Robust control method for close encounter trajectory in multi-target tracking

Abstract

The present application relates to a kind of close approach trajectory robust control method in multi-target tracking, it is related to optimal control problem analytical objective function, constraint establishment and robust approach trajectory control scheme, belong to spacecraft situation awareness and control field.The present application first establishes optimal trajectory control problem, considers information gain and security constraint comprehensively, to establish the model basis of robust control instruction.Second, by establishing the analytical expression of Hellinger distance in optimal control problem under the theory of Outer Probability Measures (OPMs), 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 select the optimal control instruction.At the same time, by establishing the analytical upper and lower bound expression of the void probability in the constraint condition of optimal control problem under the theory of OPMs, the void probability of the approach trajectory at any time under different control instructions can be efficiently calculated, so as to evaluate the safety of the approach trajectory and select the control instruction that meets the constraint condition.Finally, a robust trajectory control and a possibility label multiple Bernoulli filter module are designed to form a close approach trajectory robust control scheme, which realizes the goal of generating optimal control instructions in real time during the approach and tracking process, and achieves the effect of maximizing information gain and ensuring the safety of the approach trajectory.

Description

TECHNICAL FIELD

[0001] The present application relates to a close approach trajectory robust control method in multi-target tracking, and relates to an optimal control problem analysis target function, constraint establishment and robust approach trajectory control scheme, and belongs to the field of spacecraft situation awareness and control. BACKGROUND

[0002] Spacecraft close approach is an effective way to accurately track space targets. Spacecraft approaches multiple observation targets to obtain more accurate observation results. However, when the observation targets are space debris, which are non-cooperative space objects, the observation process may have cognitive uncertainty. It is a challenge to ensure observation accuracy and safety of the approach trajectory.

[0003] Traditional multi-target tracking methods based on the theory of random finite set (RFS) can better observe and track multiple dynamic targets and provide decision basis for trajectory control. However, this theory does not consider the case of cognitive uncertainty, which may lead to loss of tracking trajectory and inaccurate estimation. Multi-target tracking methods based on the theory of outer probability measures (OPMs) consider the case of cognitive uncertainty. However, in the optimal control problem under this theoretical framework, the analytical formulas for information gain evaluation and safety constraints are still lacking, which cannot efficiently provide decision basis for trajectory control. In addition, there is limited research on the close approach trajectory robust control method for the problem of cognitive uncertainty in the multi-target tracking scenario.

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

[0005] This invention aims to provide a method for close-range contact with space debris using a rigid-flexible variable mechanism. First, the method establishes an optimal trajectory control problem, comprehensively considering information gain and safety constraints to build a model foundation for robust control commands. Second, by establishing an analytical expression for the Hellinger distance in the optimal control problem under OPMs theory, the difference between the prior and posterior estimates of the target state is effectively evaluated, and the information gain value under different control commands is calculated to select the optimal control command. Simultaneously, by establishing analytical upper and lower bound expressions for the hole probability in the constraints of the optimal control problem under OPMs theory, the hole probability of the rendezvous trajectory at any time under different control commands can be efficiently calculated, thereby evaluating the safety of the rendezvous trajectory and selecting control commands that meet the constraints. Finally, two modules, robust trajectory control and probability label multi-Bernoulli filtering, are designed to form a robust control scheme for close-range rendezvous trajectories, achieving the goal of generating optimal control commands in real time during approach and tracking, thus maximizing information gain and ensuring the safety of the rendezvous trajectory.

[0006] The robust control method for close-range intersection trajectory in multi-target tracking disclosed in this invention includes 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 robust trajectory control commands;

[0008] The goal of the optimal trajectory control problem is to optimize the trajectory control of a spacecraft during close rendezvous with multiple targets, considering cognitive uncertainty, to improve target tracking performance. Therefore, a control scheme needs to be designed to autonomously select the optimal command by maximizing information gain to obtain the observation results with the most information. Furthermore, avoiding collisions is crucial during close rendezvous, and safety constraints must also be considered. Accordingly, based on the current time t... k The objective function for the optimal trajectory control problem is:

[0009]

[0010] Where max represents the maximization operation, α is the control command, A is the discrete control command space, and α∈A indicates that the control command is selected from the discrete control command space. Represents the expected value. Let k be the information gain objective function, k be the current time, and H be the length of the control time domain.

