Detector power descent robust optimal guidance method based on uncertainty quantization

Abstract

The invention relates to a detector power descent robust optimal guidance method based on uncertainty quantization. The method comprises the steps that a dynamic descent robust fuel optimal guidance model considering the uncertainty of an initial state and a model environment is constructed, the optimal guidance model is converted into a deterministic problem through an uncertainty quantification method based on chaos polynomial expansion, the deterministic optimization problem is solved through a sequence convex optimization method, and the dynamic descent robust fuel optimal guidance model is obtained. And a robust optimal landing trajectory and a corresponding feedback guidance law are obtained. According to the method, a complex nonlinear optimal control problem containing randomness can be converted into a convex optimization problem easy to solve, the solving efficiency is improved on the premise that the solving success rate is guaranteed, the designed optimal track can meet various constraints under the uncertain condition, and the obtained corresponding feedback guidance law can be directly applied online.

Description

Technical Field

[0001] The invention relates to a robust optimal guidance method for detector power descent based on uncertainty quantification, and belongs to the technical field of detector power descent control. Background Art

[0002] With the enhancement of the onboard computing power of the probe and the increasing maturity of the technology of linear trajectory planning represented by convex optimization, optimal guidance has become the development trend of future Mars powered descent guidance technology. Optimal guidance has the following main features: 1. Numerical algorithms are used to replace the guidance law with fixed structures, and the generation of guidance instructions is highly dependent on a large amount of onboard calculations; 2. Guidance instructions are generated based on models or data, and do not require specific reference trajectories and a large amount of offline design; 3. Pursuit of optimality. The above three features enable optimal guidance to ensure the optimality of the target (in the powered descent phase of the probe, it is often manifested as fuel optimality) while ensuring the satisfaction of various constraints. This advantage is unmatched by traditional explicit guidance laws. Many existing studies on optimal guidance also focus on fast trajectory optimization algorithms and the corresponding guidance law generation.

[0003] During the powered descent and landing process, the probe is often affected by various uncertainties, such as the uncertainty of the system initial state and the uncertainty of the system parameters. In order to achieve high-precision and high-safety landing, it is necessary to incorporate the influence of the above uncertainties on the trajectory into the design of the guidance law, that is, to construct a robust optimal guidance problem considering uncertainty. However, in the robust optimal guidance problem, the system dynamics, problem constraints and even the objective function are often random, making the robust optimal guidance problem a stochastic optimal control problem. According to the existing methods, it is impossible to solve it directly. Therefore, it is necessary to convert these random functions into deterministic functions. Uncertainty quantification is an effective means to quantitatively describe and evaluate the uncertainty and its evolution in the system. Uncertainty quantification mainly includes uncertainty characterization and uncertainty propagation. Uncertainty characterization is the process of establishing a mathematical model based on the data of uncertainty variables; uncertainty propagation is to study the propagation of the random state of the system with the propagation of system dynamics in the presence of uncertainty. The uncertainty quantification methods of the system can be mainly divided into two categories: linear and nonlinear. Among them, the linear covariance propagation method uses the linear system propagation law to analyze the evolution of the system mean and covariance. However, for nonlinear systems such as Mars powered descent, the accuracy of linear methods is often limited. Summary of the invention

[0004] The present invention provides a robust optimal guidance method for detector power descent based on uncertainty quantification, aiming to solve at least one of the technical problems existing in the prior art.

[0005] The technical solution of the present invention relates to a robust optimal guidance method for detector power descent based on uncertainty quantification. The method according to the present invention comprises the following steps:

[0006] S100, construct a robust fuel optimal guidance model for powered descent considering the uncertainty of initial state and model environment;

[0007] S200, converting the optimal guidance model into a deterministic problem by using an uncertainty quantification method based on chaotic polynomial expansion;

[0008] S300. Solve the deterministic optimization problem by using a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law.

