Method and apparatus for planning the ascent and rendezvous trajectory of a lunar ascent vehicle

Abstract

This invention relates to a method and apparatus for planning the ascent rendezvous trajectory of a lunar ascender. First, the state of the ascender at the end of the vertical ascent segment is calculated. Then, this state is transformed to a lunar-centric spherical coordinate system to obtain initial trajectory optimization values. Next, an optimized lunar ascent rendezvous trajectory model is obtained based on the ascender's dynamic model in the lunar-centric spherical coordinate system. Subsequently, a direct ascent rendezvous trajectory optimization model and an ascent phasing rendezvous trajectory optimization model are established based on the lunar ascent rendezvous trajectory optimization model. Finally, the trajectory calculated by the ascent rendezvous trajectory optimization model corresponding to the rendezvous mode with the shortest rendezvous time is selected as the target ascent rendezvous trajectory. This method uses the trajectory calculated by the rendezvous trajectory optimization model corresponding to the rendezvous mode with the shortest rendezvous time as the rendezvous estimate. The short rendezvous time and short trajectory calculation time enable real-time online trajectory planning for the spacecraft during actual flight.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, and in particular to a method and apparatus for planning the ascent rendezvous trajectory of a lunar ascender. Background Technology

[0002] The lunar surface environment is harsh, and landers or probes may encounter unforeseen circumstances during sampling or exploration activities, requiring an emergency return. In such cases, the ascender needs to autonomously plan a suitable ascent and rendezvous trajectory. The ascender faces various constraints during its lunar ascent and rendezvous with the orbiter, such as fuel constraints, rendezvous trajectory constraints, and rendezvous time constraints. To meet the requirements of an emergency return, the planned emergency ascent and rendezvous trajectory should minimize the ascent and rendezvous time while satisfying all constraints.

[0003] In traditional autonomous ascent and rendezvous methods, the ascent vehicle first reaches the designated trajectory via the ascent phase, and then reaches the rendezvous trajectory via multiple pulse orbital changes. This method separates the ascent and rendezvous phases, but due to the mutual influence between them, the ascent and rendezvous process is time-consuming, making it unsuitable for emergency return. The emergency ascent and rendezvous method based on sequential quadratic programming is an improvement on the traditional autonomous ascent and rendezvous method. It is a joint trajectory optimization method capable of emergency return, but its computational speed is slow, making online trajectory planning for the ascent vehicle during actual flight impossible. Summary of the Invention

[0004] Therefore, it is necessary to provide a method and apparatus for planning the ascent and rendezvous trajectory of a lunar ascender that is time-efficient and can achieve online trajectory planning in emergency return mode, in order to address the above-mentioned technical problems.

[0005] In a first aspect, the present invention provides a method for planning the ascent rendezvous trajectory of a lunar ascender, comprising:

[0006] Calculate the state of the ascender at the end of the vertical ascent segment;

[0007] Transforming the state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system can yield initial values ​​for trajectory optimization.

[0008] An optimized model of the lunar surface ascent rendezvous trajectory was obtained based on the dynamic model of the ascender in the lunar spherical coordinate system.

[0009] Based on the lunar surface rising rendezvous trajectory optimization model, establish a direct rising rendezvous trajectory optimization model and a rising phase-modulated rendezvous trajectory optimization model;

[0010] Input the initial trajectory optimization values ​​into the direct ascending intersection trajectory optimization model to obtain the direct ascending intersection time and the direct ascending intersection trajectory; input the initial trajectory optimization values ​​into the ascending phase intersection trajectory optimization model to obtain the ascending phase intersection trajectory and the ascending phase intersection time.

[0011] Compare the direct ascent rendezvous time and the ascent phase rendezvous time. If the direct ascent rendezvous time is longer than the ascent phase rendezvous time, then the ascent phase rendezvous is determined to be the target ascent rendezvous mode. If the direct ascent rendezvous time is shorter than the ascent phase rendezvous time, then the direct ascent rendezvous is determined to be the target ascent rendezvous mode.

[0012] Determine if the waiting time for the ascender to leave the lunar surface is less than 20 seconds. If so, the ascending rendezvous trajectory corresponding to the determined target ascender rendezvous mode is the target ascending rendezvous trajectory. Otherwise, after waiting for the ascender to leave the lunar surface to be less than 20 seconds, obtain the initial value for trajectory optimization update, and input the initial value for trajectory optimization update into the rendezvous trajectory optimization model corresponding to the target ascender rendezvous mode to obtain the ascending rendezvous updated trajectory as the target ascending rendezvous trajectory.

[0013] In one embodiment, calculating the state of the ascender at the end of the vertical ascent segment includes:

[0014] Obtain the vertical ascent parameters of the ascender, which include the start time, start position, and start velocity vector of the vertical ascent segment;

[0015] Substitute the vertical ascent parameters of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the state of the ascender at the end of the vertical ascent segment.

[0016] Specifically, the calculation model for the vertical ascent trajectory of the ascender is as follows:

[0017] (1)

[0018] In the formula, Represents a position vector. This represents the velocity vector. The subscript "vaf" indicates the end point of the vertical ascent segment, and the subscript "va0" indicates the start point of the vertical ascent segment. For flight time, and These are the position vectors of the start and end points of the vertical upward segment, respectively. and The velocity vectors at the beginning and end of the vertical ascent segment. and These are the masses of the ascenders at the beginning and end points of the vertical ascent segment, respectively. The magnitude of the main engine thrust. The specific impulse of the ascender's main engine. The gravitational constant of the moon, This is due to Earth's gravitational acceleration.

[0019] In one embodiment, obtaining the initial value for trajectory optimization update includes:

[0020] Obtain the updated parameters for the vertical ascent segment of the ascender;

[0021] Substitute the update parameters of the vertical ascent segment of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the update status of the ascender at the end of the vertical ascent segment.

