Robust optimal guidance method for probe powered descent based on uncertainty quantification

Abstract

The present invention relates to a robust optimal guidance method for powered descent of a probe based on uncertainty quantification. The method comprises: constructing a robust fuel optimal guidance model for powered descent that accounts for the uncertainties of the initial state and model environment; transforming the optimal guidance model into a deterministic problem using an uncertainty quantification method based on chaotic polynomial expansion; and solving the deterministic optimization problem using a sequential convex optimization method to obtain a robust optimal landing trajectory and corresponding feedback guidance law. This method transforms complex nonlinear optimal control problems involving randomness into easily solvable convex optimization problems, improving solution efficiency while ensuring a high solution success rate. The designed optimal trajectory can satisfy various constraints even under uncertainty, and the 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 increasing computing power of onboard probes and the maturation of linear trajectory planning techniques, particularly convex optimization, optimal guidance has become a key development trend in future Mars powered descent guidance technology. Optimal guidance has the following key features: 1. Numerical algorithms replace fixed-structure guidance laws, where guidance command generation relies heavily on extensive onboard computation; 2. Guidance commands are generated based on models or data, eliminating the need for specific reference trajectories and extensive offline design; and 3. The pursuit of optimality. These three features enable optimal guidance to ensure target optimality (often manifested as fuel optimality during a probe's powered descent) while satisfying various constraints. This advantage is unmatched by traditional explicit guidance laws. Existing research on optimal guidance has primarily focused on fast trajectory optimization algorithms and the generation of corresponding guidance laws.

[0003] During powered descent and landing, probes are often subject to various uncertainties, such as uncertainty in the system's initial state and system parameters. To achieve high-precision and high-safety landings, it is necessary to incorporate the impact of these uncertainties on the trajectory into the design of the guidance law, that is, to construct a robust optimal guidance problem that accounts for uncertainty. However, in robust optimal guidance problems, the system dynamics, problem constraints, and even the objective function are often stochastic, making the robust optimal guidance problem a stochastic optimal control problem. Existing methods cannot directly solve it, so these stochastic functions need to be converted into deterministic ones. Uncertainty quantification is an effective means of quantitatively describing and evaluating uncertainty and its evolution in a system. Uncertainty quantification mainly involves uncertainty characterization and uncertainty propagation. Uncertainty characterization is the process of building a mathematical model based on data from uncertainty variables. Uncertainty propagation studies the propagation of the system's random states along the system dynamics in the presence of uncertainty. System uncertainty quantification methods can be mainly divided into linear and nonlinear methods. The linear covariance propagation method uses the propagation law of linear systems 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 dynamic 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 probe 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 that takes into account the uncertainty of the initial state and model environment;

[0007] S200, converting the optimal guidance model into a deterministic problem through 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 powered descent robust fuel optimal guidance model, 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(t0)=m0(ξ)

[0022] Where 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; Represent the given terminal position and terminal velocity expectations respectively; 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. A larger ε value means a smaller probability of the constraint being broken.

[0023] Furthermore, in step S100,

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

[0025]

[0026] Where, 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] Where K rl ,K vl are the feedback gains of position and velocity errors in the l direction respectively.

[0029] Furthermore, 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] Furthermore, 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] Where R, V, and M represent the high-dimensional polynomial coefficient vectors obtained by expanding the position, velocity, and mass of the detector through 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] Furthermore, 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] Furthermore, 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 the linearized dynamic system, which is expressed as follows:

[0047]

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

[0049] The obtained linearized dynamic system is discretized using the Euler method, with the discrete time interval Δt being Δt, and we can obtain:

[0050]

[0051] Then we can get:

[0052]

[0053] Where,

[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] Furthermore, in step S300:

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

[0057]

[0058] The constraints of the optimization problem include:

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

[0060]

[0061] Where, 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 substitution variables Performing linear expansion we can get:

[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 having program instructions stored thereon, 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 descent 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 addresses the problem of powered descent on Mars and proposes robust optimal guidance based on uncertainty quantification technology. This approach constructs an optimal guidance model that takes into account the uncertainties of the initial state and model environment, transforms it into a deterministic problem using an uncertainty quantification method based on chaotic polynomial expansion, and solves the deterministic optimization problem using a sequential convex optimization method, thereby obtaining a robust optimal landing trajectory and a corresponding feedback guidance law. The present invention can transform complex nonlinear optimal control problems involving randomness into easily solvable convex optimization problems, improving solution efficiency while ensuring a high success rate. The present invention can take into account the uncertainties of the model and environment while designing the optimal trajectory, enabling the designed optimal trajectory to satisfy various constraints even under uncertain conditions. While optimizing the trajectory, the present invention also obtains a corresponding feedback guidance law, which can be directly applied online, reducing the burden of online computation. 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 over time according to the method of the present invention.

