An optimal method for generating lunar surface hovering flyby trajectories

Abstract

The invention relates to an optimal lunar surface hovering flyby trajectory generation method, belonging to the field of trajectory design of celestial body surface flight probes. The method comprises the following steps: step one, dividing the flyby trajectory into three stages; step two, establishing a motion model in a two-dimensional plane of the flyby trajectory; step three, setting constraint conditions of control quantities in each stage; step four, setting initial conditions and terminal conditions in each stage; step five, setting the optimal control quantity form in each stage according to the motion model, control quantity constraint conditions, initial conditions and terminal conditions obtained in steps two to four; step six, obtaining the corresponding optimal trajectory in each stage through one-dimensional search according to the motion model, control quantity constraint conditions, initial conditions and terminal conditions, and optimal control quantity form obtained in steps two to five; and step seven, combining the optimal trajectories of each stage obtained in step six to generate a final optimal lunar surface hovering flyby trajectory. The method is simple and reliable, and is suitable for offline or online calculation.

Description

Technical Field

[0001] The invention belongs to the field of trajectory design of a celestial body surface flying probe, and relates to an optimal lunar surface circling flyby trajectory generation method. Background Art

[0002] Flying probes can place scientific payloads on the surface of a predetermined celestial body, build a network as a signal site, and play an important role in establishing bases and mapping the surface of celestial bodies. In addition, flying probes can also be used to verify landing technology, attitude determination technology, energy generation and storage technology, sensor technology, material technology, and communication technology, providing powerful technical verification for the exploration of planets, satellites, asteroids, comets, and other celestial bodies. At present, there are trajectory design methods for the descent process such as lunar landing, planetary landing, and re-entry to the earth, as well as ascending trajectory design methods such as takeoff from the surface of a celestial body and ground launch. Existing technologies cannot complete flight exploration missions. Summary of the invention

[0003] The technical problem solved by the present invention is to overcome the deficiencies of the prior art and propose an optimal lunar surface hovering flyby trajectory generation method which is simple, reliable and suitable for offline or online calculation.

[0004] The solution of the present invention is:

[0005] A method for generating an optimal lunar surface hovering flyby trajectory, comprising:

[0006] Step 1: Divide the flight trajectory into three stages;

[0007] Step 2: Set the target landing position as the origin and establish a two-degree-of-freedom motion model at each stage in the two-dimensional plane of the flight trajectory;

[0008] Set the constraints of the control quantity at each stage;

[0009] Set the initial and terminal conditions for each stage;

[0010] Step 3: According to the two-degree-of-freedom motion model, control quantity constraint conditions, initial conditions and terminal conditions obtained in step 2, set the optimal control quantity form in each stage;

[0011] Step 4: According to the two-degree-of-freedom motion model, control quantity constraint conditions, initial conditions and terminal conditions, and optimal control quantity form obtained in step 2, the corresponding optimal trajectory is obtained through one-dimensional search in each stage;

[0012] Step 5: Combine the optimal trajectories of each stage obtained in step 4 to generate the final optimal lunar surface circling flyby trajectory.

[0013] In the above-mentioned method for generating an optimal lunar hovering flyby trajectory, in step 1, the three stages of the flyby trajectory are respectively a vertical ascent stage, a translation stage, and a vertical descent stage.

[0014] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in step 2, the two-degree-of-freedom motion model of the vertical ascent segment and the vertical descent segment is:

[0015] a x (t k )=F(t k ) / m(t k )-g m

[0016] v x (t k+1 )=v x (t k )+a x (t k )T

[0017] x(t k+1 )=x(t k )+v x (t k )T

[0018] m(t k+1 )=m(t k )-F(t k )T / I sp

[0019] Where, t k is the k-th shot time;

[0020] t k+1 is the k+1th beat time;

[0021] F is the main engine thrust;

[0022] m is the mass of the vehicle, which changes with the propellant consumption m during the leap;

[0023] g m is the magnitude of the gravitational acceleration of the moon;

[0024] I sp is the main engine specific impulse;

[0025] T is the trajectory update period;

[0026] a x is the vertical acceleration, which is positive when it is upward;

[0027] v x is the vertical speed;

[0028] x is the vertical position.

