CN117902068A - Planetary landing guidance method for optimal control and quick search - Google Patents

Abstract

The invention discloses an optimal control rapid search planetary landing guidance method, and belongs to the technical field of spacecraft guidance and control. The implementation method of the invention comprises the following steps: decoupling the lander dynamics model into a controlled dynamics model and an uncontrolled dynamics model; constructing an optimization model of the reachable region by taking the thrust amplitude constraint and the thrust direction constraint as constraint conditions, and solving a controllable movement reachable region in a prediction time domain; constructing a burnup optimization model by taking different positions in an reachable region as virtual endpoints, obtaining burnup optimal control of landers reaching the designated virtual endpoint positions through offline optimization, storing the optimal control as an optimal control database, and storing the corresponding virtual endpoint states as an endpoint state database; and superposing the uncontrolled motion and the end point state database in the landing process to obtain a state prediction space of the lander, searching the state of the optimal terminal to obtain a corresponding optimal control instruction in the optimal control database, and realizing planetary landing guidance according to the optimal control instruction.

Description

Planetary landing guidance method for optimal control and quick search

Technical Field

The invention relates to a spacecraft guidance method, in particular to a planet landing guidance method for optimal control and rapid search, and belongs to the technical field of spacecraft guidance and control.

Background

Planetary detection is an important means for realizing the extraterrestrial survival of human cognition universe law. The accurate landing technology of the planet surface is a key technology of planet detection activity and is also a precondition for carrying out tasks such as in-situ detection, sampling and returning of the surface of an extraterrestrial celestial body. The power down leg is a critical stage of the landing of the planetary surface, and relates to whether the lander can safely and accurately reach the desired landing site. The trajectory of the power down leg needs to meet a variety of constraints, including position and velocity constraints at the landing site, as well as thrust magnitude and direction constraints during landing. In addition, the limited burnup and satellite-borne computing resources of the lander bring practical engineering constraints to the design of the planetary landing guidance method. Therefore, in order to achieve accurate landing of the planetary surface, it is necessary to develop a landing guidance method that can satisfy multiple constraints.

The existing related researches are designed aiming at a planet landing guidance method, and the method mainly comprises a tracking guidance method based on a nominal track and an explicit guidance method without the nominal track. The tracking guidance method based on the nominal track can process various constraints, but the track is generally designed in advance, so that the method has poor adaptability to the initial deviation of the task; explicit guidance methods without nominal trajectories have better adaptability to initial condition deviations, but are difficult to handle complex constraints effectively. The model predictive control combines the characteristics of the two, and has the capability of coping with initial condition deviation and complex constraint processing. The basic idea is to solve the optimal control problem in the limited time domain by online scrolling. Because of the need of solving the complex optimization problem on line, the model predictive control cannot ensure that the real-time requirement of landing guidance can be met. Therefore, facing the requirements of safe and accurate landing guidance of the planetary surface, the conventional planetary landing guidance method needs to be improved, and a planetary landing guidance method capable of processing complex constraints and having higher real-time performance is developed.

Disclosure of Invention

Aiming at the contradiction between complex constraint processing and real-time demand satisfaction in a planetary power descent phase, the main purpose of the invention is to provide a planetary landing guidance method for quickly searching optimal control starting from the demand of meeting the accurate landing and the fuel consumption reduction of a lander, the lander dynamics model is decoupled into a controlled dynamics model and a non-controlled dynamics model, a reachable area of controlled movement in a prediction time domain is solved, the fuel consumption optimal control of the lander reaching different positions in the reachable area is obtained offline, and the optimal control and the lander end state are respectively stored as an optimal control database and an end state database. And superposing the uncontrolled motion and the end point state database in the landing process to obtain a state prediction space of the lander, searching the state of the optimal terminal to obtain a corresponding optimal control instruction in the optimal control database, and realizing planetary landing guidance according to the optimal control instruction.

The aim of the invention is achieved by the following technical scheme.

The invention discloses an optimal control quick search planetary landing guidance method, which comprises the following steps:

Step one, establishing a dynamic model of the lander under a solid coordinate system of a planetary landing site, and decoupling the dynamic model of the lander into a controlled dynamic model and an uncontrolled dynamic model, wherein the controlled dynamic model corresponds to the movement of the lander when only being pushed, and the uncontrolled dynamic model corresponds to the movement of the lander when only being pulled.