[0022] Transforming the update state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system yields the initial values ​​for trajectory optimization.

[0023] In one embodiment, obtaining the optimized lunar ascent rendezvous trajectory model based on the ascent dynamics model in the lunar spherical coordinate system includes:

[0024] The dynamic model of the ascender in the lunar spherical coordinate system is transformed into...

[0025] (2)

[0026] In the formula: Radial distance, The phase angle, Polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system; , and These are the components of the ascender thrust direction in the lunar spherical coordinate system. The magnitude of the ascender thrust. For the mass of the riser, This refers to the riser's second consumption.

[0027] Establish initial state constraints for the ascender, rendezvous constraints between the ascender and the orbiter, lunar center distance constraints, and ascender thrust magnitude constraints.

[0028] Specifically, the initial state constraints of the ascender are as follows:

[0029] (3);

[0030] In the formula: The initial radial distance, The initial phase angle, The initial polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system; The initial mass of the ascender, This is the initial time;

[0031] The rendezvous constraint between the ascender and the orbiter is

[0032] (4);

[0033] In the formula: The radius of the long-distance rendezvous track; The initial phase angle of the orbiter, The angular velocity of the orbiter; The speed of the long-distance rendezvous track; The mass of the ascender structure and load; For terminal flight time;

[0034] The lunar distance constraint is

[0035] (5);

[0036] In the formula: The radius is the radius of the moon.

[0037] Ascendant thrust magnitude constraint is

[0038] (6);

[0039] The lunar ascent rendezvous trajectory optimization model is obtained by constraining equation (2) using the initial state constraints of the ascender, the rendezvous constraints between the ascender and the orbiter, the lunar center distance constraints, and the ascender thrust magnitude constraints.

[0040] (7).

[0041] In one embodiment, the direct ascent rendezvous includes two segments: the first segment is the main engine operating segment, and the second segment is the thruster operating segment. The direct ascent rendezvous trajectory optimization model is established based on the lunar surface ascent rendezvous trajectory optimization model, including:

[0042] A direct ascent rendezvous optimization model is established based on the lunar ascent rendezvous trajectory optimization model.

[0043] (8);

[0044] In the formula: and These are the initial values ​​and intersection constraints, respectively. and These are the state and control variables for the first segment. and These are the state and control variables for the second segment; , and These are the initial time, time, and terminal time of the first segment, respectively. , and These are the initial time, time, and terminal time of the second segment, respectively. The right-hand side of the dynamic equation system representing equation (2) The inequality constraints representing equations (5) and (6);

[0045] Discretization and convexification of the direct upward intersection optimization model yields the direct upward intersection trajectory optimization model.

[0046] (9);

[0047] In the formula, Waiting time on the moon The number of discrete points in the first segment. This is the first discrete time step. The number of discrete points in the second segment. This is the second discrete time step. These are the constraint variables for the first segment of virtual control variables. The penalty function coefficients for the first segment of virtual control quantity. These are the constraint variables for the second segment of virtual control variables. The penalty function coefficients for the second segment of virtual control quantity. This represents the slack in the terminal constraint. for The penalty function coefficients, This represents the state variables of the first segment. This represents the right-hand side term of the transformed first section of the dynamic equations. This indicates the inequality constraints in the first paragraph. This represents the state variable of the second segment. This represents the right-hand side term of the transformed second-segment dynamic equation system. Let represent the inequality constraint in the second paragraph. This is to avoid situations where the performance metric reaches its minimum value. In the case of negative infinity, , , and These are the specific impulses of the main engine and the thruster, respectively.

[0048] In one embodiment, the rising phase intersection includes a rising segment and a phase intersection segment, and the rising phase intersection trajectory model includes a rising segment trajectory optimization model and a phase intersection segment trajectory optimization model.

[0049] Specifically, the trajectory optimization model for the ascending segment is as follows:

[0050] (10);

[0051] In the formula: The number of discrete points in the ascending segment. The discrete time step of the rising segment. This represents the state variable during the rising phase. This represents the right-hand side term of the dynamic equations after the transformation of the ascending segment. Indicates the inequality constraints in the ascending segment. To adjust the orbital radius, For phase-adjusting track speed;

[0052] The trajectory optimization model for the phase intersection segment is as follows:

[0053] (11);

[0054] In the formula: , and These represent the number of discrete points in the first, second, and third segments of the phase-intersection segment, respectively. , and To adjust the discrete times of the first, second, and third segments in the phase intersection segment, Waiting time on the moon This refers to the time the ascender travels in the sliding track. This represents the slack in the terminal constraint. for The penalty function coefficients, , and These are the state quantities of the first, second, and third segments in the phase intersection segment, respectively. , and These are the right-hand terms of the transformed dynamic equations for the first, second, and third segments of the phase intersection section, respectively. , and These are the inequality constraints for the first, second, and third segments of the intersection segment, respectively. For terminal inequality constraints, This refers to the mass of the riser after it reaches the phasing track.

[0055] Secondly, the present invention also provides an ascending rendezvous trajectory planning device for a lunar ascender, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements an ascending rendezvous trajectory planning method for the lunar ascender.

[0056] The beneficial effects of this invention are:

[0057] (1) The present invention selects the rendezvous mode corresponding to the shortest time of the direct ascent rendezvous time and the direct ascent rendezvous time, and then uses the direct ascent rendezvous trajectory optimization model and the ascent phase-modulation rendezvous trajectory optimization model corresponding to the rendezvous mode of the time period to calculate the target ascent rendezvous trajectory. Thus, the ascent rendezvous trajectory planning method of the lunar ascent vehicle of the present invention has a short rendezvous time between the ascent vehicle and the orbiter.

[0058] (2) In this invention, when the ascender and the orbiter meet, the ascender only needs to circle the moon once to complete the meeting. Unlike the prior art, which requires multiple pulse orbit changes to reach the meeting orbit, it has the characteristic of short meeting time.

