CN113741193A - Weak-gravity small celestial body surface bounce track correction control method - Google Patents

Weak-gravity small celestial body surface bounce track correction control method Download PDF

Info

Publication number
CN113741193A
CN113741193A CN202111038247.9A CN202111038247A CN113741193A CN 113741193 A CN113741193 A CN 113741193A CN 202111038247 A CN202111038247 A CN 202111038247A CN 113741193 A CN113741193 A CN 113741193A
Authority
CN
China
Prior art keywords
detector
potential function
braking
small celestial
celestial body
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111038247.9A
Other languages
Chinese (zh)
Other versions
CN113741193B (en
Inventor
朱圣英
杨哲
崔平远
徐瑞
梁子璇
葛丹桐
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN202111038247.9A priority Critical patent/CN113741193B/en
Publication of CN113741193A publication Critical patent/CN113741193A/en
Application granted granted Critical
Publication of CN113741193B publication Critical patent/CN113741193B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • 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
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—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
    • 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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G1/00—Cosmonautic vehicles
    • B64G1/16—Extraterrestrial cars
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B64—AIRCRAFT; AVIATION; COSMONAUTICS
    • B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
    • B64G4/00—Tools specially adapted for use in space
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

Landscapes

  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Software Systems (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Health & Medical Sciences (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Artificial Intelligence (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

The invention discloses a control method for correcting a bounce trajectory of a small celestial body surface under weak gravity, relates to a control method for correcting a detector trajectory through potential function guidance in the bounce movement process of the small celestial body surface under weak gravity, and belongs to the field of deep space detection. Aiming at the existing correction method of the bouncing movement track of the surface of the small celestial body, the pulse speed maneuver and the obstacle processing are not considered when the position error is large in the bouncing process, and only the correction of the small position deviation can be carried out. The implementation method of the invention comprises the following steps: when the detector causes large track deviation due to speed errors after take-off, the track is corrected in a pulse motor-driven mode, a correction repulsive force potential function representing an obstacle is introduced and is superposed with a gravitational force potential function to obtain a correction potential function, the pulse motor-driven speed is obtained through the correction potential function, and the detector performs weak-gravity small celestial body surface bounce track correction control through the braking speed pulse, so that the position accuracy of the movement of the detector is improved.