The specific implementation method of the first step is as follows:

Defining a landing site fixed coordinate system O-XYZ: with the landing site as the origin O of the coordinate system, the OX axis points to the local east, the OY axis points to the local north, and the OZ axis points to the local zenith.

Neglecting the effects of planetary rotation and aerodynamic force, taking the planetary gravitational acceleration as a constant, and establishing a lander dynamics model under a landing site fixed coordinate system:

Wherein r and v respectively represent a position vector and a speed vector of the lander under a landing site fixed coordinate system, a represents a thrust acceleration vector of the lander, T represents a thrust vector of the lander, m represents a mass of the lander, g represents a gravitational acceleration vector of a planet surface, I _sp represents a specific impulse of an engine of the lander, and g ₀ represents a numerical value of gravitational acceleration of the earth sea level.

According to the motion independence principle, the motion of the lander can be regarded as the synthesis of two partial motions driven by thrust and gravity respectively, and the two partial motions are independently carried out and are not interfered with each other. The position and velocity equations in equation (1) are integrated to obtain:

Where t represents the motion time, and r ₀ and v ₀ represent the position vector and the velocity vector, respectively, at the initial time.

Decoupling the kinetic equation into a controlled kinetic model and an uncontrolled kinetic model by analyzing the position and velocity equation as shown in formula (2), as shown in formula (3) and formula (4), respectively:

In the controlled dynamics model, the initial position and the initial speed of the lander are 0 and only receive the thrust action; in the uncontrolled kinetic model, the initial position and speed of the lander are r ₀ and v ₀ respectively, and are only affected by gravity.

Setting a prediction time domain, constructing an optimization model of the reachable region by taking the thrust amplitude constraint and the thrust direction constraint as constraint conditions according to the controllable dynamic model in the first step, and solving a controllable movement reachable region in the prediction time domain according to the optimization model; and constructing a fuel consumption optimization model by taking different positions in the reachable region as virtual endpoints, taking fuel consumption as an optimization target and taking thrust amplitude constraint and thrust direction constraint as constraint conditions, obtaining fuel consumption optimal control of the lander reaching a designated virtual endpoint position according to offline optimization of the fuel consumption optimization model, storing the optimal control as an optimal control database, and storing a corresponding virtual endpoint state as an endpoint state database.

The specific implementation method of the second step is as follows:

The control constraints to which the lander is subjected include thrust magnitude constraints and thrust direction constraints, as shown in equation (5):

Where T _min and T _max represent the minimum and maximum values of the thrust amplitude, respectively, n _z represents a unit vector in the positive direction of the Z axis, and θ _max represents the maximum value of the engine swing angle, which is defined as the maximum angle between the thrust vector and the positive direction of the Z axis.

The prediction time domain is set to t _N. And solving the controllable movement reachable area in the prediction time domain offline. Considering the rotational symmetry of the thrust force about the Z axis, the two-dimensional reachable area of the lander in the first quadrant of XOZ can be solved first, and then the two-dimensional reachable area can be obtained by rotating around the Z axis for one circle. According to the controllable dynamics model in the first step, constructing an optimization model of the two-dimensional reachable region by taking thrust amplitude constraint and thrust direction constraint as constraint conditions, wherein the optimization model is shown in a formula (6):

wherein, all vectors are two-dimensional vectors, X _i and Z _i respectively represent X-axis and Z-axis coordinates which can be reached by the lander, different Z _i are selected, the furthest X-axis position X _i which can be reached by the lander at the moment is obtained through optimization, the envelope formed by the coordinates (X _i,z_i) is a two-dimensional reachable area, and the three-dimensional reachable area can be obtained through rotation around the Z axis.

Selecting different positions r _i as virtual endpoints in the reachable region, taking optimal burnup as an optimization target, taking thrust amplitude constraint and thrust direction constraint as constraint conditions as shown in a formula (5), establishing an optimization model as shown in a formula (7), and obtaining optimal burnup control of the lander reaching a specified virtual endpoint position according to offline optimization of the optimization model as shown in the formula (7).