[0009] Further, for step S100,

[0010] In the robust fuel optimal guidance model for powered descent, the objective function of the optimization problem is expressed as follows:

[0011]

[0012] The constraints of the optimization problem include:

[0013] The dynamic system of the Mars rover under uncertainty is expressed as follows:

[0014]

[0015] The constraint used to limit the thrust amplitude to a given range with a high probability is expressed as follows:

[0016]

[0017] The constraint used to ensure that the probe does not collide with the ground with a high probability is expressed as follows:

[0018] μ(r z (t;ξ))-εσ(r z (t;ξ))≥0

[0019] The initial and terminal conditions of the optimization problem are expressed as follows:

[0020]

[0021] m(t 0 )=m 0 (ξ)

[0022] In the formula, l∈{x,y,z} represents a dimension in three-dimensional space; r l (t;ξ) and v l(t;ξ) respectively represent the position and velocity of the detector in the l direction under the influence of system randomness; Respectively represent the given terminal position and terminal velocity expectations; They represent the upper bounds of the standard deviation of the given terminal position and terminal velocity, respectively; m(t; ξ) represents the detector mass; r l0 (ξ),v l0 (ξ),m 0 (ξ) represent the initial position, velocity and mass of the detector respectively; t f represents the given terminal time; g represents the Martian gravity acceleration vector; α(ξ) represents the thruster parameter; is the thrust vector of the thruster; ρ 1 ,ρ 2 They represent the lower and upper bounds of the thrust norm respectively; ε is a constant used to measure robustness. The larger the ε value, the smaller the probability of the constraint being broken.

[0023] Further, in step S100,

[0024] Thrust vector It is decomposed into two parts: nominal thrust and state feedback, which are expressed as follows

[0025]

[0026] In the formula, is the deterministic nominal thrust vector, Designed for μ(r l (t f ξ)) and μ(v l (t f ξ)) is the linear feedback control quantity, where

[0027]

[0028] In the formula, K rl ,K vl are the feedback gains of position and velocity errors in direction l respectively.

[0029] Further, in step S200:

[0030] The intrusive chaotic polynomial expansion method used is expressed as follows:

[0031]

[0032] In the formula, <·,·> represents the j}The inner product in the expanded Hilbert space is

[0033] <f(ξ)g(ξ)>=∫f(ξ)g(ξ)W(ξ)dξ

[0034] Where W(ξ) represents the corresponding weight function selected according to the probability density function of the uncertainty source ξ.

[0035] Further, in step S200:

[0036] The stochastic dynamic uncertainty of the Mars rover dynamic system under uncertainty is quantified based on the chaotic polynomial expansion method, and the deterministic form of the objective function of the robust fuel optimal guidance model for powered descent is obtained;

[0037] The deterministic system obtained after uncertainty quantification of the robust fuel optimal guidance model for powered descent is expressed as follows:

[0038]

[0039] Among them, the vectors containing all corresponding chaotic polynomial coefficients are expressed as follows:

[0040]

[0041] In the formula, R, V, and M represent the high-dimensional polynomial coefficient vectors obtained after the detector position, velocity, and mass are expanded by chaotic polynomials respectively; Represents the vector consisting of all state quantities in the deterministic system obtained after uncertainty quantification; Represents the vector composed of the system control quantity; For the introduction Substitution variables satisfy

[0042] Further, in step S300:

[0043] Based on the construction method of convex programming problem, discretization and linearization are used to convexify the system dynamics, problem constraints and objective function, and trust region constraints and virtual control constraints are added to facilitate the solution using sequential convex optimization technology.

[0044] Further, in step S300:

[0045] The sequential convex optimization method comprises:

[0046] In the reference system state and control quantity X * (t),U * Taylor expansion of the deterministic system dynamics (10) is performed at (t) to obtain a linearized dynamic system, which is expressed as follows:

[0047]

[0048] In the formula, is the linearized system state matrix and control matrix;

[0049] The obtained linearized dynamic system is discretized using the Euler method, and the discrete time interval is Δt, and it can be obtained:

[0050]

[0051] Then we can get:

[0052]

[0053] In the formula,

[0054] They represent the system state / control matrix, system state / control quantity and system reference state / control quantity at discrete time point t k The value below.

