CN113641190A - Complex small celestial body surface landing obstacle avoidance constant thrust control method - Google Patents

Complex small celestial body surface landing obstacle avoidance constant thrust control method Download PDF

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CN113641190A
CN113641190A CN202111052976.XA CN202111052976A CN113641190A CN 113641190 A CN113641190 A CN 113641190A CN 202111052976 A CN202111052976 A CN 202111052976A CN 113641190 A CN113641190 A CN 113641190A
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lander
landing
obstacle
potential function
area
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CN113641190B (en
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朱圣英
杨贺
崔平远
徐瑞
梁子璇
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Beijing Institute of Technology BIT
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    • G05—CONTROLLING; REGULATING
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    • G05D1/10—Simultaneous control of position or course in three dimensions
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Abstract

The invention relates to a complex small celestial body surface landing obstacle avoidance constant-thrust control method, and belongs to the technical field of deep space exploration. The method comprises the steps of establishing a lander kinetic equation under a landing point fixed connection coordinate system; designing a sliding mode surface and a gravitational potential function coefficient by adopting a method of combining a linear sliding mode surface and an improved artificial potential function; the method comprises the following steps of carrying out 'dangerous area', 'expansion early warning area' and 'safe area' zoning on a space near a terrain obstacle, combining and enclosing all obstacles, simplifying the terrain obstacle, providing a novel repulsive force potential function, and verifying that the lander, a target point and an obstacle dangerous cylinder can effectively escape from a local minimum point under the condition that the lander, the target point and the obstacle dangerous cylinder are aligned in the horizontal direction and the obstacle dangerous cylinder is arranged between the lander, the target point and the obstacle dangerous cylinder; designing and improving a constant thrust control law; the control method of the obstacle avoidance constant thrust for the landing of the asteroid is applied to the control of the landing of the complex small celestial body surface, so that the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively avoided.

Description

Complex small celestial body surface landing obstacle avoidance constant thrust control method
Technical Field
The invention relates to a method for controlling the normal thrust of complex small celestial body surface landing obstacle avoidance, which is suitable for a small celestial body lander taking the normal thrust as a propulsion mode and belongs to the technical field of deep space exploration.
Background
Landing is a crucial step in the small celestial body detection task, is an effective guarantee for acquiring effective scientific data information of the small celestial body surface, and is also a necessary precondition for executing the small celestial body surface sample collection and return tasks. With the continuous development of space science and technology and aerospace technology, the small celestial body detection task seeks to land in complex areas with higher scientific value or more special resources, and the areas are often complex in environment, rugged in terrain, widely distributed in ridges, valleys, pits and hills, and threaten the accurate and safe landing task of a lander, so that the difficulty of the landing task on the surface of the small celestial body is increased. Therefore, the autonomous obstacle avoidance control method capable of ensuring the safe landing of the lander in the complex terrain environment is an important research direction of the small celestial body landing segment detection technology. At present, a potential function guidance method is a commonly used autonomous obstacle avoidance method for a lander, however, the problem of local minimum value generated by the potential function guidance method can be caused by a complex terrain environment of a small celestial body, so that the lander falls into a local minimum value area and cannot reach a target landing point.
In the developed potential function landing obstacle avoidance control method, in the prior art [1] (Yuan, X., et al., Probasic-based hawzard altitude guidance for a planar landing.ActaAstronica, 2018.144: p.12-22.), from the viewpoint of probabilistic description of obstacle threats, a landing obstacle avoidance control method based on collision Probability is provided, the probabilistic description of obstacle threats is performed by calculating the real-time collision Probability of landers and star surface obstacles under uncertain conditions, and an analyzed obstacle control law is deduced based on the real-time collision Probability, so that the real-time obstacle avoidance capability under uncertain conditions is improved, the real-time uncertainty avoidance control method has adaptability to the real-time change of the uncertain conditions, and the robustness of obstacle avoidance control and the autonomous landing safety are improved. However, the algorithm does not consider the problem of local minimum value, and the lander falls into a local minimum value area under complex terrain and cannot reach a target landing point.
In the prior art [2] (see Juezhining et al. Small celestial body landing obstacle avoidance constant thrust control method based on an expansion early warning region, China, ZL 202010766827.9[ P ],2020-08-03), the expansion early warning region is defined based on the influence of a landing obstacle region, and the traditional artificial potential function is improved; the designed improved artificial potential function gradient is introduced into the linear sliding mode surface, corresponding parameters of the artificial potential function are designed, a sliding mode control law suitable for a constant-thrust engine is designed, a dead zone is introduced for control law improvement, obstacle avoidance and accurate landing of the lander in a complex area under the action of constant thrust are achieved, and the service life of the lander is prolonged. However, the algorithm does not consider the problem of local minimum value which can be generated, and the lander falls into the local minimum value area under the complex terrain and cannot reach the target landing point.
