CN110775300A - Method for suppressing landing error of irregular small celestial body surface by using attitude maneuver - Google Patents
Method for suppressing landing error of irregular small celestial body surface by using attitude maneuver Download PDFInfo
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Abstract
The invention discloses a method for restraining landing errors of an irregular small celestial body surface by utilizing attitude maneuver, and belongs to the technical field of aerospace. The implementation method of the invention comprises the following steps: the lander pre-estimates the landing position and speed according to the release condition, establishes a small celestial body surface coordinate system and a contact dynamic model, and optimizes the optimal landing attitude according to constraint; planning attitude motion of the lander according to the current attitude and the optimal landing attitude, controlling the lander through an attitude control mechanism to meet the landing attitude obtained by solving, enabling the normal speed of the probe to be smaller than a threshold value after the probe is contacted with the surface through one or more attitude maneuvers, sliding on the surface and staying on the surface of the small celestial body by using friction force. According to the invention, the landing attitude of the probe is changed, so that the speed direction of the probe after the probe is contacted with the small celestial body is changed, the landing rebound track is further changed, the landing error caused by rebound in the landing process is reduced, and the reliability and precision of the surface landing of the small celestial body are improved.
Description
Technical Field
The invention relates to an error suppression method for an irregular small celestial body surface during landing, in particular to a landing trajectory error suppression method suitable for the irregular small celestial body surface, and belongs to the technical field of aerospace.
Background
The small celestial body detection is a hot topic in the current deep space detection field, has rich information of solar system formation and evolution, is rich in rich mineral resources, and is an important link for people to move to deep space for detection, development and utilization.
The detection modes of the small celestial bodies include fly-by detection, intersection detection, landing attachment detection and the like, wherein the landing attachment detection is the most complex detection mode and is also a detection mode which obtains the most scientific return. By releasing the lander to the small celestial body surface, the material composition and topography of the small celestial body can be measured and analyzed in detail. Therefore, landing detection is also the current main detection method. And the landing trajectory design and the attachment control are key steps for realizing the landing detection. Because the small celestial body has the characteristics of weak attraction, small size, irregular shape and the like, the landing device is generally limited in size, and part of the landing device does not have the capability of thrust control, so that the landing device can be contacted with the surface of the small celestial body at a certain speed, rebounds at a certain contact speed, and can stay on the surface of the small celestial body after being contacted for many times, and the landing error is large.
The developed design method for landing tracks of small celestial bodies adopts a convex optimization method to optimize the landing tracks in the prior art [1] (see Pinson R M, LuP. transport design estimation and regulation for the landing on linearly shaped lands [ J ]. Journal of Guidance, Control, and Dynamics,2018,41(6):1243-1256.), but the method is only suitable for landers with thrust Control and not suitable for landers without thrust.
In the prior art [2] (see Ulamec S, Biele J, Blazquez A, et al, Rosetta lander-Philae: mapping preparations [ J ] Acta Astronautica,2015,107:79-86.) the lander is attached to the surface of a small celestial body by means of anchoring by a fish fork mechanism, but the problem of anchoring failure occurs in the actual task, so that the landing error of the lander on the surface is large.
Disclosure of Invention
The invention discloses a method for restraining landing errors of irregular small celestial body surfaces by utilizing attitude maneuver, which aims to solve the technical problems that: aiming at the small celestial body lander which is released by the track and is not controlled by thrust, the landing attitude of the lander is adjusted in the landing process, and the contact speed of the lander is changed, so that the landing error is reduced, and the landing reliability and precision of the small celestial body lander are improved.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for restraining landing errors of irregular small celestial body surfaces by utilizing attitude maneuver. Planning attitude motion of the lander according to the current attitude and the optimal landing attitude, controlling the lander through an attitude control mechanism to meet the landing attitude obtained by solving, enabling the normal speed of the probe to be smaller than a threshold value after the probe is contacted with the surface through one or more attitude maneuvers, sliding on the surface and staying on the surface of the small celestial body by using friction force. According to the invention, the landing attitude of the probe is changed, so that the speed direction of the probe after the probe is contacted with the small celestial body is changed, the landing rebound track is further changed, the landing error caused by rebound in the landing process is reduced, and the reliability and precision of the surface landing of the small celestial body are improved.