[0029] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in step 2, the two-degree-of-freedom motion model of the translation segment is:

[0030] F(t k )=m(t k ) m / cosθ(t k )

[0031] a y (t k ) = g m tanθ(t k )

[0032] v y (t k+1 )=v y (t k )+a y (t k )T

[0033] y(t k+1 )=y(t k )+v y (t k )T

[0034] θ(t k+1 )=θ(t k )+ω(t k )T

[0035] m(t k+1 )=m(t k )-F(t k )T / I sp

[0036] Where θ is the angle between the longitudinal axis of the aircraft and the vertical direction, and the nose-lead angle is positive;

[0037] a y is the horizontal acceleration, which is positive when pointing in the launching direction;

[0038] v y is the horizontal speed;

[0039] y is the horizontal position;

[0040] ω is the pitch angular velocity, which is positive when lowering the head forward.

[0041] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in the step 2, the constraints of the control quantities in each stage are:

[0042] Vertical ascending section: 0≤F≤F max ;

[0043] Translation segment: ω≤ω max ;

[0044] Vertical descent section: 0≤F≤F max ;

[0045] Among them, F max is the maximum thrust of the main engine;

[0046] ω max It is the preset maximum angular velocity of the aircraft.

[0047] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in the step 2, the initial conditions and terminal conditions of each flight phase are respectively:

[0048] Vertical ascending section: x(0)=0, v x (0)=0, m(0)=m0, x(T1)=x1,v x (T1) = 0;

[0049] Translation segment: y(T1)=y1,v y (T1) = 0, y(T2) = 0, v y (T2) = 0;

[0050] Vertical descent section: x(T2)=x1,v x (T2)=0, m(T2)=m2, x(T3)=0, v x (T3) = 0;

[0051] Among them, T1, T2, and T3 are the end times of the vertical ascent segment, the translation segment, and the vertical descent segment respectively;

[0052] x1 is the preset flight altitude;

[0053] y1 is the horizontal position of the take-off point;

[0054] m0 is the initial takeoff mass;

[0055] m1 is the initial mass of the translation segment;

[0056] m2 is the initial mass of the vertical descent section.

[0057] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in step 3, the optimal control amount of each stage is in the form of:

[0058] Vertical ascent section:

[0059] Translation segment:

[0060] Vertical descent section: Among them, T 11 It is the preset shutdown time of the vertical ascent stage;

[0061] T 31 It is the preset start time of the vertical descent section.

[0062] In the above-mentioned optimal lunar hovering flyby trajectory generation method, in the step 4, the golden section method is used for one-dimensional search in each stage;

[0063] The method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical ascent segment is:

[0064] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage; through one-dimensional search, T is changed successively. 11 value, until the vertical speed v x When it is 0, the absolute value of the difference between the vertical position and x1 is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical ascent segment obtained by search, and the end time of the trajectory is T1, and the mass corresponding to the end time is m1.

[0065] In the above-mentioned optimal lunar hovering flyby trajectory generation method, the method for obtaining the corresponding optimal trajectory through one-dimensional search in the translation segment is:

[0066] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form of this stage, the T2 value is changed successively through one-dimensional search until the absolute value of the horizontal position y(T2) is less than 0.001m when the time reaches T2, and the iteration is stopped; the trajectory generated for the last time is the optimal trajectory of the translation segment obtained by the search, and the mass at the end of the trajectory is m2.

[0067] In the above-mentioned optimal lunar hovering flyby trajectory generation method, the method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical descent stage is:

[0068] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage, T is changed successively through one-dimensional search. 31 value, until the vertical speed v x When it is 0, the absolute value of the vertical position is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical descent segment obtained by search, and the end time of the trajectory is T3.

[0069] The beneficial effects of the present invention compared with the prior art are:

[0070] (1) The trajectory generated by the present invention can complete the altitude-fixed flight detection mission without a translation engine. Currently, no special design method for this special mission has been found. The method of the present invention is more applicable to this special mission.

[0071] (2) The method of the present invention has been rigorously theoretically proven to consume less propellant than other existing numerical optimization methods and is globally optimal;

[0072] (3) The present invention only requires one-dimensional search, which is simpler to operate than other optimization methods, more conducive to online use, and more practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 Generate a flow chart for the flight trajectory of the present invention;

[0074] Figure 2 Schematic diagram of the trajectory of the aircraft of the present invention. DETAILED DESCRIPTION

[0075] The present invention will be further described below in conjunction with the embodiments.