[0055] Further, in step S300:

[0056] The robust fuel optimal guidance model for powered descent is constructed as a convex programming problem, which is expressed as follows:

[0057]

[0058] The constraints of the optimization problem include:

[0059] The dynamic constraints obtained after convexification of the deterministic system of the robust fuel optimal guidance model for powered descent are expressed as follows:

[0060]

[0061] In the formula, They represent the state matrix and control matrix of the high-dimensional system after chaotic polynomial expansion and its linearization, respectively; V k represents the virtual control quantity;

[0062] Convex constraints including linear equality constraints or second-order cone inequality constraints are expressed as follows:

[0063]

[0064]

[0065] For the substitution variable relation Linear expansion yields:

[0066]

[0067] The constraint of the difference Δ between the optimization state and the control quantity in two adjacent rounds is expressed as follows:

[0068]

[0069] Where K is the total length of the discrete time domain; are the linearized system state matrix and control matrix respectively.

[0070] The technical solution of the present invention also relates to a computer-readable storage medium on which program instructions are stored, and the above-mentioned method is implemented when the program instructions are executed by a processor.

[0071] The technical solution of the present invention also relates to a detector power reduction robust optimal guidance method for an autoencoder and a graph attention network, wherein the system includes a computer device comprising the above-mentioned computer-readable storage medium.

[0072] The beneficial effects of the present invention are as follows:

[0073] The present invention proposes a robust optimal guidance based on uncertainty quantification technology for the problem of powered descent on Mars. The optimal guidance model that takes into account the uncertainty of the initial state and the model environment is constructed, and the uncertainty quantification method based on the chaotic polynomial expansion is used to convert it into a deterministic problem, and the deterministic optimization problem is solved by a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law. The present invention can convert a complex nonlinear optimal control problem containing randomness into a convex optimization problem that is easy to solve, thereby improving the solution efficiency while ensuring the success rate of the solution. The present invention can take the uncertainty of the model and the environment into consideration while designing the optimal trajectory, so that the designed optimal trajectory can also meet various constraints under uncertain conditions. The present invention also obtains the corresponding feedback guidance law while optimizing the trajectory, and the feedback guidance law can be directly applied online, reducing the burden of online calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a basic flow chart of the method according to the present invention.

[0075] Figure 2 Schematic diagram of the detector trajectory dispersion according to the method of the present invention.

[0076] Figure 3 It is a schematic diagram of the change of the three-axis thrust of the detector with time according to the method of the present invention.

[0077] Figure 4 It is a schematic diagram of the change of the thrust second norm of the detector with time according to the method of the present invention.

[0078] Figure 5 It is a schematic diagram of the change of the detector state over time according to the method of the present invention.

[0079] Figure 6 It is a schematic diagram of the distribution of the falling points of the detectors according to the method of the present invention. DETAILED DESCRIPTION

[0080] The concept, specific structure and technical effects of the present invention will be clearly and completely described below in combination with the embodiments and drawings to fully understand the purpose, scheme and effect of the present invention.

[0081] It should be noted that, unless otherwise specified, when a feature is referred to as being "fixed" or "connected" to another feature, it may be directly fixed or connected to another feature, or it may be indirectly fixed or connected to another feature. The singular forms of "," "said" and "the" used herein are also intended to include the plural forms, unless the context clearly indicates otherwise. In addition, unless otherwise defined, all technical and scientific terms used herein have the same meaning as those generally understood by those skilled in the art. The terms used in this specification are intended to describe specific embodiments only and are not intended to limit the invention. The term "and / or" used herein includes any combination of one or more of the related listed items.

[0082] It should be understood that, although the term first, second, third etc. may be adopted to describe various elements in the present disclosure, these elements should not be limited to these terms. These terms are only used to distinguish the same type of elements from each other. For example, without departing from the scope of the present disclosure, the first element may also be referred to as the second element, and similarly, the second element may also be referred to as the first element. The use of any and all examples or exemplary language ("for example", "such as" etc.) provided herein is only intended to better illustrate embodiments of the present invention, and unless otherwise required, the scope of the present invention will not be limited.

[0083] Reference Figures 1 to 4 In some embodiments, the robust optimal guidance method for probe power descent based on uncertainty quantification according to the present invention comprises at least the following steps:

[0084] S100, construct a robust fuel optimal guidance model for powered descent considering the uncertainty of initial state and model environment;

[0085] S200, transforming the optimal guidance model into a deterministic problem through uncertainty quantification method based on chaotic polynomial expansion;

[0086] S300. Solve the deterministic optimization problem by using a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law.