Disclosure of Invention
The invention aims to solve the problem that the lander falls into a local minimum value area and cannot reach a target landing point due to the existing potential function guidance method. The method of the invention divides the space near the terrain obstacle into a dangerous area, an expansion early warning area and a safety area, divides the complex obstacle terrain into a plurality of obstacle areas which are not mutually influenced by combining and surrounding each obstacle, simplifies the complex obstacle terrain, and avoids the problem that the repulsion potential functions generated by a plurality of obstacles are excessively superposed in a certain area to generate local minimum values. Meanwhile, a novel repulsive force potential function is defined, and the lander can effectively escape from a local minimum value point and finally reaches the target landing point under the condition that the lander, the target point and the barrier dangerous cylinder are aligned in the horizontal direction and the barrier dangerous cylinder is arranged between the lander and the target dangerous cylinder.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a method for controlling the landing obstacle avoidance constant thrust of a complex small celestial body surface, which comprises the steps of establishing a lander dynamic equation under a landing point fixed connection coordinate system; designing a sliding mode surface and a gravitational potential function coefficient by adopting a method of combining a linear sliding mode surface and an improved artificial potential function; the method comprises the following steps of carrying out 'dangerous area', 'expansion early warning area' and 'safe area' zoning on a space near a terrain obstacle, combining and enclosing all obstacles, simplifying the terrain obstacle, providing a novel repulsive force potential function, and verifying that the lander, a target point and an obstacle dangerous cylinder can effectively escape from a local minimum point under the condition that the lander, the target point and the obstacle dangerous cylinder are aligned in the horizontal direction and the obstacle dangerous cylinder is arranged between the lander, the target point and the obstacle dangerous cylinder; designing and improving a constant thrust control law; the control method for the asteroid landing by the complex small celestial body surface landing obstacle avoidance constant thrust is applied to control the small planet landing, so that the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively avoided, and obstacle avoidance and accurate landing of the lander under the action of constant thrust are guaranteed.
The invention discloses a method for controlling the normal thrust of complex small celestial body surface landing obstacle avoidance, which comprises the following steps:
step 1: establishing a fixed connection coordinate system sigma of small celestial bodiesbCoordinate system sigma fixed with landing pointlUsing landers in sigmabDeducing sigma through a landing kinetic equation under the system and a position and speed conversion relation between two coordinate systemslLander dynamics equations are followed.
The specific implementation method of the step 1 comprises the following steps:
using the centroid of the small celestial body as the origin ObThe minor celestial spin axis being zbAxis, minimum axis of inertia of small celestial body being xbAxis, definition of y by right hand rulebFixed connection coordinate system O of small celestial body established by shaftb-xbybzb(Σb) (ii) a Using the target landing point as the origin Ol，OlIs located in the out-of-plane normal direction zlAxis to lie in zlOlzbPlane and perpendicular to zlThe south pole direction of the axis pointing to the small celestial body is xlAxis, definition of y by right hand rulelLanding point fixed connection coordinate system O of small celestial body established by shaftl-xlylzl(Σl)。
Lander in sigmabThe following kinetic equation is:
Figure BDA0003249861150000021
wherein r isbAnd vbLander in sigma, respectivelybA position vector and a velocity vector under the system; ω ═ 0,0, ω]TFor small celestial body rotation angular velocity vectors, assuming that the small celestial body rotates uniformly, i.e.
Figure BDA0003249861150000022
Figure BDA0003249861150000023
The acceleration of the small celestial body gravity on the lander; dbIs sigmabThe lower disturbance acceleration is tied and represents the influence of small celestial body gravitational field deviation, sunlight pressure and third body perturbation on the lander in the motion process; a iscbIs sigmabControlling the acceleration under the control;
Σbsum-sigmalThe position and the speed of the lander have the following coordinate conversion relationship:
Figure BDA0003249861150000031
wherein r islAnd vlLander in sigma, respectivelylPosition and velocity vectors under the system,/bIs composed of
Figure BDA0003249861150000032
In sigmabIs determined.
Figure BDA0003249861150000033
To be derived from ∑lTo sigmabThe coordinate transformation matrix below.
Lander in sigmabThe following kinetic equation is:
Figure BDA0003249861150000034
wherein d islIs sigmalDisturbance acceleration under the system, aclIs sigmalThe acceleration is controlled. Defining the acceleration of lander caused by small celestial body gravitational field and autorotation effect
Figure BDA0003249861150000035
Comprises the following steps:
Figure BDA0003249861150000036
substituting the formula (4) into the formula (3), and introducing a control acceleration expression to obtain a simplified landing dynamics equation:
Figure BDA0003249861150000037
wherein, TclControl thrust vector generated for lander self-contained thruster and having TcliE { -T,0, + T } (i { -1, 2,3), where T is the magnitude of thrust generated by a single axis of the lander, and subscript i denotes the components of the x, y, z axes of the variables; m is the mass of the lander, g0Is the standard gravitational acceleration at sea level of the earth; i isspIs the thrust device specific impulse.
Step 2: a method of combining a linear sliding mode surface and an improved artificial potential function is adopted to design the sliding mode surface and design a gravitational potential function coefficient.
