A preset time trajectory tracking control method for planetary probe under input saturation

Abstract

The application discloses a preset time trajectory tracking control method for a planetary probe under input saturation. The method comprises the following steps: establishing an initial dynamic model of the planetary probe in an atmospheric entry section; setting a reference radial distance of the planetary probe; determining an initial height tracking compensation error and a first-order height tracking compensation error of the planetary probe based on an actual radial distance in the initial dynamic model and the reference radial distance; obtaining a second-order height tracking compensation error based on the initial dynamic model, the initial height tracking compensation error and the first-order height tracking compensation error; and setting an initial sliding mode variable, processing the initial sliding mode variable, and obtaining a first-order sliding mode variable. The application solves the technical problem that the planetary probe cannot achieve high-precision landing within a preset time in a complex space environment.

Description

Technical Field

[0001] This invention relates to the field of planetary exploration control technology, and more specifically, to a method for tracking and controlling a planetary probe's preset time trajectory under input saturation. Background Technology

[0002] With the development of planetary exploration missions, future planetary probes are expected to provide rapid and accurate landings under uncertainties and external interference. In the complex space environment, trajectory tracking control methods are more suitable for the entry phase guidance of planetary probes. Previously, most methods employed finite-time sliding mode control, but this method results in the system's convergence time being constrained by initial conditions, which are generally difficult to know in advance. To address this challenge, fixed-time sliding mode control schemes were proposed. However, since the fixed convergence time is related to the system's structural parameters, it is difficult for users to adjust the system's convergence time independently. Summary of the Invention

[0003] This invention provides a method for tracking and controlling a planetary probe's trajectory within a preset time under input saturation, in order to at least solve the technical problem that planetary probes cannot achieve high-precision landing within a preset time in complex space environments.

[0004] According to one aspect of the present invention, a method for tracking and controlling a planetary probe's preset time trajectory under input saturation is provided. The method may include: establishing an initial dynamic model of the planetary probe during its atmospheric entry phase; setting a reference radial distance for the planetary probe; determining the initial altitude tracking compensation error and the first-order altitude tracking compensation error based on the actual radial distance and the reference radial distance in the initial dynamic model; obtaining the second-order altitude tracking compensation error based on the initial dynamic model, the initial altitude tracking compensation error, and the first-order altitude tracking compensation error; setting an initial sliding mode variable and processing it to obtain a first-order sliding mode variable; setting an auxiliary system model when the control input of the planetary probe system is saturated, and obtaining an updated second-order altitude tracking compensation error based on the auxiliary system model; obtaining an updated first-order sliding mode variable based on the updated second-order altitude tracking compensation error and the first-order sliding mode variable; obtaining a first Lyapunov function and a second Lyapunov function; and determining the trajectory tracking convergence of the planetary probe within a target preset time under control input saturation based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error, wherein the target preset time is determined based on a first preset time of the initial sliding mode variable and a second preset time in the auxiliary system model.

[0005] Optionally, determining the initial altitude tracking compensation error of the planetary probe based on the actual radial distance and the reference radial distance in the initial dynamic model includes: determining the difference between the actual radial distance and the reference radial distance in the initial dynamic model as the initial altitude tracking compensation error of the planetary probe.

[0006] Optionally, the process for determining the first-order altitude tracking compensation error is as follows: the first-order altitude tracking compensation error is obtained by differentiating the initial altitude tracking compensation error.

[0007] Optionally, the step of processing the initial sliding mode variable to obtain the first-order sliding mode variable includes: taking the derivative of the initial sliding mode variable to obtain the first-order sliding mode variable.

[0008] Optionally, obtaining the updated second-order altitude tracking compensation error based on the auxiliary system model includes: replacing the control input of the planetary probe system with the auxiliary system model to obtain the updated second-order altitude tracking compensation error.

[0009] Optionally, determining the trajectory tracking convergence of the planetary probe within a predetermined target time under control input saturation based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error includes: determining that the initial sliding mode variable converges to near zero within a first predetermined time based on the updated first-order sliding mode variable and the first Lyapunov function; when the initial sliding mode variable converges to near zero within the first predetermined time, determining that the initial altitude tracking compensation error converges to near zero within a second predetermined time based on the initial sliding mode variable and the second Lyapunov function; when the initial altitude tracking compensation error converges to near zero within the second predetermined time, the trajectory tracking of the planetary probe within the predetermined target time under control input saturation converges.