The invention discloses a method for restraining landing errors of an irregular small celestial body surface by utilizing attitude maneuver, which comprises the following steps:
the method comprises the following steps: and estimating the landing position and speed according to the release condition of the lander.
The motion near the small celestial body is typically analyzed in a fixed relationship while a main system is established with the main inertia axis of the landing gear as the coordinate axis. The velocity and position after the lander release are r
i,v
i. Estimating the time T of the contact of the lander and the small celestial body by using the kinetic equation (1)
fAnd landing position r
fAnd landing velocity v
f。
Wherein the spin angular velocity of the celestial bodies is omega
a＝[0,0,ω
0]
T. To take into accountThe irregular shape and surface topography of the small celestial body are calculated by adopting a small celestial body polyhedral model
And (3) judging the contact condition of the lander and the small celestial body through a formula (2).
Wherein ω is
fIntegrating the formula (1) and judging the formula (2) if the edge parameters of the small celestial body polyhedron model, G is the gravitation coefficient and sigma is the small celestial body density
It indicates that the lander is in contact with a small celestial body and the integration is terminated. The corresponding terminal state is the landing position and speed of the lander, and the integration time is the landing time.
Step two: and establishing a small celestial body surface coordinate system by taking the landing point as an origin, establishing contact dynamics, and solving the contact speed and the angular speed of the lander after the lander is contacted with the surface.
Since the lander is in contact with the surface at a relative speed, the lander rebounds in consideration of energy loss after collision, and is considered to stay on the surface when the contact speed is sufficiently small.
And establishing a coordinate system of the surface of the small celestial body by taking the landing point as an origin and the external normal direction of the surface of the landing point as a Z axis, wherein the Y axis of the coordinate system points to the rotation axis of the small celestial body, and the X axis is determined according to a right-hand rule. Obtaining the landing speed V under the surface coordinate system according to the surface coordinate system and the transformation matrix M of the small celestial body solid connection system
l -＝Mv
f。
Angular velocity of small celestial body during landing is omega
-The contact point of the lander and the small celestial body is r under the fixed connection position
cThen the contact velocity of the contact point is V
c -＝V
l -+N(Ω
-×r
c) Where N represents the transformation matrix from the body system to the surface system. The mass of the lander is m, and the inertia matrix is J
sDefinition of
Wherein d ═ l
1,l
2)
TWl
3,l
1＝[1,0,0]
T,l
2＝[0,1,0]
T,l
3＝[0,0,1]
TRespectively, basis vectors. The lander contact velocity is numerically solved by the contact dynamics equation
Wherein: e denotes the total mechanical energy of the system, I
pThe total impulse generated to the lander during contact is indicated. Gamma denotes the tangential velocity of the point of contact along the surface,
V
czis the normal velocity of the perpendicular surface of the contact point. Mu.s
dReferring to the friction factor of the surface, the coefficient of restitution e of the surface also needs to be considered in the calculation. According to different landing postures N and posture angular velocity omega
-And obtaining corresponding lander speed and angular speed after contact and respectively recording as V
+，Ω
+。
Step three: and optimizing the landing attitude and attitude angular speed of the lander according to different constraints and performance indexes according to the contact dynamics established in the step two.
Landing attitude N and attitude angular velocity omega of lander
-Therefore, the landing attitude of the lander is simplified into a landing angle α representation, the attitude angular velocity is represented by a spin velocity omega, and different contact speeds of the lander can be obtained by selecting different landing angles and spin velocities and combining the landing velocities.
Contact velocity optimization is performed with α and Ω as optimization variables, and the landing angle and spin velocity are first selected to be 0, α is 0, and Ω is 0, and calculation is performed, and this is doneThe corresponding landing mode is a surface landing mode. When the contact velocity normal component V is calculated according to the formula (3)
z +Less than threshold delta
1And then, the lander is kept on the surface of the small celestial body after one landing, optimization is not needed, and the posture of the lander during the landing is selected to be the corresponding situation.
When the calculated contact velocity normal component is larger than the threshold value delta
1It means that the surface landing will generate many bounces, and the edge landing mode needs to be selected. At contact velocity normal component V
z +The minimum is optimized for the target.