[0059] (3) The present invention can calculate the rendezvous trajectory within 20 seconds and realize online trajectory planning of the ascender in actual flight.

[0060] (4) The present invention has a short rendezvous time and can calculate the real-time rendezvous trajectory, which can realize trajectory planning in emergency return state. Attached Figure Description

[0061] Figure 1 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention;

[0062] Figure 2 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention;

[0063] Figure 3 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention;

[0064] Figure 4 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention;

[0065] Figure 5 This is a schematic diagram of the orbital coordinate system provided in an embodiment of the present invention;

[0066] Figure 6 This is a schematic diagram of the lunar spherical coordinate system provided in an embodiment of the present invention;

[0067] Figure 7 This is a schematic diagram of the thrust direction provided in an embodiment of the present invention;

[0068] Figure 8 This is a schematic diagram of an emergency ascent rendezvous provided in an embodiment of the present invention;

[0069] Figure 9 This is a comparison of simulation results for two schemes, direct rising intersection and rising phase-modulated intersection, provided in this embodiment of the invention. Figure 9(a) is a plan view of the direct ascent rendezvous flight trajectory. Figure 9 (b) is a plan view of the ascending phase intersection flight trajectory. Figure 9 (c) is the direct ascent intersection velocity curve. Figure 9 The middle (d) graph is the velocity curve of the rising phase intersection. Figure 9 (e) is the direct upward thrust curve. Figure 9 The middle (f) is the thrust curve of the rising phase intersection.

[0070] Figure 10 This is a comparison of simulation results between two schemes provided in this embodiment of the invention: direct rising intersection and rising phase-modulated intersection. Figure 10 (a) is a plan view of the direct ascent rendezvous flight trajectory. Figure 10 (b) is a plan view of the ascending phase intersection flight trajectory. Figure 10 (c) is the direct ascent intersection velocity curve. Figure 10 The middle (d) graph is the velocity curve of the rising phase intersection. Figure 10 (e) is the direct upward thrust curve. Figure 10 The middle (f) is the thrust curve of the rising phase intersection. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0072] In one embodiment, such as Figure 1 As shown, Figure 1 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention, including the following steps:

[0073] S101. Calculate the state of the ascender at the end of the vertical ascent segment.

[0074] To eliminate the effects of the takeoff platform tilt, the ascender needs to take off vertically for a period of time before ascending and rendezvous. When the ascender rendezvous with the orbiter, its initial state is the same as the state at the end of the vertical ascent phase.

[0075] S102. Transforming the state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system can obtain the initial value for trajectory optimization.

[0076] S103. Obtain the optimized model of the lunar surface ascent rendezvous trajectory based on the dynamic model of the ascender in the lunar center spherical coordinate system.

[0077] S104. Based on the lunar surface rising rendezvous trajectory optimization model, establish a direct rising rendezvous trajectory optimization model and a rising phase-modulated rendezvous trajectory optimization model.

[0078] S105. Input the initial trajectory optimization value into the direct ascending intersection trajectory optimization model to obtain the direct ascending intersection time and the direct ascending intersection trajectory. Input the initial trajectory optimization value into the ascending phase intersection trajectory optimization model to obtain the ascending phase intersection trajectory and the ascending phase intersection time.

[0079] S106. Compare the direct ascent rendezvous time and the ascent phase rendezvous time. If the direct ascent rendezvous time is greater than the ascent phase rendezvous time, then the ascent phase rendezvous is determined to be the target ascent rendezvous mode. If the direct ascent rendezvous time is less than the ascent phase rendezvous time, then the direct ascent rendezvous is determined to be the target ascent rendezvous mode.

[0080] Specifically, in this embodiment, the ascending rendezvous trajectory optimization model corresponding to the rendezvous mode with the shortest rendezvous time is selected to calculate the rendezvous trajectory between the ascender and the orbiter. The rendezvous time of the corresponding trajectory is short, which is beneficial for emergency return.

[0081] S107. Determine whether the waiting time for the ascender to leave the lunar surface is less than 20 seconds. If so, the ascending rendezvous trajectory corresponding to the determined target ascender rendezvous mode is the target ascending rendezvous trajectory. Otherwise, after waiting for the ascender to leave the lunar surface to be less than 20 seconds, obtain the initial value of trajectory optimization update, and input the initial value of trajectory optimization update into the rendezvous trajectory optimization model corresponding to the target ascender rendezvous mode to obtain the ascending rendezvous updated trajectory as the target ascending rendezvous trajectory.

[0082] Specifically, in this embodiment, it is determined whether the waiting time for the ascender to leave the lunar surface is less than 20 seconds. That is, it can be assumed that the ascender can calculate the shortest trajectory rendezvous scheme for the current state within a 20-second interval, and can leave the lunar surface and achieve emergency return in a short time in case of an emergency.

[0083] In addition, the target ascent and rendezvous trajectory was calculated only 20 seconds before the ascent vehicle left the lunar surface, and the calculated trajectory was less affected by the moon's rotation.

[0084] In one embodiment, such as Figure 2 As shown, Figure 2 This is one of the flowcharts illustrating the ascent and rendezvous trajectory planning method for a lunar ascender provided in this embodiment of the invention. This embodiment relates to how to calculate the state of the ascender at the end of the vertical ascent segment. Based on the above embodiment, step S101 includes:

[0085] S201. Obtain the vertical ascent parameters of the ascender. The vertical ascent parameters of the ascender include the start time, start position and start velocity vector of the vertical ascent segment.

[0086] S202. Substitute the vertical ascent parameters of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the state of the ascender at the end of the vertical ascent segment.

