CN113741193B - Weak attraction small celestial body surface bouncing track correction control method - Google Patents

Weak attraction small celestial body surface bouncing track correction control method Download PDF

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CN113741193B
CN113741193B CN202111038247.9A CN202111038247A CN113741193B CN 113741193 B CN113741193 B CN 113741193B CN 202111038247 A CN202111038247 A CN 202111038247A CN 113741193 B CN113741193 B CN 113741193B
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detector
braking
potential function
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track
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CN113741193A (en
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朱圣英
杨哲
崔平远
徐瑞
梁子璇
葛丹桐
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Beijing Institute of Technology BIT
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
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    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
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Abstract

The invention discloses a control method for correcting a bouncing track of the surface of a weak-attraction small celestial body, relates to a control method for correcting a detector track through potential function guidance in the bouncing movement process of the surface of the weak-attraction small celestial body, and belongs to the field of deep space detection. Aiming at the existing small celestial body surface bouncing movement track correction method, the pulse speed maneuver and the obstacle treatment are not considered when the position error is large in the bouncing process, and only the correction of the tiny position deviation can be carried out. The implementation method of the invention comprises the following steps: when the track deviation is larger due to the speed error after the detector is tripped, the track is corrected in a pulse maneuver mode, a correction potential function is obtained by introducing a correction repulsive force potential function representing an obstacle and overlapping a power potential function, the pulse maneuver speed is obtained through the correction potential function, and the detector carries out weak attraction small celestial body surface bounce track correction control through the braking speed pulse, so that the moving position precision of the detector is improved.

Description

Weak attraction small celestial body surface bouncing track correction control method
Technical Field
The invention relates to a control method for correcting a detector track through potential function guidance in the process of bouncing and moving of the surface of a weak-attraction small celestial body, and belongs to the field of deep space detection.
Background
After lunar and planetary exploration, the asteroid landing exploration is gradually becoming a popular field of deep space exploration. Currently, there are three main approaches to the detection of asteroid: the ground observation station is used for observation and research, the emission detector is used for carrying out close-range surrounding flight detection or leap observation on the asteroid, and the emission detector is used for carrying out landing detection on the surface of the asteroid. With the advancement of technology, the task of detecting asteroid with soft landing and sampling return of surfaces is becoming the primary way to detect asteroid. Unlike the planetary surface environment, the asteroid has extremely tiny gravity and complex and changeable surface environment, so that the traditional wheel type planetary detector has extremely difficult walking and control on the surface, and the internationally recognized surface movement mode is bouncing movement at present. The bouncing movement has the advantages of being capable of crossing an obstacle, being capable of realizing long-distance movement in a short time, and the like, but at the same time, a small deviation of the initial state of the bouncing movement can cause a large deviation of the final position of the movement. Therefore, methods for trajectory modification during detector bounce need to be studied to achieve precise control of detector surface movement.
In the development of the developed small celestial body surface movement detection guidance method, a guidance algorithm is designed based on a parabolic motion model aiming at the small celestial body surface bouncing movement problem in the prior art [1] (see Bellerose J, scheeres D J. Dynamics and Control for Surface Exploration of Small Bodies [ C ]. AIAA/AAS 2008Astrodynamics Specialist Conference,Honolulu,Hawaii,Aug.18-21,2008:AIAA 2008-6251 ]), but the method is based on a simplified motion model, so that the control accuracy is poor.
In the prior art [2] (see Shen H, zhang T, li Z, li H.multiple-Hopping Trajectories Near a Rotating Asteroid [ J ]. Astrophysics and Space Science,2017,362:45 ]) a particle swarm optimization algorithm is applied to study the problem of optimizing the track of the movement of the bouncing detector on the surface of the small celestial body, and although an accurate dynamics model is adopted in the method, the thrust design based on an optimization method is an open-loop idea and is greatly influenced by external interference and unknown dynamics characteristics.