Description

Weak-gravity small celestial body surface bounce 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 movement of the surface of a small celestial body with weak gravity, belonging to the field of deep space detection.
Background
After lunar and planet exploration, the detection of asteroid landing gradually becomes the hot field of deep space exploration. Currently, there are three main schemes for detecting small planets: observation research is carried out through a ground observation station, the transmitting detector carries out close-range surrounding flight detection or flying observation on the asteroid, and the transmitting detector carries out landing detection on the surface of the asteroid. With the advancement of technology, the task of asteroid detection with soft landing on the surface and return sampling is becoming the main way to detect asteroids. Different from the surface environment of a planet, the gravity of a small planet is tiny, the surface environment is complex and changeable, the walking and the control of the traditional wheel type planet detector on the surface of the small planet become extremely difficult, and a surface moving mode which is internationally recognized at present is bouncing movement. While bouncing movement has the advantage of being able to pass over obstacles and achieve long-distance movement in a short time, small initial state deviations of bouncing may cause large positional deviations of the movement end point. Therefore, there is a need to develop methods for trajectory modification during probe bounce to achieve precise control of probe 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 movement model aiming at the Small celestial body Surface bounce movement problem in the prior art [1] (see Bellerose J, Scheers D J.Dynamics and Control for Surface expansion of Small celestial Bodies [ C ]. AIAA/AAS 2008 dynamics concrete Conference, Honolulu, Hawaii, aug.18-21,2008: AIAA 2008-.
In the prior art [2] (see Shen H, Zhang T, Li Z, Li H. multiple-bearing objectives Near a Rotating optical [ J ]. interactions and Space Science,2017,362:45.) a particle swarm optimization algorithm is applied to research the track optimization problem of the movement of the bounce detector on the surface of a small celestial body, although the method adopts an accurate kinetic model, the thrust design based on the optimization method is an open-loop idea and is greatly influenced by external interference and uncertain kinetic characteristics.
In the prior art [3] (see Liu Yanjie, small celestial body attachment detection track optimization and guidance method research [ D ]. Beijing university of science and technology, 2017.), tracking of a first-order sliding mode surface is realized by designing a second-order sliding mode surface, an analytic expression of guidance acceleration is deduced by using the second-order sliding mode surface, and accurate transfer of single bounce of a detector is realized by using the obtained guidance acceleration. However, this method does not mention a method of processing an obstacle, and needs to correct a trajectory using a plurality of pulses, and cannot cope with a trajectory correction case with a large error.
Disclosure of Invention
Aiming at the existing correction method of the bouncing movement track of the surface of the small celestial body, the pulse speed maneuver and the obstacle processing are not considered when the position error is large in the bouncing process, and only the correction of the small position deviation can be carried out. The invention discloses a correction control method for the surface bounce track of a small celestial body with weak gravity, which mainly solves the following problems: when the detector causes large track deviation due to speed errors after take-off, the track is corrected in a pulse motor-driven mode, a correction repulsive force potential function representing an obstacle is introduced and is superposed with a gravitational force potential function to obtain a correction potential function, the pulse motor-driven speed is obtained through the correction potential function, and the detector performs weak-gravity small celestial body surface bounce track correction control through the braking speed pulse, so that the position accuracy of the movement of the detector is improved.
The invention is realized by the following technical scheme.
The invention discloses a weak-gravitation small celestial body surface bounce trajectory correction control method, aiming at the problem of single bounce movement of a detector, and respectively establishing a dynamic equation of the detector after bouncing under a small celestial body fixed connection coordinate system and a small celestial body surface coordinate system. And (4) taking external interference factors received by the detector in the take-off process into consideration to obtain an actual bounce track kinetic equation of the detector containing unknown interference. And obtaining a nominal track through the non-interference dynamic model, giving a maximum position deviation allowed in a track error range, and judging whether the detector needs track correction or not according to a position difference value between an actual motion track and a reference track of the detector at the same moment. And when the detector needs to correct the track, planning the path by using an artificial potential function guidance method. Establishing a potential function relative to the position of the detector relative to a collision point, representing the spherical obstacle in the nominal track range of the detector by using a repulsive 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, and the potential field value is ensured to be gradually reduced in the process from the detector to the collision point. The relation between the pulse maneuvering speed and the potential function of the braked detector is obtained by deriving the potential function, the braked pulse maneuvering speed and the position of the braking moment are used as the initial state of the detector after braking, the minimum potential field value which finally reaches the collision point after the residual time is used as a performance index to design a guidance method, and therefore the bounce correction track of the detector on the surface of the weak-gravity small celestial body is obtained, and the position accuracy of movement is improved.
The invention discloses a method for correcting and controlling the bounce track of the surface of a small celestial body with weak gravity, which comprises the following steps:
step 1: and respectively establishing a kinetic equation under a small celestial body fixed connection coordinate system and a surface coordinate system, and considering external interference factors received by the detector in the take-off process to obtain an actual bounce track kinetic equation of the detector containing unknown interference.
Aiming at the problem of single bounce movement of the detector, under the condition that the small celestial body is fixedly connected with a coordinate system, the kinetic equation of the detector after jumping is expressed as
Figure BDA0003248159100000031
Wherein r isB、vBPosition and velocity vectors of the detector, omega is the spin angular velocity of the small celestial body, aBV is a gravitational potential function for other accelerations not taking into account perturbation forces.
In the surface coordinate system, the kinetic equation of the detector is
Figure BDA0003248159100000032
Wherein r and v are respectively the position and velocity vector of the detector, rho is the position vector of the origin of the surface coordinate system relative to the center of the small celestial body, and u is the position vector of the origin of the surface coordinate system relative to the center of the small celestial bodyBThe thrust vector of the coordinate system of the detector body,
Figure BDA0003248159100000036
for the matrix transformed from the body coordinate system to the surface coordinate system, a is the acceleration of the other not considered perturbation forces.
Considering that various uncertainties exist in a dynamic model of the detector, the 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 to
Figure BDA0003248159100000033
Integral the kinetic equation to
Figure BDA0003248159100000034
Wherein n isiAnd (i-r, v) is an unknown interference quantity.
Step 2: and (4) carrying out linear solution on a kinetic equation under the small celestial body surface coordinate system to obtain the relation between the braking time and the braking speed.
Selecting the position and the speed of the detector under the surface coordinate system of the small celestial body as state variables, namely
Figure BDA0003248159100000035
In an initial state X0Linearizing the dynamic equation (1) to obtain a linearized equation of the detector bouncing motion
Figure BDA0003248159100000041
Figure BDA0003248159100000042
Wherein
Figure BDA0003248159100000043
Figure BDA0003248159100000044
Figure BDA0003248159100000045
Figure BDA0003248159100000046
And
Figure BDA0003248159100000047
respectively as a function of gravitational potential in an initial state X0The first and second derivatives of the position r.
The linear system (5) of the detector bounce motion is a linear steady system, and the solution of the system is
Figure BDA0003248159100000048
Since u is a constant matrix and the matrix
Figure BDA0003248159100000049
Is reversible, therefore
Figure BDA00032481591000000410
The solution of the system is expressed as
X(t)＝e(A+δ)tX0+(A+δ)-1[e(A+δ)t-I6×6]u (12)
The brake time of the thruster is tsThe probe speed before braking is v-After braking probe speed is v+Detector state transition matrix of
Figure BDA00032481591000000411
Constant value vector is
Figure BDA00032481591000000412
The required velocity 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).
And step 3: establishing a gravitational potential function with respect to the location of the detector relative to the collision point; meanwhile, a repulsive force function with a high potential field value is used for representing the spherical obstacle in the range of the nominal track of the detector. And correcting the repulsive force potential function to enable the repulsive force potential function to meet the Lyapunov stability condition, and further enabling the repulsive force potential function to be converged at the collision point. And superposing the gravitational potential function and the corrected repulsive potential function to obtain a corrected potential function.
Selecting a gravitational potential function of
Figure BDA0003248159100000051
Wherein the content of the first and second substances,
Figure BDA0003248159100000052
rlthe position r of the detector in the coordinate system of the small celestial body surface is expressed as
rl＝r-rt (18)
Wherein r istThe position of the collision point in the coordinate system of the surface of the small celestial body. The gravitational potential function is defined as a function of the detector position and is positive, if and only if r ═ rtI.e. the detector reaches the collision point, the gravitational 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 points which are the same distance from the collision point are closer to the connecting line of the braking point and the target point of the detector, the potential field value is lower, and the selected parameter is
kx＝ky＝k＞1 (19)
Introducing a region with a high potential function to represent the limiting condition of a motion path, wherein a spherical obstacle exists on a bounce path of the detector, the gradient value of the high value potential function region represents the magnitude of a repulsive force applied to the detector to avoid the obstacle, and the repulsive potential function in the form of a Gaussian function is selected as
Figure BDA0003248159100000053
Wherein r isoIs a position vector of the spherical center of the cataract obstacle in a coordinate system of the surface of the small celestial body, lambda1、λ2The height and width of the repulsive force. Consider when r ═ rtWhen the value is not zero, the formula (20) does not satisfy the Lyapunov stability condition. In order to make the potential function after the repulsive potential energy is added converge at the collision point, equation (20) is modified to
Figure BDA0003248159100000061
Wherein
Figure BDA0003248159100000062
px＞1,py＞1,pz＞1 (23)
The modified potential function is
Figure BDA0003248159100000063
And 4, 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 maneuvering speed of the pulse 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 delta r | | r-re||≥rmaxWhen the engine is ignited, the detector is subjected to brake control, and the expected speed after braking is selected as
Figure BDA0003248159100000064
The first derivative of equation (24) with respect to time is
Figure BDA0003248159100000065
Bringing formula (25) into formula (26) to obtain
Figure BDA0003248159100000066