[0087] Specifically, the calculation model for the vertical ascent trajectory of the ascender is as follows:

[0088] (1)

[0089] In the formula, Represents a position vector. This represents the velocity vector. The subscript "vaf" indicates the end point of the vertical ascent segment, and the subscript "va0" indicates the start point of the vertical ascent segment. For flight time, and These are the position vectors of the start and end points of the vertical upward segment, respectively. and The velocity vectors at the beginning and end of the vertical ascent segment. and These are the masses of the ascenders at the beginning and end points of the vertical ascent segment, respectively. The magnitude of the main engine thrust. The specific impulse of the ascender's main engine. The gravitational constant of the moon, This is due to Earth's gravitational acceleration.

[0090] In one embodiment, such as Figure 3 As shown, Figure 3 This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention. This embodiment relates to how to obtain initial values ​​for trajectory optimization and update. Based on the above embodiment, obtaining initial values ​​for trajectory optimization and update includes:

[0091] S301, Obtain the update parameters for the vertical ascent segment of the ascender.

[0092] Specifically, the updated parameters refer to the starting time, starting position, and starting velocity vector of the current vertical ascent segment.

[0093] S302. Substitute the update parameters of the vertical ascent segment of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the update status of the ascender at the end of the vertical ascent segment.

[0094] S303. By converting the update state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system, the initial value for trajectory optimization update can be obtained.

[0095] In an optional embodiment, such as Figure 4 As shown, Figure 4This is one of the flowcharts illustrating the lunar ascent rendezvous trajectory planning method provided in this embodiment of the invention. This embodiment relates to how to obtain an optimized lunar ascent rendezvous trajectory model based on the ascent dynamics model in the lunar spherical coordinate system. Based on the above embodiment, step S103 includes:

[0096] S401. Convert the ascent dynamics model in the lunar spherical coordinate system to...

[0097] (2)

[0098] In the formula: Radial distance, The phase angle, Polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system; , and These are the components of the ascender thrust direction in the lunar spherical coordinate system. The magnitude of the ascender thrust. For the mass of the riser, This represents the riser's second consumption.

[0099] Specifically, the coordinate systems involved in this invention include: lunar-centered inertial coordinate system, orbital coordinate system, and lunar-centered spherical coordinate system. The following is a brief introduction to the relevant coordinate systems.

[0100] (1) Lunar inertial coordinate system

[0101] Origin of the lunar inertial coordinate system At the heart of the moon, Within the lunar equatorial plane, pointing towards the lunar zero longitude line; The axis points in the direction of the moon's rotation; shaft and The planes are perpendicular and form a right-handed coordinate system. The lunar-centered inertial coordinate system remains stationary after the lander lands.

[0102] (2) Orbital coordinate system

[0103] like Figure 5 As shown, Figure 5 This is a schematic diagram of the orbital coordinate system provided in an embodiment of the present invention. The origin of the orbital coordinate system. At the heart of the moon, The axis is within the target orbital plane, pointing towards the projection of the midpoint of the line connecting A and B onto the orbital plane. A and B are the positions of the landing point and the original takeoff point in inertial space, respectively. The axis is perpendicular to the orbital plane. The axis points to the orbiter as it passes through The direction of flight when the axis is aligned; Axis perpendicular to The plane forms a right-handed coordinate system.

[0104] (3) Lunar spherical coordinate system

[0105] like Figure 6 As shown, Figure 6 This is a schematic diagram of the lunar spherical coordinate system provided in an embodiment of the present invention. The origin of the lunar spherical coordinate system is shown. At the heart of the moon, Connecting the lunar center to the spacecraft Length; for The axis rotates counterclockwise to the angle through which the projection of the spacecraft in the orbital plane rotates; for The angle with the orbital plane. Define the direction of the unit vector. as follows: along The direction; In plane Inside, perpendicular to , pointing to The direction of increase; Perpendicular to , pointing to The direction of increase, and with and This forms a rectangular coordinate system.

[0106] In the lunar center inertial coordinate system, the dynamic equations of the ascender are established as shown in equation (12).

[0107] (12)

[0108] In the formula: and These are the position and velocity vectors of the ascender in the lunar inertial frame, respectively. For the thrust of the ascender, , and This represents the component of the ascent thrust direction in the lunar center inertial frame; It is the gravitational constant of the moon; For the mass of the ascender, The specific impulse of the ascender engine. This is due to Earth's gravitational acceleration.

[0109] The dynamic equations of the ascender are obtained by establishing a system of equations (13) in the lunar center spherical coordinate system.

[0110] (13)

[0111] In the formula: , and For the speed of the ascender The following components; , and For the riser thrust in The following components, .

[0112] Then, for the dynamic equations of the ascender, the control variables are transformed as follows:

[0113] (14)

[0114] In the formula: This is the unit vector of thrust in spherical coordinates. Since the magnitude of the thrust is fixed, it is taken as a constant. Therefore, the dynamic equations can be transformed into equation (2).

[0115] This embodiment assumes that the orbiter remains on its parking orbit before the ascent vehicle reaches the rendezvous orbit, and that the parking orbiter's parking orbit is a circular orbit. The dynamic equations of the orbiter are established in the lunar spherical coordinate system. During the ascent and rendezvous phase of the ascent vehicle, only the phase angle of the orbiter changes, i.e.:

[0116] (15)

[0117] In the formula: The phase angle of the orbiter, Let be the angular velocity of the orbiter on its parking track.

[0118] S402. Establish the initial state constraints of the ascender, the rendezvous constraints between the ascender and the orbiter, the lunar center distance constraints, and the ascender thrust magnitude constraints.

[0119] Specifically, the initial state constraints of the ascender are as follows:

[0120] (3);

[0121] In the formula: The initial radial distance, The initial phase angle, The initial polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system; The initial mass of the ascender, This is the initial time;

[0122] The rendezvous constraint between the ascender and the orbiter is

[0123] (4);

[0124] In the formula: The radius of the long-distance rendezvous track; The initial phase angle of the orbiter, The angular velocity of the orbiter; The speed of the long-distance rendezvous track; The mass of the ascender structure and load; For terminal flight time;

[0125] The lunar distance constraint is

[0126] (5);

[0127] In the formula: The radius is the radius of the moon.