In the prior art [3] (see Liu Yanjie. Research on small celestial body attachment detection track optimization and guidance method [ D ]. Beijing university of technology, 2017.), tracking of a first-order sliding surface is achieved by designing a second-order sliding surface, an analytical expression of guidance acceleration is deduced by using the second-order sliding surface, and single bounce accurate transfer of the detector is achieved by using the obtained guidance acceleration. However, this method does not mention a method for processing an obstacle, and requires a plurality of pulses to correct the trajectory, and cannot cope with a trajectory correction situation in which an error is large.
Disclosure of Invention
Aiming at the existing small celestial body surface bouncing movement track correction method, the pulse speed maneuver and the obstacle treatment are not considered when the position error is large in the bouncing process, and only the correction of the tiny position deviation can be carried out. The invention discloses a weak attraction small celestial body surface bouncing track correction control method, which mainly solves the problems that: when the track deviation is larger due to the speed error after the detector is tripped, the track is corrected in a pulse maneuver mode, a correction potential function is obtained by introducing a correction repulsive force potential function representing an obstacle and overlapping a power potential function, the pulse maneuver speed is obtained through the correction potential function, and the detector carries out weak attraction small celestial body surface bounce track correction control through the braking speed pulse, so that the moving position precision of the detector is improved.
The invention is realized by the following technical scheme.
The invention discloses a weak-attraction small celestial body surface bouncing track correction control method, which aims at the problem of single bouncing movement of a detector and respectively establishes a dynamic equation of the detector after the detector jumps under a small celestial body fixedly connected coordinate system and a small celestial body surface coordinate system. And (3) taking external interference factors received by the detector in the take-off process into consideration to obtain an actual bouncing trajectory dynamics equation of the detector containing unknown interference. And obtaining a nominal track through the non-interference dynamic model, giving out a maximum allowable position deviation in a track error range, and judging whether the detector needs track correction or not through the position difference value between the actual motion track and the reference track of the detector at the same time. When the detector needs to carry out track correction, a path planning is carried out by using an artificial potential function guidance method. Establishing a potential function related to the position of the detector relative to the collision point, representing the spherical obstacle in the nominal track range of the detector by using a repulsive force potential function with a high potential field value, and superposing the two potential functions to obtain a corrected potential function. The direction of the descending path of the detector is changed by adjusting the parameters of the direction matrix, so that the potential field value is gradually reduced in the process of the detector reaching the collision point. The relation between the pulse maneuvering speed of the braked detector and the potential function is obtained by deriving the potential function, the pulse maneuvering speed after the braking and the position at the moment of the braking are used as initial states of the detector after the braking, and the minimum potential field value at the collision point which is finally reached by the residual time is used as a performance index to design a guidance method, so that the surface bouncing correction track of the detector on the weak attraction small celestial body is obtained, and the moving position accuracy is improved.
The invention discloses a weak-attraction small celestial body surface bouncing track correction control method, which comprises the following steps:
step 1: and respectively establishing a dynamic equation under the celestial body fixed connection coordinate system and the surface coordinate system, and obtaining an actual bouncing track dynamic equation of the detector containing unknown interference by considering external interference factors received by the detector in the tripping process.
Aiming at the problem of single bouncing movement of the detector, under the small celestial body fixedly connected coordinate system, the dynamic equation of the detector after taking off is expressed as
Wherein r is B 、v B The position and velocity vectors of the detector, ω is the angular spin velocity of the celestial body, a B For other accelerations where the perturbation is not taken into account, V is a gravitational potential function.
Under the surface coordinate system, the dynamic equation of the detector is that
Wherein r and v are the position and speed vectors of the detector, ρ is the position vector of the center of the small celestial body relative to the origin of the surface coordinate system, u B For the thrust vector of the detector body coordinate system,for the matrix converted from the bulk coordinate system to the surface coordinate system, a is the other acceleration without taking the perturbation into account.