Wherein f (V)
l -,Ω
-α) represents the contact kinetics, if the result is optimized
The result is the optimal attitude for landing. Otherwise, the lander is turned over on the surface through the arris landing, so that the optimization index is changed into
I.e. to minimize the tangential component of the landing gear's contact velocity, where delta, in the case where the contact velocity normal component satisfies the constraint
2The minimum bounce speed corresponding to the time required for adjusting the posture of the lander is related to the gravitational field coefficient of the small celestial body. Obtaining the corresponding optimal landing attitude and landing attitude angular velocity according to the optimization target, and recording the optimal landing attitude and landing attitude angular velocity as
And
step four: and according to the optimized optimal landing attitude and the current attitude of the lander, adopting an attitude track in a polynomial form and realizing the landing of the optimal landing attitude by controlling the attitude.
The attitude of the lander is expressed by adopting an exponential form chi, and the conversion relation between the attitude matrix and the attitude matrix is shown as the formula
Wherein I
3×3Is a third order identity matrix with a corresponding attitude kinematics equation of
Wherein
The attitude change trajectory is represented as
χ(t)＝a
0+a
1t+a
2t
2+a
3t
3(9)
Wherein a is
0,a
1,a
2,a
3And determining the coefficients according to the landing time, the initial attitude of the lander, the terminal attitude and the attitude angular speed. And the lander lands along the designed attitude change track through tracking control.
Step five, the lander realizes the landing process according to the optimal posture, and when the normal component of the contact speed is larger than the threshold value delta
1If so, the lander is popped up from the surface again, the process is regarded as a new release process of the lander, the attitude and the position speed of the new lander are obtained again, and the steps from the first step to the fourth step are repeated; if the normal component of the contact velocity is less than the threshold value delta
1It means that the lander will stay on the surface to slide. And solving the sliding track by utilizing the sliding dynamics to obtain the final landing position of the lander.
When the normal component of the contact velocity is less than the threshold value delta
1It indicates that the lander is finally determined to be surface landing, and the contact speed is V
l +The sliding dynamics under the surface system are shown below
Wherein the supporting force F
N＝f
3l
3Friction force
The sliding speed of the lander on the surface is gradually reduced under the influence of friction force when V
l| | is less than threshold δ
3The lander is considered to be stopped at the surface and this position is the final landing position for the lander. And combining the bounce orbit of the steps to obtain a complete landing orbit. And calculating the landing error of the lander according to the stopping position and the position of the lander which is firstly contacted with the surface.
Step six: and (4) combining the bounce track obtained in the first step to the fifth step to obtain a complete landing track, and calculating to obtain a landing error of the lander according to the staying position and the position of the lander which is firstly contacted with the surface. Landing according to the obtained optimal landing attitude and landing attitude angular velocity can reduce landing errors and improve the landing reliability and precision of the small celestial body lander.
Has the advantages that:
1. the invention discloses a method for restraining landing errors of an irregular small celestial body surface by utilizing attitude maneuver, which changes the contact speed of a lander by adopting the attitude maneuver, thereby changing the landing rebound track, shortening the bounce distance and effectively restraining the landing errors.
2. The invention discloses a method for restraining the landing error of an irregular small celestial body surface by utilizing attitude maneuver, which combines surface landing and edge landing to give the logic sequence of the attitude maneuver and ensure the reliability of the landing process.
3. The method for restraining the landing error of the irregular small celestial body surface by utilizing attitude maneuver, disclosed by the invention, can plan the optimal landing attitude according to the current state, can effectively correct the release error of the lander and has good robustness.
Drawings
FIG. 1 is a flow chart of a method for suppressing a landing error of an irregular small celestial body surface by attitude maneuver.
FIG. 2 is a landing configuration diagram of the landing gear of the present invention.
FIG. 3 is a flowchart illustrating a second step of selecting a landing attitude optimization target according to the present invention.
Figure 4 small celestial Bennu landing trajectory with attitude maneuver in the present example.
Figure 5 zenith Bennu landing trajectory without attitude maneuver in the present example.
Detailed Description
To better illustrate the objects and advantages of the present invention, the present invention is explained in detail below by an example analysis of a small celestial body Bennu vicinity transfer orbit design.