[0076] The present invention provides an optimal lunar hovering flyby trajectory generation method. According to different mission constraints during the flight, the flight trajectory is divided into three stages: vertical ascent stage, translation stage, and vertical descent stage. The optimal trajectory is obtained through one-dimensional search. The present invention fully considers the actual mission requirements and constraints, is simple and reliable, can be used offline or online, and provides a general trajectory design method for fixed-altitude flight detection missions without translation engines on the surface of celestial bodies.

[0077] The optimal lunar surface hovering flyby trajectory generation method is as follows: Figure 1 As shown, the specific steps include:

[0078] Step 1: Figure 2 As shown in the figure, the flight trajectory is divided into three stages; the three stages of the flight trajectory are vertical ascent, translation, and vertical descent. In order to ensure safe takeoff, the aircraft can only fly translationally after reaching a certain height. When the aircraft reaches the landing point, it begins to descend until it touches the ground and shuts down. Therefore, the flight trajectory is divided into three stages: vertical ascent, translation, and vertical descent.

[0079] Step 2: Set the target landing position as the origin and establish the two-degree-of-freedom motion model of each stage in the two-dimensional plane of the flight trajectory; the two-degree-of-freedom motion model of the vertical ascent stage and the vertical descent stage is:

[0080] a x (t k )=F(t k ) / m(t k )-g m

[0081] v x (t k+1 )=v x (tk )+a x (t k )T

[0082] x(t k+1 )=x(t k )+v x (t k )T

[0083] m(t k+1 )=m(t k )-F(t k )T / I sp

[0084] Where, t k is the k-th shot time;

[0085] t k+1 is the k+1th beat time;

[0086] F is the main engine thrust;

[0087] m is the mass of the vehicle, which changes with the propellant consumption m during the leap;

[0088] g m is the gravitational acceleration of the moon, 1.62m / s 2 ;

[0089] I sp is the main engine specific impulse;

[0090] T is the trajectory update period;

[0091] a x is the vertical acceleration, which is positive when it is upward;

[0092] v x is the vertical speed;

[0093] x is the vertical position.

[0094] The two-degree-of-freedom motion model of the translation segment is:

[0095] F(t k )=m(t k ) m / cosθ(t k )

[0096] a y (t k ) = g m tanθ(t k )

[0097] v y (t k+1 )=v y(t k )+a y (t k )T

[0098] y(t k+1 )=y(t k )+v y (t k )T

[0099] θ(t k+1 )=θ(t k )+ω(t k )T

[0100] m(t k+1 )=m(t k )-F(t k )T / I sp

[0101] Where θ is the angle between the longitudinal axis of the aircraft and the vertical direction, and the nose-lead angle is positive;

[0102] a y is the horizontal acceleration, which is positive when pointing in the launching direction;

[0103] v y is the horizontal speed;

[0104] y is the horizontal position;

[0105] ω is the pitch angular velocity, which is positive when lowering the head forward.

[0106] Step 3: Set the constraints of the control quantity at each stage; the constraints of the control quantity at each stage are:

[0107] The control quantity of the vertical ascent phase is the engine thrust, and the constraint condition is: 0≤F≤F max ;

[0108] The engine thrust in the translation phase can be obtained by real-time calculation of the pitch attitude according to the balanced gravity requirement. This phase achieves horizontal acceleration and deceleration by adjusting the pitch attitude. The actual control quantity is the pitch angular velocity, and its constraint is: ω≤ω max ;ω max It is the preset maximum angular velocity of the aircraft.

[0109] The control quantity of the vertical descent phase is the engine thrust, and the constraint condition is: 0≤F≤F max Among them, F max The maximum thrust of the main engine.

[0110] Step 4: Set the initial and terminal conditions for each stage.

