Close-range intersection trajectory robust control method in multi-target tracking

Abstract

The invention relates to a close-range intersection trajectory robust control method in multi-target tracking, relates to an optimal control problem analysis objective function, constraint establishment and robust approach trajectory control scheme, and belongs to the field of spacecraft situation awareness and control. The method comprises the following steps: firstly, establishing an optimal trajectory control problem, and comprehensively considering information gain and security constraints to establish a model basis of a robust control instruction; and secondly, by establishing an analytical expression of a Hellinger distance in an optimal control problem under an OPMs (Out Probability Measurement) theory, effectively evaluating a difference between prior estimation and posteriori estimation of a target state, and further calculating information gain values under different control instructions so as to screen out an optimal control instruction. Meanwhile, by establishing an upper and lower bound analysis expression of the void probability in the optimal control problem constraint condition under the OPMs theory, the void probability of the rendezvous trajectory at any moment under different control instructions can be efficiently calculated, so that the safety of the rendezvous trajectory is evaluated, and the control instructions meeting the constraint condition are screened out. And finally, designing a robust trajectory control module and a possibility label multi-Bernoulli filtering module, forming a close-range rendezvous trajectory robust control scheme, and realizing the target of generating an optimal control instruction in real time in the approaching and tracking process so as to achieve the effects of maximizing information gain and ensuring the rendezvous trajectory safety.

Description

Technical Field

[0001] The present invention relates to a close-range rendezvous trajectory robust control method in multi-target tracking, involves an optimal control problem analytical objective function, constraint establishment and a robust approach trajectory control scheme, and belongs to the field of spacecraft situation awareness and control. Background Art

[0002] Close rendezvous of spacecraft is an effective way to accurately track space targets. Spacecraft can obtain more accurate observation results by approaching multiple targets to be observed. However, when the target to be observed is a non-cooperative space object such as space debris, there may be cognitive uncertainty in the observation process. How to ensure both the observation accuracy and the safety of the approach trajectory is a major challenge.

[0003] Traditional multi-target tracking methods based on the Random Finite Set (RFS) theory can observe and track multiple dynamic targets well and provide a decision basis for trajectory control. However, this theory does not consider the existence of epistemic uncertainty, which may lead to loss of tracking trajectory and inaccurate estimation. Multi-target tracking methods based on the Outer Probability Measures (OPMs) theory take into account the situation of epistemic uncertainty. However, in the optimal control problem under this theoretical framework, the analytical formulas for information gain evaluation and safety constraints are still lacking, and it is impossible to efficiently provide a decision basis for trajectory control. In addition, in the close-range rendezvous trajectory robust control method, research on the problem of epistemic uncertainty in multi-target tracking scenarios is also very limited.

[0004] Therefore, the close-range rendezvous trajectory robust control method has the problem of difficult to ensure observation accuracy and trajectory safety in scenarios with multi-target tracking and cognitive uncertainty. It is of great significance to study the strong robust rendezvous trajectory control under high-precision tracking. Summary of the invention

[0005] The present invention aims to provide a method for a rigid-flexible variable mechanism to approach space debris. The method first establishes an optimal trajectory control problem, comprehensively considers information gain and safety constraints, and establishes a model basis for robust control instructions. Secondly, by establishing an analytical expression of the Hellinger distance in the optimal control problem under the OPMs theory, the difference between the prior estimate and the posterior estimate of the target state is effectively evaluated, and then the information gain value under different control instructions is calculated to screen out the optimal control instruction. At the same time, by establishing the analytical upper and lower bound expressions of the void probability in the constraints of the optimal control problem under the OPMs theory, the void probability of the rendezvous trajectory at any time under different control instructions can be efficiently calculated, thereby evaluating the safety of the rendezvous trajectory and screening out the control instructions that meet the constraints. Finally, two modules, robust trajectory control and possibility label multi-Bernoulli filtering, are designed to form a close-range rendezvous trajectory robust control scheme, which achieves the goal of generating the optimal control instruction in real time during the approach and tracking process, so as to achieve the effect of maximizing information gain and ensuring the safety of the rendezvous trajectory.