Where m ₀ represents the mass of the lander at the initial time.

All virtual end positions r _i, v _i when the lander reaches r _i, and burnup Δm of the lander are stored as an end state database, the corresponding optimal control acceleration a _i is stored as an optimal control database, and for convenience of storage, the optimal control acceleration a _i is scattered into an optimal control acceleration sequence a _i,j to be stored, wherein j=1, 2, … and t _N/t_g,t_g represent guidance periods, and t _N is an integer multiple of t _g.

Step three, calculating the state of the lander after undergoing a prediction time domain uncontrolled motion according to an uncontrolled dynamics model in the landing process, and superposing the uncontrolled motion end state and the end state database obtained in the step two to generate a state prediction space of the lander in a prediction time domain; eliminating state points which violate control constraint due to quality change in a state prediction space; the lander mass in a prediction time domain is approximately equivalent to a constant, a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass, and burnup is corrected according to the burnup correction factor alpha; and traversing and searching an optimal state in the state prediction space to obtain a corresponding optimal control instruction in an optimal control database, and realizing planetary landing guidance according to the optimal control instruction.

The specific implementation method of the third step is as follows:

At the time t of the landing process, calculating the state of the lander after undergoing a predicted time domain uncontrolled motion according to an uncontrolled dynamics model, as shown in formula (8):

Where r _u、v_u and m _u represent the position vector, velocity vector and mass, respectively, of the lander after a predicted time-domain uncontrolled motion.

Superposing the final state of uncontrolled motion and the final state of controlled motion in the final state database to generate a state prediction space X _N of the lander at the moment t in a prediction time domain, wherein the state prediction space X _N is shown as a formula (9):

X_N＝{(r_N,v_N,m_N)|r_N＝r_u+r_i,v_N＝v_u+v_i,m_N＝m_u-Δm_i,i＝1,2,...,n} (9)

Where r _N、v_N and m _N represent the position vector, velocity vector and mass of the lander after passing a prediction horizon, respectively, and n represents the number of controlled end-of-motion states in the end-point state database.

Considering that the initial mass of the lander in the formula (7) is m ₀, and the variable in the optimal control database is the acceleration a, when the mass of the lander at the moment t is reduced to m (t), the optimal control acceleration a _e which partially meets the lower limit constraint of the thrust amplitude in the optimal control database does not meet the constraint condition at this time, namely:

For a _e, the corresponding state point X _e in the lander state prediction space X _N is removed, so as to ensure that the optimal control meets the thrust constraint, and the state prediction space X is shown in the formula (11):

X＝X_N-X_e (11)

During landing, the rate of change of the lander mass is proportional to the thrust amplitude, which is proportional to the lander mass. The change in lander mass also affects the value of burnup in the state prediction space X. The lander mass in a prediction time domain is approximately equivalent to a constant, and a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass as shown in a formula (12):

At time t of the landing process, selecting performance indexes as shown in formulas (13) - (15):

Where λ <0 represents the burnup weight coefficient, k represents the speed weight coefficient, r _x、r_y and r _z represent the current time lander triaxial position, v _x、v_y and v _z represent the current time lander triaxial speed, t _go represents the lander residual flight time, and d >0 is a constant that prevents Q from singular occurrence.

According to the performance indexes shown in formulas (13) to (15), the optimal state X ^* is searched in the lander state prediction space X in a traversing way, and the lander is driven to move towards the target point by taking the first item a _i,1 of the optimal control sequence a _i,j corresponding to the optimal state X ^* in the optimal control database as the actual optimal control.

And executing the terminal state prediction and the optimal control search once in each guidance period, and performing planetary landing guidance according to the optimal control instruction obtained by the search until the lander reaches a target landing site.

The beneficial effects are that:

1. Aiming at the problems that the planet landing has various constraints such as thrust amplitude constraint, direction constraint and the like, the planet landing guidance method for the optimal control quick search disclosed by the invention calculates an reachable area of the lander offline, solves the burnup optimal control meeting the thrust constraint in the reachable area range, stores the burnup optimal control in an optimal control database, searches the optimal control online, and ensures that the control quantity obtained by searching meets constraint conditions. In the landing process, the optimal control search range is dynamically adjusted according to the quality change of the lander, the burnup data is corrected, and the planetary landing guidance is further ensured not to violate the control constraint condition. According to the guidance method, the optimal control meeting the constraint conditions is solved offline, and the data is corrected online, so that the control constraint of the lander can be guaranteed to be met.