The step 2 is realized by the following specific method:
at ΣlThe expression of the state vector for the desired landing target point is rld＝[0,0,0]Tm, to rldDerivation, expression for obtaining desired landing speed
Figure BDA0003249861150000038
Define the relative position σ ═ rl-rldAnd relative velocity
Figure BDA0003249861150000039
On the basis of the above-mentioned information, the relative velocity vector is used
Figure BDA00032498611500000310
Establishing a linear sliding mode surface with an artificial potential function gradient:
Figure BDA00032498611500000311
wherein:
Figure BDA00032498611500000312
for the gradient operator symbol, phi is an artificial potential function,
Figure BDA00032498611500000313
is the gradient of the artificial potential function phi to the lander position vector.
In the landing control process of the lander, in order to achieve obstacle avoidance and accurate soft landing of the lander, a non-negative scalar function phi is often introduced into a control system to describe terrain obstacle information and relative position state information of the spacecraft in the landing process, and the potential function value at a target landing point is the lowest. φ generally consists of two parts: gravitational potential function phiaAnd repulsive force potential function phir. The expression of φ is:
φ＝φa+φr (7)
the gravitational potential function is used for describing the relative position relationship between the position of the lander and the target landing point, the longer the relative distance between the position of the lander and the target landing point is, the larger the numerical value of the gravitational potential function and the attractive force is, under the action of the attractive force, the lander moves to the position with reduced potential energy and finally converges to the target landing point, when the lander reaches the target landing point, the global minimum value of the gravitational potential function and the attractive force is 0, the attractive force does not act any more, and the common form of the gravitational potential function is a quadratic function:
Figure BDA0003249861150000041
wherein, Kt＝diag(kt1；kt2；kt3) Is a semi-positive definite matrix.
When the lander is not affected by obstacles during landing, only the gravitational potential function is activated at this time, and the sliding mode surface shown in formula (6) can be simplified into a linear sliding mode surface shown in formula (9):
Figure BDA0003249861150000042
σ when the lander moves on a linear sliding surface shown in equation (9)i,
Figure BDA0003249861150000043
All analytic solutions exist:
Figure BDA0003249861150000044
wherein, tiThe time of the lander moving on the linear sliding mode surface,
Figure BDA0003249861150000045
for landers to reach the relative position of the slip-form faces, and exist
Figure BDA0003249861150000046
Wherein σ0＝[(σ1)0,(σ2)0,(σ3)0]For initiation of landersThe relative position can be known from the formulas (10) and (11), when the lander moves on the linear sliding mode surface only under the action of the gravitation, the relative position of each shaft is | | | σi| and magnitude of relative velocity
Figure BDA0003249861150000047
Are all exponentially and monotonically decreased along with the increase of time and finally approach to 0, and the convergence speed depends on the parameter k of the artificial potential functionti(i ═ 1,2, 3). Before landing, the lander needs to reach a desired position in the horizontal direction to prevent the lander from colliding with the ground of the small celestial body during landing, so that the convergence speed of the z-axis should be slower than those of the other two axes, namely, the z-axis exists
Figure BDA0003249861150000048
Escape velocity V due to small celestial bodyescapeAnd the landing speed of the lander is strictly controlled in the detection task of the small celestial body, so that the escape phenomenon is avoided. Namely, it is
Figure BDA0003249861150000049
And step 3: and (3) partitioning a dangerous area, an expansion early warning area and a safety area in the space near the terrain obstacle, and establishing a repulsive force potential function form for effectively avoiding the lander from falling into a local minimum value.
The specific implementation method of the step 3 is as follows:
the cylinder is adopted to just surround the obstacle, and the surrounding area is a 'dangerous area', namely an area which can not be contacted by the landing device; outside the dangerous area, another cylindrical area is defined in a preset range, and the area is an expansion early-warning area; the expansion early-warning area surrounds a danger area; the area outside the inflated precaution area is the "safe zone".
When the expansion early warning areas of a plurality of obstacles are overlapped, all overlapped areas are surrounded by a cylinder, and the areas are regarded as a whole, namely a dangerous area; outside the dangerous area, another cylindrical area is defined in a preset range, and the cylindrical area is an expansion early-warning area;
when the lander enters the expansion early warning area, the repulsive force potential function is rapidly increased to generate repulsive force, the lander is pushed to be away from the obstacle until the lander enters the safety area to fly, the repulsive force potential function is reduced to zero, the obstacle does not interfere with the flight of the lander any more, and the lander is only acted by the attractive force and gradually converges to a preset target landing point.
When the expansion early warning areas of a plurality of obstacles are overlapped, the obstacles are combined and surrounded, the complex obstacle terrain is divided into a plurality of obstacle areas which are not mutually influenced, the complex obstacle terrain is simplified, and the problem that the repulsion force potential functions generated by a plurality of obstacles are excessively overlapped in a certain area to generate a local minimum value is avoided.