[0087] In some embodiments, the present invention proposes a robust optimal guidance scheme based on uncertainty quantification technology for the Mars powered descent problem, which first constructs an optimal guidance problem considering the initial state and model environment uncertainty. Specifically, a general nonlinear system with system initial state and parameter uncertainty:

[0088]

[0089] In the formula, Respectively represent the state vector of the system and its initial value including uncertainty; represents the system parameter vector containing uncertainty; represents the system control input containing uncertainty. The above initial state and parameter uncertainties are caused by different uncertainty sources and are expressed as At the same time, these uncertainty sources each satisfy their corresponding probability distribution.

[0090] Furthermore, x 0 (ξ),u(ξ) and a(ξ) can be expressed with respect to their respective nominal values a n ,u n Function of the uncertainty source ξ:

[0091]

[0092] In some embodiments, the present invention converts the optimal guidance model into a deterministic problem through an uncertainty quantification method based on chaotic polynomial expansion.

[0093] Specifically, according to the chaotic polynomial theory, the random variables x(ξ), u(ξ), and a(ξ) can be represented by the corresponding chaotic polynomial expansion model. Furthermore, due to the consideration of computational complexity, it is often necessary to Truncation, where p is the order selected for a single uncertainty source, as shown in equations (5) to (7):

[0094]

[0095] In the formula, represents a random variable (·) i The j-th order chaotic polynomial coefficient of , Φ(ξ) is an orthogonal polynomial basis selected according to the form of the uncertainty source ξ, and the random distribution of the uncertainty source is selected as a standard random distribution that satisfies the Askey scheme.

[0096] Through the chaotic polynomial expansion of the form (5) to (7), the deterministic time-varying chaotic polynomial coefficients and It can be decoupled from the orthogonal polynomial basis Φ(ξ) containing the random characteristics of the system. By eliminating ξ through appropriate mathematical methods, the original stochastic differential equation (1) can be solved.

[0097] Furthermore, this patent adopts the intrusive chaotic polynomial expansion method, substituting equations (5) to (7) into equation (1) and projecting both sides of the equation onto Φ(ξ) at the same time, and we can get

[0098]

[0099] In formula (8), <·,·> represents the j}The inner product in the expanded Hilbert space is

[0100]

[0101] Where W(ξ) represents the corresponding weight function selected according to the probability density function of the uncertainty source ξ.

[0102] Furthermore, the optimal orthogonal polynomial basis functions corresponding to common distribution types are given in Table 1. It can be understood that the probability density function corresponding to the same distribution type is similar to the weight function form, which can ensure that these orthogonal polynomial bases are optimal for a certain probability distribution type.

[0103] Table 1 Orthogonal polynomials corresponding to different random variables

[0104]

[0105] On the right side of equation (8), the <Φ l 2 The term (ξ)> can be obtained analytically according to the definition of the inner product (9). However, for the numerator, due to the nonlinearity of the system dynamics, the integral term is difficult to obtain analytically, and it is often necessary to use numerical integration methods to obtain it, such as the full factor numerical integration method.

[0106] In the present invention, formula (8) transforms the original random system containing n random states into a random system containing n s =n·P′ states, where P′=P+1:

[0107]

[0108] Where X, U, a represent all polynomial coefficients used to construct the chaotic polynomial expansion of x, u, a respectively:

[0109]

[0110] The deterministic system described by equation (10) constitutes a proxy model of the original random system (1), and its state can be efficiently obtained using system evolution methods such as the Euler method and the fourth-order Runge-Kutta method. Furthermore, in order to describe the state statistical characteristics of the random system (1), the mean μ(x i ) and variance σ(x i ) can be obtained analytically using the chaotic polynomial coefficient X:

[0111]

[0112] Where E[·] represents the expected value of the corresponding random variable.