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

[0012]

[0013] Where min represents the minimization operation, i is the discrete time in the control time domain, and P k+i For the tth k+i The probability of a void in the void region S at any given time, where the void probability represents the probability that no object exists in the given region S, P. void The void probability threshold is used to assess whether a spacecraft is in a safe zone; the void zone represents a safety warning zone for the spacecraft, and when a target enters this zone, it is considered to pose a significant safety hazard. s Let be the spacecraft state value, T be the spacecraft state transition matrix, and Φ be the constraint function of the control command α.

[0014] Step 2: Establish an analytical expression for the Hellinger distance in the optimal control problem under OPMs theory, enabling efficient evaluation of the difference between the prior and posterior estimates of the target state, and subsequently calculating the information gain value under different control commands. To select the optimal control command;

[0015] The construction of the objective function relies on the reasonable assumption that the posterior estimate is generally more information-rich than its prior estimate. Therefore, the objective function can be designed to maximize the information gain under control commands. This is achieved by evaluating the difference between the prior state estimate π0 and the posterior estimate π1, utilizing the Hellinger distance... To calculate the information gain, the traditional Hellinger distance typically quantifies the similarity between two probability density functions. Therefore, we first define the Hellinger distance within the framework of OPMs theory:

[0016]

[0017] Within the theoretical framework of OPMs, the prior state estimate π0 and the posterior estimate π1 can be written in the following form:

[0018]

[0019] In the formula, X represents the multi-objective state variable. This represents a label indicator symbol, where δ is the generalized Kronecker notation, and |X| represents the number of all labels. The numbers represent the number of distinct labels, w0 and w1 represent weight coefficients with a maximum value of 1, and f0(·) and f1(·) represent the probability functions of the target. Based on this, the specific expression for the Hellinger distance within the OPMs framework can be given:

[0020]

[0021] In the formula, L represents the target label. For tag space, This indicates that the target tag is in the tag space.

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

[0023]

[0024] In the formula, l represents the label of a single target, and x represents the state of a single target. Let be a Gaussian probability function. and Let l be the mean state of the target. and Let l be the state covariance of the spatial label target.

[0025] The analytical Hellinger distance expression can then be derived:

[0026]

[0027] Where ∑ is the summation symbol and ∏ is the multiplication symbol. The specific expression is as follows:

[0028]

[0029] At this point, the analytical expression for the Hellinger distance under the OPMs framework has been established, and the objective function can be expressed as:

[0030]

[0031] in This is a pseudo-prior estimate. This is a pseudo-posterior estimate.

[0032] Step 3: Establish the void probability P in the constraints of the optimal control problem. k+i The analytical upper and lower bound expressions under OPMs theory enable efficient calculation of the hole probability of the intersection trajectory at any time under different control commands, thereby evaluating the safety of the intersection trajectory and selecting control commands that meet the constraints.

[0033] During close encounters in multi-target tracking, ensuring spacecraft safety is paramount. To prevent potential collisions, a void region must be maintained around the spacecraft, within which no object is permitted to enter. This safety constraint can be quantified using the concept of void probability, which measures the risk of collision by assessing the likelihood that no target is present within the void region.

[0034] First, define the existence function F.p (S) and the non-existent function F a (S), the existence function represents the confidence that at least one point exists in the hole region, while the non-existence function represents the confidence that the hole region does not contain any points. The specific definitions are as follows:

[0035]

[0036] In the formula, P represents the probability function, X is the unlabeled multi-objective state, and ∩ is the intersection operation. This is an empty set. Therefore, the specific expressions for existing and non-existent functions under the OPMs framework can be obtained as follows:

[0037]

[0038] Here, sup represents the upper bound operation. For a multi-objective state space, An augmented space representing the target state and label within the void region. To remove the target state and label augmented space from the empty region, f(·) is a Gaussian probability function.

[0039] Based on this, the analytical expressions for existing and non-existent functions can be derived.

[0040]

[0041]

[0042] For a void region S, the void probability P k+i It is restricted by the existence and non-existence functions, that is:

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

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

[0045] Step 4: Based on Steps 1, 2, and 3, design two modules: robust trajectory control and probability label multi-Bernoulli filtering. Finally, a robust control scheme for close-range rendezvous trajectory is formed, which enables the generation of optimal control commands in real time during the approach and tracking process, achieving the effect of maximizing information gain and ensuring safe rendezvous trajectory.