[0006] The present invention discloses a method for robustly controlling a close-range intersection trajectory in multi-target tracking, comprising the following steps:

[0007] Step 1: Establish the optimal trajectory control problem, comprehensively consider information gain and safety constraints, and provide a model basis for generating trajectory robust control instructions;

[0008] The goal of the optimal trajectory control problem is to optimize the trajectory control of the spacecraft in a close-range rendezvous of multiple targets under the premise of considering cognitive uncertainty to improve the target tracking performance. Therefore, it is necessary to design a control scheme that autonomously selects the best instructions by maximizing information gain to obtain the observation results with the most information. In addition, it is crucial to avoid collisions during a close-range rendezvous, and safety constraints must also be considered. Based on this, at the current time t k The objective function of the optimal trajectory control problem is:

[0009]

[0010] Where max represents the maximization operation, α is the control instruction, A is the discrete control instruction space, α∈A means that the control instruction is selected from the discrete control instruction space, represents the expected value, is the information gain objective function, k is the current moment, and H is the control time domain length.

[0011] Then the constraints of the optimal trajectory control problem are established:

[0012]

[0013] Where min represents the minimization operation, i is the discrete moment in the control time domain, and P k+i For the tth k+i The hole probability in the hole area S at the moment, which represents the probability that no object exists in a given area S, P void is the hole probability threshold, which is used to evaluate whether the spacecraft is in a safe area; the hole area represents the safety warning area of ​​the spacecraft. When the target enters this area, it is considered to have a greater safety hazard. s is the spacecraft state value, T is the spacecraft state transfer matrix, and Φ is the constraint function of the control instruction α.

[0014] Step 2: Establish an analytical expression for the Hellinger distance in the optimal control problem under OPMs theory, so that the difference between the prior estimate and the posterior estimate of the target state can be efficiently evaluated, and then the information gain value under different control instructions can be calculated. To select the optimal control instructions;

[0015] The construction of the objective function relies on a reasonable assumption that the posterior estimate is usually higher in information than its prior estimate. Therefore, the objective function can be designed to maximize the information gain value under the control command. By evaluating the difference between the prior state estimate π0 and the posterior estimate π1, the Hellinger distance To calculate the information gain value, the traditional Hellinger distance usually quantifies the similarity between two probability density functions, so first define the Hellinger distance in the OPMs theoretical framework:

[0016]

[0017] In the OPMs theoretical framework, the prior state estimate π0 and the posterior estimate π1 can be written as follows:

[0018]

[0019] Where X represents the multi-objective state variable, represents a label indicator symbol, where δ is the generalized Kronecker symbol, |X| represents the number of all labels, represents the number of different labels, w0 and w1 represent weight coefficients with a maximum value of 1, and f0(·) and f1(·) represent the possibility function of the target. Based on this, the specific expression of Hellinger distance in the OPMs framework can be given:

[0020]

[0021] Where L represents the target label, is the label space, Indicates that the target label is in the label space.

[0022] The Gaussian likelihood function is the most commonly used likelihood function in OPMs theory. Here, the Gaussian likelihood function is used to derive the analytical Hellinger distance expression. The following Gaussian likelihood function is given:

[0023]

[0024] Where l represents the label of a single target, x is the state of a single target, is the Gaussian likelihood function, and is the state mean of the target with label l, and is the state covariance of the target with spatial label l.

[0025] Then the analytical Hellinger distance expression can be derived:

[0026]

[0027] Among them, ∑ is the summation symbol, ∏ is the multiplication symbol, The specific expression is as follows:

[0028]

[0029] So far, the analytical expression of Hellinger distance under the OPMs framework has been established, and the objective function can be expressed as:

[0030]

[0031] in is a pseudo-priori estimate, is a pseudo-posteriori estimate.