Various uncertainties exist in the dynamic model of the detector, wherein the uncertainties form factors comprising model parameter errors, unknown high-order gravitational field models and unmodeled perturbation forces, and the dynamic changes caused by the uncertainties form factors are attributed to model-free acceleration.
Order theIntegrating the kinetic equation
Wherein n is i (i=r, v) is an unknown interference amount.
Step 2: and carrying out linearization solution on a dynamic equation under the celestial body surface coordinate system to obtain the relationship between the braking time and the braking speed.
Selecting the position and speed of the detector under the surface coordinate system of the celestial body as state variables, namely
In the initial state X 0 Linearizing the dynamics equation (1) to obtain a linearization equation of the bouncing motion of the detector
Wherein the method comprises the steps of
And->Respectively the gravitation bit function is in the initial state X 0 The first derivative and the second derivative of the position r.
The linearization system (5) of the bouncing motion of the detector is a linear steady system, and the solution of the system is
Since u is a constant matrix and the matrixIs reversible, thus
The solution of the system is expressed as
X(t)＝e (A+δ)t X 0 +(A+δ) -1 [e (A+δ)t -I 6×6 ]u (12)
The braking time of the thruster is t s The detector speed before braking is v - The detector speed after braking is v + The detector state transition matrix is
Constant vector is
The required speed pulse is
Δv＝v + -v - (15)
Namely, the relationship between the braking time and the braking speed established by the equations (12), (13), (14) and (15).
Step 3: establishing a potential function of the force of the detector relative to the position of the collision point; while spherical obstructions within the nominal trajectory of the detector are represented by repulsive potential functions having high potential field values. And correcting the repulsive force potential function to enable the repulsive force potential function to meet the Lyapunov stability condition, so that the repulsive force potential function is converged at the collision point. And superposing the attraction potential function and the corrected repulsion potential function to obtain a corrected potential function.
Selecting the potential function of the attraction force as
Wherein,
r l for the position of the detector relative to the collision point in the small celestial surface coordinate system, the position r of the detector in the small celestial surface coordinate system is expressed as
r l ＝r-r t (18)
Wherein r is t Is the location of the collision point in the celestial surface coordinate system. The defined potential function of the force is a function of the detector position and is positive if and only if at r=r t I.e. the detector reaches the collision point, the force potential function is zero.
The matrix M determines the direction of the detector jumping to the landing point, and in order to ensure that the closer to the point of the detector braking point and the connecting line of the target point, the lower the potential field value is, the parameters are selected as
k x ＝k y ＝k＞1 (19)
Introducing a limiting condition that a region with a high potential function represents a motion path, wherein spherical obstacles exist on the bouncing path of the detector, gradient values of the region with the high potential function represent the repulsive force applied to the detector for avoiding the obstacles, and selecting a repulsive force potential function in a Gaussian function form as the repulsive force potential function
Wherein r is o Is the position vector lambda of the sphere center of the obstacle in the small celestial body surface coordinate system 1 、λ 2 Is the height and width of the repulsive force potential. Consider when r=r t In the case where formula (20) is not zero, the lyapunov stability condition is not satisfied. In order to converge the potential function after the repulsive potential is added at the collision point, equation (20) is modified to
Wherein the method comprises the steps of
p x ＞1,p y ＞1,p z ＞1 (23)
The modified potential function is
Step 4: and (3) substituting the judgment condition of the maneuvering position of the detector and the expected speed after braking into the correction potential function in the step (3) to obtain the magnitude of the pulse maneuvering speed after braking.
When the error value of the actual track and the reference track of the detector is larger than the allowable maximum error, namely Deltar= |r-r e ||≥r max When send outThe detector is braked by ignition of the engine, and the expected speed after braking is selected as
The first derivative of equation (24) with respect to time is
Bringing formula (25) into formula (26) to obtain
K is the magnitude of the pulse maneuvering speed of the detector after braking, and K is more than 0, so that the derivative of the potential function on time can be ensured to be negative after the braking. Knowing that the potential function is positive, the velocity direction determined in equation (25) ensures that the detector position eventually converges to the desired end state, i.e., the predetermined target collision point, in accordance with the lispro's steady state theorem.