[0113] In an application embodiment, the present invention can be applied to the robust optimal guidance problem. It can be understood that the main purpose of the robust optimal guidance problem is to use statistical moments (such as mean, variance, etc.) to quantify the dispersion of trajectories and plan the corresponding minimum fuel consumption thrust sequence to ensure that the trajectory generated under the thrust sequence can still ensure the satisfaction of constraints under uncertain conditions. Specifically, in the power descent robust fuel optimal guidance model, the objective function of the optimization problem is expressed as follows:

[0114]

[0115] Subject to the following constraints (constraints of the optimization problem):

[0116]

[0117] μ(r z (t;ξ))-εσ(r z (t;ξ))≥0 (22)

[0118]

[0119] m(t 0 )=m 0 (ξ) (25)

[0120] In the formula, l∈{x,y,z} represents a dimension in three-dimensional space; r l (t;ξ) and v l (t;ξ) respectively represent the position and velocity of the detector in the l direction under the influence of system randomness; Respectively represent the given terminal position and terminal velocity expectations; They represent the upper bounds of the standard deviation of the given terminal position and terminal velocity, respectively; m(t; ξ) represents the detector mass; r l0 (ξ),v l0 (ξ),m 0 (ξ) represent the initial position, velocity and mass of the detector respectively; tf represents the given terminal time; g represents the Martian gravity acceleration vector; α(ξ) represents the thruster parameter; is the thrust vector of the thruster; ρ 1 ,ρ 2 They represent the lower and upper bounds of the thrust norm respectively; ε is a constant used to measure robustness. The larger the ε value, the smaller the probability of the constraint being broken.

[0121] It can be understood that the above equation (16) is the objective function of the optimization problem, and equations (17) to (25) are the constraints of the optimization problem. Among them, equations (17) to (19) represent the dynamics of the Mars probe under uncertainty, equations (20) and (21) limit the thrust amplitude to be within a given range with a high probability, ensuring that the probe can achieve the desired trajectory; equation (22) ensures that the probe does not collide with the ground with a high probability, ensuring the safety of the probe under uncertainty conditions; equations (23) to (25) give the initial conditions and terminal conditions of the optimization problem.

[0122] Furthermore, the thrust vector It can be decomposed into two parts: nominal thrust and state feedback, namely

[0123]

[0124] In the formula, is the deterministic nominal thrust vector, Designed for μ(r l (t f ξ)) and μ(v l (t f ξ)) is the linear feedback control quantity, where

[0125]

[0126] In the formula, K rl ,K vl are the feedback gains of position and velocity errors in direction l respectively.

[0127] In some embodiments, the above-mentioned power descent robust fuel optimal guidance problem is a nonlinear programming problem involving random variables. In order to solve such an optimization problem, the present invention first uses an uncertainty quantification method based on chaotic polynomial expansion to convert it into a deterministic problem. Further, in order to improve the solution efficiency of the obtained deterministic nonlinear programming problem, it can be constructed as a convex programming problem. The convex programming problem requires that the objective function and constraints of the system are both convex functions.

[0128] Specifically, first, in the reference system state and control quantity X * (t),U* Taylor expansion of the deterministic system dynamics (10) is performed at (t) to obtain the linearized dynamic system:

[0129]

[0130] In the formula, are the linearized system state matrix and control matrix.

[0131] Furthermore, the obtained linear system (28) is discretized using the Euler method, and the discrete time interval is Δt, then:

[0132]

[0133] Rearranging formula (29), we get:

[0134]

[0135] In the formula,

[0136]

[0137] Specific implementation of steps S100 and S200

[0138] In the model construction and uncertainty quantification of the robust guidance problem of the present invention, the robust fuel optimal guidance model of the power descent considering the uncertainty of the initial state and system parameters as shown in equations (16) to (25) is first constructed for the robust fuel optimal guidance problem of the power descent. In order to solve the robust fuel optimal guidance problem of the power descent, the present invention adopts an uncertainty quantification method based on chaotic polynomials to transform the random variables containing uncertainty in the robust fuel optimal guidance problem of the power descent into deterministic ones, which specifically includes the uncertainty quantification of random dynamics, problem constraints and objective functions.

[0139] Specifically, the stochastic dynamics equations (17) to (19) of the system are subjected to the stochastic dynamics uncertainty quantification based on the chaotic polynomial expansion method shown in equation (8), and the obtained result is:

[0140]

[0141]

[0142] Due to the existence of the uncertain thrust norm in the numerator on the right side of equation (33), the inner product term in the numerator is very difficult to obtain, so the substitution variable is introduced And satisfy the corresponding equality constraints:

[0143]

[0144] The uncertainty of equation (34) is quantified as shown in equation (8), and we get:

[0145]

[0146] Using the random variable statistical moment solution method described by equations (14) and (15) for equations (20) to (25), we obtain:

[0147]

[0148] The objective function in the powered descent robust fuel optimal guidance model, equation (16), can be rewritten in the following deterministic form:

[0149]

[0150] in,

[0151]

[0152] are vectors containing all corresponding chaotic polynomial coefficients. For simplicity, the deterministic system obtained after uncertainty quantization is recorded as:

[0153]

[0154] Where a represents the polynomial coefficient vector obtained after the uncertain parameter a is expanded by the chaotic polynomial; t represents time.