Example 1:
taking a small celestial body Bennu as an example, the landing trajectory design of the irregular small celestial body surface by using attitude maneuver is utilized, as shown in fig. 1, the method for suppressing the landing error of the irregular small celestial body surface by using attitude maneuver disclosed in this embodiment specifically includes the following implementation steps:
the method comprises the following steps: and estimating the landing position and speed according to the release condition of the lander.
The motion near the small celestial body is typically analyzed in a fixed relationship while a main system is established with the main inertia axis of the landing gear as the coordinate axis. Let the velocity and position after lander release be r respectively
i,v
i. Estimating the time T of the contact of the lander and the small celestial body by using the kinetic equation (1)
fAnd landing position r
fAnd landing velocity v
f。
And (3) judging the contact condition of the lander and the small celestial body through a formula (2).
Wherein ω is
fIntegrating the formula (1) and judging the formula (2) if the edge parameters of the small celestial body polyhedron model, G is the gravitation coefficient and sigma is the small celestial body density
It indicates that the lander is in contact with a small celestial body and the integration is terminated. The corresponding terminal state is the landing position and speed of the lander, and the integration time is the landing time.
The spin velocity of the small celestial body Bennu is equal to 4.0679 × 10
-4rad/s, selected density rho 1.26g/cm
3. The initial state after the lander release is
r
i＝[-10.3,-13.8,368.3]
Tm,v
i＝[0.0017,0.0013,-0.0051]
Tm/s
The nominal landing position speed of the lander is calculated to be
r
f＝[-6.0,-14.8,249.1]
Tm,v
i＝[0.0032,-0.004,-0.1163]
Tm/s
The landing time was 2232.0 seconds.
Step two: and establishing a small celestial body surface coordinate system by taking the landing point as an origin, establishing contact dynamics, and solving the contact speed and the angular speed of the lander after the lander is contacted with the surface.
Since the lander is in contact with the surface at a certain speed, the lander will rebound at a certain contact speed considering the energy loss after collision, and the lander is considered to stay on the surface when the contact speed is sufficiently small.
And establishing a coordinate system of the surface of the small celestial body by taking the landing point as an origin and the external normal direction of the surface of the landing point as a Z axis, wherein the Y axis of the coordinate system points to the rotation axis of the small celestial body, and the X axis is determined according to a right-hand rule. Obtaining the landing speed V under the surface coordinate system according to the surface coordinate system and the transformation matrix M of the small celestial body solid connection system
l -＝Mv
f. Obtaining a transfer matrix from the landing surface information as
Corresponding V
l -＝[0.00315,-0.00396,-0.116253]
Tm/s。
Angular velocity when a small celestial body lands is Ω
-The contact point of the lander and the small celestial body is r under the fixed connection position
cThen the contact velocity of the contact point is V
c -＝V
l -+N(Ω
-×r
c) Where N represents the transformation matrix from the body system to the surface system. Assume that the mass of the lander is m and the inertia matrix is J
sDefinition of
Wherein d ═ l
1,l
2)
TWl
3,l
1＝[1,0,0]
T,l
2＝[0,1,0]
T,l
3＝[0,0,1]
TRespectively, basis vectors. The lander contact velocity is numerically solved by the contact dynamics equation
Wherein E represents the total mechanical energy of the system, I
pThe total impulse generated to the lander during contact is indicated. Gamma denotes the tangential velocity of the point of contact along the surface,
V
czis the normal velocity of the perpendicular surface of the contact point. Mu.s
dReferring to the friction factor of the surface, the coefficient of restitution e of the surface also needs to be considered in the calculation. Obtaining corresponding lander speed and angular speed after contact and respectively recording the speed and the angular speed as V according to different landing attitudes N and omega-of attitude angular speed
+，Ω
+. The landing gear mass was chosen to be 2.3kg, J ═ diag ([0.025875,0.025875, 0.025875)])kg·m
2The contact dynamics calculation was carried out with the surface friction coefficient μ of the small celestial body equal to 1 and the recovery coefficient e equal to 0.6.
Step three: and optimizing the landing attitude and attitude angular speed of the lander according to different constraints and performance indexes according to the contact dynamics established in the step two.