Step 5: with the residual time t after the detector is braked go Potential field value phi at the final target point f And 3, determining the magnitude K of the pulse maneuvering speed of the detector after the braking by using the correction potential function established in the step 3 to obtain braking speed pulses required by the track correction of the detector, and performing weak attraction small celestial body surface bouncing track correction control by the detector through the braking speed pulses to improve the moving position accuracy of the detector.
After the detector passes the braking, the residual time t is passed under the action of uncontrolled force go Potential field value phi at the final target point f At least as a performance index, i.e
Determining the magnitude K of the pulse maneuvering speed of the detector after the braking, wherein the residual time t go Is the time it takes for the detector to complete the entire bouncing process from the current state.
The state of the detector after braking is
Then from phi f Minimum requirement
Combining the linearization model (5) to obtain a unique solution of K
In which a is i For braking time t s The expression of which is as follows:
if i=1, 2,3
If i=4, 5,6
Due to
The K value given by equation (31) is such that the potential field value phi at the collision point is given f The minimum post-braking detector pulse maneuver speed magnitude. The desired braking speed pulse is determined by equation (25)Is that
And the detector corrects and controls the surface bounce track of the weak attraction celestial body through the braking speed pulse Deltav, so that the moving position precision of the detector is improved.
The beneficial effects are that:
1. aiming at the existing small celestial body surface bouncing movement track correction method, the pulse speed maneuver and the obstacle treatment are not considered when the position error is large in the bouncing process, and only the correction of the tiny position deviation can be carried out. According to the method for controlling the surface bounce trajectory correction of the weak-attraction small celestial body, disclosed by the invention, the artificial potential function guidance method is introduced into the control for the surface bounce trajectory correction of the weak-attraction small celestial body, the pulse speed maneuver and the obstacle treatment are considered when the position error is large in the bounce process, the small celestial body surface bounce trajectory correction can be realized in a pulse maneuver mode, and the trajectory correction efficiency is improved.
2. The invention discloses a method for controlling the surface bounce track of a weak attraction small celestial body, which comprises the steps that when track deviation is larger due to speed error after taking off, a detector corrects the track in a pulse maneuver mode, a correction potential function is obtained by superposing an obstacle potential function with a high potential field value and a power potential function, pulse maneuver speed is obtained through the correction potential function, and the detector carries out the surface bounce track correction control of the weak attraction small celestial body through the braking speed pulse, so that the moving position precision of the detector is improved.
3. The invention discloses a method for controlling the correction of the surface bounce track of a weak attraction small celestial body, which uses a repulsive force potential function with a high potential field value to represent a spherical obstacle in the range of the nominal track of a detector, corrects the repulsive force potential function to enable the spherical obstacle to meet the Lyapunov stability condition, further enables the repulsive force potential function to converge at a collision point, and enables a correction potential function obtained by superposing the repulsive force potential function and the corrected repulsive force potential function to converge at the collision point, thereby improving the correction control precision of the surface bounce track of the weak attraction small celestial body.
Drawings
FIG. 1 is a schematic flow chart of a method for controlling the modification of the bouncing track of the surface of a weak attraction celestial body;
FIG. 2 is a schematic diagram of a nominal trajectory, an actual trajectory, and a corrected trajectory of a detector bouncing process in accordance with an embodiment of the present invention;
fig. 3 is a schematic diagram of the distribution of the actual track error and the corrected track error obtained by performing the monte carlo simulation 300 times in the example of the present invention.
Detailed Description
For a better description of the objects and advantages of the present invention, the following description will be given with reference to the accompanying drawings and examples.