K is the magnitude of the maneuvering speed of the detector pulse after braking, and K is more than 0, so that the derivative of the potential function to time after the braking is negative and definite can be ensured. Given that the potential function is positive, the velocity direction determined in equation (25) ensures that the probe position eventually converges to the desired end state, i.e., the predetermined target collision point, according to the Lyapunov theorem of stability.
And 5: the remaining time t after the braking of the detectorgoThe potential field value phi at the finally reached target pointfAnd (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) as the minimum performance index, further obtaining a braking speed pulse required by the detector for track correction, and performing the track correction control of the bounce of the surface of the small celestial body with weak gravity by using the braking speed pulse by using the detector, thereby improving the position accuracy of the movement of the detector.
After the detector passes the brake, the remaining time t passes under the action of the uncontrolled forcegoThe potential field value phi at the finally reached target pointfMinimum is a performance index, i.e.
Figure BDA0003248159100000071
Determining the magnitude K of the pulse motor-driven speed of the detector after the brake, wherein the residual time tgoIs the time it takes for the detector to complete the entire bounce process from the current state.
The detector state after braking is
Figure BDA0003248159100000072
Then by phifMinimum requirements
Figure BDA0003248159100000073
Combining the linearized model (5) to find the unique solution of K
Figure BDA0003248159100000074
In the formula aiFor a braking time tsA function of, a table ofThe expression is as follows:
if i is 1,2,3
Figure BDA0003248159100000075
If i is 4,5,6
Figure BDA0003248159100000076
Due to the fact that
Figure BDA0003248159100000077
The K value given by equation (31) is therefore such that the potential field value φ at the point of impact is given under given conditionsfMinimum post-braking detector pulse maneuver speed magnitude. The required braking speed pulse is determined by equation (25) as
Figure BDA0003248159100000078
And the detector performs the correction control on the bounce track of the surface of the small celestial body with weak gravity through the braking speed pulse delta v, so that the moving position precision of the detector is improved.
Has the advantages that:
1. aiming at the existing correction method of the bouncing movement track of the surface of the small celestial body, the pulse speed maneuver and the obstacle processing are not considered when the position error is large in the bouncing process, and only the correction of the small position deviation can be carried out. The invention discloses a correction control method for the surface bounce trajectory of a small celestial body with weak gravity, which introduces an artificial potential function guidance method into correction control for the surface bounce trajectory of the small celestial body with weak gravity, considers pulse speed maneuver and treatment of obstacles when the position error is large in the bounce process, can realize the correction of the surface bounce trajectory of the small celestial body in a pulse maneuver mode, and improves the trajectory correction efficiency.
2. The invention discloses a correction control method for the surface bounce trajectory of a weak-gravity small celestial body, which is characterized in that when a detector has larger trajectory deviation caused by speed error after takeoff, the trajectory is corrected in a pulse maneuvering mode, a correction potential function is obtained by introducing an obstacle potential function with a high potential field value and superposing the obstacle potential function with the gravity potential function, the pulse maneuvering speed is obtained through the correction potential function, and the detector performs correction control on the surface bounce trajectory of the weak-gravity small celestial body through braking speed pulses, so that the moving position precision of the detector is improved.
3. The invention discloses a correction control method for a bounce track of a small celestial body surface with weak attraction, which is characterized in that a repulsive force potential function with a high potential field value is used for representing a spherical obstacle in a nominal track range of a detector, the repulsive force potential function is corrected to meet the Lyapunov stability condition, so that the repulsive force potential function is converged at a collision point, a corrected potential function obtained by superposing a gravitational force potential function and the corrected repulsive force potential function is converged at the collision point, and the correction control precision of the bounce track of the small celestial body surface with weak attraction is improved.
Drawings
FIG. 1 is a schematic flow chart of a method for correcting and controlling the bounce trajectory of the surface of a small celestial body with weak gravity according to the present invention;
FIG. 2 is a schematic illustration of a nominal, actual and modified trajectory of a detector bounce process in an example of the invention;
FIG. 3 is a schematic diagram of the distribution of actual trajectory errors and corrected trajectory errors obtained from 300 Monte Carlo simulations performed in an example of the present invention.
Detailed Description
For a better understanding of the objects and advantages of the present invention, reference should be made to the following detailed description taken in conjunction with the accompanying drawings and examples.
As shown in fig. 1, the method for correcting and controlling the bounce trajectory of the small celestial body surface with weak gravity disclosed in this embodiment includes the following specific steps:
step 1: and respectively establishing a kinetic equation under a small celestial body fixed connection coordinate system and a surface coordinate system, and considering external interference factors received by the detector in the take-off process to obtain an actual bounce track kinetic equation of the detector containing unknown interference.