[0010] The beneficial effects of this invention are:

[0011] This invention proposes a pre-set time trajectory tracking control method for planetary probes under input saturation. First, a dynamic model of the planetary probe's entry phase is established. Based on this, a terminal sliding mode variable is designed. Continuous functions are used in the controller design to eliminate chattering. Furthermore, a pre-set time convergence method is adopted to achieve faster convergence and allow users to customize the convergence time. Finally, an input saturation auxiliary function is used to limit the control input, ensuring the invention's applicability in practice. This invention, combining sliding mode control, input saturation, and the pre-set time convergence method, not only ensures accurate guidance under disturbances but also converges the tracking error to near the origin within a user-preset time, improving the landing accuracy of the planetary probe. Attached Figure Description

[0012] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and, together with their description, serve to explain the invention and do not constitute an undue limitation thereof. In the drawings:

[0013] Figure 1 This is a flowchart of a planetary probe preset time trajectory tracking control method under input saturation according to an embodiment of the present invention;

[0014] Figure 2 This is a schematic diagram illustrating the relationship between a planetary inertial coordinate system, a fixed coordinate system, and a geographic coordinate system according to an embodiment of the present invention.

[0015] Figure 3 This is a schematic diagram of trajectory tracking error and height curve under target preset time control input according to an embodiment of the present invention;

[0016] Figure 4 This is a schematic diagram of the control input curve under the preset target time control input according to an embodiment of the present invention;

[0017] Figure 5 This is a schematic diagram of the convergence curve of the sliding mode variable controlled by the preset target time according to an embodiment of the present invention. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0019] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and to describe a specific order or sequence. It should be understood that such terms can be used interchangeably where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0020] Example 1

[0021] According to an embodiment of the present invention, a method for tracking and controlling a planetary probe's preset time trajectory under input saturation is provided. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system containing at least one set of computer-executable instructions. Furthermore, although a logical order is shown in the flowchart, in some cases, the steps shown or described may be executed in a different order than that shown here.

[0022] Figure 1 This is a flowchart of a planetary probe preset time trajectory tracking control method under input saturation according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method may include the following steps:

[0023] Step S101: Establish the initial dynamic model of the planetary probe during the atmospheric entry phase.

[0024] In the technical solution provided by step S101 of the present invention, the planetary probe operates for a very short time during the atmospheric entry phase, and the accuracy requirements for the gravitational field are not high. Therefore, the simplified gravitational field model is as follows:

[0025] (1)

[0026] Wherein, in equation (1) Planetary gravitational acceleration, The gravitational constant of a planet. Let the distance be the distance from the center of mass of the planetary probe to the center of mass of the planet. A simplified atmospheric density model is as follows:

[0027] (2)

[0028] Among them, in equation (2) This represents the atmospheric density at the location of the probe. This represents the atmospheric density at atmospheric elevation. The radius of the planet. Atmospheric elevation, Figure 2 This is a schematic diagram illustrating the relationship between the planetary inertial coordinate system, the fixed coordinate system, and the geographic coordinate system according to an embodiment of the present invention.

[0029] Assuming the planetary probe is a rigid body, we only consider the motion of its center of mass. Furthermore, throughout the entry process, the planet can be treated as a near-perfect sphere with no rotation, and we assume a uniformly distributed atmosphere. Based on these reasonable assumptions, we establish the initial dynamic model of the planetary probe during the atmospheric entry phase:

[0030] (3)

[0031] (4)

[0032] (5)

[0033] (6)

[0034] (7)

[0035] (8)

[0036] in, Let be the radial distance between the center of mass of the planetary probe and the center of mass of the planet. This represents the longitude of the planetary probe. It is the latitude of the planetary probe. For the flight speed of the planetary probe, The flight path angle, It is the heading angle. The angle of inclination. For lift, As resistance, This is the gravitational acceleration of the planet. The expressions for the mass, lift, and drag of the planetary probe are as follows:

[0037] (9)

[0038] in This is the reference area for the planetary probe. and These are the lift coefficient and drag coefficient, respectively.