[0155] Specific implementation of step S300

[0156] The present invention is based on a construction method of convex programming problems, uses discretization and linearization to convexify system dynamics, problem constraints and objective functions, and adds trust region constraints and virtual control constraints to facilitate solving using sequential convex optimization technology.

[0157] Specifically, the convex programming problem of robust fuel optimal guidance for power descent is

[0158]

[0159] Subject to the following constraints (constraints of the optimization problem):

[0160]

[0161]

[0162] Where K is the total length of the discrete time domain; are the linearized system state matrix and control matrix.

[0163] It should be noted that equation (51) is the dynamic constraint obtained by convexifying equation (49) with reference to the method shown in equation (30), equation (58) is the linear expansion of the substitution variable relationship equation (35), and equations (52) to (57) contain a series of linear equality constraints or second-order cone inequality constraints, all of which are convex constraints, so no additional convexification is required. In order to prevent the "artificial infeasibility" problem caused by local linearized dynamics, a virtual control variable V is added to equation (51) k ; At the same time, in order to reduce the error caused by linearization, equation (59) constrains the difference between the optimization state and the control quantity of two adjacent rounds, represented by Δ. Finally, add V to the objective function k ,Δ and its corresponding weight w V ,w Δ .

[0164] The present invention solves the robust guidance problem by a sequential convex optimization method. The sequential convex optimization method approximates the solution of the original problem by continuously solving the convex subproblems obtained by expanding at the current reference state. The process is shown in Algorithm 1:

[0165]

[0166] Here, a specific embodiment is used to simulate and verify the present invention.

[0167] Specifically, the simulation and optimization algorithm parameters are shown in the table:

[0168] Table 2 Mars environment and probe related parameter values

[0169]

[0170] Assuming thruster coefficient α, initial position r 0 There is uncertainty. The specific uncertainty information and the corresponding PCE are shown in Table 3:

[0171] Table 3 Uncertainty of dynamical system

[0172]

[0173] It should be noted that the hardware platform used for the simulation is as follows: CPU is AMD R7-5800H (8 cores and 16 threads), main frequency is 2.5GHz; running memory is 32GB. The convex optimization problem is solved using the MOSEK solver.

[0174] The effectiveness of the present invention is verified. First, a robust optimal guidance problem is constructed according to Table 2 and Table 3, and a sequential convex optimization technique is used to solve it. The linear feedback gain K obtained by the solution is used rl (t),K vl (t) and nominal thrust Tl (t) Constructing the feedback guidance law. Next, a Monte Carlo simulation is performed: using the uncertainty in the dynamic system given in Table 2, 2000 sets of samples are generated, and the resulting feedback guidance law is used for landing guidance.

[0175] in, Figure 2 The trajectory dispersion is given, and it can be seen that under the action of the designed robust optimal feedback guidance law, the probe can achieve soft landing in the presence of initial state uncertainty and parameter uncertainty. Figure 3 and Figure 4 The three-axis thrust and thrust norm of the probe under uncertain conditions are given respectively. It can be seen that even under the influence of uncertainty, the designed robust optimal feedback guidance law can still ensure that the thrust norm is within the given interval. In addition, the thrust norm still has a bang-bang form, which is similar to the deterministic optimal thrust situation.

[0176] In order to further clarify the effectiveness of the designed robust optimal feedback guidance law, Figure 5 The position and velocity of the detector are plotted over time. It can be seen that the z-axis height of the detector is always greater than zero, and the proposed algorithm can ensure the safety of the detector under uncertain conditions. Figure 6 The falling point scatter diagram is given, and it can be seen that in most cases, the falling point of the detector is constrained within the preset μ±3σ range ( Figure 6 ellipsoid).