[0111] The vertical ascent phase starts on the lunar surface with zero velocity, the terminal velocity is zero and the altitude is the target altitude; the initial conditions of the translation phase are the terminal conditions of the vertical ascent phase, the terminal velocity is zero and the position is directly above the target point; the initial conditions of the vertical descent phase are the terminal conditions of the translation phase, the terminal velocity is zero and the position is the target point. Therefore, the initial conditions and terminal conditions of each flight phase are:

[0112] Vertical ascending section: x(0)=0, v x (0)=0, m(0)=m0, x(T1)=x1,v x (T1) = 0;

[0113] Translation segment: y(T1)=y1,v y (T1) = 0, y(T2) = 0, v y (T2) = 0;

[0114] Vertical descent section: x(T2)=x1,v x (T2)=0, m(T2)=m2, x(T3)=0, v x (T3) = 0;

[0115] Among them, T1, T2, and T3 are the end times of the vertical ascent segment, the translation segment, and the vertical descent segment respectively;

[0116] x1 is the preset flight altitude;

[0117] y1 is the horizontal position of the take-off point;

[0118] m0 is the initial takeoff mass;

[0119] m1 is the initial mass of the translation segment;

[0120] m2 is the initial mass of the vertical descent section.

[0121] Step 5: According to the motion model, control quantity constraint conditions, initial conditions and terminal conditions obtained from steps 2 to 4, set the optimal control quantity form for each stage.

[0122] According to the results of theoretical proof, the control amount corresponding to the optimal trajectory of the vertical ascent stage is the stick-stick control form, that is, first the maximum thrust, then shut down the engine; the control amount corresponding to the optimal trajectory of the translation stage is first the maximum positive angular velocity for a quarter of the time, then the maximum negative angular velocity for a half of the time, and then the maximum positive angular velocity for a quarter of the time; the control amount corresponding to the optimal trajectory of the vertical descent stage is the stick-stick control form, that is, first shut down the engine, then the maximum thrust. Therefore, the optimal control amount form of each stage is:

[0123] Vertical ascent section:

[0124] Translation segment:

[0125] Vertical descent section: Among them, T 11 It is the preset shutdown time of the vertical ascent stage;

[0126] T 31 It is the preset start time of the vertical descent section.

[0127] Step 6: According to the two-degree-of-freedom motion model, control quantity constraint conditions, initial conditions and terminal conditions, and optimal control quantity form obtained from steps 2 to 5, the corresponding optimal trajectory is obtained through one-dimensional search in each stage; the golden section method is used for one-dimensional search in each stage;

[0128] The method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical ascent segment is:

[0129] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage; through one-dimensional search, T is changed successively. 11 value, until the vertical speed v x When it is 0, the absolute value of the difference between the vertical position and x1 is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical ascent segment obtained by search, and the end time of the trajectory is T1, and the mass corresponding to the end time is m1.

[0130] The method for obtaining the corresponding optimal trajectory through one-dimensional search for the translation segment is:

[0131] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form of this stage, the T2 value is changed successively through one-dimensional search until the absolute value of the horizontal position y(T2) is less than 0.001m when the time reaches T2, and the iteration is stopped; the trajectory generated for the last time is the optimal trajectory of the translation segment obtained by the search, and the mass at the end of the trajectory is m2.

[0132] The method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical descent section is:

[0133] Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage, T is changed successively through one-dimensional search. 31 value, until the vertical speed v x When it is 0, the absolute value of the vertical position is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical descent segment obtained by search, and the end time of the trajectory is T3.

[0134] Step 7: Combine the optimal trajectories of each stage obtained in step 6 to generate the final optimal lunar surface circling flyby trajectory, as shown in Figure 2 shown.

[0135] The trajectory generated by the present invention can complete the altitude-fixed flight detection mission without a translation engine. Currently, no special design method for this special mission has been found. The method of the present invention is more applicable to this special mission. The method has been strictly theoretically proven to consume less propellant than other existing numerical optimization methods and is globally optimal. Moreover, the present invention only requires one-dimensional search, which is simpler to calculate than other optimization methods, more conducive to online use, and more practical.