Repulsive potential function phirIs represented as follows:
Figure BDA0003249861150000051
wherein r islx、rly、rlzAnd the position of the lander at the current moment is shown under the landing site fixed coordinate system.
Figure BDA0003249861150000052
Characterised by the distance, k, of the current position of the lander in the horizontal direction from the jth obstacle centrerFor the weight coefficient to be designed, and requires krIs greater than 0. n is the total number of obstacles. x is the number ofjo、yjo、zjoAnd djoIs the center position, height and cylinder radius of the danger zone cylinder corresponding to the jth obstacle in the horizontal direction, deltajoAnd deltajhArtificially defined threshold values respectively representing the height and the radius of the cylinder of the warning area corresponding to the jth obstacle and satisfying deltajo＞djo> 0 and deltajh＞zjo＞0。
To quantify the surfaceForce function of repulsionrRange of influence of each obstacle, kja、kjha、kjoAnd kjhoThe design of (2) is as follows:
Figure BDA0003249861150000053
Figure BDA0003249861150000054
Figure BDA0003249861150000055
Figure BDA0003249861150000056
the obtained novel artificial potential function form is as follows:
Figure BDA0003249861150000057
the repulsion potential function form can effectively avoid the problem that the lander falls into a local minimum value.
And 4, step 4: and (3) designing a sliding mode control law suitable for the constant-thrust engine on the basis of the sliding mode surface established in the step (2) and the potential function obtained in the step (3), and introducing a dead zone to improve the control law so as to reduce buffeting and fuel consumption caused by frequently switching the thrust direction of the engine.
The specific implementation method of the step 4 is as follows:
the control law is designed as follows:
Figure BDA0003249861150000061
wherein sgn is a sign function.
The dead zone is introduced to equation (21) for control law improvement:
Figure BDA0003249861150000062
wherein, f(s)i)tIs defined as:
Figure BDA0003249861150000063
wherein, χi(i ═ 1,2,3) and ψi(i ═ 1,2,3) is an artificially set dead zone threshold, and ψ existsi＜χi(i ═ 1,2,3) are all positive numbers, and subscripts t- Δ t indicate the control amount at the previous time.
The control law is improved by equations (20) to (22), and buffeting and fuel consumption caused by frequent switching of the thrust direction of the engine are reduced.
Further comprising the step 5: the control method for the asteroid landing by the complex small celestial body surface landing obstacle avoidance constant thrust control method is applied, so that the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively solved, and obstacle avoidance and accurate landing of the lander under the action of constant thrust are guaranteed.
Advantageous effects
The invention discloses a method for controlling the normal thrust of a complex small celestial body surface landing obstacle avoidance, which is characterized in that a dangerous area, an expansion early warning area and a safety area are partitioned in the space near a terrain obstacle, and the space is combined and surrounded to simplify the land obstacle, so that a novel repulsive force potential function is provided, the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively avoided, and the obstacle avoidance and accurate landing of the lander under the action of the normal thrust are ensured.
Drawings
Fig. 1 is a flow chart of a complex small celestial body surface-based landing obstacle avoidance constant thrust control method.
FIG. 2 is a fixed coordinate system sigma of the small celestial body in step 1bCoordinate system sigma fixed with landing pointlSchematic representation.
Fig. 3 is a schematic diagram of the "danger zone", "expansion early warning zone", and "safety zone" in step 3. Wherein, the diagram (a) is a basic diagram, and the diagram (b) is a basic diagram of the situation that the obstacles are merged.
FIG. 4 is a schematic diagram of local minimum problem verification in step 3.
Fig. 5 is a schematic diagram of the simulated terrain in step 5.
Fig. 6 is a landing obstacle avoidance trajectory diagram using a gaussian potential function guidance method.
Fig. 7 is a simulation analysis result of the control method. Wherein, the diagram (a) is a landing obstacle avoidance trajectory diagram of the lander, the diagram (b) is a three-axis position change curve diagram of the lander, and the diagram (c) is a three-axis speed change curve diagram of the lander.
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.
Example 1:
in order to verify the feasibility of the method, the irregular asteroid 2063Bacchus is used as a target celestial body to carry out landing obstacle avoidance control, a polyhedron model is adopted to establish a small celestial body gravitational field, and a fixed connection coordinate system sigma of the small celestial body is establishedbCoordinate system sigma fixed with landing pointl. The volume density of the small planet is 2.0g/cm3The autorotation period is 14.9 h. In sigmabNext, the selected target landing site is [ 130-210,100 ]]And m is selected. In sigmalThe initial landing gear position is [40,40,10 ]]m, initial velocity of [0,0 ]]m/s, target termination velocity of [0, 0%]m/s, semi-positive definite matrix KtIs diag (0.006; 0.006; 0.002), and has a weighting coefficient of kr0.002. Initial mass of lander is m0200kg, the thrust of each shaft of the lander is T40N, and the specific impulse of the lander is Isp300 s. Dead zone thresholds for the control laws are set to [0.01,0.01 ]]。
As shown in fig. 1, the method for controlling normal thrust based on obstacle avoidance during landing on the surface of a small complex celestial body disclosed in this embodiment includes the following specific steps:
step 1: establishing a fixed connection coordinate system sigma of small celestial bodiesbCoordinate system sigma fixed with landing pointlUsing landers in sigmabDeducing sigma through a landing kinetic equation under the system and a position and speed conversion relation between two coordinate systemslLander dynamics equations are followed.