[0046] First, a probability-labeled multi-Bernoulli filter is designed for state estimation, given time t. k The posterior state π kIn the control time domain, a predict-update recursive process for the filter is executed, where the observations used for updating are generated after the spacecraft executes the optimal control command. Since observations may not be generated at every moment, and in the absence of measurements, the posterior state estimate is considered equal to the prior state estimate. Next, 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. * To maximize the corresponding objective function value and satisfy safety constraints, a robust control scheme for the intersection trajectory is finally formed based on the above two modules. The specific steps are as follows:

[0047] For a control instruction α that satisfies safety constraints j Propagate the state of the spacecraft and target forward to t k+H Time. Subsequently, based on the pseudo-prior estimate obtained from sampling. and pseudo-measurement values Perform probability label multi-Bernoulli filter updates. The above process is carried out throughout the control period t. k+i The process is repeated within the range i = 1, ..., H, and then a posterior pseudo-estimation is used. and prior pseudo-estimation The Hellinger distance is calculated, and then the optimal control problem from step one is solved to obtain the optimal control command in the current control time domain. These two modules need to be executed repeatedly in consecutive control time domains to ultimately obtain the optimal trajectory control command for the entire rendezvous process.

[0048] Beneficial effects:

[0049] 1. The robust control method for close-range rendezvous trajectory in multi-target tracking disclosed in this invention establishes the analytical form of Hellinger distance and hole probability under OPMs theory, which enables efficient solution of the information gain objective function and safety constraints of the optimal control problem in close-range rendezvous tracking, thereby solving the problem of close-range multi-target tracking under cognitive uncertainty.

[0050] 2. The robust control method for close-range rendezvous trajectory in multi-target tracking disclosed in this invention forms a robust control scheme for close-range rendezvous trajectory by designing two modules: a state estimation filter and a trajectory control module. This enables the spacecraft to obtain observation and tracking results with maximum information gain while ensuring the safety of the approach trajectory. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of a multi-target tracking scenario in this invention;

[0052] Figure 2 This is a flowchart of the robust control scheme for close-range rendezvous trajectory in a multi-target tracking scenario designed in this invention;

[0053] Figure 3 The image shows a spacecraft trajectory heatmap based on the OPMs method and the traditional RFS method, where yellow dots represent the initial point and green dots represent the endpoint of the target trajectory.

[0054] Figure 4 A comparison chart of void region analysis based on the OPMs method and the traditional RFS method;

[0055] Figure 5 Simulation diagram of metric evaluation and multi-objective quantity estimation based on optimal submode allocation (OSPA(2)); Detailed Implementation

[0056] To better illustrate the purpose and advantages of the present invention, the specific embodiments and effects of the present invention will be further described in detail below with reference to examples and accompanying drawings.

[0057] The robust control method for close-range intersection trajectory in multi-target tracking disclosed in this embodiment is 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 robust trajectory control commands;

[0059] Consider the attached diagram Figure 1 The multi-target tracking scenario shown contains seven fragmented targets. The entire approach tracking process lasts 200 seconds, during which multiple collision events cause the targets to disappear, as detailed in Table 1. The actual trajectories of the seven targets are shown in the attached figure. Figure 1 As shown by the black curves, these trajectories can be clearly divided into two groups, A and B. The scenario was intentionally designed to simulate the aggregation change between the two groups of targets; that is, the initial aggregation of group A is higher, and it shifts to group B after the collision.

[0060] Table 1 Initial conditions for the optimal model

[0061]

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

[0063] Step 2: Establish an analytical expression for the Hellinger distance in the optimal control problem under OPMs theory, enabling efficient evaluation of the difference between the prior and posterior estimates of the target state, and subsequently calculating the information gain value under different control commands. To select the optimal control command;

[0064] Based on the analytical Hellinger distance expression established by formula (8), Monte Carlo integration is used to approximate the expected value in formula (1). First, the posterior estimate is... Perform sampling and propagate to t k+H At time 1, a set of pseudo-observations is generated, and then updated to obtain the posterior estimate after sampling. The expected value is approximated using the following formula:

[0065]

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

[0067] In the attached diagram Figure 3 A heatmap of the spacecraft trajectory obtained through 100 Monte Carlo simulations is presented, with brighter lines indicating regions 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 a collision with the target. This reflects the effect of the information gain objective function, which maximizes information gain by approaching regions with higher target concentration. However, in the RFS-based method, the spacecraft path primarily exhibits a pattern around group A, implying a potential decrease in the accuracy of observations of targets in group B. This also confirms the effectiveness of the proposed method for calculating the information gain objective function based on OPMs theory.

[0068] Step 3: Establish the void probability P in the constraints of the optimal control problem. k+i The analytical upper and lower bound expressions under OPMs theory enable efficient calculation of the hole probability of the intersection trajectory at any time under different control commands, thereby evaluating the safety of the intersection trajectory and selecting control commands that meet the constraints.