2. Aiming at engineering reality constraint conditions such as limited calculation and storage capacity of a planetary lander computer, the optimal control quick search planetary landing guidance method disclosed by the invention decouples a dynamics model of the lander into a controlled dynamics model and an uncontrolled dynamics model, only stores data related to controlled movement in a terminal state database, and reduces the data storage capacity of the spaceborne computer and the calculation amount of online search; and (3) taking different positions in the reachable region as virtual endpoints, taking burnup as an optimization target, taking thrust amplitude constraint and thrust direction constraint as constraint conditions, constructing a burnup optimal control optimization model, and solving the optimization problem offline according to the burnup optimization model, wherein only two databases are required to be called and optimal control is searched in the landing process, the optimization problem is not required to be solved online, and the workload of the spaceborne computer is reduced. The guidance method has the advantages of small calculated amount and high searching speed, and can meet the calculation performance constraint of the spaceborne computer.

3. According to the planetary landing guidance method for the optimal control quick search, disclosed by the invention, on the basis of realizing the beneficial effects 1 and 2, planetary landing guidance under the optimal condition of burning up can be realized, and meanwhile, the landing position precision and the speed precision of the lander meet the terminal constraint, so that the accurate landing on the surface of the planetary can be realized.

Drawings

FIG. 1 is a schematic flow chart of an optimal control fast search planetary landing guidance method disclosed by the invention;

FIG. 2 is an optimal acceleration magnitude profile in an optimal control database;

FIG. 3 is a plot of the three axis position of the lander;

FIG. 4 is a graph of lander triaxial speed;

FIG. 5 is a plot of total thrust amplitude for a lander;

Fig. 6 is a graph of lander engine swing angle.

Detailed Description

For a better description of the objects and advantages of the present invention, the following description of the invention refers to the accompanying drawings and examples.

In order to verify the feasibility of the method, taking landing tasks of landers on Mars as an example, simulation of a planetary landing guidance method for optimal control and quick search is performed. The detector enters a Mars landing power descent section from an initial position r ₀＝[2000,0,1500]^T (unit: m), and the initial speed is v ₀＝[100,0,-75]^T (unit: m/s). The initial mass of the lander m=1905 kg, the flight time T _f =200 s, the maximum engine thrust T _max =13258N, the minimum thrust T _min =4971N, the maximum engine swing angle θ _max =30°, the engine specific impulse I _sp =225 s, the earth sea level gravitational acceleration g ₀＝9.80665m/s², the Mars surface gravitational acceleration g= [0, -3.72] ^T (unit: m/s ²) are set.

As shown in fig. 1, the implementation steps of the planetary landing guidance method for optimal control and rapid search disclosed in this embodiment are as follows:

Step one, establishing a dynamic model of the lander under a solid coordinate system of a planetary landing site, and decoupling the dynamic model of the lander into a controlled dynamic model and an uncontrolled dynamic model, wherein the controlled dynamic model corresponds to the movement of the lander when only being pushed, and the uncontrolled dynamic model corresponds to the movement of the lander when only being pulled.

The specific implementation method of the first step is as follows:

Defining a landing site fixed coordinate system O-XYZ: with the landing site as the origin O of the coordinate system, the OX axis points to the local east, the OY axis points to the local north, and the OZ axis points to the local zenith.

Neglecting the effects of planetary rotation and aerodynamic force, taking the planetary gravitational acceleration as a constant, and establishing a lander dynamics model under a landing site fixed coordinate system:

Wherein r and v respectively represent a position vector and a velocity vector of the lander under a landing site fixed coordinate system, a represents a thrust acceleration vector of the lander, T represents a thrust vector of the lander, m represents a mass of the lander, g= [0, -3.72] ^T (unit: m/s ²) represents a gravity acceleration vector of a Mars surface, I _sp =225 s represents a thrust of an engine of the lander, and g ₀＝9.80665m/s² represents a numerical value of a gravity acceleration of the earth sea surface.