Establishing a fixed coordinate system sigma of the small celestial body as shown in FIG. 2bCoordinate system sigma fixed with landing pointlLander in sigmabThe following kinetic equation is:
Figure BDA0003249861150000081
wherein r isbAnd vbLander in sigma, respectivelybA position vector and a velocity vector under the system; ω ═ 0,0, ω]TFor small celestial body rotation angular velocity vectors, assuming that the small celestial body rotates uniformly, i.e.
Figure BDA0003249861150000082
Figure BDA0003249861150000083
The acceleration of the small celestial body gravity on the lander; dbIs sigmabThe lower disturbance acceleration is tied and represents the influence of small celestial body gravitational field deviation, sunlight pressure and third body perturbation on the lander in the motion process; a iscbIs sigmabControlling the acceleration under the control;
Σbsum-sigmabThe position and the speed of the lander have the following coordinate conversion relationship:
Figure BDA0003249861150000084
wherein r islAnd vlLander in sigma, respectivelylPosition vector and velocity under the systemDegree vector,/bIs composed of
Figure BDA0003249861150000085
In sigmabIs determined.
Figure BDA0003249861150000086
Is from ΣlTobThe coordinate transformation matrix below.
Lander in sigmabThe following kinetic equation is:
Figure BDA0003249861150000087
wherein d islIs sigmalDisturbance acceleration under the system, aclIs sigmalThe acceleration is controlled. Defining the acceleration of lander caused by small celestial body gravitational field and autorotation effect
Figure BDA0003249861150000088
Comprises the following steps:
Figure BDA0003249861150000089
substituting the formula (26) into the formula (25) and introducing a control acceleration expression to obtain a simplified landing dynamics equation:
Figure BDA00032498611500000810
wherein, TclControl thrust vector generated for lander self-contained thruster and having TcliE { -T,0, + T } (i { -1, 2,3), where T is the magnitude of thrust generated by a single axis of the lander, and subscript i denotes the components of the x, y, z axes of the variables; m is the mass of the lander, g0Is the standard gravitational acceleration at sea level of the earth; i isspIs the thrust device specific impulse.
Step 2: a method of combining a linear sliding mode surface and an improved artificial potential function is adopted to design the sliding mode surface and design a gravitational potential function coefficient.
At ΣlThe expression of the state vector for the desired landing target point is rld＝[0,0,0]Tm, to rldDerivation, expression for obtaining desired landing speed
Figure BDA00032498611500000811
Define the relative position σ ═ rl-rldAnd relative velocity
Figure BDA00032498611500000812
On the basis of the above-mentioned information, the relative velocity vector is used
Figure BDA00032498611500000813
Establishing a linear sliding mode surface with an artificial potential function gradient:
Figure BDA00032498611500000814
wherein:
Figure BDA0003249861150000091
for the gradient operator symbol, phi is an artificial potential function,
Figure BDA0003249861150000092
is the gradient of the artificial potential function phi to the lander position vector.
The artificial potential function φ is generally composed of two parts: gravitational potential function phiaAnd repulsive force potential function phir. The expression of φ is:
φ＝φa+φr (29)
when the lander reaches the target landing point, the gravitational potential function and the attractive force are minimum and 0, and the commonly used gravitational potential function is in the form of a quadratic function:
Figure BDA0003249861150000093
wherein, Kt＝diag(kt1；kt2；kt3) Is a semi-positive definite matrix.
Before landing, the lander needs to reach a desired position in the horizontal direction to prevent the lander from colliding with the ground of the small celestial body during landing, so the convergence speed of the z-axis should be slower than those of the other two axes, i.e. the z-axis
Figure BDA0003249861150000094
Escape velocity V due to small celestial bodyescapeAnd the landing speed of the lander is strictly controlled in the detection task of the small celestial body, so that the escape phenomenon is avoided. Namely, it is
Figure BDA0003249861150000095
And step 3: a 'dangerous area', 'expansion early warning area' and 'safe area' are partitioned in the space near a terrain obstacle, a novel repulsive force potential function form is established, and the problem of local minimum value can be avoided through verification.
As shown in fig. 3(a) and (b), the space near the terrain obstacle is divided into a dangerous area, an expansion early warning area and a safe area, and the complex obstacle terrain is divided into a plurality of obstacle areas which do not influence each other, so that the complex obstacle terrain is simplified. The traditional repulsion potential function is improved based on the defined expansion early-warning area, and the repulsion potential function phi obtained after improvementrThe formula of (1) is:
Figure BDA0003249861150000096
wherein r islx、rly、rlzAnd the position of the lander at the current moment is shown under the landing site fixed coordinate system.