And (3) optimally designing the contact velocity by using α and omega as optimization variables, firstly selecting a landing angle and a spin velocity of 0, wherein α is 0, and omega is 0, and calculating, wherein the corresponding landing mode is a surface landing mode, and if the normal component V of the contact velocity obtained by calculation according to the formula (3) is a surface landing mode
z +Less than threshold delta
1And then, the lander is kept on the surface of the small celestial body after one landing, optimization is not needed, and the posture of the lander during the landing is selected to be the corresponding situation.
If the calculated contact velocity normal component is larger than the threshold value delta
1It means that the surface landing will generate many bounces, and the edge landing mode needs to be selected. At contact velocity normal component V
z +The minimum is optimized for the target.
Wherein f (V)
l -,Ω
-α) represents the contact kinetics, if the result is optimized
The result is the optimal attitude for landing. Otherwise, the lander is turned over on the surface through the arris landing, so that the optimization index is changed into
I.e. to make the tangential component of the contact velocity of the lander as small as possible, δ, with the normal component of the contact velocity satisfying the constraint
2The minimum bounce speed corresponding to the time required for adjusting the posture of the lander is related to the gravitational field coefficient of the small celestial body. Obtaining the corresponding optimal landing attitude and landing angular velocity according to the optimization target, and recording the optimal landing attitude and landing angular velocity as
And
selection of delta
1＝0.002m/s,δ
2Calculating V corresponding to the found surface landing at 0.0025m/s
z +＝0.06578m/s＞δ
1Therefore, it is necessary to optimize the landing by using the edge landing and find the landing speed obtained by using the minimum normal speed as an index
Then re-optimization is performed by using the minimum tangential component of the contact velocity as an index to obtain the optimal landing attitude angle α of 80.1 degrees and the angular velocity omega
-0.3965rad/s, corresponding to a contact velocity V
+＝[-0.06208,-0.02739,0.00280]m/s。
Step four: and according to the optimized optimal landing attitude and the current attitude of the lander, adopting an attitude track in a polynomial form and realizing the optimal landing attitude through control.
The attitude of the lander is expressed by adopting an exponential form chi, and the conversion relation between the attitude matrix and the attitude matrix is shown as the formula
Corresponding attitude kinematics equation of
Wherein
The attitude change trajectory is represented as
χ(t)＝a
0+a
1t+a
2t
2+a
3t
3(9)
Wherein a is
0,a
1,a
2,a
3As a function of landing time and landerInitial and terminal poses and pose angular velocities are determined. And through tracking control, the lander can realize the expected landing process along the designed attitude change track.
Initial angular velocity of the lander is [0,0,0.0001 ]]rad/s, exponential attitude χ
i＝[-3.1341,-1.1534,1.2542]Converting the landing attitude and attitude angular velocity obtained by solving into an exponential form chi, and substituting the exponential form chi into transfer time to obtain a corresponding polynomial coefficient a
0＝[1.3811,0,-0.3789],a
1＝[0,0,0],a
2＝[-0.0005,-0.0022,-0.0018],a
3＝[0.0505,0.2193,0.1840]×10
-4And generating a posture change track.
Step five, the lander realizes the landing process according to the optimal posture, if the normal component of the contact speed is larger than the threshold value delta
1If so, the lander is popped up from the surface again, the process is regarded as a new release process of the lander, the attitude and the position speed of the new lander are obtained again, and the steps from the first step to the fourth step are repeated; if the normal component of the contact velocity is less than the threshold value delta
1It means that the lander will stay on the surface to slide. And solving the sliding track by utilizing the sliding dynamics to obtain the final landing position of the lander.
The normal component of the contact velocity being less than a threshold value delta
1It indicates that the lander is finally determined to be surface landing, and the contact speed is V
l +The sliding dynamics under the surface system are shown below
Wherein the supporting force F
N＝f
3l
3Friction force
The sliding speed of the lander on the surface is gradually reduced under the influence of friction force when V
l||Less than threshold delta
3The lander is considered to be stopped at the surface and this position is the final landing position for the lander. And combining the bounce orbit of the steps to obtain a complete landing orbit. And calculating the landing error of the lander according to the stopping position and the position of the lander which is firstly contacted with the surface.
By calculating that the contact speed corresponding to the first landing is more than delta
1Therefore, the steps from one to four need to be repeated, the landing device slides on the surface after 2 landings, and the final landing position is r
s＝[-42.6,-18.9,235.1]
Tm.