[0177] It should be noted that in recent years, most studies on optimal guidance have only focused on deterministic trajectory planning problems, that is, the model and environmental uncertainties and the impact of external disturbances on the trajectory are not considered during trajectory planning, so that only a nominal trajectory that satisfies the constraints and has optimality under deterministic conditions can be obtained. Although, in the traditional "trajectory planning-trajectory tracking" guidance scheme, the offset of disturbances and uncertainties can be achieved by designing a robust tracking controller that outputs online tracking of nominal trajectory guidance instructions without putting it in the trajectory planning link, and according to their design principles, these tracking controllers can be roughly divided into two types: active compensation controllers based on feedforward and passive compensation controllers based on feedback. However, no matter which tracking controller is used, the tracking controller and the optimal trajectory in this scheme are designed independently, and the optimal trajectory cannot consider the output of the tracking controller, which will inevitably affect the optimality of the actual trajectory.

[0178] It should be appreciated that the method steps in the embodiments of the present invention can be implemented or implemented by computer hardware, a combination of hardware and software, or by computer instructions stored in a non-transitory computer readable memory. The method can use standard programming techniques. Each program can be implemented in a high-level process or object-oriented programming language to communicate with a computer system. However, if necessary, the program can be implemented in an assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, the program can be run on a programmed ASIC for this purpose.

[0179] Furthermore, the operations of the processes described herein may be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The processes described herein (or variations and / or combinations thereof) may be performed under the control of one or more computer systems configured with executable instructions, and may be implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors, by hardware, or a combination thereof. The computer program includes a plurality of instructions that may be executed by one or more processors.

[0180] Further, the method can be implemented in any type of computing platform that is operably connected to a suitable computer, including but not limited to a personal computer, a minicomputer, a mainframe, a workstation, a network or distributed computing environment, a separate or integrated computer platform, or in communication with a charged particle tool or other imaging device, etc. Various aspects of the present invention can be implemented in machine-readable code stored on a non-transitory storage medium or device, whether removable or integrated into a computing platform, such as a hard disk, an optical read and / or write storage medium, an RSM, a ROM, etc., so that it can be read by a programmable computer, and when the storage medium or device is read by the computer, it can be used to configure and operate the computer to perform the process described herein. In addition, the machine-readable code, or portions thereof, can be transmitted via a wired or wireless network. When such media includes instructions or programs that implement the steps described above in conjunction with a microprocessor or other data processor, the invention described herein includes these and other different types of non-transitory computer-readable storage media. When programmed according to the methods and techniques of the present invention, the present invention can also include the computer itself.

[0181] The computer program can be applied to input data to perform the functions described herein, thereby converting the input data to generate output data stored in a non-volatile memory. The output information can also be applied to one or more output devices such as a display. In a preferred embodiment of the present invention, the converted data represents physical and tangible objects, including specific visual depictions of physical and tangible objects produced on the display.

[0182] The above is only a preferred embodiment of the present invention. The present invention is not limited to the above implementation. As long as the technical effect of the present invention is achieved by the same means, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of protection of the present invention. Within the scope of protection of the present invention, its technical scheme and / or implementation method may have various modifications and changes.

Claims

1. A robust optimal guidance method for detector power descent, characterized in that: The method comprises the following steps: S100, construct a robust fuel optimal guidance model for powered descent considering the uncertainty of initial state and model environment; S200, converting the optimal guidance model into a deterministic problem by using an uncertainty quantification method based on chaotic polynomial expansion; S300. Solve the deterministic optimization problem by using a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law.

2. The method according to claim 1, characterized in that For step S100, In the robust fuel optimal guidance model for powered descent, the objective function of the optimization problem is expressed as follows: The constraints of the optimization problem include: The dynamic system of the Mars rover under uncertainty is expressed as follows: The constraint used to limit the thrust amplitude to a given range with a high probability is expressed as follows: The constraint used to ensure that the probe does not collide with the ground with a high probability is expressed as follows: μ(r z (t;ξ))-εσ(r z (t;ξ))≥0 The initial and terminal conditions of the optimization problem are expressed as follows: m(t0)=m0(ξ) In the formula, l∈{x,y,z} represents a dimension in three-dimensional space; r l (t;ξ) and v l (t;ξ) respectively represent the position and velocity of the detector in the l direction under the influence of system randomness; Respectively represent the given terminal position and terminal velocity expectations; They represent the upper bounds of the standard deviation of the given terminal position and terminal velocity, respectively; m(t; ξ) represents the detector mass; r l0 (ξ),v l0 (ξ),m0(ξ) represent the initial position, velocity and mass of the detector respectively; t f represents the given terminal time; g represents the Martian gravity acceleration vector; α(ξ) represents the thruster parameter; is the thrust vector of the thruster; ρ1 and ρ2 represent the lower and upper bounds of the thrust norm, respectively; ε is a constant used to measure robustness. The larger the ε value, the smaller the probability of the constraint being broken.