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

[0078] Figure 5 Schematic diagram of the detector status changing over time according to the method of the present invention.

[0079] Figure 6 Schematic diagram of the distribution of the detector's landing points according to the method of the present invention. DETAILED DESCRIPTION

[0080] The following will provide a clear and complete description of the concept, specific structure and technical effects of the present invention in conjunction with the embodiments and drawings to fully understand the purpose, scheme and effects 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 the other feature, or it may be indirectly fixed or connected to the other 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 commonly understood by those skilled in the art. The terms used in this specification are for the purpose of describing 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] Should be understood that, although the present disclosure may adopt the term first, second, third etc. to describe various elements, these elements should not be limited to these terms.These terms are only used to distinguish the elements of the same type 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, will not impose limitations on the scope of the present invention.

[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 includes at least the following steps:

[0084] S100, construct a robust fuel optimal guidance model for powered descent that takes into account the uncertainty of the 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 addresses the problem of powered descent on Mars by proposing a robust optimal guidance scheme based on uncertainty quantification technology. This scheme first constructs an optimal guidance problem that considers the uncertainty of the initial state and the model environment. Specifically, for a general nonlinear system with system initial state and parameter uncertainty:

[0088]

[0089] Where, Represent the state vector of the system and its initial value containing uncertainty; represents the system parameter vector containing uncertainty; Denotes 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, x0(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, random variables x(ξ), u(ξ), 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] Where, 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 the 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, Table 1 lists the optimal orthogonal polynomial basis functions corresponding to common distribution types. It can be understood that the probability density function and weight function corresponding to the same distribution type are similar in form, which ensures 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 formula (8), the denominator <Φ l 2 The term (ξ)> can be obtained analytically based on the definition of the inner product (9). However, for the numerator term, 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, such as the full factor numerical integration method.

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

[0107]

[0108] Where X, U, and a represent all polynomial coefficients used to construct the chaotic polynomial expansion of x, u, and 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 one embodiment, the present invention can be applied to the robust optimal guidance problem. It is understood that the main purpose of the robust optimal guidance problem is to use statistical moments (such as mean and variance) to quantify the dispersion of trajectories and plan a corresponding minimum fuel consumption thrust sequence to ensure that the trajectory generated under this thrust sequence still meets the constraints under uncertain conditions. Specifically, in the power-down 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(t0)=m0(ξ) (25)

[0120] Where 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; Represent the given terminal position and terminal velocity expectations respectively; 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. A larger ε value means a smaller 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 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] Where, 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] Where K rl ,K vl are the feedback gains of position and velocity errors in the l direction respectively.

[0127] In some embodiments, the aforementioned robust fuel optimization guidance problem for power descent is a nonlinear programming problem involving random variables. To solve this optimization problem, the present invention first utilizes an uncertainty quantification method based on chaotic polynomial expansion to transform it into a deterministic problem. Furthermore, to improve the efficiency of solving the resulting deterministic nonlinear programming problem, it can be formulated as a convex programming problem. Convex programming requires that both the system's objective function and constraints be convex.

[0128] Specifically, first, the reference system state and the 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] Where, 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] Arranging formula (29), we get:

[0134]

[0135] Where,

[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 problem for power descent is firstly addressed. The robust fuel optimal guidance model for power descent, shown in Equations (16) to (25), is constructed, taking into account the uncertainty of the initial state and system parameters. To solve the robust fuel optimal guidance problem for power descent, the present invention employs an uncertainty quantification method based on chaotic polynomials to transform the random variables containing uncertainty in the robust fuel optimal guidance problem into deterministic ones. This method specifically includes uncertainty quantification of the stochastic dynamics, problem constraints, and objective function.

[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 following is obtained:

[0140]

[0141]

[0142] Due to the existence of the uncertainty 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] By quantifying the uncertainty of equation (34) as shown in equation (8), we can obtain:

[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 robust fuel optimal guidance model for powered descent, 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 the construction method of convex programming problem, uses discretization and linearization to convexify the system dynamics, problem constraints and objective function, and adds trust region constraints and virtual control constraints to facilitate the solution 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 linearization dynamics, a virtual control variable V is added to Equation (51). kAt 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, which is represented by Δ. Finally, V is added to the objective function k ,Δ and its corresponding weight w V ,w Δ .