[0032] Step 3: Establish the hole probability P in the optimal control problem constraints k+i The analytical upper and lower bound expressions under the OPMs theory enable efficient calculation of the hole probability of the rendezvous trajectory at any time under different control instructions, and then evaluate the safety of the rendezvous trajectory to select the control instructions that meet the constraints;

[0033] During close encounters with multiple targets, it is critical to ensure the safety of the spacecraft. To prevent potential collisions, a void zone around the spacecraft must be maintained, within which no object is allowed to enter. This safety constraint can be quantified using the concept of void probability, which measures the risk of collision by evaluating the probability that no target exists within the void zone.

[0034] First, define the existence function Fp (S) and there is no function F a (S), the existence function indicates the credibility that there is at least one point in the hole region, while the non-existence function indicates the credibility that the hole region does not contain any point, which is specifically defined as follows:

[0035]

[0036] Where P represents the probability function, X is the multi-target state without labels, ∩ ​​is the intersection operation, is an empty set. Thus, we can get the specific expressions of the existence and non-existence of functions in the OPMs framework:

[0037]

[0038] Among them, sup is the upper bound operation, is the multi-objective state space, represents the augmented space of target states and labels in the hole region, is the augmented space of target states and labels that removes empty regions, and f(·) is the Gaussian likelihood function.

[0039] Based on this, we can derive analytical expressions for the existence and non-existence of functions.

[0040]

[0041]

[0042] For the hole area S, the hole probability P k+i is restricted by the existence function and the non-existence function, namely:

[0043] 1-F p (S)≤P k+i (S)≤F a (S) (15)

[0044] So far, the hole probability P is established k+i Analytical upper and lower bound expressions under OPMs theory.

[0045] Step 4: Based on steps 1, 2, and 3, two modules, robust trajectory control and possibility label multi-Bernoulli filtering, are designed to eventually form a close-range rendezvous trajectory robust control scheme, which enables real-time generation of optimal control instructions during the approach and tracking process, achieving maximum information gain and safe rendezvous trajectory.

[0046] First, a multi-Bernoulli filter with the possibility label is designed for state estimation. Given the time t k The posterior state π under k, the prediction-update recursive process of the filter is performed in the control time domain, where the observations used for updating are generated by the spacecraft after executing the optimal control command. Since the observations may not be generated at every moment, in the absence of measurement values, the posterior state estimate is considered to be equal to the prior state estimate. Secondly, a trajectory control module is designed to generate the optimal control command. The goal of the trajectory control module is to select the optimal control α from the discrete control command space at the current moment * , so that it maximizes the corresponding objective function value and satisfies the safety constraints. Finally, a robust control scheme for the rendezvous trajectory is formed based on the above two modules. The specific steps are as follows:

[0047] For a control instruction α that satisfies the safety constraint j , propagating the states of the spacecraft and the target forward to t k+H Then, based on the pseudo-priori estimate obtained by sampling and pseudo-measurements Execute the possibility label multi-Bernoulli filter update. The above process is performed during the entire control period t k+i , i = 1, ..., H, and then use the posterior pseudo estimate and a priori pseudo-estimates Calculate the Hellinger distance, and then solve the optimal control problem in step 1 to obtain the optimal control command in the current control time domain. These two modules need to be repeatedly executed in the continuous control time domain to finally obtain the optimal trajectory control command in the entire rendezvous process.

[0048] Beneficial effects:

[0049] 1. The robust control method for close-range rendezvous trajectories in multi-target tracking disclosed in the present invention, by establishing the analytical form of Hellinger distance and hole probability under OPMs theory, makes it possible to efficiently solve the information gain objective function and safety constraints of the optimal control problem in the close-range rendezvous tracking process, thereby solving the close-range multi-target tracking problem under cognitive uncertainty.