[0039] Step S102: Set the reference radial distance of the planetary probe.

[0040] In the technical solution provided by step S102 of the present invention, the definition is... denoted as the second-order differentiable reference radial distance of the planetary probe.

[0041] Step S103: Based on the actual radial distance and reference radial distance in the initial dynamic model, determine the initial altitude tracking compensation error and the first-order altitude tracking compensation error of the planetary probe.

[0042] In the technical solution provided by step S103 of the present invention, Given the actual radial distance, the initial altitude tracking compensation error of the planetary probe can be expressed as: The first-order height tracking compensation error can be expressed as: .

[0043] Step S104: Based on the initial dynamic model, the initial altitude tracking compensation error, and the first-order altitude tracking compensation error, the second-order altitude tracking compensation error is obtained.

[0044] In the technical solution provided in step S104 of the present invention, based on the initial dynamic model (3)-(8) of the planetary probe in the atmospheric entry phase, considering the uncertainties of atmospheric density, drag coefficient, and lift coefficient in the entry phase, the atmospheric density, drag coefficient, and lift coefficient in the above formula can be expressed as follows: , , .in, , and These are the nominal atmospheric density, drag coefficient, and lift coefficient, respectively. , and The uncertainties in atmospheric density, drag coefficient, and lift coefficient are considered. Therefore, the second-order altitude tracking compensation error can be expressed as:

[0045] (10)

[0046] in, This indicates the control input; the remaining parts are as follows:

[0047]

[0048] in, Bounded uncertain disturbance, satisfying F(t) represents the normal state function of the planetary probe system, and H(t) represents the control state gain function of the planetary probe system. This invention will subsequently... F(t), H(t) and Briefly describe the planetary probe system status as follows: , , and .

[0049] Step S105: Set the initial sliding mode variable and process the initial sliding mode variable to obtain the first-order sliding mode variable.

[0050] In the technical solution provided in step S105 of the present invention, the expression for the initial sliding mode variable is defined as follows:

[0051] (11)

[0052] in, It is a parameter related to the scheduled time, satisfying... and It is an even number. It is an odd number. Indicates the gain before sliding mode, This represents the gain behind the sliding mode surface; both are positive constants. For parameters related to a predetermined time on the sliding surface, where These are the parameters before conversion. These are the converted parameters. A positive constant given by the user, representing the time constant of the sliding surface.

[0053] Differentiating the initial sliding mode variables yields the first-order sliding mode variables.

[0054] Step S106: When the control input of the planetary probe system is saturated, set the auxiliary system model and obtain the updated second-order altitude tracking compensation error based on the auxiliary system model.

[0055] In the technical solution provided by step S106 of the present invention, since input saturation exists in practical applications, the control input is nonlinear, and the control input saturation is expressed as follows:

[0056] (12)

[0057] in, This represents the ideal control effect. and These are the upper and lower bounds of the input saturation limit;

[0058] The auxiliary system model is defined as follows:

[0059] (13)

[0060] in, This refers to the status of the auxiliary planetary probe system. To enhance the gain of the planetary probe system, For auxiliary state segment values, It is a bounded control input error. Definition

[0061] (14)

[0062] This represents the preset time correlation quantity of the auxiliary planetary probe system, where This indicates the gain of the auxiliary planetary probe system before the preset time. This indicates the gain of the auxiliary planetary probe system after a preset time. To assist the planetary probe system in presetting time parameters and It is an even number, used as a preset even time parameter for the auxiliary planetary probe system. It is an odd number, which is used to preset odd time parameters for the auxiliary planetary probe system. To assist the planetary probe system in pre-determined total time gain and To assist the planetary probe system in converting parameters before the conversion, To assist the planetary probe system in converting parameters, A positive constant given by the user, representing the time constant of the auxiliary planetary probe system state.

[0063] By replacing the control input in formula (10) with the auxiliary system model, the updated second-order height tracking compensation error is obtained.