As shown in fig. 1, the method for controlling the modification of the surface bounce trajectory of the weak attraction celestial body disclosed in the embodiment specifically includes the following implementation steps:
step 1: and respectively establishing a dynamic equation under the celestial body fixed connection coordinate system and the surface coordinate system, and obtaining an actual bouncing track dynamic equation of the detector containing unknown interference by considering external interference factors received by the detector in the tripping process.
The minor planet is constructed by adopting a triaxial ellipsoidal model, and the spin angular velocity of the minor planet is 1.407 multiplied by 10 -4 rad/s, the accuracy of determination of the gravitational coefficient is 0.0015×10 5 m 3 /s 2 The uncertainty of 5% exists in each order coefficient of the gravitation bit function, and the speed error of each external influence is expressed by a normally distributed random number. Establishing a surface coordinate system by taking the initial jump position of the detector as an origin, wherein the initial jump position is r 0 ＝[0,0,0] T m, initial take-off speed v 0 ＝[2,3,2] T m/s, the predicted time for one jump motion is 40s, the ideal gravitational acceleration of the celestial body is g=0.1 m/s 2 . The initial conditions are taken into an error-free kinetic equation (36) to determine the position of the target point of the detector as r t ＝[80,120,0] T m。
Various uncertainties exist in the dynamic model of the detector, wherein the uncertainties form factors comprising model parameter errors, unknown high-order gravitational field models and unmodeled perturbation forces, and the dynamic changes caused by the uncertainties form factors are attributed to model-free acceleration.
Order theThe actual collision position of the detector obtained by integrating the dynamics equation with the initial state value is r n ＝[78.2417,106.6747,0] T m。
Wherein n is i (i=r, v) is an unknown interference amount.
Step 2: and carrying out linearization solution on a dynamic equation under the celestial body surface coordinate system to obtain the relationship between the braking time and the braking speed.
Selecting the position and speed of the detector in the asteroid surface coordinate system as state variables, namely
In the initial state X 0 ＝[0,0,0,2,3,2] T The dynamics equation (36) is linearized to obtain a linearization equation of the bouncing motion of the detector
Wherein the method comprises the steps of
And->Respectively the gravitation bit function is in the initial state X 0 The first derivative and the second derivative of the position r.
The linearization system (39) of the bouncing motion of the detector is a linear steady system, the solution of which is
Since u is a constant matrix and the matrixIs reversible, thus
The solution of the system is expressed as
X(t)＝e (A+δ)t X 0 +(A+δ) -1 [e (A+δ)t -I 6×6 ]u (46)
When the error value of the actual track and the reference track of the detector is larger than the allowable maximum error, namely Deltar= |r-r e ||≥r max When the engine is ignited, the detector is startedBrake control, where r max =3.5m, thruster braking time t s =3.5 s, detector speed before braking v - ＝[2.1638,2.9501,0.4436] T m/s. The detector state transition matrix is
Constant vector is
The required speed pulse is
Δv＝v + -v - (49)
Namely, the relationship between the braking time and the braking speed established by the equations (46) (47) (48) (49).
Step 3: establishing a potential function of the force of the detector relative to the position of the collision point; while spherical obstructions within the nominal trajectory of the detector are represented by repulsive potential functions having high potential field values. And correcting the repulsive force potential function to enable the repulsive force potential function to meet the Lyapunov stability condition, so that the repulsive force potential function is converged at the collision point. And superposing the attraction potential function and the corrected repulsion potential function to obtain a corrected potential function.
Selecting the potential function of the attraction force as
Wherein,
r l for the position of the detector relative to the collision point in the asteroid surface coordinate system, the position r of the detector in the asteroid surface coordinate system is expressed as
r l ＝r-r t (52)
Wherein r is t Is the location of the collision point in the celestial surface coordinate system. The defined potential function of the force is a function of the detector position and is positive if and only if at r=r t I.e. the detector reaches the collision point, the force potential function is zero.