[0050] 2. The robust control method for close-range rendezvous trajectory in multi-target tracking disclosed in the present invention forms a robust control scheme for close-range rendezvous trajectory by designing two modules, namely, state estimation filter and trajectory control. This enables the spacecraft to obtain observation and tracking results with maximum information gain while ensuring the safety of the approach trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 A schematic diagram of a multi-target tracking scenario in the present invention;

[0052] Figure 2 A flow chart of the close-range rendezvous trajectory robust control scheme in a multi-target tracking scenario designed in the present invention;

[0053] Figure 3 The heat map of spacecraft trajectory based on OPMs method and traditional RFS method, where the yellow point represents the initial point and the green point represents the end point of the target trajectory;

[0054] Figure 4 Comparison diagram of cavity area analysis based on OPMs method and traditional RFS method;

[0055] Figure 5 This is a simulation diagram based on the Optimal Sub-Pattern Allocation (OSPA(2)) metric evaluation and multi-objective quantity estimation; DETAILED DESCRIPTION

[0056] In order to better illustrate the purpose and advantages of the present invention, the specific implementation methods and effects of the present invention are further described in detail below with reference to examples and drawings.

[0057] The robust control method for close-range intersection trajectories in multi-target tracking disclosed in this embodiment is specifically implemented in the following steps:

[0058] Step 1: Establish the optimal trajectory control problem, comprehensively consider information gain and safety constraints, and provide a model basis for generating trajectory robust control instructions;

[0059] Consider the attached figure Figure 1 The multi-target tracking scene shown in the figure has 7 debris targets. The entire approach tracking process lasts for 200 seconds, during which there are multiple collision events that cause the targets to disappear, as shown in Table 1. The actual trajectories of the 7 targets are shown in the figure. Figure 1 As shown by the black curve, these trajectories can be clearly divided into two groups, A and B. This scene is deliberately designed to simulate the change in aggregation between the two groups of targets, that is, the aggregation of group A is higher at first, and it shifts to group B after the collision.

[0060] Table 1 Optimal model initial value conditions

[0061]

[0062] Considering the existence of a circular reference orbit, the spacecraft state transfer matrix T can be described by the Clohessy-Wiltshire (CW) equation. Based on the above conditions, the optimal trajectory control problem in the close-range multi-target tracking scenario can be established according to formulas (1) and (2).

[0063] Step 2: Establish an analytical expression for the Hellinger distance in the optimal control problem under OPMs theory, so that the difference between the prior estimate and the posterior estimate of the target state can be efficiently evaluated, and then the information gain value under different control instructions can be calculated. To select the optimal control instructions;

[0064] Based on the analytical Hellinger distance expression established in formula (8), Monte Carlo integration is used to approximate the expected value in formula (1). First, the posterior estimate Sampling is performed and propagated to t k+H time, then generate a set of pseudo observations, and then update them to obtain the sampled posterior estimate The expected value is approximated by the following formula:

[0065]

[0066] Where N is the number of Monte Carlo sampling.

[0067] In the attached figure Figure 3 The heat map of spacecraft trajectories obtained through 100 Monte Carlo simulations is shown, and the brighter lines indicate areas where the trajectory passes through more frequently. The results show that for the OPMs-based method, the spacecraft initially approaches group A and then moves to group B after the target collision, which reflects the effect of the information gain objective function, that is, maximizing information gain by approaching areas with higher target concentration. However, in the RFS-based method, the spacecraft path is mainly shown around group A, which means that the observation accuracy of the targets in group B may decrease. At the same time, it also confirms the effectiveness of the information gain objective function calculation method proposed in the present invention under the OPMs theory.

[0068] Step 3: Establish the hole probability P in the optimal control problem constraints k+i The analytical upper and lower bound expressions under the OPMs theory enable efficient calculation of the hole probability of the rendezvous trajectory at any time under different control instructions, and then evaluate the safety of the rendezvous trajectory to select the control instructions that meet the constraints;

[0069] Based on formula (15), the boundary average is used to approximate the void probability:

[0070]

[0071] And the safety constraint requires that P k+i (S) <P void In the attached figure Figure 4 The comparison of the hole area analysis based on the OPMs method and the traditional RFS method is shown. The results show that the OPMs-based method significantly reduces the probability of the target entering the hole area, which means that it has higher safety in close-range rendezvous. It also confirms the effectiveness of the safety constraint calculation method proposed in this invention under the OPMs theory.