Figure BDA0003249861150000097
Characterised by the distance, k, of the current position of the lander in the horizontal direction from the jth obstacle centrerFor the weight coefficient to be designed, and requires krIs greater than 0. n is the total number of obstacles. x is the number ofjo、yjo、zjoAnd djoIs the center position, height and cylinder radius of the danger zone cylinder corresponding to the jth obstacle in the horizontal direction, deltajoAnd deltajhArtificially defined threshold values respectively representing the height and the radius of the cylinder of the warning area corresponding to the jth obstacle and satisfying deltajo＞djo> 0 and deltajh＞zjo＞0。
To quantitatively express the repulsive potential function phirRange of influence of each obstacle, kja、kjha、kjoAnd kjhoThe design of (2) is as follows:
Figure BDA0003249861150000098
Figure BDA0003249861150000101
Figure BDA0003249861150000102
Figure BDA0003249861150000103
the improved artificial potential function is in the form of:
Figure BDA0003249861150000104
as shown in fig. 4, after the complex obstacle terrain is segmented, the local minimum point may occur only in a case where the lander, the target point, and the obstacle hazard cylinder are aligned in the horizontal direction with the obstacle hazard cylinder in between.
For the horizontal direction, equation (38) can be simplified as:
Figure BDA0003249861150000105
suppose the horizontal center coordinate of the obstacle is (x)1o,y1o) The local minimum point may appear at a position of
Figure BDA0003249861150000106
From the geometric relationship:
Figure BDA0003249861150000107
therefore exist
Figure BDA0003249861150000108
x1o、
Figure BDA0003249861150000109
The same number;
Figure BDA00032498611500001010
y1o、
Figure BDA00032498611500001011
the same number.
For conditions where the extreme is taken by a binary function
Figure BDA00032498611500001012
Existence of
Figure BDA00032498611500001013
K is obtained by substituting equation (40) into equation (41)t1＝kt2The second derivative is obtained by:
Figure BDA00032498611500001014
Figure BDA00032498611500001015
Figure BDA00032498611500001016
simultaneous reaction (40) - (44), available as AC-B2Less than 0, the condition of taking an extreme value by a binary function is known,
Figure BDA0003249861150000111
is the saddle point of the potential function phi, and can escape under the action of the minimal interference force in the formula (5)
Figure BDA0003249861150000112
And finally to the target landing site.
And 4, step 4: and (3) designing a sliding mode control law suitable for the constant-thrust engine on the basis of the sliding mode surface established in the step (2) and the potential function designed in the step (3), and introducing a dead zone to improve the control law so as to reduce buffeting and fuel consumption caused by frequently switching the thrust direction of the engine.
The control law is designed as follows:
Figure BDA0003249861150000113
wherein sgn is a sign function.
The dead zone introduced by equation (45) is modified by the control law:
Figure BDA0003249861150000114
wherein, f(s)i)tIs defined as:
Figure BDA0003249861150000115
wherein, χi(i ═ 1,2,3) and ψi(i ═ 1,2,3) is an artificially set dead zone threshold, and ψ existsi＜χi(i ═ 1,2,3) are all positive numbers, and subscripts t- Δ t indicate the control amount at the previous time.
The control law is improved by equations (45) to (47), and buffeting and fuel consumption caused by frequent switching of the thrust direction of the engine are reduced.
Further comprising the step 5: the control method for the asteroid landing by the complex small celestial body surface landing obstacle avoidance constant thrust control method is applied, so that the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively solved, and obstacle avoidance and accurate landing of the lander under the action of constant thrust are guaranteed.
Establishing a terrain obstacle three-dimensional graph of a simulated landing area as shown in FIG. 5, respectively controlling a lander by using a potential function guidance method and a complex small celestial body surface landing obstacle avoidance constant thrust control method under given initial conditions and terminal conditions, landing the simulated landing area with the special terrain obstacle given in FIG. 5, and finally obtaining simulation results as shown in FIGS. 6 and 7, wherein the results show that the lander finally falls into a minimum value area due to a potential function guidance method, and the complex small celestial body surface landing obstacle avoidance constant thrust control method realizes that the lander effectively escapes from the minimum value area and successfully realizes obstacle avoidance in the landing process, and meanwhile, the speed and the position are converged to corresponding target values, so that accurate landing is realized.