3. The method according to claim 1, characterized in that In the step S100, Thrust vector It is decomposed into two parts: nominal thrust and state feedback, which are expressed as follows In the formula, is the deterministic nominal thrust vector, Designed for μ(r l (t f ξ)) and μ(v l (t f ξ)) is the linear feedback control quantity, where In the formula, K rl ,K vl are the feedback gains of position and velocity errors in direction l respectively.

4. The method according to claim 2, characterized in that: In step S200: The intrusive chaotic polynomial expansion method used is expressed as follows: In the formula, <·,·> represents the j }The inner product in the expanded Hilbert space is <f(ξ)g(ξ)> =∫f(ξ)g(ξ)W(ξ)dξ Where W(ξ) represents the corresponding weight function selected according to the probability density function of the uncertainty source ξ.

5. The method according to claim 4, characterized in that In step S200: The stochastic dynamic uncertainty of the Mars rover dynamic system under uncertainty is quantified based on the chaotic polynomial expansion method, and the deterministic form of the objective function of the robust fuel optimal guidance model for powered descent is obtained; The deterministic system obtained after uncertainty quantification of the robust fuel optimal guidance model for powered descent is expressed as follows: Among them, the vectors containing all corresponding chaotic polynomial coefficients are expressed as follows: In the formula, R, V, and M represent the high-dimensional polynomial coefficient vectors obtained after the detector position, velocity, and mass are expanded by chaotic polynomials respectively; Represents the vector consisting of all state quantities in the deterministic system obtained after uncertainty quantification; Represents the vector composed of the system control quantity; For the introduction Substitution variables satisfy 6. The method according to claim 5, characterized in that In step S300: Based on the construction method of convex programming problem, discretization and linearization are used to convexify the system dynamics, problem constraints and objective function, and trust region constraints and virtual control constraints are added to facilitate the solution using sequential convex optimization technology.

7. The method according to claim 6, characterized in that In step S300: The sequential convex optimization method comprises: In the reference system state and control quantity X * (t),U * Taylor expansion of the deterministic system dynamics (10) is performed at (t) to obtain a linearized dynamic system, which is expressed as follows: In the formula, is the linearized system state matrix and control matrix; The obtained linearized dynamic system is discretized using the Euler method, and the discrete time interval is Δt, and it can be obtained: Then we can get: In the formula, X k =X(t k ),U k =U(t k ), They represent the system state / control matrix, system state / control quantity and system reference state / control quantity at discrete time point t k The value below.

8. The method according to claim 7, characterized in that In step S300: The robust fuel optimal guidance model for powered descent is constructed as a convex programming problem, which is expressed as follows: The constraints of the optimization problem include: The dynamic constraints obtained after convexification of the deterministic system of the robust fuel optimal guidance model for powered descent are expressed as follows: In the formula, They represent the state matrix and control matrix of the high-dimensional system after chaotic polynomial expansion and its linearization, respectively; V k represents the virtual control quantity; Convex constraints including linear equality constraints or second-order cone inequality constraints are expressed as follows: For the substitution variable relationship Linear expansion yields: The constraint of the difference Δ between the optimization state and the control quantity in two adjacent rounds is expressed as follows: Where K is the total length of the discrete time domain; are the linearized system state matrix and control matrix respectively.

9. A computer-readable storage medium having program instructions stored thereon, wherein the program instructions are executed by a processor to implement the method according to any one of claims 1 to 8.

10. The robust optimal guidance method for detector power descent is characterized by: include: A computer device comprising a computer readable storage medium according to claim 9.

Images