According to the motion independence principle, the motion of the lander can be regarded as the synthesis of two partial motions driven by thrust and gravity respectively, and the two partial motions are independently carried out and are not interfered with each other. The position and velocity equations in equation (1) are integrated to obtain:

Where t represents the motion time, and r ₀ and v ₀ represent the position vector and the velocity vector, respectively, at the initial time.

Decoupling the kinetic equation into a controlled kinetic model and an uncontrolled kinetic model by analyzing the position and velocity equation as shown in formula (2), as shown in formula (3) and formula (4), respectively:

In the controlled dynamics model, the initial position and the initial speed of the lander are 0 and only receive the thrust action; in the uncontrolled kinetic model, the initial position and speed of the lander are r ₀ and v ₀ respectively, and are only affected by gravity.

Setting a prediction time domain, constructing an optimization model of the reachable region by taking the thrust amplitude constraint and the thrust direction constraint as constraint conditions according to the controllable dynamic model in the first step, and solving a controllable movement reachable region in the prediction time domain according to the optimization model; and constructing a fuel consumption optimization model by taking different positions in the reachable region as virtual endpoints, taking fuel consumption as an optimization target and taking thrust amplitude constraint and thrust direction constraint as constraint conditions, obtaining fuel consumption optimal control of the lander reaching a designated virtual endpoint position according to offline optimization of the fuel consumption optimization model, storing the optimal control as an optimal control database, and storing a corresponding virtual endpoint state as an endpoint state database. The specific implementation method of the second step is as follows:

The control constraints to which the lander is subjected include thrust magnitude constraints and thrust direction constraints, as shown in equation (5):

Where T _min =4971N and T _max =13258N denote a minimum value and a maximum value of the thrust amplitude, respectively, N _z denotes a unit vector in the Z-axis forward direction, and θ _max =30° denotes an engine pivot angle maximum value.

The prediction time domain is set to t _N =10s. And solving the controllable movement reachable area in the prediction time domain offline. Considering the rotational symmetry of the thrust force about the Z axis, the two-dimensional reachable area of the lander in the first quadrant of XOZ can be solved first, and then the two-dimensional reachable area can be obtained by rotating around the Z axis for one circle. According to the controllable dynamics model in the first step, constructing an optimization model of the two-dimensional reachable region by taking thrust amplitude constraint and thrust direction constraint as constraint conditions, wherein the optimization model is shown in a formula (6):

Wherein, all vectors are two-dimensional vectors, X _i and Z _i respectively represent the X-axis and Z-axis coordinates that the lander can reach, different Z _i are selected, in this example, Z _i =130, 140,150, …,350 are optimized to obtain the furthest X-axis position X _i that the lander can reach at this time, the envelope formed by the coordinates (X _i,z_i) is a two-dimensional reachable region, and the three-dimensional reachable region can be obtained by rotating around the Z axis.

Selecting different positions r _i as virtual endpoints in the reachable region, taking optimal burnup as an optimization target, taking thrust amplitude constraint and thrust direction constraint as constraint conditions as shown in a formula (5), establishing an optimization model as shown in a formula (7), and obtaining optimal burnup control of the lander reaching a specified virtual endpoint position according to offline optimization of the optimization model as shown in the formula (7). In this example, virtual endpoints constitute a collection Wherein C represents a three-dimensional reachable region.

Where m ₀ =1905 kg represents the mass of the lander at the initial time.

All virtual end positions r _i, v _i when the lander reaches r _i, and burnup Δm _i of the lander are stored as an end state database, corresponding optimal control acceleration a _i is stored as an optimal control database, and for convenience of storage, the optimal control acceleration a _i is scattered into an optimal control acceleration sequence a _i,j to be stored, wherein j=1, 2, …, and t _N/t_g,t_g =1s represent a guidance period.

Step three, calculating the state of the lander after undergoing a prediction time domain uncontrolled motion according to an uncontrolled dynamics model in the landing process, and superposing the uncontrolled motion end state and the end state database obtained in the step two to generate a state prediction space of the lander in a prediction time domain; eliminating state points which violate control constraint due to quality change in a state prediction space; the lander mass in a prediction time domain is approximately equivalent to a constant, a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass, and burnup is corrected according to the burnup correction factor alpha; and traversing and searching an optimal state in the state prediction space to obtain a corresponding optimal control instruction in an optimal control database, and realizing planetary landing guidance according to the optimal control instruction.