[0064] Step S107: Based on the updated second-order height tracking compensation error and the first-order sliding mode variable, the updated first-order sliding mode variable is obtained.

[0065] In the technical solution provided in step S107 of the present invention, the expression for the first-order sliding mode variable is:

[0066] (15)

[0067] Substituting equation (10) into equation (15), that is, based on the updated second-order height tracking compensation error and the first-order sliding mode variable, the expression for the updated first-order sliding mode variable is obtained as follows:

[0068] (16)

[0069] in, This is a new state variable for a planetary probe system model.

[0070] Theorem 1: For a planetary probe with unknown perturbations, in order to achieve accurate trajectory tracking during the entry phase, the following ideal control input is designed:

[0071] (17)

[0072] in, The hyperbolic tangent function is used to cancel out the total uncertainty and A positive integer represents a small range boundary.

[0073] Step S108: Obtain the first Lyapunov function and the second Lyapunov function.

[0074] Step S109: Based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error, determine the trajectory tracking convergence of the planetary probe within the target preset time under control input saturation. The target preset time is determined based on the first preset time of the initial sliding mode variable and the second preset time in the auxiliary system model.

[0075] In the technical solution provided by step S109 of the present invention, based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error, the trajectory tracking convergence of the planetary probe within a preset time under control input saturation is obtained.

[0076] The method described in this embodiment will be further described below.

[0077] As an optional embodiment, step S103, determining the initial altitude tracking compensation error of the planetary probe based on the actual radial distance and the reference radial distance in the initial dynamic model, includes: determining the difference between the actual radial distance and the reference radial distance in the initial dynamic model as the initial altitude tracking compensation error of the planetary probe.

[0078] In this embodiment, the difference between the actual radial distance and the reference radial distance in the initial dynamic model is defined as the expression for the initial altitude tracking compensation error of the planetary probe:

[0079]

[0080] in, This is to compensate for the initial altitude tracking error of the planetary probe.

[0081] As an optional embodiment, step S103, the process of determining the first-order altitude tracking compensation error is as follows: the first-order altitude tracking compensation error is obtained by differentiating the initial altitude tracking compensation error.

[0082] In this embodiment, the expression for the first-order altitude tracking compensation error is obtained by differentiating the initial altitude tracking compensation error:

[0083]

[0084] in, This is for first-order height tracking error compensation.

[0085] As an optional embodiment, step S105, processing the initial sliding mode variable to obtain the first-order sliding mode variable, includes: taking the derivative of the initial sliding mode variable to obtain the first-order sliding mode variable.

[0086] As an optional embodiment, step S106, obtaining the updated second-order altitude tracking compensation error based on the auxiliary system model, includes: replacing the control input of the planetary probe system with the auxiliary system model to obtain the updated second-order altitude tracking compensation error.

[0087] In this embodiment, the control input of the planetary probe system is replaced by an auxiliary system model to obtain an updated second-order altitude tracking compensation error.

[0088] As an optional embodiment, step S109, determining the trajectory tracking convergence of the planetary probe within a predetermined target time under control input saturation based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error, includes: determining that the initial sliding mode variable converges to near zero within a first predetermined time based on the updated first-order sliding mode variable and the first Lyapunov function; when the initial sliding mode variable converges to near zero within the first predetermined time, determining that the initial altitude tracking compensation error converges to near zero within a second predetermined time based on the initial sliding mode variable and the second Lyapunov function; when the initial altitude tracking compensation error converges to near zero within the second predetermined time, the trajectory tracking of the planetary probe within the predetermined target time under control input saturation is considered converged.

[0089] In this embodiment, the Lyapunov stability of the planetary probe system at a predetermined target time is proven below. Before presenting the proof, the following lemma is introduced:

[0090] Lemma 1: If a nonlinear planetary probe system has a Lyapunov function that satisfies:

[0091] (18)

[0092] in, It is a time constant. For preset time parameters, The gain before the function, If ε is the gain of the function and a positive constant representing a small boundary value of the function, then the trajectory of the planetary probe system converges within the actual preset time. Furthermore, the convergence time is... ,in These are the relevant adjustment parameters for the planetary probe system, and the convergence region is expressed as follows:

[0093] (19)

[0094] Specifically, when ε=0, the state of the planetary probe system in time... The interior tends towards 0.