Step six: and (4) combining the bounce track obtained in the first step to the fifth step to obtain a complete landing track, and calculating to obtain a landing error of the lander according to the staying position and the position of the lander which is firstly contacted with the surface. Landing according to the obtained optimal landing attitude and landing attitude angular velocity, reducing landing errors and improving the landing reliability and precision of the small celestial body lander.
The lander lands according to the obtained landing attitude and landing attitude angular velocity, and the final landing trajectory is shown in fig. 4. The landing error between the final landing position and the initial landing position was 35.2 m. In contrast, the landing trajectory without attitude maneuver is shown in fig. 5, the landing error reaches 167.6m, and the method effectively restrains the error to 20% and improves the landing accuracy. Meanwhile, the method optimizes the landing attitude according to different initial states, and can effectively correct initial errors and make landing areas more concentrated.
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. A method for suppressing the landing error of an irregular small celestial body surface by using attitude maneuver is characterized by comprising the following steps: comprises the following steps of (a) carrying out,
the method comprises the following steps: estimating the landing position and speed according to the release condition of the lander;
step two: establishing a small celestial body surface coordinate system by taking the landing point as an origin, establishing contact dynamics, and solving the contact speed and the angular speed of the lander after the lander is contacted with the surface;
step three: optimizing the landing attitude and attitude angular speed of the lander according to different constraints and performance indexes according to the contact dynamics established in the step two;
step four: according to the optimized optimal landing attitude and the current attitude of the lander, the attitude trajectory in a polynomial form is adopted, and the optimal landing attitude is landed by controlling the attitude;
step five, the lander realizes the landing process according to the optimal posture, and when the normal component of the contact speed is larger than the threshold value delta
1If so, the lander is popped up from the surface again, the process is regarded as a new release process of the lander, the attitude and the position speed of the new lander are obtained again, and the steps from the first step to the fourth step are repeated; if the normal component of the contact velocity is less than the threshold value delta
1Then it means the lander will stay on the surface to slide; solving a sliding track by utilizing sliding dynamics to obtain a final landing position of the lander;
step six: obtaining a complete landing track by combining the bounce track obtained in the first step to the fifth step, and calculating a landing error of the lander according to the staying position and the position of the lander which is firstly contacted with the surface; landing according to the obtained optimal landing attitude and landing attitude angular velocity can reduce landing errors and improve the landing reliability and precision of the small celestial body lander.
2. The method for suppressing the landing error of the irregular small celestial body surface by attitude maneuver according to claim 1, wherein: the first implementation method comprises the following steps of,
the motion near the small celestial body is usually analyzed under a fixed connection system, and a main system taking the main inertia axis of the lander as a coordinate axis is established; the velocity and position after the lander release are r
i,v
i(ii) a Estimating lander using equation of dynamics (1)Time T of contact with small celestial body
fAnd landing position r
fAnd landing velocity v
f；
Wherein the spin angular velocity of the celestial bodies is omega
a＝[0,0,ω
0]
T(ii) a In order to consider the irregular shape and surface topography of the small celestial body, a small celestial body polyhedral model is adopted to calculate the gravitational acceleration
Judging the contact condition of the lander and the small celestial body through a formula (2);
wherein ω is
fIntegrating the formula (1) and judging the formula (2) if the edge parameters of the small celestial body polyhedron model, G is the gravitation coefficient and sigma is the small celestial body density
Then indicating that the lander is in contact with the small celestial body and the integration is terminated; the corresponding terminal state is the landing position and speed of the lander, and the integration time is the landing time.