[0128] To facilitate solving the trajectory optimization problem, the control constraints of equation (2) are relaxed as follows: the ascender thrust magnitude constraint is...

[0129] (6);

[0130] S403. Using the initial state constraints of the ascender, the rendezvous constraints between the ascender and the orbiter, the lunar center distance constraints, and the ascender thrust magnitude constraints, Equation (2) is constrained to obtain the lunar surface ascending rendezvous trajectory optimization model.

[0131] (7).

[0132] In an optional embodiment, the direct ascent rendezvous includes two segments: the first segment is the main engine operating segment, and the second segment is the thruster operating segment. The direct ascent rendezvous trajectory optimization model, established based on the lunar surface ascent rendezvous trajectory optimization model, includes:

[0133] A direct ascent rendezvous optimization model is established based on the lunar ascent rendezvous trajectory optimization model.

[0134] (8);

[0135] In the formula: and These are the initial values ​​and intersection constraints, respectively. and These are the state and control variables for the first segment. and These are the state and control variables for the second segment; , and These are the initial time, time, and terminal time of the first segment, respectively. , and These are the initial time, time, and terminal time of the second segment, respectively. The right-hand side of the dynamic equation system representing equation (2) The inequality constraints of expressions (5) and (6) are represented.

[0136] It should be noted that the thrust of the ascender remains constant in each flight phase, so the mass is only related to time. In this embodiment, the flight time of each segment is used as the variable, so the mass variable in the state variables can be neglected.

[0137] Discretization and convexification of the direct ascending intersection optimization model yields the direct ascending intersection trajectory optimization model (DAR-ODP).

[0138] (9);

[0139] In the formula, Waiting time on the moon The number of discrete points in the first segment. This is the first discrete time step. The number of discrete points in the second segment. This is the second discrete time step. These are the constraint variables for the first segment of virtual control variables. The penalty function coefficients for the first segment of virtual control quantity. These are the constraint variables for the second segment of virtual control variables. The penalty function coefficients for the second segment of virtual control quantity. This represents the slack in the terminal constraint. for The penalty function coefficients, This represents the state variables of the first segment. This represents the right-hand side term of the transformed first section of the dynamic equations. This indicates the inequality constraints in the first paragraph. This represents the state variable of the second segment. This represents the right-hand side term of the transformed second-segment dynamic equation system. Let represent the inequality constraint in the second paragraph. This is to avoid situations where the performance metric reaches its minimum value. In the case of negative infinity, , , and These are the specific impulses of the main engine and the thruster, respectively.

[0140] Specifically, the Direct Ascending Intersection Optimization (DAR-OCP) model is an infinite-dimensional nonlinear optimization problem. To solve DAR-OCP quickly, it needs to be discretized and made convex. First, DAR-OCP is discretized. To ensure discretization accuracy and the sparsity of the optimization problem, this embodiment uses the trapezoidal discretization method to discretize the dynamic equations of DAR-OCP. The first segment is taken... A discrete point, discrete time step It is expressed as follows:

[0141] (16)

[0142] Therefore, we can conclude that: Then, the dynamic equations of the first segment, after trapezoidal discretization, can be expressed as:

[0143] (17)

[0144] In the formula: , For the sake of brevity, Abbreviated as .

[0145] because Since this is a system of nonlinear equations, it needs to be linearized using a Taylor expansion, i.e.:

[0146] ((18)

[0147] In the formula: Indicates the reference trajectory. Indicates the first The dynamic equations at each reference point are vectors. In solving... right When the partial derivatives are obtained, due to and The changes are relatively small, so we can ignore the differentiation of these two terms and directly use the reference trajectory results for calculation.

[0148] To avoid the pseudo-infeasibility caused by the inaccuracy of the initial conjecture and the linearization process, a virtual control variable is added to equation (18), namely:

[0149] (19)

[0150] Adding virtual control variables Then, a penalty function for this term should be added to the objective function to avoid the influence of the virtual control quantity on the final result, that is:

[0151] (20)

[0152] In the formula, These are constraint variables for virtual control quantities. Let be the penalty function coefficients of the virtual control variable. To avoid the unbounded phenomenon in the optimization problem caused by the addition of the virtual control variable, trust region constraints should be added to the variables related to the performance indicators, i.e.:

[0153] (twenty one)

[0154] In the formula: and These are the upper and lower boundary parameters of the trust region constraint, respectively.

[0155] Regarding the constraint on the rate of change of attitude angle, this embodiment assumes that the thrust direction is along the longitudinal axis of the ascender. Therefore, the constraint on the rate of change of attitude angle can be converted into a constraint on the thrust direction, such as... Figure 7 As shown, Figure 7 middle, This represents the maximum attitude change angle within the discrete time step. Figure 7 From the geometric relationship, we can know that:

[0156] (twenty two)

[0157] In the formula: Let be the maximum rate of change of the ascender's attitude angle. The rate of change of attitude angle can then be expressed as follows:

[0158] (twenty three)

[0159] Since the optimization model in this embodiment is established in a spherical coordinate system, which changes with the position of the ascender, the attitude angle constrained by equation (23) will have a deviation due to the change in the coordinate system. However, since the time between the two discrete points is very short, that is, the coordinate system deviation between the two discrete points is very small, the attitude angle constraint deviation caused by the change in the coordinate system can be ignored.

[0160] For the sake of brevity in the following expression, take This represents an inequality constraint, namely:

[0161] (twenty four)

[0162] In the formula: This is the maximum attitude angle change rate of the main engine operating section.

[0163] This completes the transformation of the trajectory optimization problem for the main engine operating section. The transformation of the trajectory optimization problem for the thruster operating section follows the same method, taking the number of discrete points in the second section as... Discrete time step The formula is as follows:

[0164] (25)

[0165] Right-hand side of the dynamic equations The formula is as follows:

[0166] (26)

[0167] Inequality constraints The formula is as follows:

[0168] (27)

[0169] In the formula: This represents the maximum rate of change of attitude angle during the thruster's operating phase.