The asteroid is constructed by adopting a triaxial ellipsoid model, and the spin angular velocity of the asteroid is 1.407 multiplied by 10-4rad/s, the precision of the determination of the gravitational coefficient is 0.0015X 105m3/s2And 5% of uncertainty exists in each order coefficient of the gravitational potential function, and the speed error of each external influence is represented by a normally distributed random number. Establishing a surface coordinate system by taking the initial jump starting position of the detector as an origin, wherein the initial jump starting position is r0＝[0,0,0]Tm, initial take-off speed v0＝[2,3,2]Tm/s, the predicted time of one jump motion is 40s, and the ideal gravitational acceleration of the small celestial body is g which is 0.1m/s2. The initial condition is brought into a dynamic equation (36) without error, and the target point position r of the detector is obtainedt＝[80,120,0]Tm。
Figure BDA0003248159100000091
Considering that various uncertainties exist in a dynamic model of the detector, the 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 to
Figure BDA0003248159100000092
The equation (37) is substituted into the initial state value to integrate the kinetic equation to obtain the actual collision position r of the detectorn＝[78.2417,106.6747,0]Tm。
Figure BDA0003248159100000093
Wherein n isiAnd (i-r, v) is an unknown interference quantity.
Step 2: and (4) carrying out linear solution on a kinetic equation under the small celestial body surface coordinate system to obtain the relation between the braking time and the braking speed.
Selecting the position and the speed of the detector under the surface coordinate system of the minor planet as state variables, namely
Figure BDA0003248159100000094
In an initial state X0＝[0,0,0,2,3,2]TLinearizing the dynamic equation (36) to obtain the linearized equation of the detector bounce motion
Figure BDA0003248159100000101
Figure BDA0003248159100000102
Wherein
Figure BDA0003248159100000103
Figure BDA0003248159100000104
Figure BDA0003248159100000105
Figure BDA0003248159100000106
And
Figure BDA0003248159100000107
respectively as a function of gravitational potential in an initial state X0The first and second derivatives of the position r.
The linear system (39) for the detector bouncing movement is a linear steady system, the solution of which is
Figure BDA0003248159100000108
Since u is a constant matrix and the matrix
Figure BDA0003248159100000109
Is reversible, therefore
Figure BDA00032481591000001010
The solution of the system is expressed as
X(t)＝e(A+δ)tX0+(A+δ)-1[e(A+δ)t-I6×6]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 delta r | | r-re||≥rmaxThe engine is ignited to brake and control the detector, wherein rmax3.5m, the brake time of the thruster is tsAt 3.5s, the probe speed before braking is v-＝[2.1638,2.9501,0.4436]Tm/s. The detector state transition matrix is
Figure BDA00032481591000001011
Constant value vector is
Figure BDA0003248159100000111
The required velocity pulse is
Δv＝v+-v- (49)
I.e. the relationship between the braking time and the braking speed established by the equations (46) (47) (48) (49).
And step 3: establishing a gravitational potential function with respect to the location of the detector relative to the collision point; meanwhile, a repulsive force function with a high potential field value is used for representing the spherical obstacle in the range of the nominal track of the detector. And correcting the repulsive force potential function to enable the repulsive force potential function to meet the Lyapunov stability condition, and further enabling the repulsive force potential function to be converged at the collision point. And superposing the gravitational potential function and the corrected repulsive potential function to obtain a corrected potential function.
Selecting a gravitational potential function of
Figure BDA0003248159100000112
Wherein the content of the first and second substances,
Figure BDA0003248159100000113
rlthe position of the detector relative to the collision point in the minor planet surface coordinate system is represented by the position r of the detector in the minor planet surface coordinate system
rl＝r-rt (52)
Wherein r istThe position of the collision point in the coordinate system of the surface of the small celestial body. The gravitational potential function is defined as a function of the detector position and is positive, if and only if r ═ rtI.e. the detector reaches the collision point, the gravitational 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 points which are the same distance from the collision point are closer to the connecting line of the braking point and the target point of the detector, the potential field value is lower, and the selected parameter is
kx＝ky＝k＞1, k＝2 (53)
Introducing a region with a higher potential function to represent the limiting condition of a motion path, wherein a spherical obstacle exists on a bounce path of the detector, the gradient value of the high-value potential function region represents the magnitude of a repulsive force applied to the detector to avoid the obstacle, and the repulsive potential function in the form of a Gaussian function is selected as
Figure BDA0003248159100000114
Wherein r isoIs a position vector of the spherical center of the cataract obstacle in a coordinate system of the surface of the small celestial body, lambda1＝1000,λ2900 is the height and width of the repulsive potential. Consider when r ═ rtWhen the value is not zero, the formula (54) does not satisfy the Lyapunov stability condition. In order to make the potential function after the repulsive potential energy is added converge at the collision point, equation (54) is corrected to
Figure BDA0003248159100000121
Wherein
Figure BDA0003248159100000122
Figure BDA0003248159100000123
The modified potential function is
Figure BDA0003248159100000124
And 4, 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 maneuvering speed of the pulse 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 delta r | | r-re||≥rmaxWhen the engine is ignited, the detector is subjected to brake control, and the expected speed after braking is selected as
Figure BDA0003248159100000125
The first derivative of equation (58) with respect to time is
Figure BDA0003248159100000126
Bringing formula (59) into formula (60) to obtain
Figure BDA0003248159100000127
K is the magnitude of the maneuvering speed of the detector pulse after braking, and K is more than 0, so that the derivative of the potential function to time after the braking is negative and definite can be ensured. Given that the potential function is positive, the velocity direction determined in equation (59) ensures that the probe position eventually converges to the desired end state, i.e., the predetermined target collision point, according to the Lyapunov theorem of stability.