The matrix M determines the direction of the detector jumping to the landing point, and in order to ensure that the closer to the point of the detector braking point and the connecting line of the target point, the lower the potential field value is, the parameters are selected as
k x ＝k y ＝k＞1, k＝2 (53)
Introducing a region with a higher potential function to represent a limiting condition of a motion path, wherein spherical obstacles exist on the bouncing path of the detector, the gradient value of the region with the higher potential function represents the repulsive force applied to the detector to avoid the obstacles, and selecting the repulsive force potential function in the form of a Gaussian function as
Wherein r is o Is the position vector lambda of the sphere center of the obstacle in the small celestial body surface coordinate system 1 ＝1000,λ 2 =900 is the high and wide of the repulsive force potential. Consider when r=r t When formula (54) is not zero, the lyapunov stability condition is not satisfied. In order to converge the potential function after the repulsive potential is added at the collision point, equation (54) is modified to
Wherein the method comprises the steps of
The modified potential function is
Step 4: and (3) substituting the judgment condition of the maneuvering position of the detector and the expected speed after braking into the correction potential function in the step (3) to obtain the magnitude of the pulse maneuvering speed after braking.
When the error value of the actual track and the reference track of the detector is larger than the allowable maximum error, namely Deltar= |r-r e ||≥r max When the engine is ignited, the detector is braked, and the expected speed after braking is selected as
The first derivative of equation (58) with respect to time is
Bringing formula (59) into formula (60) to obtain
K is the magnitude of the pulse maneuvering speed of the detector after braking, and K is more than 0, so that the derivative of the potential function on time can be ensured to be negative after the braking. Knowing that the potential function is positive, the velocity direction determined in equation (59) ensures that the detector position eventually converges to the desired end state, i.e., the predetermined target collision point, in accordance with the lispro's steady state theorem.
Step 5: with the residual time t after the detector is braked go Potential field value phi at the final target point f The minimum is the performance index, and the current braking postdetection is determined through the correction potential function established in the step 3The magnitude K of the pulse maneuvering speed of the detector is measured, so that braking speed pulses required by the detector for track correction are obtained, and the detector performs weak attraction small celestial body surface bouncing track correction control through the braking speed pulses, so that the moving position accuracy of the detector is improved.
After the detector passes the braking, the residual time t is passed under the action of uncontrolled force go Potential field value phi at the final target point f At least as a performance index, i.e
Determining the expected speed K of the detector after the braking, wherein the residual time t go Is the time it takes for the detector to complete the entire bouncing process from the current state.
The state of the detector after braking is
Then from phi f Minimum requirement
By combining the linearization model (39), a unique solution of K can be obtained
In which a is i For braking time t s The expression of which is as follows:
if i=1, 2,3
If i=4, 5,6
/>
Due to
The K value given by equation (65) is such that the potential field value phi at the collision point is given f The minimum post-braking detector pulse maneuver speed magnitude. The desired braking speed pulse can be determined to be by equation (59)
Substituting the data to obtain Deltav= [1.8725,3.4351, -1.0348 ]] T m/s, braking time t= 13.6441s, remaining time t go 22.5154s, the braking position is r= [29.5231,40.2517,15.3601 ]] T m, the final collision point of the corrected track is r s ＝[80.3195,120.6092,0] T m. As shown in FIG. 2, by using the method for controlling the surface bounce trajectory correction of the weak-attraction celestial body disclosed by the invention, when a larger trajectory deviation occurs in the bouncing process of the detector, the maneuvering of the speed pulse can be completed rapidly, and the position accuracy of the bouncing movement of the detector is further improved.
As shown in fig. 3, 300 Monte Carlo simulations show that the method disclosed by the invention can well correct the error interference track of the detector in the take-off process, so that the detector is optimized near the target position at the collision position with larger original error.