[0095] Lemma 2: For state ,parameter and ,have Established.

[0096] Lemma 3: When the sliding mode variables satisfy Planetary probe system status At the second preset time It converges to 0.

[0097] Lemma 4: For any state Let n be the power parameter and n represent the state order. The following inequalities hold:

[0098]

[0099] Substituting (17) into (16) yields the first derivative of the sliding mode variable:

[0100] (20)

[0101] Among them, the total uncertainty of the planetary probe system is calculated as follows: .

[0102] Choose a suitable first Lyapunov function as follows:

[0103] (twenty one)

[0104] when When the planetary probe system is operational, according to (20) and (13), the derivative of the Lyapunov function is:

[0105] (twenty two)

[0106] Among them, tiny errors Furthermore, Lemmas 2 and 4 are used in the above derivation. Because It is bounded, as can be seen from Lemma 1, the state and At the first preset time ( () converges internally, where It is and The relevant parameters of the planetary probe system are constants. Therefore, the Lyapunov function of the planetary probe system will converge to...

[0107] (twenty three)

[0108] when At that time, the input saturation problem did not occur, that is The same result as equation (22) can be obtained.

[0109] According to Lemma 3, a suitable second Lyapunov function is chosen as follows:

[0110] (twenty four)

[0111] The known sliding mode variables are derived from the above. It will remain constant within a domain, which we will call the region of convergence of the sliding mode variable. Under these conditions, the following equations hold:

[0112] (25)

[0113] After differentiating (24), substituting (25) into it, we get the derivative of the second Lyapunov function as follows:

[0114] (26)

[0115] According to Lemma 1, the state of the planetary probe system... At the second preset time ( The system will converge to near the origin within a certain timeframe. Therefore, the planetary probe system will reach the target location within the preset timeframe. Internal stability.

[0116] Figure 3 This is a schematic diagram of trajectory tracking error and height curve under target preset time control input according to an embodiment of the present invention; by Figure 3 It can be seen that the tracking error of the planetary probe system can be successfully converged within 200 seconds.

[0117] Figure 4 This is a schematic diagram of the control input curve under the preset target time control input according to an embodiment of the present invention; by Figure 4 It can be seen that the control input of the planetary probe system is limited to the upper and lower limits, thus achieving control under input saturation.

[0118] Figure 5 This is a schematic diagram of the convergence curve of the sliding mode variable controlled by the preset target time according to an embodiment of the present invention. Figure 5 It can be seen that the sliding mode variables of the planetary probe system converge within 200s.

[0119] In this embodiment of the invention, an initial dynamic model of the planetary probe during its atmospheric entry phase is established; a reference radial distance of the planetary probe is set; based on the actual radial distance and the reference radial distance in the initial dynamic model, the initial altitude tracking compensation error and the first-order altitude tracking compensation error of the planetary probe are determined; based on the initial dynamic model, the initial altitude tracking compensation error, and the first-order altitude tracking compensation error, the second-order altitude tracking compensation error is obtained; an initial sliding mode variable is set, and the initial sliding mode variable is processed to obtain the first-order sliding mode variable; when the control input of the planetary probe system is saturated, an auxiliary system model is set, and based on the auxiliary system model, the updated second-order altitude tracking compensation error is obtained; based on the updated second-order altitude tracking compensation error and the first-order sliding mode variable, the updated first-order sliding mode variable is obtained. The algorithm obtains the first and second Lyapunov functions. Based on the updated first-order sliding mode variables, the first and second Lyapunov functions, the initial sliding mode variables, and the initial altitude tracking compensation error, it determines the trajectory tracking convergence of the planetary probe within a preset time under control input saturation. The preset time is determined based on the first preset time of the initial sliding mode variables and the second preset time in the auxiliary system model. This solves the technical problem that planetary probes cannot achieve high-precision landing within a preset time in complex space environments. It achieves the technical effect of enabling planetary probes to land with high precision within a preset time in complex space environments by designing a preset time non-singular terminal sliding mode variable, combining it with a continuous function, and introducing an input saturation auxiliary system into the control input.

