the equilibrium of the participants in the narrow space. For two participants, the forces acting on them in equilibrium can be expressed as

[0057]

[0058] In a non-cooperative task, the goal of the participants is to achieve the leveling goal as quickly as possible. To fully study the problem of achieving leveling with a net force of zero, the following assumptions are made:

[0059] (1) The participants are non-cooperative opponents, and both parties know each other's current state information;

[0060] (2) Participants have the ability to independently level, and should try their best to achieve the goal of zero combined force;

[0061] (3) During the continuous movement of the planar motor above the servo platform, assuming that the resultant force acting on the system changes slightly in adjacent time periods, it can be approximately regarded as remaining constant, and the motion mode of the motor can be simplified to uniformly accelerated linear motion.

[0062] (4) Take the minimum value R and define the successful resultant force F of the leveling task i The judgment condition of (t) is

[0063] F i (t)<R (2)

[0064] In the game process, the set of the participant's currently available movement strategies is called the participant's strategy set, and Indicates that the subscript i represents the i-th step strategy to be executed, represents the strategy of the servo-following system at step i, is the angle (°) that the servo platform will move in step i, represents the strategy of the planar motor in step i, is the electromagnetic force (N) that the planar motor needs to output in step i.

[0065] The core goal of the single-step game strategy is to keep the net force on the air-floating microgravity test platform close to zero, that is, to minimize the net force, while ensuring that the following two key constraints are met:

[0066] Planar motor displacement distance constraint: Ensures that after each strategy step is executed, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from leaving the servo platform.

[0067] Planar motor static state constraint: Furthermore, the planar motor's moving speed is required to be strictly zero. This condition not only simplifies the system dynamic model and prevents the planar motor from leaving the platform, but also may reduce energy consumption in specific application scenarios. It is of great significance for maintaining the long-term stable operation of the system.

[0068] Based on the above, the optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows:

[0069]

[0070] Among them, the angle θ between the servo platform and the horizontal plane i As the decision vector in this problem, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in step i, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set. F em,i represents the actual electromagnetic force output by the planar motor under the strategy in step i, which can be obtained from the electromagnetic characteristics of the planar motor, and h is the maximum allowable displacement of the planar motor. The speed of the planar motor can be obtained from the principles of classical dynamics. To simplify the analysis, it is assumed that its direction of movement is the same as the direction of the force, and its speed can be expressed as where v i-1That is, the speed (mm / s) of step i-1. In the initial state, v0 = 0, m is the weight of the plane motor, and t is the movement time. Therefore, during the leveling process, the optimization constraints of the system's next strategy depend on the execution results of the previous strategy.

[0071] In the construction of a cooperative control system for a simulated microgravity platform, the planar motor and the servo platform are two key players. The non-cooperative game theory method is used to achieve effective coordination between them to ensure the stability of the platform, that is, the net force approaches zero. When the game forms a situation, in order to evaluate the pros and cons of the situation, the profit function I is introduced. i , as a participant Evaluation criteria for strategy selection. In order to effectively achieve non-cooperative goals while maintaining a competitive relationship between participants, the following profit function is constructed:

[0072] 1. Combined benefits of the air-floating microgravity test platform

[0073] The difference between the current resultant force generated by the participant (air-floating microgravity test platform) and the desired target (i.e., the minimum value R that the resultant force approaches) is set as

[0074] F i,goal (θ i ,F em,i )=F i (θ i ,F em,i )-R (4)

[0075] In order to assess whether the current resultant force (i.e. the force generated by the participants or their contribution to the resultant force) is within a safe range, a resultant force threshold F is preset. safe,i , its initial value (i=1) is taken as 10N, and its final value (i=∞) is taken as 0. At each control step, according to the current control effect and the resultant force state, in order to gradually approach the optimal resultant force control state, the safety value is adjusted by dichotomy, that is:

[0076]

[0077] Combined benefits of the air-floating microgravity test platform Expressed as:

[0078]

[0079] When the difference between the total force generated by each participant and the target is F i,goal (θ i ,F em,i ) is within the safety threshold, the smaller its value is, the greater the benefits the participants will gain. i,goal (θ i ,F em,i ) is greater than Fsafe,i When , the system resultant force may not meet the requirements. In order to avoid this situation, the resultant force sub-item benefit value is set to zero.

[0080] 2. Speed ​​Gains of Air-Floating Microgravity Test Platform

[0081] Current speed value v of the planar motor i (θ i ) can be calculated by the planar motor moving speed solution model. In order to evaluate whether the current planar motor moving speed is within the safe range, the preset speed threshold v safe,i , the initial value (i=1) is taken as 200mm / s, and the final value (i=∞) is taken as 0. At each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the safety value v is adjusted by dichotomy. safe,i Right now:

[0082]

[0083] Servo / air float system speed gain Expressed as:

[0084]

[0085] When the planar motor speed is less than the safety value v safe,i When v i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i In order to avoid entering this state, the payoff value is set to zero.