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 (1)

1. The method for controlling the correction of the surface bounce track of the weak attraction small celestial body is characterized by comprising the following steps: comprises the following steps of the method,
step 1: respectively establishing a dynamic equation under a celestial body fixed connection coordinate system and a surface coordinate system, and taking external interference factors received by the detector in the take-off process into consideration to obtain an actual bouncing track dynamic equation of the detector containing unknown interference;
the implementation method of the step 1 is that,
aiming at the problem of single bouncing movement of the detector, under the small celestial body fixedly connected coordinate system, the dynamic equation of the detector after taking off is expressed as
Wherein r is B 、v B The position and velocity vectors of the detector, ω is the angular spin velocity of the celestial body, a B For other accelerations not taking into account the perturbation force, V is a gravitational potential function;
under the surface coordinate system, the dynamic equation of the detector is that
Wherein r and v are the position and speed vectors of the detector, ρ is the position vector of the center of the small celestial body relative to the origin of the surface coordinate system, u B For the thrust vector of the detector body coordinate system,a is a matrix converted from a body coordinate system to a surface coordinate system, and a is other acceleration without taking the perturbation power into consideration;
taking various uncertainties of a dynamic model of the detector into consideration, wherein uncertainty forming factors comprise model parameter errors, an unknown high-order gravitational field model and unmodeled perturbation force, and dynamic changes caused by the uncertainty forming factors are attributed to model-free acceleration;
order theIntegrating the kinetic equation
Wherein n is i (i=r, v) is an unknown interference amount;
step 2: carrying out linearization solution on a dynamic equation under a celestial body surface coordinate system to obtain a relationship between braking time and braking speed;
the implementation method of the step 2 is that,
selecting the position and speed of the detector under the surface coordinate system of the celestial body as state variables, namely
In the initial state X 0 Linearizing the dynamics equation (1) to obtain a linearization equation of the bouncing motion of the detector
Wherein the method comprises the steps of
And->Respectively the gravitation bit function is in the initial state X 0 A first derivative and a second derivative of the position r;
the linearization system (5) of the bouncing motion of the detector is a linear steady system, and the solution of the system is
Since u is a constant matrix and the matrixIs reversible, thus
The solution of the system is expressed as
The braking time of the thruster is t s The detector speed before braking is v - The detector speed after braking is v + The detector state transition matrix is
Constant vector is
The required speed pulse is
Δv＝v + -v - (15)
Namely, the relationship between the braking time and the braking speed established by the formulas (12), (13), (14) and (15);
step 3: establishing a potential function of the force of the detector relative to the position of the collision point; meanwhile, a repulsive force potential function with a high potential field value is used for representing the spherical obstacle in the range of the nominal track of the detector; the repulsive force potential function is corrected to meet the Lyapunov stability condition, so that the repulsive force potential function is converged at the collision point; superposing the attraction potential function and the corrected repulsion potential function to obtain a corrected potential function;
the implementation method of the step 3 is that,
selecting the potential function of the attraction force as
Wherein,
r l for the position of the detector relative to the collision point in the small celestial surface coordinate system, the position r of the detector in the small celestial surface coordinate system is expressed as
r l ＝r-r t (18)
Wherein r is t Is the collision point in the surface coordinate system of the small celestial bodyA location; the defined potential function of the force is a function of the detector position and is positive if and only if at r=r t I.e. when the detector reaches the collision point, the potential function of the force is zero;
the matrix M determines the direction of the detector jumping to the landing point, and in order to ensure that the closer to the point of the detector braking point and the connecting line of the target point, the lower the potential field value is, the parameters are selected as
k x ＝k y ＝k＞1 (19)