[0072] Step 4: Based on steps 1, 2, and 3, two modules, robust trajectory control and possibility label multi-Bernoulli filtering, are designed to eventually form a close-range rendezvous trajectory robust control scheme, which enables real-time generation of optimal control instructions during the approach and tracking process, achieving maximum information gain and safe rendezvous trajectory.

[0073] In the attached figure Figure 2 The flowchart of the robust control scheme for close-range rendezvous trajectory in the multi-target tracking scenario designed in the present invention is shown. Based on the control scheme, the spacecraft trajectory can be controlled to obtain the following figure. Figure 5 The optimal sub-pattern allocation (OSPA) (2) )Metric evaluation and multi-target number estimation simulation diagram, which shows the performance comparison between the proposed OPMs-based method and the traditional RFS-based method. The results show that the proposed method performs better in post-collision state and target number estimation, and can achieve higher observation accuracy while ensuring the safety of the rendezvous trajectory.

[0074] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A robust control method for close-range rendezvous trajectory in target tracking, characterized by: The steps include: Step 1: Establish the optimal trajectory control problem, comprehensively consider information gain and safety constraints, and provide a model basis for generating trajectory robust control instructions; Step 2: Establish an analytical expression of the Hellinger distance in the optimal control problem under the theory of Outer Probability Measures (OPMs), so that the difference between the prior estimate and the posterior estimate of the target state can be efficiently evaluated, and then the information gain value under different control instructions can be calculated. To select the optimal control instructions; Step 3: Establish the hole probability P in the optimal control problem constraints k+i The analytical upper and lower bound expressions under the OPMs theory enable efficient calculation of the hole probability of the rendezvous trajectory at any time under different control instructions, and then evaluate the safety of the rendezvous trajectory to select the control instructions that meet the constraints; Step 4: Based on steps 1, 2, and 3, two modules, robust trajectory control and possibility label multi-Bernoulli filtering, are designed to eventually form a close-range rendezvous trajectory robust control scheme, which enables real-time generation of optimal control instructions during the approach and tracking process, achieving maximum information gain and a safe rendezvous trajectory.

2. The method for robust control of close-range intersection trajectories in target tracking according to claim 1, characterized in that: The implementation method of step one is: The goal of the optimal trajectory control problem is to optimize the trajectory control of the spacecraft in a close-range rendezvous of multiple targets under the premise of considering cognitive uncertainty to improve the target tracking performance. Therefore, it is necessary to design a control scheme that autonomously selects the best instructions by maximizing information gain to obtain the observation results with the most information. In addition, it is crucial to avoid collisions during a close-range rendezvous, and safety constraints must also be considered. Based on this, at the current time t k The objective function of the optimal trajectory control problem is: Where max represents the maximization operation, α is the control instruction, A is the discrete control instruction space, α∈A means that the control instruction is selected from the discrete control instruction space, represents the expected value, is the information gain objective function, k is the current moment, and H is the control time domain length. Then the constraints of the optimal trajectory control problem are established: Where min represents the minimization operation, i is the discrete moment in the control time domain, and P k+i For the tth k+i The hole probability in the hole area S at the moment, which represents the probability that no object exists in a given area S, P void is the hole probability threshold, which is used to evaluate whether the spacecraft is in a safe area; the hole area represents the safety warning area of ​​the spacecraft. When the target enters this area, it is considered to have a greater safety hazard. s is the spacecraft state value, T is the spacecraft state transfer matrix, and Φ is the constraint function of the control instruction α.