[0164] The present invention solves the robust guidance problem through a sequential convex optimization method. The sequential convex optimization method approximates the solution to the original problem by continuously solving 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 Martian environment and probe related parameter values

[0169]

[0170] Assuming the thruster coefficient α, the initial position r0 has uncertainty. The specific uncertainty information and the corresponding PCE are shown in Table 3:

[0171] Table 3 Uncertainty of dynamical system

[0172]

[0173] The simulations were conducted on an AMD R7-5800H processor (8 cores, 16 threads) with a clock speed of 2.5 GHz and 32 GB of RAM. The convex optimization problem was 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 solved using sequential convex optimization technology. The linear feedback gain K obtained by the solution is used. rl (t),K vl (t) and nominal thrust T l (t) Constructing a feedback guidance law. Next, a Monte Carlo simulation is performed: using the uncertainties 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 presented. 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 range. Furthermore, the obtained thrust norm still has a bang-bang form, similar to the deterministic optimal thrust case.

[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 landing point scatter diagram is given, and it can be seen that in most cases, the landing point of the detector is constrained within the preset μ±3σ range ( Figure 6 colored ellipsoid).

[0177] It should be noted that in recent years, most research on optimal guidance has focused solely on deterministic trajectory planning. This means that trajectory planning fails to consider the effects of model and environmental uncertainties, or external disturbances, on the trajectory. Consequently, only a nominal trajectory that satisfies constraints and achieves optimality under deterministic conditions can be obtained. However, in traditional "trajectory planning-tracking" guidance schemes, the cancellation of disturbances and uncertainties can be achieved by designing a robust tracking controller that outputs guidance commands to track the nominal trajectory online, without requiring a trajectory planning step. Based on their design principles, these tracking controllers can be broadly categorized as either active compensation controllers based on feedforward or passive compensation controllers based on feedback. However, regardless of the tracking controller employed, the tracking controller and the optimal trajectory are designed independently, and the optimal trajectory cannot take into account the output of the tracking controller, which inevitably compromises 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 executed 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 procedural or object-oriented programming language to communicate with the computer system. However, if desired, the program can be implemented in assembly or machine language. In any case, the language can be a compiled or interpreted language. In addition, for this purpose, the program can be run on a programmed application-specific integrated circuit.

[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 the 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 can 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 as 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 over 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 that is 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 a physical and tangible object, including a specific visual depiction of the physical and tangible object produced on the display.

[0182] The above description is merely a preferred embodiment of the present invention. The present invention is not limited to the aforementioned embodiments. As long as the technical effects of the present invention are achieved by the same means, any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention. Within the scope of protection of the present invention, various modifications and variations of the technical solutions and / or implementation methods are possible.

Claims

1. A robust optimal guidance method for detector dynamic descent based on uncertainty quantification, characterized by: The method comprises the following steps: S100, construct a robust fuel optimal guidance model for powered descent that takes into account the uncertainty of the initial state and model environment; S200, converting the optimal guidance model into a deterministic problem through an uncertainty quantification method based on chaotic polynomial expansion; S300, solving a deterministic optimization problem using a sequential convex optimization method to obtain a robust optimal landing trajectory and a corresponding feedback guidance law; Wherein, for the step S100, In the powered descent robust fuel optimal guidance model, 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 is expressed as follows: The constraints used to ensure that the probe does not collide with the ground are 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) Where 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; Represent the given terminal position and terminal velocity expectations respectively; 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. A larger ε value means a smaller probability of the constraint being broken.

2. 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 Where, 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 Where K rl ,K vl are the feedback gains of position and velocity errors in the l direction respectively.

3. The method according to claim 1, 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.

4. The method according to claim 3, 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: Where R, V, and M represent the high-dimensional polynomial coefficient vectors obtained by expanding the position, velocity, and mass of the detector through 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 5. The method according to claim 4, 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.

6. The method according to claim 5, 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 the linearized dynamic system, which is expressed as follows: Where, is the linearized system state matrix and control matrix; The obtained linearized dynamic system is discretized using the Euler method, with the discrete time interval Δt being Δt, to obtain: Then we get: Where, X k = X(t k ), U k = U(t k ), Minute The system state / control matrix, system state / control quantity and system reference state / control quantity are expressed separately at discrete time point t k The value below.

7. The method according to claim 6, characterized in that In step S300: The robust fuel optimal guidance model for powered descent is formulated as a convex programming problem, which is expressed as follows: The constraints of the optimization problem include: The dynamic constraints obtained by convexifying the deterministic system of the robust fuel optimal guidance model for powered descent are expressed as follows: Where, 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 substitution variables Performing 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. 8 . A computer-readable storage medium having program instructions stored thereon, wherein the program instructions are configured to implement the method according to claim 1 when executed by a processor.

9. The robust optimal guidance method for detector power descent is characterized by: include: A computer device comprising the computer-readable storage medium according to claim 8.

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