Introducing a limiting condition that a region with a high potential function represents a motion path, wherein spherical obstacles exist on the bouncing path of the detector, gradient values of the region with the high potential function represent the repulsive force applied to the detector for avoiding the obstacles, and selecting a repulsive force potential function in a Gaussian function form as the repulsive force potential function
Wherein r is o Is the position vector lambda of the sphere center of the obstacle in the small celestial body surface coordinate system 1 、λ 2 The height and width of the repulsive force potential; consider when r=r t When the formula (20) is not zero, the lyapunov stability condition is not satisfied; in order to converge the potential function after the repulsive potential is added at the collision point, equation (20) is modified to
Wherein the method comprises the steps of
p x ＞1,p y ＞1,p z ＞1 (23)
The modified potential function is
Step 4: substituting the judging conditions of the maneuvering positions of the detectors and the expected speed after braking into the correction potential function in the step 3 to obtain the pulse maneuvering speed after braking;
the implementation method of the step 4 is that,
when the error value of the actual track and the reference track of the detector is larger than the allowable maximum error, namely Deltar= |r-r e ||≥r max When the engine is ignited, the detector is braked, and the expected speed after braking is selected as
The first derivative of equation (24) with respect to time is
Bringing formula (25) into formula (26) to obtain
K is the pulse maneuvering speed of the detector after braking, and K is more than 0, so that the derivative of the potential function on time after the braking is ensured to be negative; knowing that the potential function is positive, the velocity direction determined in equation (25) ensures that the detector position eventually converges to the desired end state, i.e., the predetermined target collision point, in accordance with the lispro stability theorem;
step 5: with the residual time t after the detector is braked go Potential field value phi at the final target point f The minimum is the performance index, and the magnitude K of the pulse maneuvering speed of the detector after the braking is determined through the correction potential function established in the step 3, therebyThe method comprises the steps that braking speed pulses required by the detector for track correction are obtained, and the detector carries out weak-attraction celestial body surface bouncing track correction control through the braking speed pulses, so that the moving position accuracy of the detector is improved;
the implementation method of the step 5 is that,
after the detector passes the braking, the residual time t is passed under the action of uncontrolled force go Potential field value phi at the final target point f At least as a performance index, i.e
Determining the magnitude K of the pulse maneuvering speed of the detector after the braking, wherein the residual time t go The time it takes for the detector to complete the entire bouncing process from the current state;
the state of the detector after braking is
Then from phi f Minimum requirement
Combining with linearization system (5) to obtain unique solution of K
In which a is i For braking time t s The expression of which is as follows:
if i=1, 2,3
If i=4, 5,6
Due to
The K value given by equation (31) is such that the potential field value phi at the collision point is given f The minimum post-braking detector pulse maneuver speed magnitude; then the desired braking speed pulse is determined to be by equation (25)
And the detector corrects and controls the surface bounce track of the weak attraction celestial body through the braking speed pulse Deltav, so that the moving position precision of the detector is improved.
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Publication number Priority date Publication date Assignee Title
JP2001322600A (en) * 2000-05-16 2001-11-20 Sumitomo Heavy Ind Ltd Planet probe
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CN112269390A (en) * 2020-10-15 2021-01-26 北京理工大学 Small celestial body surface fixed-point attachment trajectory planning method considering bounce
CN112896560A (en) * 2021-01-25 2021-06-04 北京理工大学 Small celestial body surface safe bounce movement track planning method
CN112947533A (en) * 2021-04-14 2021-06-11 北京理工大学 Complex small celestial body surface movement sequence trajectory planning method

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP2001322600A (en) * 2000-05-16 2001-11-20 Sumitomo Heavy Ind Ltd Planet probe
CN111361760A (en) * 2020-01-13 2020-07-03 北京理工大学 Small celestial body surface movement track tolerance optimization method
CN112269390A (en) * 2020-10-15 2021-01-26 北京理工大学 Small celestial body surface fixed-point attachment trajectory planning method considering bounce
CN112896560A (en) * 2021-01-25 2021-06-04 北京理工大学 Small celestial body surface safe bounce movement track planning method
CN112947533A (en) * 2021-04-14 2021-06-11 北京理工大学 Complex small celestial body surface movement sequence trajectory planning method

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