The specific implementation method of the third step is as follows:

At the time t of the landing process, calculating the state of the lander after undergoing a predicted time domain uncontrolled motion according to an uncontrolled dynamics model, as shown in formula (8):

Where r _u、v_u and m _u represent the position vector, velocity vector and mass, respectively, of the lander after a predicted time-domain uncontrolled motion.

Superposing the final state of uncontrolled motion and the final state of controlled motion in the final state database to generate a state prediction space X _N of the lander at the moment t in a prediction time domain, wherein the state prediction space X _N is shown as a formula (9):

X_N＝{(r_N,v_N,m_N)|r_N＝r_u+r_i,v_N＝v_u+v_i,m_N＝m_u-Δm_i,i＝1,2,...,n} (9)

Where r _N、v_N and m _N represent the position vector, velocity vector and mass of the lander after a prediction horizon, respectively, and n= 1969128 represents the number of controlled end-of-motion states in the end-state database.

Considering that the initial mass of the lander in the formula (7) is m ₀, and the variable in the optimal control database is the acceleration a, when the mass of the lander at the moment t is reduced to m (t), the optimal control acceleration a _e which partially meets the constraint of the lower limit of the thrust amplitude in the optimal control database does not meet the constraint condition at this time, namely:

For a _e, the corresponding state point X _e in the lander state prediction space X _N is removed, so as to ensure that the optimal control meets the thrust constraint, and the state prediction space X is shown in the formula (11):

X＝X_N-X_e (11)

During landing, the rate of change of the lander mass is proportional to the thrust amplitude, which is proportional to the lander mass. The change in lander mass also affects the value of burnup in the state prediction space X. The lander mass in a prediction time domain is approximately equivalent to a constant, and a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass as shown in a formula (12):

At time t of the landing process, selecting performance indexes as shown in formulas (13) - (15):

where λ <0 represents the burnup weight coefficient, in this example λ= -500, k represents the velocity weight coefficient, in this example k=100, r _x、r_y and r _z represent the current time lander triaxial position, v _x、v_y and v _z represent the current time lander triaxial velocity, t _go represents the lander residual flight time, d >0 is a constant that prevents Q from singular, in this example d=0.01.

According to the performance indexes shown in formulas (13) to (15), the optimal state X ^* is searched in the lander state prediction space X in a traversing way, and the lander is driven to move towards the target point by taking the first item a _i,1 of the optimal control sequence a _i,j corresponding to the optimal state X ^* in the optimal control database as the actual optimal control.

And executing the terminal state prediction and the optimal control search once in each guidance period, and performing planetary landing guidance according to the optimal control instruction obtained by the search until the lander reaches a target landing site.

FIG. 2 shows the optimal acceleration amplitude distribution in the corresponding optimal control database when the virtual endpoint in the endpoint state database is in the XOZ plane. Fig. 3 shows a three-axis position curve of the lander, where r _x、r_y and r _z represent three-axis position components of the lander in the coordinate system of the satellite landing site, respectively, and fig. 4 shows a three-axis velocity curve of the lander, where v _x、v_y and v _z represent three-axis velocity components of the lander in the coordinate system of the satellite landing site, respectively, it can be seen that the lander achieves accurate landing satisfying the terminal constraints. Fig. 5 shows the overall thrust amplitude curve of the lander, fig. 6 shows the engine swing angle curve, the engine swing angle is defined as the angle between the thrust direction of the lander and the positive direction of the Z axis, and it can be seen that the thrust amplitude and the direction constraint are satisfied in the whole landing process. The average time spent on searching the optimal control of each guidance period is 7.29ms, and the longest time spent is 8.34ms, so that the real-time requirement of guidance is met. Simulation shows that the designed guidance method is suitable for the planetary landing task.

While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.