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 (1)

1. The method for controlling the normal thrust of the complex small celestial body surface for landing obstacle avoidance is characterized by comprising the following steps of: the method comprises the following steps:
step 1: establishing a fixed connection coordinate system sigma of small celestial bodiesbCoordinate system sigma fixed with landing pointlUsing landers in sigmabDeducing sigma through a landing kinetic equation under the system and a position and speed conversion relation between two coordinate systemslLanding gear dynamic equations under the system;
using the centroid of the small celestial body as the origin ObThe minor celestial spin axis being zbAxis, minimum axis of inertia of small celestial body being xbAxis, definition of y by right hand rulebFixed connection coordinate system O of small celestial body established by shaftb-xbybzb(Σb) (ii) a Using the target landing point as the origin Ol，OlIs located in the out-of-plane normal direction zlAxis to lie in zlOlzbPlane and perpendicular to zlThe south pole direction of the axis pointing to the small celestial body is xlAxis, definition of y by right hand rulelLanding point fixed connection coordinate system O of small celestial body established by shaftl-xlylzl(Σl)；
Lander in sigmabThe following kinetic equation is:
Figure FDA0003249861140000011
wherein r isbAnd vbLander in sigma, respectivelybA position vector and a velocity vector under the system; ω ═ 0,0, ω]TFor small celestial body rotation angular velocity vectors, assuming that the small celestial body rotates uniformly, i.e.
Figure FDA0003249861140000012
Figure FDA0003249861140000013
The acceleration of the small celestial body gravity on the lander; dbIs sigmabUnder-tie disturbance accelerationDegree, which represents the influence of small celestial body gravitational field deviation, sunlight pressure and third body perturbation on the lander in the motion process; a iscbIs sigmabControlling the acceleration under the control;
Σbsum-sigmalThe position and the speed of the lander have the following coordinate conversion relationship:
Figure FDA0003249861140000014
wherein r islAnd vlLander in sigma, respectivelylPosition and velocity vectors under the system,/bIs composed of
Figure FDA0003249861140000015
In sigmabA position vector of (1);
Figure FDA0003249861140000016
to be derived from ∑lTo sigmabA lower coordinate transformation matrix;
lander in sigmabThe following kinetic equation is:
Figure FDA0003249861140000017
wherein d islIs sigmalDisturbance acceleration under the system, aclIs sigmalControlling the acceleration under the control; defining the acceleration of lander caused by small celestial body gravitational field and autorotation effect
Figure FDA0003249861140000018
Comprises the following steps:
Figure FDA0003249861140000019
substituting the formula (4) into the formula (3), and introducing a control acceleration expression to obtain a simplified landing dynamics equation:
Figure FDA0003249861140000021
wherein, TclControl thrust vector generated for lander self-contained thruster and having TcliE { -T,0, + T } (i { -1, 2,3), where T is the magnitude of thrust generated by a single axis of the lander, and subscript i denotes the components of the x, y, z axes of the variables; m is the mass of the lander, g0Is the standard gravitational acceleration at sea level of the earth; i isspIs thrust device specific impulse;
step 2: designing a sliding mode surface by adopting a method of combining a linear sliding mode surface and an improved artificial potential function, and designing a gravitational potential function coefficient;
at ΣlThe expression of the state vector for the desired landing target point is rld＝[0,0,0]Tm, to rldDerivation, expression for obtaining desired landing speed
Figure FDA0003249861140000022
Define the relative position σ ═ rl-rldAnd relative velocity
Figure FDA0003249861140000023
On the basis of the above-mentioned information, the relative velocity vector is used
Figure FDA0003249861140000024
Establishing a linear sliding mode surface with an artificial potential function gradient:
Figure FDA0003249861140000025
wherein:
Figure FDA0003249861140000026
for gradient operator symbols, phiThe potential function of the artificial potential is adopted,
Figure FDA0003249861140000027
the gradient of the artificial potential function phi to the lander position vector is shown;
in the landing control process of the lander, in order to achieve obstacle avoidance and accurate soft landing of the lander, a non-negative scalar function phi is often introduced into a control system to describe terrain obstacle information and relative position state information of the spacecraft in the landing process, and the potential function value at a target landing point is the lowest; φ generally consists of two parts: gravitational potential function phiaAnd repulsive force potential function phir(ii) a The expression of φ is:
φ＝φa+φr (7)
the gravitational potential function is used for describing the relative position relationship between the position of the lander and the target landing point, the longer the relative distance between the position of the lander and the target landing point is, the larger the numerical value of the gravitational potential function and the attractive force is, under the action of the attractive force, the lander moves to the position with reduced potential energy and finally converges to the target landing point, when the lander reaches the target landing point, the global minimum value of the gravitational potential function and the attractive force is 0, the attractive force does not act any more, and the common form of the gravitational potential function is a quadratic function:
Figure FDA0003249861140000028
wherein, Kt＝diag(kt1；kt2；kt3) Is a semi-positive definite matrix;
when the lander is not affected by obstacles during landing, only the gravitational potential function is activated at this time, and the sliding mode surface shown in formula (6) can be simplified into a linear sliding mode surface shown in formula (9):
Figure FDA0003249861140000029
when the lander moves on the linear sliding mode surface shown in the formula (9)，
Figure FDA00032498611400000210
All analytic solutions exist:
Figure FDA0003249861140000031
wherein, tiThe time of the lander moving on the linear sliding mode surface,
Figure FDA0003249861140000032
for landers to reach the relative position of the slip-form faces, and exist
Figure FDA0003249861140000033
Wherein σ0＝[(σ1)0,(σ2)0,(σ3)0]For the initial relative position of the lander, as can be seen from the equations (10) and (11), when the lander moves on the linear sliding mode surface only under the action of gravity, the relative position of each axis is | | | σ |, andi| and magnitude of relative velocity
Figure FDA0003249861140000034
Are all exponentially and monotonically decreased along with the increase of time and finally approach to 0, and the convergence speed depends on the parameter k of the artificial potential functionti(i ═ 1,2, 3); before landing, the lander needs to reach a desired position in the horizontal direction to prevent the lander from colliding with the ground of the small celestial body during landing, so that the convergence speed of the z-axis should be slower than those of the other two axes, namely, the z-axis exists
Figure FDA0003249861140000035
Escape velocity V due to small celestial bodyescapeSmaller, in the sense of a small celestial bodyIn service, the landing speed of the lander is strictly controlled, so that the escape phenomenon is avoided; namely, it is
Figure FDA0003249861140000036
And step 3: carrying out 'dangerous area', 'expansion early warning area' and 'safe area' zoning on the space near the terrain obstacle, and establishing a repulsive force potential function form for effectively avoiding the lander from falling into a local minimum value;
the cylinder is adopted to just surround the obstacle, and the surrounding area is a 'dangerous area', namely an area which can not be contacted by the landing device; outside the dangerous area, another cylindrical area is defined in a preset range, and the area is an expansion early-warning area; the expansion early-warning area surrounds a danger area; the area outside the expansion early warning area is a safety area;
when the expansion early warning areas of a plurality of obstacles are overlapped, all overlapped areas are surrounded by a cylinder, and the areas are regarded as a whole, namely a dangerous area; outside the dangerous area, another cylindrical area is defined in a preset range, and the cylindrical area is an expansion early-warning area;
when the lander enters the expansion early warning area, the repulsive force potential function is rapidly increased to generate repulsive force, the lander is pushed to be away from the obstacle until the lander enters the safety area to fly, the repulsive force potential function is reduced to zero, the obstacle does not interfere with the flight of the lander any more, and the lander is only acted by the attractive force and gradually converges to a preset target landing point;
when the expansion early warning areas of a plurality of obstacles are overlapped, the complex obstacle terrain is divided into a plurality of obstacle areas which are not mutually influenced by combining and surrounding each obstacle, the complex obstacle terrain is simplified, and the problem that a repulsion force potential function generated by a plurality of obstacles is excessively overlapped in a certain area to generate a local minimum value is further avoided;
repulsive potential function phirIs represented as follows:
Figure FDA0003249861140000037
wherein r islx、rly、rlzRepresenting the position of the lander at the current moment under the landing site fixed coordinate system;
Figure FDA0003249861140000041
characterised by the distance, k, of the current position of the lander in the horizontal direction from the jth obstacle centrerFor the weight coefficient to be designed, and requires krIs greater than 0; n is the total number of obstacles; x is the number ofjo、yjo、zjoAnd djoIs the center position, height and cylinder radius of the danger zone cylinder corresponding to the jth obstacle in the horizontal direction, deltajoAnd deltajhArtificially defined threshold values respectively representing the height and the radius of the cylinder of the warning area corresponding to the jth obstacle and satisfying deltajo＞djo> 0 and deltajh＞zjo＞0；
To quantitatively express the repulsive potential function phirRange of influence of each obstacle, kja、kjha、kjoAnd kjhoThe design of (2) is as follows:
Figure FDA0003249861140000042
Figure FDA0003249861140000043
Figure FDA0003249861140000044
Figure FDA0003249861140000045
the obtained novel artificial potential function form is as follows:
Figure FDA0003249861140000046
the repulsion force potential function form can effectively avoid the problem that the lander falls into a local minimum value;
and 4, step 4: designing a sliding mode control law suitable for a constant-thrust engine on the basis of the sliding mode surface established in the step 2 and the potential function obtained in the step 3, and introducing a dead zone to improve the control law so as to reduce buffeting and fuel consumption caused by frequently switching the thrust direction of the engine;
the specific implementation method of the step 4 is as follows:
the control law is designed as follows:
Figure FDA0003249861140000051
wherein sgn is a sign function;
the dead zone is introduced to equation (21) for control law improvement:
Figure FDA0003249861140000052
wherein, f(s)i)tIs defined as:
Figure FDA0003249861140000053
wherein, χi(i ═ 1,2,3) and ψi(i ═ 1,2,3) is an artificially set dead zone threshold, and ψ existsi＜χi(i ═ 1,2,3) are all positive numbers, and subscript t- Δ t denotes the control amount at the previous time;
the control law is improved through formulas (20) - (22), and buffeting and fuel consumption caused by frequently switching the thrust direction of the engine are reduced;
further comprising the step 5: the control method for the asteroid landing by the complex small celestial body surface landing obstacle avoidance constant thrust control method is applied, so that the problem that the lander falls into a local minimum value area due to a potential function guidance method can be effectively solved, and obstacle avoidance and accurate landing of the lander under the action of constant thrust are guaranteed.
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