[0086] In game theory, when no strategy adopted by any player can increase their payoff, the combination of strategies chosen by each player is called a Nash equilibrium. In game theory, a Nash equilibrium can be understood as finding a strategy that, given all payoffs, leaves no player motivated to change their strategy. Clearly, a Nash equilibrium is the optimal strategy for each player.

[0087] In the coordinated control of air-floating microgravity test platform, Denotes the Nash equilibrium solution of the participant in step i, which satisfies

[0088]

[0089] in, Represents two profit functions, namely, equation (6) and equation (8), θ i ,x i ,vi They are respectively the currently measured platform tilt angle value, plane motor displacement distance value and speed value.

[0090] To find the Nash equilibrium solution of the non-cooperative game in the air-floating microgravity test platform First, we need to give the strategy for step 0, that is, the initial control cycle servo platform and planar motor. To simplify the analysis process, θ0 is the angle of the servo platform in the initial state, and F0 is the electromagnetic force that needs to be output when the planar motor starts.

[0091] In each subsequent control step, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the benefit of each participant according to formula (6) and formula (8). When the first iteration is performed, substitute the currently measured platform tilt angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (9), if the expected value of the platform inclination angle can be obtained Expected displacement distance of the planar motor Planar motor speed expectation The minimum value of is used as the strategy for the next step. The iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the next strategy, and the iteration ends. To simplify the calculation, each strategy is set to iterate a maximum of 5 times. If the minimum of all expected values ​​cannot be found after 5 iterations, the expected value used in the 5th iteration is used, and the current strategy combination is considered to be a Nash equilibrium solution and used as the next strategy.

[0092] Find the executable strategy for each participant in step i Then, the first two steps strategy is and Resubstitute the profit function, take the strategy with the largest profit, and form the strategy set T i , T i The strategy that the servo platform and planar motor can achieve the optimal performance at step i is defined as:

[0093]

[0094] The solution process of the servo / air floating platform collaborative control game strategy is as follows Figure 9 As shown. Figure 9 The process is modeled and simulated using the MATLAB / Simulink platform to verify the effectiveness of the control strategy.

[0095] Assuming that the initial resultant force of the system is a sinusoidal change with an amplitude of 1.55 and a frequency of 100 Hz, the game model is used to solve the resultant force output response curves of the planar motor and the servo follower system. Figure 3 and Figure 4 .according to Figure 5 As shown in the figure, the initial combined force is 1.55 N, and after 0.8 seconds, the combined force on the platform drops to 0 N. This shows that the platform can be leveled after the non-cooperative game, reducing the individual force output of the air-floating microgravity test platform and lowering energy consumption, proving the feasibility of the scheme.

[0096] Assuming that the initial resultant force of the system is a sinusoidal change with an amplitude of 1.55 and a frequency of 10 Hz, the game model is used to solve the resultant force output response curves of the planar motor and the servo follower system. Figure 6 and Figure 7 .according to Figure 8 As shown in the figure, the initial resultant force is 1.55 N, and after 0.6 seconds, the platform resultant force drops to 0 N. This shows that the platform can be leveled after the non-cooperative game, reducing the individual force output of the air-floating microgravity test platform and lowering energy consumption. In addition, as the frequency of the system's resultant force changes decreases, the system's adjustment speed becomes faster, proving the feasibility of this solution.

Claims

1. A non-cooperative game collaborative control method for an air-floating microgravity test platform. The air-floating microgravity test platform comprises an upper support structure, a measurement baseplate, and an air-floating bearing. A planar motor and a servo platform are defined as two participants in a non-cooperative game when the air-floating microgravity test platform is operating. In the non-cooperative task, the participants aim to achieve leveling as quickly as possible. The motion mode of the planar motor is simplified to uniformly accelerated linear motion. Each participant knows each other's current state information. The non-cooperative game collaborative control method comprises: In the game process, the set of the participant's currently available movement strategies is called the participant's strategy set, and Indicates that the subscript i represents the i-th step strategy to be executed, represents the strategy of the servo-following system at step i, θ i * is the angle (°) that the servo platform will move in step i, represents the strategy of the planar motor in step i, is the electromagnetic force required to be output by the planar motor in step i (N); The core goal of the game strategy is to keep the net force on the air-floating microgravity test platform close to zero, that is, to minimize the net force, while ensuring that the following two constraints are met: Planar motor displacement distance constraint: Ensures that after each strategy step, the position of the planar motor on the servo platform is always within the maximum allowable displacement range to prevent the motor from detaching from the servo platform; Planar motor static state constraint: requires the moving speed of the planar motor to be strictly 0; Determine the optimization problem of the step game strategy; When the game forms a situation, the profit function is introduced as the participant s i j To evaluate the strategy selection criteria, two profit functions were constructed: one is the combined force profit of the air-floating microgravity test platform: a combined force threshold is preset, and at each control step, based on the current control effect and combined force state, in order to gradually approach the optimal combined force control state, when the difference between the combined force generated by each participant and the target is within the combined force threshold, the smaller the value, the greater the participant's profit; otherwise, the combined force sub-item profit value is set to zero; the other is the speed profit of the air-floating microgravity test platform: a speed threshold is preset, and when the planar motor speed value is less than the speed threshold, the smaller the planar motor speed value, the greater the participant's profit; otherwise, the speed sub-item profit value is set to zero; The final result of the game is the Nash equilibrium solution, which requires determining the initial control strategy for the periodic servo platform and the planar motor; performing iterative solution to obtain a strategy set consisting of Nash equilibrium solutions.

2. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 1 is characterized in that: The optimization problem of the i-th (i=1,2,...,n) step game strategy is defined as follows: Among them, the angle θ between the servo platform and the horizontal plane under the i-th step game strategy is i As the decision vector, F i (θ i ,F em,i ) represents the actual value of the horizontal force of the planar motor under the game strategy in step i, expressed as F i (θ i ,F em,i )=F em,i -G i sinθ i , is the mapping of the decision vector on the target set; F em,i represents the actual output electromagnetic force of the planar motor under the strategy of step i, which is obtained from the electromagnetic characteristics of the planar motor, G i Represents the gravity acting on the planar motor; x i represents the displacement of the planar motor under the game strategy in step i, and its absolute value |x i |, h is the maximum allowable displacement of the planar motor; for the movement speed of the planar motor, assuming that its movement direction is in the same direction as the force, its movement speed is expressed as where v i-1 That is, the speed of the i-1th step (mm / s). In the initial state, v0=0, m is the weight of the planar motor, and t is the movement time.

3. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 1, characterized in that: Combined benefits of the air-floating microgravity test platform The definition is as follows: Assume that the difference between the current total force generated by each participant and the expected target is F i,goal (θ i ,F em,i ), F i,goal (i i ,F em,i )=F i (i i ,F em,i )-R (1) Where, F i (θ i ,F em,i ) is the current resultant force generated by each participant, and the desired target is the minimum value R that the resultant force approaches; Preset resultant force threshold F safe,i , combined benefit of air-floating microgravity test platform I i 1 Expressed as: When the difference between the total force generated by each participant and the target is F i,goal (θ i ,F em,i ) is within the combined force threshold, the smaller its value is, the greater the benefits the participants will gain. i,goal (θ i ,F em,i ) is greater than F safe,i When , let the resultant component benefit be zero.

4. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 3 is characterized in that: At each control step, according to the current control effect and resultant force state, in order to gradually approach the optimal resultant force control state, the resultant force threshold F is adjusted by dichotomy. safe,i .

5. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 1, characterized in that: Speed ​​Gains of Air-Floating Microgravity Experimental Platform The definition is as follows: Let v i (θ i ) is the current speed value of the planar motor, which is calculated by the planar motor moving speed solution model; the preset speed threshold v safe,i ; Speed ​​Gains of Air-Floating Microgravity Experimental Platform Expressed as: When the planar motor speed is less than the speed threshold v safe,i When v i (θ i ) is smaller, the greater the benefit the participant gets. i (θ i ) is greater than v safe,i When , let the speed sub-item benefit value be zero.

6. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 5, characterized in that: At each control step, according to the current control effect and speed state, in order to gradually approach the state of speed being 0, the speed threshold v is adjusted by dichotomy. safe,i .

7. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 1, characterized in that: The strategy for the initial control period servo platform and planar motor is as follows: θ0 takes the angle of the servo platform in the initial state, and F0 takes the electromagnetic force required to be output when the planar motor starts.

8. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 1, characterized in that: The strategy set is solved by the Nash equilibrium of the game model Composition, θ i * is the angle that the servo platform will move in step i, is the displacement of the planar motor in the i-th step, is the speed at which the planar motor will move in the i-th step, satisfy Where, the subscript i represents the i-th step, j = 1, 2 represents two types of profit functions, namely, formula (2) and formula (3), θ i ,x i ,v i They are the platform tilt angle value, plane motor displacement distance value and speed value measured in the i-th step, collectively referred to as the measured state value.

9. The non-cooperative game collaborative control method for an air-floating microgravity test platform according to claim 8, characterized in that: The method for iterative solution to obtain a strategy set consisting of Nash equilibrium solutions is: The number of iterations is preset. At each step of control, first, the measured state value and the resultant force threshold F safe,i , speed threshold v safe,i , calculate the combined force gain and speed gain of both participants; when the first iteration is performed, substitute the currently measured platform tilt angle value θ i , Planar motor displacement distance value x i With speed value v i , solve equation (4), if the expected value of the platform inclination angle can be obtained Expected displacement distance of the planar motor Planar motor speed expectation The minimum value of is used as the strategy for the next step. The iteration ends. If the minimum value of a certain expected value is found, the minimum value is used as the new expected value for re-iteration until the minimum value of all expected values ​​is found. The minimum value is used as the strategy for the next step, and the iteration ends. If the minimum value of all expected values ​​cannot be solved after reaching the number of iterations, the expected value used in the last iteration is taken, and the current strategy combination is considered to be the Nash equilibrium solution, which is used as the strategy for the next step. The executable strategy of each participant in step i is obtained. Then, the first two steps strategy is and Re-substitute the combined force benefit and speed benefit, take the strategy with the largest benefit, and form the strategy set T i .

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