And 5: the remaining time t after the braking of the detectorgoThe potential field value phi at the finally reached target pointfAnd (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) as the minimum performance index, further obtaining a braking speed pulse required by the detector for track correction, and performing the track correction control of the bounce of the surface of the small celestial body with weak gravity by using the braking speed pulse by using the detector, thereby improving the position accuracy of the movement of the detector.
After the detector passes the brake, the remaining time t passes under the action of the uncontrolled forcegoThe potential field value phi at the finally reached target pointfMinimum is a performance index, i.e.
Figure BDA0003248159100000131
Determining the expected speed K of the detector after the brake, wherein the residual time tgoIs the time it takes for the detector to complete the entire bounce process from the current state.
The detector state after braking is
Figure BDA0003248159100000132
Then by phifMinimum requirements
Figure BDA0003248159100000133
Combining the linearized model (39) to obtain a unique solution for K
Figure BDA0003248159100000134
In the formula aiFor a braking time tsIs expressed as follows:
if i is 1,2,3
Figure BDA0003248159100000135
If i is 4,5,6
Figure BDA0003248159100000136
Due to the fact that
Figure BDA0003248159100000137
The K value given by equation (65) is therefore the value of the potential field at the point of impact φ under the given conditionsfMinimum post-braking detector pulse maneuver speed magnitude. Then the required brake speed pulse can be determined by equation (59) as
Figure BDA0003248159100000141
Substituting the data to obtain Δ v ═ 1.8725,3.4351, -1.0348]Tm/s, braking time t is 13.6441s, and residual time t isgo22.5154s, and r is [29.5231,40.2517,15.3601 ═ braking position]Tm, repairThe final collision point of the positive track is rs＝[80.3195,120.6092,0]TAnd m is selected. As shown in FIG. 2, by using the method for correcting and controlling the bounce trajectory of the surface of the small celestial body with weak gravity, disclosed by the invention, when a detector has a large trajectory deviation in the bouncing process, the speed pulse maneuver can be rapidly completed, so that the position accuracy of bouncing movement of the detector is improved.
As shown in FIG. 3, 300 Monte Carlo simulations show that the method of the present invention better corrects the error interference trajectory of the detector during the take-off process, so that the detector is optimized near the target position at the collision position where the original error is larger.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. The weak-gravity small celestial body surface bounce track correction control method is characterized by comprising the following steps of: comprises the following steps of (a) carrying out,
step 1: respectively establishing a dynamic equation under a small celestial body fixed connection coordinate system and a surface coordinate system, and considering external interference factors received by the detector in a take-off process to obtain an actual bounce track dynamic equation of the detector containing unknown interference;
step 2: carrying out linear solution on a kinetic equation under a small celestial body surface coordinate system to obtain a relation between braking time and braking speed;
and step 3: establishing a gravitational potential function with respect to the location of the detector relative to 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; correcting the repulsive force potential function to enable the repulsive force potential function to meet the Lyapunov stability condition, and further enabling the repulsive force potential function to be converged at a collision point; superposing the gravitational potential function and the corrected repulsive potential function to obtain a corrected potential function;
and 4, step 4: obtaining the magnitude of the braking pulse maneuvering speed by giving out the detector maneuvering position judgment condition and the braking expected speed and substituting the condition into the correction potential function in the step 3;
and 5: the remaining time t after the braking of the detectorgoThe potential field value phi at the finally reached target pointfAnd (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) as the minimum performance index, further obtaining a braking speed pulse required by the detector for track correction, and performing the track correction control of the bounce of the surface of the small celestial body with weak gravity by using the braking speed pulse by using the detector, thereby improving the position accuracy of the movement of the detector.
2. The weak-gravity small celestial surface bounce trajectory correction control method of claim 1, wherein: the step 1 is realized by the method that,
aiming at the problem of single bounce movement of the detector, under the condition that the small celestial body is fixedly connected with a coordinate system, the kinetic equation of the detector after jumping is expressed as
Figure FDA0003248159090000011
Wherein r isB、vBPosition and velocity vectors of the detector, omega is the spin angular velocity of the small celestial body, aBFor other accelerations without considering the perturbation force, V is a gravitational potential function;
in the surface coordinate system, the kinetic equation of the detector is
Figure FDA0003248159090000021
Wherein r and v are respectively the position and velocity vector of the detector, rho is the position vector of the origin of the surface coordinate system relative to the center of the small celestial body, and u is the position vector of the origin of the surface coordinate system relative to the center of the small celestial bodyBThe thrust vector of the coordinate system of the detector body,
Figure FDA0003248159090000027
a is a matrix converted from a body coordinate system to a surface coordinate system, and a is the acceleration of other not considered perturbation forces;
considering that various uncertainties exist in a dynamic model of a detector, 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 summarized into model-free acceleration;
order to
Figure FDA0003248159090000022
Integral the kinetic equation to
Figure FDA0003248159090000023
Wherein n isiAnd (i-r, v) is an unknown interference quantity.
3. The weak-gravity small celestial surface bounce trajectory correction control method of claim 2, wherein: the step 2 is realized by the method that,