Claims (4)

1. The planet landing guidance method for optimal control and quick search is characterized by comprising the following steps of: comprises the following steps of the method,

Step one, establishing a dynamic model of a lander under a solid coordinate system of a planetary landing site, and decoupling the dynamic model of the lander into a controlled dynamic model and an uncontrolled dynamic model, wherein the controlled dynamic model corresponds to the movement of the lander when only being pushed, and the uncontrolled dynamic model corresponds to the movement of the lander when only being pulled;

setting a prediction time domain, constructing an optimization model of the reachable region by taking the thrust amplitude constraint and the thrust direction constraint as constraint conditions according to the controllable dynamic model in the first step, and solving a controllable movement reachable region in the prediction time domain according to the optimization model; taking different positions in an reachable area as virtual endpoints, taking burnup as an optimization target, taking thrust amplitude constraint and thrust direction constraint as constraint conditions, constructing a burnup optimization model, obtaining burnup optimal control of the lander reaching a designated virtual endpoint position according to offline optimization of the burnup optimization model, storing the optimal control as an optimal control database, and storing a corresponding virtual endpoint state as an endpoint state database;

Step three, calculating the state of the lander after undergoing a prediction time domain uncontrolled motion according to an uncontrolled dynamics model in the landing process, and superposing the uncontrolled motion end state and the end state database obtained in the step two to generate a state prediction space of the lander in a prediction time domain; eliminating state points which violate control constraint due to quality change in a state prediction space; the lander mass in a prediction time domain is approximately equivalent to a constant, a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass, and burnup is corrected according to the burnup correction factor alpha; and traversing and searching an optimal state in the state prediction space to obtain a corresponding optimal control instruction in an optimal control database, and realizing planetary landing guidance according to the optimal control instruction.

2. The optimally controlled fast search planetary landing guidance method of claim 1, wherein: the specific implementation method of the first step is that,

Defining a landing site fixed coordinate system O-XYZ: taking the landing point as a coordinate system origin O, wherein an OX axis points to the local east direction, an OY axis points to the local north direction, and an OZ axis points to the local zenith direction;

neglecting the effects of planetary rotation and aerodynamic force, taking the planetary gravitational acceleration as a constant, and establishing a lander dynamics model under a landing site fixed coordinate system:

Wherein r and v respectively represent a position vector and a speed vector of the lander under a landing site fixed coordinate system, a represents a thrust acceleration vector of the lander, T represents a thrust vector of the lander, m represents a mass of the lander, g represents a gravity acceleration vector of a planet surface, I _sp represents a specific impulse of an engine of the lander, and g ₀ represents a numerical value of a gravity acceleration of the earth sea level;

According to the motion independence principle, the motion of the lander can be regarded as the synthesis of two partial motions driven by thrust and gravity respectively, and the two partial motions are independently carried out and are not interfered with each other; the position and velocity equations in equation (1) are integrated to obtain:

Wherein t represents movement time, and r ₀ and v ₀ represent a position vector and a velocity vector at an initial time, respectively;

Decoupling the kinetic equation into a controlled kinetic model and an uncontrolled kinetic model by analyzing the position and velocity equation as shown in formula (2), as shown in formula (3) and formula (4), respectively:

In the controlled dynamics model, the initial position and the initial speed of the lander are 0 and only receive the thrust action; in the uncontrolled kinetic model, the initial position and speed of the lander are r ₀ and v ₀ respectively, and are only affected by gravity.

3. The optimally controlled fast search planetary landing guidance method of claim 2, wherein: the specific implementation method of the second step is as follows:

The control constraints to which the lander is subjected include thrust magnitude constraints and thrust direction constraints, as shown in equation (5):

Wherein, T _min and T _max respectively represent the minimum value and the maximum value of the thrust amplitude, n _z represents a unit vector in the positive direction of the Z axis, and theta _max represents the maximum value of the swing angle of the engine, which is defined as the maximum included angle between the thrust vector and the positive direction of the Z axis;

Setting a prediction time domain as t _N; offline solving a controllable movement reachable area in a prediction time domain; considering the rotational symmetry of the thrust force about the Z axis, the two-dimensional reachable area of the lander in the first quadrant of the XOZ can be solved first, and then the two-dimensional reachable area can be obtained after rotating around the Z axis for one circle; according to the controllable dynamics model in the first step, constructing an optimization model of the two-dimensional reachable region by taking thrust amplitude constraint and thrust direction constraint as constraint conditions, wherein the optimization model is shown in a formula (6):