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

[0070]

[0071] Furthermore, the safety constraints require that P be satisfied within the control time domain. k+i (S) <P void In the attached image Figure 4 A comparison of cavity region analysis based on the OPMs method and the traditional RFS method is presented. The results show that the OPMs-based method significantly reduces the probability of the target entering the cavity region, implying higher safety in close-range encounters. This also confirms the effectiveness of the safety constraint calculation method based on OPMs theory proposed in this invention.

[0072] Step 4: Based on Steps 1, 2, and 3, design two modules: robust trajectory control and probability label multi-Bernoulli filtering. Finally, a robust control scheme for close-range rendezvous trajectory is formed, which enables the generation of optimal control commands in real time during the approach and tracking process, achieving the effect of maximizing information gain and ensuring safe rendezvous trajectory.

[0073] In the attached diagram Figure 2 The flowchart of the robust control scheme for close-range rendezvous trajectory in a multi-target tracking scenario designed in this invention is shown. Based on this control scheme, the spacecraft trajectory can be controlled to obtain the result shown in the attached figure. Figure 5 The diagram shows the optimal subpattern allocation (OSPA) (2) The figure shows a simulation of metric evaluation and multi-target quantity estimation, illustrating the performance comparison between the proposed OPMs-based method and the traditional RFS-based method. The results demonstrate that the proposed method outperforms the traditional RFS-based method in estimating post-collision states and target quantities, achieving higher observation accuracy while ensuring the safety of the rendezvous trajectory.

[0074] The above detailed description further illustrates the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above description 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 within the scope of protection of the present invention.

Claims

1. A robust control method for close-range intersection trajectory in multi-target tracking, characterized by: Includes the following steps, Step 1: Taking into account information gain and security constraints, establish the optimal trajectory control problem, which is used to establish robust control commands; Step 2: Establish the analytical expression of the Hellinger distance in the optimal control problem under the external probability measure OPMs theory. This can efficiently evaluate the difference between the prior and posterior estimates of the target state, and then calculate the information gain objective function J under different control commands to screen the optimal control command. The second step is implemented as follows: The objective function is to maximize the information gain under control commands; this is achieved by evaluating the difference between the prior state estimate π0 and the posterior estimate π1, using the Hellinger distance. To calculate the information gain value; The Hellinger distance within the OPMs theoretical framework is: The prior state estimates π0 and posterior estimates π1 can be written in the following form: The posterior estimate is obtained by updating the prior estimate through observations, which are measured by optical sensors carried by the observation spacecraft; in the above formula, X represents the multi-target state variable. The label for X; This represents a label indicator symbol, where δ is the generalized Kronecker notation, and |X| represents the number of all labels. π represents the number of different labels; w0 is the weight coefficient under the prior state estimate π0, and w1 is the weight coefficient under the posterior state estimate π1. To estimate the probability function in π0 from the prior state, For the posterior state estimation, the possibility function in π1 is given. The specific expression for Hellinger distance within the OPMs framework: In the formula, e is The label of a single specific target. For tag space, This indicates that the target tag is in the tag space; The Gaussian probability function is: In the formula, x represents the state of a single target. Let be a Gaussian probability function. for The state mean in for The state mean in; for State covariance in for State covariance in; Then we obtain the analytical Hellinger distance expression: Where ∑ is the summation symbol and Π is the multiplication symbol. The specific expression is as follows: Based on the analytical expression of Hellinger distance within the OPMs framework, the information gain objective function is expressed as: in This is a pseudo-prior estimate. This is a pseudo-posterior estimate; Based on the information gain objective function under different control commands Select the optimal control command; Step 3: Establish the void probability P in the constraints of the optimal control problem. k+i Based on the analytical upper and lower bound expressions of OPMs theory, the hole probability of the intersection trajectory at any time under different control commands is calculated. The hole probability represents the probability that no object exists in a given area, thereby evaluating the safety of the intersection trajectory and screening control commands that meet the constraints. Step 4: Based on the optimal trajectory control problem established in Step 1, the information gain objective function J obtained in Step 2, and the hole probability P obtained in Step 3. k+i Two modules are designed: a robust trajectory control module and a probability label multi-Bernoulli filter module. Based on the robust trajectory control module and the probability label multi-Bernoulli filter module, robust control commands for close-range rendezvous trajectories are generated. Then, the optimal control commands are generated in real time during the approach and tracking process. Based on the optimal control commands, robust control of close-range rendezvous trajectories in multi-target tracking is performed to maximize information gain and ensure safe rendezvous trajectories in multi-target tracking.