[0120] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0121] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0122] In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented in other ways. The device embodiments described above are merely illustrative; for example, the division of units can be a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between units or modules may be electrical or other forms.

[0123] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0124] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a first processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0125] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for tracking and controlling a planetary probe's preset time trajectory under input saturation, characterized in that, include: Establish an initial dynamic model of the planetary probe during its atmospheric entry phase; Set the reference radial distance for the planetary probe; Based on the actual radial distance and reference radial distance in the initial dynamic model, the initial altitude tracking compensation error and the first-order altitude tracking compensation error of the planetary probe are determined. Based on the initial dynamics model, initial altitude tracking compensation error, and first-order altitude tracking compensation error, the second-order altitude tracking compensation error is obtained. Set initial sliding mode variables, process them to obtain first-order sliding mode variables; where the initial sliding mode variables are: , To compensate for the first-order height tracking error, To compensate for initial altitude tracking errors, satisfy and It is an even number. It is an odd number. , It is a positive number. For gain in front of sliding mode, It is the gain behind the sliding surface. , , , The first preset time; When the control input of the planetary probe system becomes saturated, an auxiliary system model is set up, and the control input in the second-order altitude tracking compensation error is replaced with the auxiliary system model to obtain the updated second-order altitude tracking compensation error; wherein, the auxiliary system model is: It is the status of the auxiliary system. To enhance the gain of the planetary probe system, For auxiliary state segment values, It is a bounded control input error. Indicates saturation control input. H represents the ideal control action, and H is the control state gain function of the planetary probe system. , This indicates the gain of the auxiliary planetary probe system before the preset time. This indicates the gain of the auxiliary planetary probe system after a preset time. and It is an even number, used as a preset even time parameter for the auxiliary planetary probe system. It is an odd number, which is the preset odd time parameter for the auxiliary planetary probe system. and , , This is the second preset time; Based on the updated second-order height tracking compensation error and the first-order sliding mode variable, the updated first-order sliding mode variable is obtained; Obtain the first and second Lyapunov functions; Based on the updated first-order sliding mode variables, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variables, and the initial altitude tracking compensation error, the trajectory tracking convergence of the planetary probe under control input saturation is determined within a target preset time. The target preset time is determined based on the first preset time of the initial sliding mode variables and the second preset time in the auxiliary system model.

2. The method according to claim 1, characterized in that, The determination of the initial altitude tracking compensation error of the planetary probe based on the actual radial distance and reference radial distance in the initial dynamic model includes: The difference between the actual radial distance and the reference radial distance in the initial dynamic model is determined as the initial altitude tracking compensation error of the planetary probe.

3. The method according to claim 1, characterized in that, The process for determining the first-order altitude tracking compensation error is as follows: the first-order altitude tracking compensation error is obtained by differentiating the initial altitude tracking compensation error.

4. The method according to claim 1, characterized in that, The process of processing the initial sliding mode variables to obtain first-order sliding mode variables includes: Differentiating the initial sliding mode variable yields the first-order sliding mode variable.

5. The method according to claim 1, characterized in that, Based on the auxiliary system model, the updated second-order height tracking compensation error is obtained, including: By replacing the control input of the planetary probe system with an auxiliary system model, the updated second-order altitude tracking compensation error is obtained.

6. The method according to claim 1, characterized in that, The determination of trajectory tracking convergence of the planetary probe within a preset time under control input saturation, based on the updated first-order sliding mode variable, the first Lyapunov function, the second Lyapunov function, the initial sliding mode variable, and the initial altitude tracking compensation error, includes: Based on the updated first-order sliding mode variable and the first Lyapunov function, it is determined that the initial sliding mode variable converges to zero within a first preset time. When the initial sliding mode variable converges to zero within a first preset time, based on the initial sliding mode variable and the second Lyapunov function, it is determined that the initial height tracking compensation error converges to zero within a second preset time. When the initial altitude tracking compensation error converges to near zero within a second preset time, the planetary probe's trajectory tracking converges within the target preset time under control input saturation.

7. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

8. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

9. A computer program product, characterized in that... It includes computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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