3. The method for robust control of close-range intersection trajectory in target tracking according to claim 1, characterized in that: The implementation method of step 2 is: The construction of the objective function relies on a reasonable assumption that the posterior estimate is usually higher in information than its prior estimate. Therefore, the objective function can be designed to maximize the information gain value under the control command. By evaluating the difference between the prior state estimate π0 and the posterior estimate π1, the Hellinger distance To calculate the information gain value, the traditional Hellinger distance usually quantifies the similarity between two probability density functions, so first define the Hellinger distance in the OPMs theoretical framework: In the OPMs theoretical framework, the prior state estimate π0 and the posterior estimate π1 can be written as follows: Where X represents the multi-objective state variable, represents a label indicator symbol, where δ is the generalized Kronecker symbol, |X| represents the number of all labels, represents the number of different labels, w0 and w1 represent weight coefficients with a maximum value of 1, and f0(·) and f1(·) represent the possibility function of the target. Based on this, the specific expression of Hellinger distance in the OPMs framework can be given: Where L represents the target label, is the label space, Indicates that the target label is in the label space. The Gaussian likelihood function is the most commonly used likelihood function in OPMs theory. Here, the Gaussian likelihood function is used to derive the analytical Hellinger distance expression. The following Gaussian likelihood function is given: Where l represents the label of a single target, x is the state of a single target, is the Gaussian likelihood function, and is the state mean of the target with label l, With P1 (l) is the state covariance of the target with spatial label l. Then the analytical Hellinger distance expression can be derived: Among them, ∑ is the summation symbol, ∏ is the multiplication symbol, The specific expression is as follows: So far, the analytical expression of Hellinger distance under the OPMs framework has been established, and the objective function can be expressed as: in is a pseudo-priori estimate, is a pseudo-posteriori estimate.

4. The method for robust control of close-range intersection trajectories in target tracking according to claim 1, characterized in that: The implementation method of step three is: During close encounters with multiple targets, it is critical to ensure the safety of the spacecraft. To prevent potential collisions, a void zone around the spacecraft must be maintained, within which no object is allowed to enter. This safety constraint can be quantified using the concept of void probability, which measures the risk of collision by evaluating the probability that no target exists within the void zone. First, define the existence function F p (S) and there is no function F a (S), the existence function indicates the credibility that there is at least one point in the hole region, while the non-existence function indicates the credibility that the hole region does not contain any point, which is specifically defined as follows: In the formula represents the probability function, X is the multi-target state without labels, ∩ ​​is the intersection operation, is an empty set. Thus, we can get the specific expressions of the existence and non-existence of functions in the OPMs framework: Among them, sup is the upper bound operation, is the multi-objective state space, represents the augmented space of target states and labels in the hole region, is the augmented space of target states and labels that removes empty regions, and f(·) is the Gaussian likelihood function. Based on this, we can derive the analytical expressions for the existence and non-existence of functions" For the hole area S, the hole probability P k+i is restricted by the existence function and the non-existence function, namely: 1-F p (S)≤P k+i (S)≤F a (S) (15) So far, the hole probability P is established k+i Analytical upper and lower bound expressions under OPMs theory.

5. The method for robust control of close-range intersection trajectory in target tracking according to claim 1, characterized in that: The implementation method of step 4 is: First, a multi-Bernoulli filter with the possibility label is designed for state estimation. Given the time t k The posterior state π under k , the prediction-update recursive process of the filter is performed in the control time domain, where the observations used for updating are generated by the spacecraft after executing the optimal control command. Since the observations may not be generated at every moment, in the absence of measurement values, the posterior state estimate is considered to be equal to the prior state estimate. Secondly, a trajectory control module is designed to generate the optimal control command. The goal of the trajectory control module is to select the optimal control α from the discrete control command space at the current moment * , so that it maximizes the corresponding objective function value and satisfies the safety constraints. Finally, a robust control scheme for the rendezvous trajectory is formed based on the above two modules. The specific steps are as follows: For a control instruction α that satisfies the safety constraint j , propagating the states of the spacecraft and the target forward to t k+H Then, based on the pseudo-priori estimate obtained by sampling and pseudo-measurements Execute the possibility label multi-Bernoulli filter update. The above process is performed during the entire control period t k+i , i = 1, ..., H, and then use the posterior pseudo estimate and a priori pseudo-estimates Calculate the Hellinger distance, and then solve the optimal control problem in step 1 to obtain the optimal control command in the current control time domain. These two modules need to be repeatedly executed in the continuous control time domain to finally obtain the optimal trajectory control command in the entire rendezvous process.

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