2. The robust control method for close-range intersection trajectory in multi-target tracking as described in claim 1, characterized in that: The implementation method for step one is as follows: The goal of the optimal trajectory control problem is to optimize the trajectory control of spacecraft in close rendezvous with multiple targets, taking into account cognitive uncertainties, so as to improve target tracking performance. By maximizing information gain, the system autonomously selects the optimal instruction to obtain observation results with the greatest information content. Based on the current time t k The objective function for the optimal trajectory control problem is: Where max represents the maximization operation, α is the control command, A is the discrete control command space, and α∈A indicates that the control command is selected from the discrete control command space. Represents the expected value. Here, k is the information gain objective function, H is the current time, and H is the length of the control time domain. Considering safety constraints, the constraints for the optimal trajectory control problem are established as follows: Where min represents the minimization operation, i is the discrete time in the control time domain, and P k+i For the tth k+i The probability of a void in the void region S at any given time, where the void probability represents the probability that no object exists in the given region S, P. void The void probability threshold is used to assess whether a spacecraft is in a safe zone; the void region represents the spacecraft's safety warning zone, and when a target enters this region, a safety hazard is determined; x s Let denot α be the spacecraft state value, T be the spacecraft state transition matrix, and Φ be the constraint function for the control command α.

3. The robust control method for close-range intersection trajectory in multi-target tracking as described in claim 2, characterized in that: The method for implementing step three is as follows: There exists a function F p (S) represents the confidence that at least one point exists in the void region; there is no function F. a (S) represents the confidence level that the void region does not contain any points. The specific expression is: Here, sup represents the upper bound operation. For a multi-objective state space, An augmented space representing the target state and label within the void region. To remove the augmented space of target states and labels in the empty region, f(·) is a Gaussian probability function; Derive the existence function F p and the non-existent function F a The parsing expression: For a void region S, the void probability P k+i It is restricted by the existence and non-existence functions, that is: 1-F p (S)≤P k+i (S)≤F a (S) (16) Equation (16) is the cavity probability P. k+i Analytical upper and lower bound expressions under OPMs theory; The hole probability of the intersection trajectory at any time under different control commands is calculated according to Equation (15), and the safety of the intersection trajectory is evaluated so as to screen the control commands that meet the constraints.

4. The robust control method for close-range intersection trajectory in multi-target tracking as described in claim 3, characterized in that: Step four is implemented as follows: For the probability label multi-Bernoulli filter module, for a given time t k The posterior state π k In the control time domain, the prediction-update recursive process of the filter is executed. The update process mainly updates the prior estimate to obtain the posterior estimate. The observations used for the update are generated after the spacecraft executes the instructions given by the optimal trajectory control problem in step one. Since the observations may not be generated at every moment, in the absence of observations, the posterior state estimate is considered to be equal to the prior state estimate. For the robust trajectory control module, control instructions that satisfy the safety constraints in step three are selected from the discrete control instruction space at the current moment. Among the control instructions that satisfy the safety constraints, the optimal control instruction that maximizes the information gain objective function in step two is selected. Based on the optimal control instruction, robust control of the close-range rendezvous trajectory in multi-target tracking is performed to maximize the information gain and ensure the safety of the rendezvous trajectory in multi-target tracking. Robust control commands for generating close-range rendezvous trajectories are generated based on a robust trajectory control module and a probability label multi-Bernoulli filtering module. The specific implementation method is as follows: Step 4.1: Based on the robust trajectory control module, select control instructions α that satisfy the safety constraints in Step 3. j ; Step 4.2: Based on the state transition matrix T from Step 1, propagate the states of the spacecraft and the target forward to t. k+H time; Step 4.3: Pseudo-prior estimation based on sampling and pseudo-observations The update process in the probability label multi-Bernoulli filter module is performed, where the pseudo-observation is different from the observation obtained by the actual observation through the optical sensor, and the pseudo-observation is only based on pseudo-prior estimation. Step 4.4: For the processes in steps 4.1 to 4.3, the entire control time domain t k+i Repeatedly execute the procedure within the range i = 1, ..., H to obtain a posterior pseudo-estimate. and prior pseudo-estimation Step 4.5: Based on posterior pseudo-estimation and prior pseudo-estimation And in step two, calculate the Hellinger distance; Step 4.6: Solve the optimal trajectory control problem in Step 1 to obtain the optimal control command in the current control time domain; Step 4.7: Substitute the optimal control command into the probability label multi-Bernoulli filter module, execute the prediction-update recursive process, and obtain the actual multi-objective state values; Step 4.8: Repeat steps 4.1 to 4.7 in the continuous control time domain until the optimal trajectory control command for the entire rendezvous process is obtained.

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