[0170] Since the direct ascent rendezvous scheme does not involve immediate takeoff, this embodiment incorporates the ascent vehicle's waiting time on the lunar surface into the terminal phase angle constraint. and relaxation terms ,Right now:

[0171] (28)

[0172] The initial phase angle minus This is because when using the direct ascent rendezvous scheme, the final phase angle deviation between the orbiter and the ascender should be... .

[0173] Therefore, a direct ascending intersection trajectory optimization model can be obtained.

[0174] In this embodiment, the stopping condition for solving the DAR-ODP model using the sequential second-order cone programming method is:

[0175] (29)

[0176] In the formula: and For the set value, Let be the discrete time step of the main engine working segment obtained by the j-th sequence optimization, and so on.

[0177] In one embodiment, the rising phase intersection includes a rising segment and a phase intersection segment, and the rising phase intersection trajectory model includes a rising segment trajectory optimization model and an intersection segment trajectory optimization model.

[0178] During the ascent phase, the main engine of the ascender operates. The number of discrete points in the ascent phase is taken as... Then the discrete time can be expressed as follows:

[0179] ((30)

[0180] In the formula: This represents the total flight time during the ascent phase. (Take...) Represents state variables. This represents the control quantity; similar to equations (18) and (19), This represents the right-hand side of the ascending segment dynamic equations after discretization, convexification, and the addition of virtual control variables, i.e.:

[0181] ((31)

[0182] This represents an inequality constraint, namely:

[0183] ((32)

[0184] To increase the phase adjustment range, the riser should reach the phase adjustment track as soon as possible, thus obtaining the trajectory optimization model (A-DOP) for the rising segment.

[0185] After reaching the phasing track, the ascender adjusts the phase angle difference with the orbiter on the phasing track, and then the ascender completes the rendezvous with the orbiter by starting the thruster twice.

[0186] After gliding to the predetermined position, the trajectory optimization problem of the ascender is a three-stage optimization problem with variable terminal times in the "push-glide-push" sequence. Let the number of discrete points in the three stages be... , and The corresponding state variables are respectively , and The control quantity is and There is no control during the gliding phase; similar to equations (18) and (19), the right-hand side terms of the three-stage dynamic equations are respectively , and The coasting segment has no control quantity, that is:

[0187] ((33)

[0188] ((34)

[0189] ((35)

[0190] Similar to equation (23), the three-stage inequality constraints are as follows: , and ,Right now:

[0191] ((36)

[0192] (36)

[0193] ((37)

[0194] After the ascender reaches the phasing trajectory, in order to correct the deviation of the taxiing trajectory and make attitude adjustments for subsequent flight, the minimum taxiing time is set in this embodiment as follows: The intersection constraints are as follows:

[0195] (38)

[0196] In the formula: This refers to the coasting time of the ascender on the phasing track. The time the ascender waits on the lunar surface. Let be the angular velocity of the ascender as it slides on the phasing track. This is the slack term of the equality constraint.

[0197] Therefore, the PR-ODP (Plan-Optimized Trajectory Model for Intersection Segments) can be obtained.

[0198] Specifically, the trajectory optimization model for the ascending segment is as follows:

[0199] (10);

[0200] In the formula: The number of discrete points in the ascending segment. The discrete time step of the rising segment. This represents the state variable during the rising phase. This represents the right-hand side term of the dynamic equations after the transformation of the ascending segment. Indicates the inequality constraints in the ascending segment. To adjust the orbital radius, This is for adjusting the track speed.

[0201] In this embodiment, the stopping condition for solving the A-ODP model using the sequential second-order cone programming method is:

[0202] (39)

[0203] In the formula: is a set value, representing the discrete time step of the rising segment obtained by the j-th sequence optimization.

[0204] The trajectory optimization model for the phase intersection segment is as follows:

[0205] (11);

[0206] In the formula: , and These represent the number of discrete points in the first, second, and third segments of the phase-intersection segment, respectively. , and To adjust the discrete times of the first, second, and third segments in the phase intersection segment, Waiting time on the moon This refers to the time the ascender travels in the sliding track. This represents the slack in the terminal constraint. for The penalty function coefficients, , and These are the state quantities of the first, second, and third segments in the phase intersection segment, respectively. , and These are the right-hand terms of the transformed dynamic equations for the first, second, and third segments of the phase intersection section, respectively. , and These are the inequality constraints for the first, second, and third segments of the intersection segment, respectively. For terminal inequality constraints, This refers to the mass of the riser after it reaches the phasing track.

[0207] In this embodiment, the stopping condition for solving the PR-ODP model using the sequential second-order cone programming method is:

[0208] ((40)

[0209] In the formula: , and The set value; Let be the first discrete time step obtained from the j-th sequence optimization, and so on for the others.

[0210] like Figure 10 As shown, Figure 10 This is a schematic diagram of an emergency lunar rendezvous and ascent of the ascender provided in an embodiment of the present invention. The lunar rendezvous and ascent trajectory of this embodiment only requires one orbit around the moon to complete the rendezvous, unlike the prior art which requires multiple pulse orbit changes to reach the rendezvous trajectory and thus requires multiple orbits around the moon, thus featuring a shorter rendezvous time.

[0211] In a specific implementation, this embodiment implements a method for planning the ascent and rendezvous trajectory of a lunar ascender in a simulation environment. The simulation environment is Visual Studio 2019, and the computer's CPU is an Intel Core i3 10100F (base frequency 3.6GHz, maximum frequency 4.3GHz), with 8GB of memory. Specifically, the ascender parameters and orbital parameters in this embodiment are shown in Table 1 and Table 2, respectively.