selecting the position and the speed of the detector under the surface coordinate system of the small celestial body as state variables, namely
Figure FDA0003248159090000024
In an initial state X0Linearizing the dynamic equation (1) to obtain a linearized equation of the detector bouncing motion
Figure FDA0003248159090000025
Figure FDA0003248159090000026
Wherein
Figure FDA0003248159090000031
Figure FDA0003248159090000032
Figure FDA0003248159090000033
Figure FDA0003248159090000034
And
Figure FDA0003248159090000035
respectively as a function of gravitational potential in an initial state X0The first and second derivatives of the position r;
the linear system (5) of the detector bounce motion is a linear steady system, and the solution of the system is
Figure FDA0003248159090000036
Since u is a constant matrix and the matrix
Figure FDA0003248159090000037
Is reversible, therefore
Figure FDA00032481590900000310
The solution of the system is expressed as
X(t)＝e(A+δ)tX0+(A+δ)-1[e(A+δ)t-I6×6]u (12)
The brake time of the thruster is tsThe probe speed before braking is v-After braking probe speed is v+Detector state transition matrix of
Figure FDA0003248159090000038
Constant value vector is
Figure FDA0003248159090000039
The required velocity 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).
4. The weak-gravity small celestial surface bounce trajectory correction control method of claim 3, wherein: the step 3 is realized by the method that,
selecting a gravitational potential function of
Figure FDA0003248159090000041
Wherein the content of the first and second substances,
Figure FDA0003248159090000042
rlthe position r of the detector in the coordinate system of the small celestial body surface is expressed as
rl＝r-rt (18)
Wherein r istThe position of a collision point in a coordinate system of the surface of the small celestial body is shown; the defined gravitational potential function being a function of the position of the detectorAnd the potential function is positive, if and only if r is equal to rtNamely, when the detector reaches a collision point, the gravitational 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 points which are the same distance from the collision point are closer to the connecting line of the braking point and the target point of the detector, the potential field value is lower, and the selected parameter is
kx＝ky＝k＞1 (19)
Introducing a region with a high potential function to represent the limiting condition of a motion path, wherein a spherical obstacle exists on a bounce path of the detector, the gradient value of the high value potential function region represents the magnitude of a repulsive force applied to the detector to avoid the obstacle, and the repulsive potential function in the form of a Gaussian function is selected as
Figure FDA0003248159090000043
Wherein r isoIs a position vector of the spherical center of the cataract obstacle in a coordinate system of the surface of the small celestial body, lambda1、λ2Height and width of repulsive force; consider when r ═ rtWhen the formula (20) is not zero, the stability condition of Lyapunov is not satisfied; in order to make the potential function after the repulsive potential energy is added converge at the collision point, equation (20) is modified to
Figure FDA0003248159090000051
Wherein
Figure FDA0003248159090000052
px＞1,py＞1,pz＞1 (23)
The modified potential function is
Figure FDA0003248159090000053
5. The weak-gravity small celestial surface bounce trajectory correction control method of claim 4, wherein: step 4, the method is realized by the following steps,
when the error value of the actual track and the reference track of the detector is larger than the allowable maximum error, namely delta r | | r-re||≥rmaxWhen the engine is ignited, the detector is subjected to brake control, and the expected speed after braking is selected as
Figure FDA0003248159090000054
The first derivative of equation (24) with respect to time is
Figure FDA0003248159090000055
Bringing formula (25) into formula (26) to obtain
Figure FDA0003248159090000056
K is the magnitude of the maneuvering speed of the detector pulse after braking, and K is more than 0, so that the derivative of the potential function to time after the braking is negative; given that the potential function is positive, the velocity direction determined in equation (25) ensures that the probe position eventually converges to the desired end state, i.e., the predetermined target collision point, according to the Lyapunov theorem of stability.
6. The weak-gravity small celestial surface bounce trajectory correction control method of claim 5, wherein: step 5 the method is realized by the following steps,
after the detector passes the brake, the remaining time t passes under the action of the uncontrolled forcegoThe potential field value phi at the finally reached target pointfMinimum is a performance index, i.e.
Figure FDA0003248159090000067
Determining the magnitude K of the pulse motor-driven speed of the detector after the brake, wherein the residual time tgoThe time spent by the detector from the current state to the completion of the whole bounce process;
the detector state after braking is
Figure FDA0003248159090000061
Then by phifMinimum requirements
Figure FDA0003248159090000062
Combining the linearized model (5) to find the unique solution of K
Figure FDA0003248159090000063
In the formula aiFor a braking time tsIs expressed as follows:
if i is 1,2,3
Figure FDA0003248159090000064
If i is 4,5,6
Figure FDA0003248159090000065
Due to the fact that
Figure FDA0003248159090000066
The K value given by equation (31) is therefore such that the potential field value φ at the point of impact is given under given conditionsfThe minimum post-braking detector pulse motor speed; the required braking speed pulse is determined by equation (25) as
Figure FDA0003248159090000071
And the detector performs the correction control on the bounce track of the surface of the small celestial body with weak gravity through the braking speed pulse delta v, so that the moving position precision of the detector is improved.
CN202111038247.9A 2021-09-06 2021-09-06 Weak attraction small celestial body surface bouncing track correction control method Active CN113741193B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111038247.9A CN113741193B (en) 2021-09-06 2021-09-06 Weak attraction small celestial body surface bouncing track correction control method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111038247.9A CN113741193B (en) 2021-09-06 2021-09-06 Weak attraction small celestial body surface bouncing track correction control method