[0136] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for generating an optimal lunar surface hovering flyby trajectory, characterized in that: include: Step 1: Divide the flight trajectory into three stages; In the step 1, the three stages of the flight trajectory are respectively a vertical ascending stage, a translation stage, and a vertical descending stage; Step 2: Set the target landing position as the origin and establish a two-degree-of-freedom motion model at each stage in the two-dimensional plane of the flight trajectory; The two-degree-of-freedom motion model of the vertical ascent section and the vertical descent section is: a x (t k )=F(t k ) / m(t k )-g m v x (t k+1 )=v x (t k )+a x (t k )T x(t k+1 )=x(t k )+v x (t k )T m(t k+1 )=m(t k )-F(t k )T / I sp Where, t k is the k-th shot time; t k+1 is the k+1th beat time; F is the main engine thrust; m is the mass of the vehicle, which changes with the propellant consumption m during the leap; g m is the magnitude of the gravitational acceleration of the moon; I sp is the main engine specific impulse; T is the trajectory update period; a x is the vertical acceleration, which is positive when it is upward; v x is the vertical speed; x is the vertical position; The two-degree-of-freedom motion model of the translation segment is: F(t k )=m(t k )g m / cosθ(t k ) a y (t k )=g m tanθ(t k ) v y (t k+1 )=v y (t k )+a y (t k )T y(t k+1 )=y(t k )+v y (t k )T θ(t k+1 )=θ(t k )+ω(t k )T m(t k+1 )=m(t k )-F(t k )T / I sp Where θ is the angle between the longitudinal axis of the aircraft and the vertical direction, and the nose-lead angle is positive; a y is the horizontal acceleration, which is positive when pointing in the launching direction; v y is the horizontal speed; y is the horizontal position; ω is the pitch angular velocity, which is positive when the head is lowered forward; The constraints of the control quantity in each stage are: Vertical ascending section: 0≤F≤F max ; Translation segment: |ω≤ω max ; Vertical descent section: 0≤F≤F max ; Among them, F max is the maximum thrust of the main engine; ω max is the preset maximum angular velocity of the aircraft; The initial conditions and terminal conditions of each flight phase are: Vertical ascending section: x(0)=0, v x (0)=0, m(0)=m0, x(T1)=x1,v x (T1) = 0; Translation segment: y(T1)=y1,v y (T1) = 0, y(T2) = 0, v y (T2) = 0; Vertical descent section: x(T2)=x1,v x (T2)=0, m(T2)=m2, x(T3)=0, v x (T3) = 0; T1, T2, and T3 are the end times of the vertical ascent segment, the translation segment, and the vertical descent segment, respectively; x1 is the preset flight altitude; y1 is the horizontal position of the take-off point; m0 is the initial takeoff mass; m1 is the initial mass of the translation segment; m2 is the initial mass of the vertical descent stage; Set the constraints of the control quantity at each stage; Set the initial and terminal conditions for each stage; Step 3: According to the two-degree-of-freedom motion model, control quantity constraint conditions, initial conditions and terminal conditions obtained in step 2, set the optimal control quantity form in each stage; The optimal control quantity of each stage is in the form of: Vertical ascent section: Translation segment: Vertical descent section: Among them, T 11 It is the preset shutdown time of the vertical ascent stage; T 31 It is the preset start time of the vertical descent section; Step 4: According to the two-degree-of-freedom motion model, control quantity constraint conditions, initial conditions and terminal conditions, and optimal control quantity form obtained in step 2, the corresponding optimal trajectory is obtained through one-dimensional search in each stage; Step 5: Combine the optimal trajectories of each stage obtained in step 4 to generate the final optimal lunar surface circling flyby trajectory.

2. The method for generating an optimal lunar hovering trajectory according to claim 1, characterized in that: In the step 4, the golden section method is used to perform one-dimensional search in each stage; The method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical ascent segment is: Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage; through one-dimensional search, T is changed successively. 11 value, until the vertical speed v x When it is 0, the absolute value of the difference between the vertical position and x1 is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical ascent segment obtained by search, and the end time of the trajectory is T1, and the mass corresponding to the end time is m1.

3. The method for generating an optimal lunar hovering trajectory according to claim 2, characterized in that: The method for obtaining the corresponding optimal trajectory through one-dimensional search for the translation segment is: Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form of this stage, the T2 value is changed successively through one-dimensional search until the absolute value of the horizontal position y(T2) is less than 0.001m when the time reaches T2, and the iteration is stopped; the trajectory generated for the last time is the optimal trajectory of the translation segment obtained by the search, and the mass at the end of the trajectory is m2.

4. The method for generating an optimal lunar hovering trajectory according to claim 3, characterized in that: The method for obtaining the corresponding optimal trajectory through one-dimensional search in the vertical descent section is: Based on the motion model, control quantity constraints, initial conditions, and optimal control quantity form at this stage, T is changed successively through one-dimensional search. 31 value, until the vertical speed v x When it is 0, the absolute value of the vertical position is less than 0.001m, and the iteration stops; the last generated trajectory is the optimal trajectory of the vertical descent segment obtained by search, and the end time of the trajectory is T3.

Images