[0212] Table 1 Ascender Parameters

[0213]

[0214] Table 2 Track Parameters

[0215]

[0216] Assuming an emergency return is required 6.4 hours after the lander touches down, what is the initial phase angle of the ascent vehicle at this time? The initial phase angle of the orbiter The simulation results of direct ascending intersection and ascending phase intersection are, for example, Figure 9 As shown, Figure 9 This is a comparison of simulation results for two schemes: direct ascending intersection and ascending phase-modulated intersection.

[0217] exist Figure 9 In the direct ascent rendezvous scenario, the ascender waits for the orbiter to reach the appropriate position before taking off. This scenario takes 7847.07 seconds, and the ascender's final mass is 370 kg. In the ascent phasing rendezvous scenario, the ascender takes off immediately and rendezvous with the orbiter after completing phasing. This scenario takes 2630.06 seconds, and the ascender's final mass is also 370 kg. Simulation results show that both flight scenarios will exhaust fuel to achieve the fastest possible rendezvous between the ascender and orbiter. Based on the principle of shortest rendezvous time, the ascent phasing rendezvous scenario should be selected.

[0218] The solution time for different optimization problems is shown in Table 3.

[0219]

[0220] Table 3. Statistics on solution time for different optimization problems

[0221] As shown in Table 3, the present invention has a short computation time and can realize online trajectory planning for lunar ascent vehicles.

[0222] Assuming an emergency return is required 6.61 hours after the lander touches down, what is the initial phase angle of the ascent vehicle at this time? The initial phase angle of the orbiter The simulation results of direct ascending intersection and ascending phase intersection are, for example, Figure 10 As shown, Figure 10 This is a comparison of simulation results between two schemes in this embodiment: direct rising intersection and rising phase-modulated intersection.

[0223] exist Figure 10 In the direct ascent rendezvous scheme, the ascender waits for the orbiter to reach the appropriate position before taking off. This scheme takes a total of 7092.87 seconds, and the ascender's final mass is 370 kg. Figure 6 In the ascending-phase rendezvous scheme, the ascender takes off immediately. However, due to the large initial phase difference between the ascender and the orbiter, the ascender needs to glide on the phasing track for a considerable time. The total time for this scheme is 7272.97 s, and the final mass of the ascender is 370 kg. Based on the principle of shortest time rendezvous, the direct ascending rendezvous scheme should be selected in this case. The solution time for different optimization problems is shown in Table 4.

[0224] Table 4. Statistics on solution time for different optimization problems

[0225]

[0226] As shown in Table 4, the present invention has a short computation time and can realize online trajectory planning for lunar ascent vehicles.

[0227] Based on the same inventive concept, embodiments of the present invention also provide an ascending rendezvous trajectory planning device for lunar ascenders to implement the above-described method for planning the ascending rendezvous trajectory of a lunar ascender. The solution provided by this device is similar to the solution described in the above-described method. Therefore, the specific limitations of one or more embodiments of the ascending rendezvous trajectory planning device for lunar ascenders provided below can be found in the limitations of the ascending rendezvous trajectory planning method for lunar ascenders described above, and will not be repeated here.

[0228] In one embodiment, the ascending rendezvous trajectory planning device for the lunar ascender includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the ascending rendezvous trajectory planning method for the lunar ascender.

[0229] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for planning the ascent rendezvous trajectory of a lunar ascender, characterized in that, include: Calculate the state of the ascender at the end of the vertical ascent segment; Transforming the state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system can yield initial values ​​for trajectory optimization. An optimized model of the lunar surface ascent rendezvous trajectory was obtained based on the dynamic model of the ascender in the lunar spherical coordinate system. Based on the lunar surface rising rendezvous trajectory optimization model, establish a direct rising rendezvous trajectory optimization model and a rising phase-modulated rendezvous trajectory optimization model; The initial trajectory optimization value is input into the direct ascending intersection trajectory optimization model to obtain the direct ascending intersection time and the direct ascending intersection trajectory. The initial trajectory optimization value is input into the ascending phase intersection trajectory optimization model to obtain the ascending phase intersection trajectory and the ascending phase intersection time. Comparing the direct ascent rendezvous time and the ascent phase rendezvous time, if the direct ascent rendezvous time is greater than the ascent phase rendezvous time, then the ascent phase rendezvous is determined to be the target ascent rendezvous mode; if the direct ascent rendezvous time is less than the ascent phase rendezvous time, then the direct ascent rendezvous is determined to be the target ascent rendezvous mode. Determine if the waiting time for the ascender to leave the lunar surface is less than 20 seconds. If so, the ascending rendezvous trajectory corresponding to the determined target ascender rendezvous mode is the target ascending rendezvous trajectory. Otherwise, after waiting for the ascender to leave the lunar surface to be less than 20 seconds, obtain the initial value for trajectory optimization update, and input the initial value for trajectory optimization update into the direct ascending rendezvous trajectory optimization model or the ascending phase-modulated rendezvous trajectory optimization model corresponding to the target ascender rendezvous mode to obtain the ascending rendezvous updated trajectory as the target ascending rendezvous trajectory.

2. The method for planning the ascent and rendezvous trajectory of a lunar ascender according to claim 1, characterized in that, The calculation of the ascender's state at the end of the vertical ascent segment includes: Obtain the vertical ascent parameters of the ascender, which include the start time, start position, and start velocity vector of the vertical ascent segment; Substitute the vertical ascent parameters of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the state of the ascender at the end of the vertical ascent segment. Specifically, the calculation model for the vertical ascent trajectory of the ascender is as follows: 　　　(1) In the formula, Represents a position vector. This represents the velocity vector. The subscript "vaf" indicates the end point of the vertical ascent segment, and the subscript "va0" indicates the start point of the vertical ascent segment. For flight time, and These are the position vectors of the start and end points of the vertical upward segment, respectively. and The velocity vectors at the beginning and end of the vertical ascent segment. and These are the masses of the ascenders at the beginning and end points of the vertical ascent segment, respectively. The magnitude of the main engine thrust. The specific impulse of the ascender's main engine. The gravitational constant of the moon, This is due to Earth's gravitational acceleration.