Wherein, all vectors are two-dimensional vectors, X _i and Z _i respectively represent X-axis and Z-axis coordinates which can be reached by the lander, different Z _i are selected, the furthest X-axis position X _i which can be reached by the lander at the moment is obtained through optimization, an envelope formed by coordinates (X _i,z_i) is a two-dimensional reachable area, and a three-dimensional reachable area can be obtained through rotation around the Z axis;

Selecting different positions r _i as virtual endpoints in an reachable region, taking optimal burnup as an optimization target, taking thrust amplitude constraint and thrust direction constraint as constraint conditions as shown in a formula (5), establishing an optimization model as shown in a formula (7), and obtaining optimal burnup control of the lander reaching a specified virtual endpoint position according to offline optimization of the optimization model as shown in the formula (7);

Wherein m ₀ represents the mass of the lander at the initial time;

All virtual end positions r _i, v _i when the lander reaches r _i, and burnup Δm of the lander are stored as an end state database, the corresponding optimal control acceleration a _i is stored as an optimal control database, and for convenience of storage, the optimal control acceleration a _i is scattered into an optimal control acceleration sequence a _i,j to be stored, wherein j=1, 2, … and t _N/t_g,t_g represent guidance periods, and t _N is an integer multiple of t _g.

4. The optimally controlled fast search planetary landing guidance method of claim 3, wherein: the specific implementation method of the third step is as follows:

At the time t of the landing process, calculating the state of the lander after undergoing a predicted time domain uncontrolled motion according to an uncontrolled dynamics model, as shown in formula (8):

Wherein r _u、v_u and m _u respectively represent the position vector, the speed vector and the quality of the lander after a predicted time domain uncontrolled motion;

Superposing the final state of uncontrolled motion and the final state of controlled motion in the final state database to generate a state prediction space X _N of the lander at the moment t in a prediction time domain, wherein the state prediction space X _N is shown as a formula (9):

X_N＝{(r_N,v_N,m_N)|r_N＝r_u+r_i,v_N＝v_u+v_i,m_N＝m_u-Δm_i,i＝1,2,…,n} (9)

wherein r _N、v_N and m _N respectively represent the position vector, the speed vector and the quality of the lander after passing through a prediction time domain, and n represents the quantity of controlled motion end states in an end state database;

Considering that the initial mass of the lander in the formula (7) is m ₀, and the variable in the optimal control database is the acceleration a, when the mass of the lander at the moment t is reduced to m (t), the optimal control acceleration a _e which partially meets the lower limit constraint of the thrust amplitude in the optimal control database does not meet the constraint condition at this time, namely:

For a _e, the corresponding state point X _e in the lander state prediction space X _N is removed, so as to ensure that the optimal control meets the thrust constraint, and the state prediction space X is shown in the formula (11):

X＝X_N-X_e (11)

During landing, the rate of change of the lander mass is proportional to the thrust amplitude, which is proportional to the lander mass; so the change in lander mass also affects the value of burnup in the state prediction space X; the lander mass in a prediction time domain is approximately equivalent to a constant, and a burnup correction factor alpha is constructed according to the ratio of the current time lander mass to the initial time mass as shown in a formula (12):

At time t of the landing process, selecting performance indexes as shown in formulas (13) - (15):

Wherein lambda <0 represents the burnup weight coefficient, k represents the speed weight coefficient, r _x、r_y and r _z respectively represent the current time lander triaxial position, v _x、v_y and v _z respectively represent the current time lander triaxial speed, t _go represents the lander residual flight time, and d >0 is a constant for preventing Q from generating singular;

According to the performance indexes shown in formulas (13) to (15), traversing and searching an optimal state X ^* in a lander state prediction space X, and driving a lander to move towards a target point by taking a first item a _i,1 of an optimal control sequence a _i,j corresponding to the optimal state X ^* in an optimal control database as actual optimal control;

and executing the terminal state prediction and the optimal control search once in each guidance period, and performing planetary landing guidance according to the optimal control instruction obtained by the search until the lander reaches a target landing site.