3. The method for suppressing the landing error of the irregular small celestial body surface by attitude maneuver according to claim 2, wherein: the second step is realized by the method that,
the lander is contacted with the surface at a relative speed, so that the lander rebounds in consideration of energy loss after collision, and the lander is considered to stay on the surface when the contact speed is small enough;
establishing a coordinate system of the surface of the small celestial body by taking the landing point as an origin and the external normal direction of the surface of the landing point as a Z axis, wherein the Y axis of the coordinate system points to the rotation axis of the small celestial body, and the X axis is determined according to a right-hand rule; according to the surface coordinate system and the small celestial bodyObtaining the landing speed under the surface coordinate system by the transformation matrix M of the fixed connection system
Angular velocity of small celestial body during landing is omega
-The contact point of the lander and the small celestial body is r under the fixed connection position
cThe contact velocity of the contact point is
Wherein N represents a transformation matrix from a body system to a surface system; the mass of the lander is m, and the inertia matrix is J
sDefinition of
P＝r
c ×,
B＝(l
1,l
2)
TW(l
1,l
2) Wherein d ═ l
1,l
2)
TWl
3,l
1＝[1,0,0]
T,l
2＝[0,1,0]
T,l
3＝[0,0,1]
TAre respectively base vectors; the lander contact velocity is numerically solved by the contact dynamics equation
Wherein: e denotes the total mechanical energy of the system, I
pRepresenting the total impulse generated to the lander during contact; gamma denotes the tangential velocity of the point of contact along the surface,
V
czis the normal velocity of the contact point perpendicular to the surface; mu.s
dThe friction factor of the surface is referred, and the recovery coefficient e of the surface is also considered in the calculation; according to different landing postures N and posture angular velocity omega
-To obtain a pairThe corresponding after-touch lander velocity and angular velocity are denoted V respectively
+，Ω
+。
4. The method for suppressing the landing error of the irregular small celestial body surface by attitude maneuver according to claim 3, wherein: the third step is to realize the method as follows,
landing attitude N and attitude angular velocity omega of lander
-The landing attitude of the lander is simplified into a landing angle α, the attitude angular velocity is expressed by a spin velocity omega, and different contact velocities of the lander can be obtained by selecting different landing angles and spin velocities and combining the landing velocities;
using α and omega as optimization variables to optimize the contact speed, firstly selecting a landing angle and a spin speed as 0, α being 0 and omega being 0, calculating, wherein the corresponding landing mode is a surface landing mode, and calculating according to a formula (3) to obtain a normal component of the contact speed
Less than threshold delta
1If so, indicating that the lander is kept on the surface of the small celestial body after one landing, and selecting the posture of the lander during the landing as a corresponding condition without optimization;
when the calculated contact velocity normal component is larger than the threshold value delta
1The method indicates that the mode of edge landing needs to be selected when the face landing will generate a plurality of bounces; with normal component of contact velocity
Optimizing for the minimum target;
wherein f (V)
l -,Ω
-α) representsContact dynamics, if optimizing the results
The result is the optimal attitude for landing; otherwise, the lander is turned over on the surface through the arris landing, so that the optimization index is changed into
I.e. to minimize the tangential component of the landing gear's contact velocity, where delta, in the case where the contact velocity normal component satisfies the constraint
2The minimum bounce speed corresponding to the time required for adjusting the posture of the lander is related to the gravitational field coefficient of the small celestial body; obtaining the corresponding optimal landing attitude and landing attitude angular velocity according to the optimization target, and recording the optimal landing attitude and landing attitude angular velocity as
And
5. the method for suppressing the landing error of the irregular small celestial body surface by attitude maneuver according to claim 4, wherein: the implementation method of the fourth step is that,
the attitude of the lander is expressed by adopting an exponential form chi, and the conversion relation between the attitude matrix and the attitude matrix is shown as the formula
Wherein I
3×3Is a third order identity matrix with a corresponding attitude kinematics equation of
Wherein
The attitude change trajectory is represented as
χ(t)＝a
0+a
1t+a
2t
2+a
3t
3(9)
Wherein a is
0,a
1,a
2,a
3Determining the coefficients according to the landing time, the initial attitude of the lander, the terminal attitude and the attitude angular speed; and the lander lands along the designed attitude change track through tracking control.
6. The method for suppressing the landing error of the irregular small celestial body surface by attitude maneuver according to claim 5, wherein: the fifth step is to realize that the method is that,
when the normal component of the contact velocity is less than the threshold value delta
1It indicates that the lander is finally determined to be surface landing, and the contact speed is V
l +The sliding dynamics under the surface system are shown below
Wherein the supporting force F
N＝f
3l
3Friction force
The sliding speed of the lander on the surface is gradually reduced under the influence of friction force when V
l| | is less than threshold δ
3Considering that the lander stops on the surface, wherein the position is the final stopping position of the lander; obtaining a complete landing track by combining the bouncing track of the steps; calculating the landing position of the lander according to the stopping position and the position of the lander in initial contact with the surfaceAnd (4) error.
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