3. The method for planning the ascent and rendezvous trajectory of a lunar ascender according to claim 2, characterized in that, The optimized model for the lunar ascent rendezvous trajectory, obtained based on the ascent dynamics model in the lunar spherical coordinate system, includes: The dynamic model of the ascender in the lunar spherical coordinate system is transformed into... 　　　(2) In the formula: Radial distance, The phase angle, Polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system. , and These are the components of the ascender thrust direction in the lunar spherical coordinate system. The magnitude of the ascender thrust. For the mass of the riser, This refers to the riser's second consumption. Establish initial state constraints for the ascender, rendezvous constraints between the ascender and the orbiter, lunar center distance constraints, and ascender thrust magnitude constraints. Specifically, the initial state constraints of the ascender are as follows: （3）； In the formula: The initial radial distance, The initial phase angle, The initial polar angle; , and These are the components of the ascent velocity in the lunar spherical coordinate system. The initial mass of the ascender, This is the initial time; The rendezvous constraint between the ascender and the orbiter is （4）； In the formula: The radius of the long-distance rendezvous track; The initial phase angle of the orbiter, The angular velocity of the orbiter; The speed of the long-distance rendezvous track; The mass of the ascender structure and load; For terminal flight time; The lunar distance constraint is （5）； In the formula: The radius of the moon; Ascendant thrust magnitude constraint is （6）； The lunar ascent rendezvous trajectory optimization model is obtained by constraining equation (2) using the initial state constraints of the ascender, the rendezvous constraints between the ascender and the orbiter, the lunar center distance constraints, and the ascender thrust magnitude constraints. （7）。 4. The method for planning the ascent and rendezvous trajectory of a lunar ascender according to claim 3, characterized in that, The direct ascent rendezvous consists of two phases: the first phase is the main engine operating phase, and the second phase is the thruster operating phase. The establishment of the direct ascent rendezvous trajectory optimization model based on the lunar surface ascent rendezvous trajectory optimization model includes: A direct ascent rendezvous optimization model is established based on the lunar ascent rendezvous trajectory optimization model. (8)； In the formula: and These are the initial state and the intersection constraint, respectively. and These are the state and control variables for the first segment. and These are the state and control variables for the second segment; , and These are the initial time, time, and terminal time of the first segment, respectively. , and These are the initial time, time, and terminal time of the second segment, respectively. The right-hand side of the dynamic equation system representing equation (2) The inequality constraints representing equations (5) and (6); Discretization and convexification of the direct upward intersection optimization model yields the direct upward intersection trajectory optimization model. （9）； In the formula, Waiting time on the moon The number of discrete points in the first segment. This is the first discrete time step. The number of discrete points in the second segment. This is the second discrete time step. These are the constraint variables for the first segment of virtual control variables. The penalty function coefficients for the first segment of virtual control quantity. These are the constraint variables for the second segment of virtual control variables. The penalty function coefficients for the second segment of virtual control quantity. This represents the slack in the terminal constraint. for The penalty function coefficients, This represents the state variables of the first segment. This represents the right-hand side term of the transformed first section of the dynamic equations. This indicates the inequality constraints in the first paragraph. This represents the state variable of the second segment. This represents the right-hand side term of the transformed second-segment dynamic equation system. Let represent the inequality constraint in the second paragraph. This is to avoid situations where the performance metric reaches its minimum value. In the case of negative infinity, , , and These are the specific impulses of the main engine and the thruster, respectively.

5. The method for planning the ascent and rendezvous trajectory of a lunar ascender according to claim 4, characterized in that, The rising phase intersection includes a rising segment and a phase intersection segment, and the rising phase intersection trajectory optimization model includes a rising segment trajectory optimization model and a phase intersection segment trajectory optimization model. Specifically, the trajectory optimization model for the ascending segment is as follows: （10）； In the formula: The number of discrete points in the ascending segment. The discrete time step of the rising segment. This represents the state variable during the rising phase. This represents the right-hand side term of the dynamic equations after the transformation of the ascending segment. Indicates the inequality constraints in the ascending segment. To adjust the orbital radius, For phase-adjusting track speed; The phase-shifting intersection segment trajectory optimization model is as follows: （11）； In the formula: , and These represent the number of discrete points in the first, second, and third segments of the phase-intersection segment, respectively. , and To adjust the discrete times of the first, second, and third segments in the phase intersection segment, Waiting time on the moon This refers to the time the ascender travels in the sliding track. This represents the slack in the terminal constraint. for The penalty function coefficients, , and These are the state quantities for the first, second, and third segments of the phase intersection segment, respectively. , and These are the right-hand terms of the transformed dynamic equations for the first, second, and third segments of the phase intersection section, respectively. , and These are the inequality constraints for the first, second, and third segments of the intersection segment, respectively. For terminal inequality constraints, This refers to the mass of the riser after it reaches the phasing track.

6. The method for planning the ascent and rendezvous trajectory of a lunar ascender according to claim 5, characterized in that, Obtaining initial values ​​for trajectory optimization and updates includes: Obtain the updated parameters for the vertical ascent segment of the ascender; Substitute the update parameters of the vertical ascent segment of the ascender into the trajectory calculation model of the vertical ascent segment of the ascender to obtain the update status of the ascender at the end of the vertical ascent segment. Transforming the update state of the ascender at the end of the vertical ascent segment to the lunar spherical coordinate system yields the initial values ​​for trajectory optimization.

7. A device for planning the ascent and rendezvous trajectory of a lunar ascent vehicle, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor; characterized in that: When the processor executes a computer program, it implements the method for planning the ascent rendezvous trajectory of the lunar ascender as described in any one of claims 1-6.

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