Publications (2)

Publication Number Publication Date
CN113741193A true CN113741193A (en) 2021-12-03
CN113741193B CN113741193B (en) 2024-02-27

Family

ID=78736004

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111038247.9A Active CN113741193B (en) 2021-09-06 2021-09-06 Weak attraction small celestial body surface bouncing track correction control method

Country Status (1)

Country Link
CN (1) CN113741193B (en)

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

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

Also Published As

Publication number Publication date
CN113741193B (en) 2024-02-27

Similar Documents

Publication Publication Date Title
CN110989644B (en) Aircraft trajectory planning method considering target point multi-terminal constraint
CN106371312B (en) Lift formula based on fuzzy controller reenters prediction-correction method of guidance
CN113602535B (en) Method for controlling micro-nano satellite in-orbit autonomous intersection and computer equipment
CN110104219A (en) A kind of method and device controlling detector landing objects outside Earth
CN110329547B (en) Small celestial body high-speed impact terminal guidance method based on speed increment corridor
CN113467241B (en) Method for optimizing burn-up of convex curvature landing track
CN112550770A (en) Rocket soft landing trajectory planning method based on convex optimization
CN110775300A (en) Method for suppressing landing error of irregular small celestial body surface by using attitude maneuver
CN111924139A (en) Small celestial body landing obstacle avoidance constant thrust control method based on expansion early warning area
CN113569391B (en) Method, device, equipment and medium for determining parameters of earth-moon transfer track
CN113343442B (en) Method and system for solving fixed-time finite fuel multi-pulse transfer orbit
Zhang et al. Piece-wise affine MPC-based attitude control for a CubeSat during orbital manoeuvres
CN108562293A (en) Planetary landing finite-time control method based on interference observer
CN111428912B (en) Mars detector orbit prediction method and system based on support vector machine
CN110723315B (en) Track generation method for missile-type flight detection of celestial body surface
CN113741193A (en) Weak-gravity small celestial body surface bounce track correction control method
CN110758775B (en) Multi-pulse area hovering method based on asteroid surface observation
CN112541266B (en) Small celestial body attachment convex track guidance method
Zhao et al. Optimal guidance for lunar soft landing with dynamic low-resolution image sequences
CN113568314A (en) Small celestial body hovering constant thrust control method based on switching boundary compensation
CN113777926A (en) Optimal control method for burning consumption of small celestial body attached three-dimensional convex track
Guo et al. Trajectory tracking method of UAV based on discrete-time terminal sliding mode
Li et al. Mars entry guidance law design with neural network based HJB approach
CN111382514A (en) Mars detection flight orbit accurate calculation method and system based on supervised learning
CN113867143B (en) Safety soft landing analysis obstacle avoidance guidance method for extraterrestrial celestial body

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant