CN112896560A - Small celestial body surface safe bounce movement track planning method - Google Patents
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Abstract
The invention relates to a planning method for a safe bounce movement track of the surface of a small celestial body, belonging to the technical field of deep space exploration. The invention takes the position information of the current position of the detector relative to the target point into consideration to construct a cost value J for measuring the motion state of the detector. Based on a given search radius and a search angle meeting normal distribution, a sample space of the detector bounce landing point is given, and a corresponding number of sample points meeting requirements are selected from the sample space. Based on the idea of multi-step prediction, a new sample space is generated for the sample points of the outer layer, the next layer of sample points is selected, and the steps are repeated until the sample points of the corresponding layer number are generated. Integrating the cost values of the multiple layers of sample points to obtain the weighted cost value of the first layer of sample points
And selecting the sample point with the minimum weighted cost value as the next intermediate landing point. Establishing detector motion based on projectile motionThe kinetic model is simplified and the detector trajectory is generated using the model. By repeating the above processes, the detector can safely and remotely move on the surface of the small celestial body.
Description
Technical Field
The invention relates to a method for planning a safe bounce movement track of the surface of a small celestial body, which is particularly suitable for the remote movement of a deep space probe on the surface of the small celestial body with irregular weak gravitation and belongs to the technical field of deep space probe.
Background
The small celestial body has many characteristics, so that the small celestial body gradually becomes one of hot spots and focuses in the international aerospace field, and the exploration mode of the small celestial body is also developed from initial observation to fly-over detection, orbit surrounding, impact detection, landing detection and sampling return. In order to further acquire detailed shape information and composition information of the small celestial body and acquire more samples with different properties, the surface movement detection of the small celestial body needs to be studied deeply. Because the small celestial body surface gravitation is weak and can not provide enough friction force, the small celestial body surface detection task usually does not select a wheel-driven detector, but adopts a bounce detector which is less influenced by the gravitation and the terrain and has a wider detection area, and meanwhile, the detector has the characteristics of simple structure and great advantage in cost. The detector is limited by self thrust and small celestial body gravity in the bouncing process, and often needs to bounce for multiple times to reach a destination, so that a research and planning method is needed to design a middle landing point and a bouncing track of the detector so as to realize safe and accurate bouncing of the detector on the surface of a small celestial body.
In the developed method for Planning the moving track of the Surface of the small celestial body, in the prior art [1] (see Kalia H, Thangvelautham J. motion Planning on an iterative Surface with Irregularg gradient Fields [ J ]. Advances in the advanced analytical Sciences,2019,17:1-11.), a detector track of single bounce is obtained by solving a Lambert edge value problem and modifying, a probability path Planning of long-distance bounce is realized by using a random sample, and an optimal bounce track is selected by using an evolutionary algorithm. However, the method has huge calculation amount and higher requirement on the calculation capability of the detector, does not consider the problem of fluctuation of the surface topography of the small celestial body, and cannot effectively avoid obstacles in the bouncing process.
In the prior art [2] (see Shen H, Zhang T, Li Z, Li H. multiple-bearing objectives Near a rolling anode [ J ]. Asprophysics and Space Science,2017,362:45.), an ant colony algorithm is adopted to plan the bounce track of the detector on the surface of a small celestial body, and an accurate dynamic model is adopted in the planning process. However, the method does not model and control the collision of the detector on the surface of the small celestial body, so that when the size of the small celestial body is small, a large error exists in the calculated surface bounce track.
Disclosure of Invention
The invention aims to solve the problem that the calculation amount, accuracy and safety cannot be considered in the bounce type detector track planning method for moving on the surface of a small celestial body in the prior art.
The purpose of the invention is realized by the following technical scheme.
The invention discloses a planning method for a safe bounce movement track of a small celestial body surface, which is used for constructing a cost value J for measuring the motion state of a detector by considering the position information of the current position of the detector relative to a target point. Based on a given search radius and a search angle meeting normal distribution, a sample space of the detector bounce landing point is given, and a corresponding number of sample points meeting requirements are selected from the sample space. Based on the idea of multi-step prediction, a new sample space is generated for the sample points of the outer layer, the next layer of sample points is selected, and the steps are repeated until the sample points of the corresponding layer number are generated. Integrating the cost values of the multiple layers of sample points to obtain a weighted cost value J of the first layer of sample pointsDiAnd selecting the sample point with the minimum weighted cost value as the next intermediate landing point. And establishing a simplified dynamic model of the detector motion based on the oblique projectile motion, and generating a detector track by using the model. By repeating the above processes, the detector can safely and remotely move on the surface of the small celestial body.
The method for planning the safe bounce movement track of the surface of the small celestial body comprises the following steps:
step 1: taking the current position of the detector as a principal point rHCalculating the cost value J of the detector principal pointH。
The cost value J is defined as follows
Wherein the content of the first and second substances,
is the current and target point vectors r of the detectortThe included angle between them; d is the distance of the detector relative to the target point; psi is the weighting coefficient of the distance, and the value psi is more than or equal to 0. Selecting d and
as a parameter of the cost value, the distance to the target point can be shortened quickly, and a rugged terrain can be avoided to a certain extent by reducing psi.
Taking the current position of the detector as a principal point rHCalculating the cost value J of the main point of the detector by substituting formula (1)H。
Step 2: and selecting a corresponding number of sample points meeting the requirement in the principal point generated sample space sigma, repeatedly generating a sample space for the new sample points, selecting a next layer of sample points in the new space, and repeating the process until M layers of sample points are generated.
Sigma is given in the form of
Wherein D is a search radius; z is a height coordinate under a surface coordinate system; d' is the search radius at height z; theta is the search azimuth angle and satisfies the normal distribution theta-N (0, sigma)2) σ is a normal distributionStandard deviation; points in the search space should fall on the small celestial body, so there are [ D 'cos θ D' sin θ z]T∈surface。
As shown in fig. 2, the surface coordinate system is established as follows: the origin s is the starting point of the detector, and T is the vector of the starting point of the single bounce pointing to the target point. g is the gravity acceleration vector at the starting point. The sn axis is the vector in the plane of T-g, perpendicular to the vector T and pointing outside the celestial object. The sk axis and the st axis and the sn axis form a right-hand system.
Generating a sample space under the surface coordinate system, and randomly selecting L sample points in the sample space to form a first layer of prediction points, wherein each point r1,iShould satisfy, r1,i∈{∑|J1,i<JH,i＝1,...,L}，J1,iIs a is and r1,iCorresponding cost values, where 1 represents a first layer sample space and i represents a first layer sample point order; establishing a surface coordinate system of the first layer of predicted points, and further generating respective sample spaces sigma of the first layer of predicted points1,iAnd in the sample space ∑1,iRandomly selecting L sample points to form a second layer of prediction points, wherein each point satisfies r2,i,j∈{∑1,i|J2,i,j<J1,i,j＝1,...,N}，J2,i,jIs a is and r2,i,jCorresponding cost values, where 2 represents the second layer sample space and j represents the second layer sample point order. And repeating the generation of the sample space and the selection of the sample points until M layers of prediction points are generated.
And step 3: computing a weighted cost value J for the first layer sample pointsDiAnd selecting the optimal prediction point.
Wherein w is a weight coefficient of each layer cost value.
Predicting the first layer in the point
The smallest intermediate landing site that acts as a bounce.
And 4, step 4: obtaining an initial speed required by transfer by using a simplified dynamic model, wherein the transfer refers to the bounce from a current principal point to an intermediate landing point; and controlling the detector to complete corresponding bouncing movement by using the pulse motor.
The detector has a small movement distance in single bounce, so that the influence caused by the change of a gravitational field can be ignored, namely the gravitational force borne by the detector in single bounce is a constant value, and the single bounce of the detector can be regarded as oblique throwing movement under a surface coordinate system. gtAnd gnThe gravity acceleration vector g is the component of the st axis and the sn axis. Given the time t required for a single bouncepThe components of the initial velocity vector v of the detector along the st axis and the sn axis under the surface coordinate system can be calculated
The trajectory and velocity of the detector are time-varying as follows
Wherein x ist，xnRespectively representing the components of the coordinate along the st axis and the sn axis along the time change in the process of transferring the detector under the surface system; v. oft，vnThe components of the speed along the st axis and the sn axis along the time change in the process of transferring the surface system lower detector are respectively; t is the time of detector transfer.
And according to the obtained initial speed, utilizing the pulse engine to realize the bouncing movement between the main point and the predicted intermediate landing point.
And 5: and (4) when the landing point of the bouncing movement in the step (4) does not reach the target point, repeating the planning control process from the step (1) to the step (4), and when the detector is transferred to the target point through the bouncing for multiple times, finishing the control of the detector on the surface of the small celestial body.
And (3) predicting a plurality of future landing sites of the detector according to the M layers of predicted points obtained in the step (2), and filtering out the locally optimal intermediate landing sites by using the multi-step predicted landing site information so as to find out the globally optimal intermediate landing sites.
Has the advantages that:
1. according to the method for planning the safe bounce movement track of the small celestial body surface, disclosed by the invention, the position information of the detector position and the sample point relative to the target point is quantized into simple and easily calculated scalar quantities by constructing the cost value J, so that the high-efficiency selection of the sample point is realized, and meanwhile, the rough terrain can be avoided to a certain extent by changing the weighting coefficient psi, so that the method has rapidity and safety.
2. The invention discloses a planning method for safe bounce movement locus of small celestial body surface, which is characterized in that multi-step predicted information is merged into a weighted cost value J through generation of a multi-layer sample space and selection of sample pointsDiThe optimal middle landing point is selected by the calculation of the step (2), and the accuracy and the rapidity of the bounce process are improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a surface coordinate system used in the generation of sample space and simplified motion modeling of the present invention;
FIG. 3 is a diagram of the bounce simulation result of the detector according to the embodiment of the present invention, wherein (a) is the track of the detector, (b) is the change of the three-axis position of the detector in the fixed coordinate system of the small celestial body, and (c) is the change of the three-axis velocity of the detector in the fixed coordinate system of the small celestial body.
Detailed Description
To better illustrate the objects and advantages of the present invention, the following further description is made with reference to the accompanying drawings and examples.
In order to verify the feasibility of the invention, the Eros 433 minor planet is taken as an example, and the simulation analysis is carried out on the method under the given initial conditions. The starting point coordinates of the probe [ -166.84; 6084.44, respectively; 1586.45]Meter, target point coordinates [ -4528.77; 7876.55, respectively; -1354.66]The method comprises the steps of measuring the single bounce time t, wherein the number L of predicted points in a sample space is 20, the number M of sample space layers is 2, the standard difference sigma of a search angle is 4.47 degrees, the search radius D is 600 metersp900 seconds, a cost value coefficient ψ 1, a multi-layer cost value weight coefficient w 1; 0.3]And performing mathematical simulation verification.
As shown in fig. 1, the method for planning the safe bounce movement track of the surface of the small celestial body disclosed by the embodiment specifically includes the following steps:
step 1: taking the current position of the detector as a principal point rHCalculating its cost value JH。
Wherein the cost value J is defined as follows
Wherein the content of the first and second substances,
is the current and target point vectors r of the detectortThe included angle between them; d is the distance of the detector relative to the target point; psi is the weighting coefficient of the distance, and the value psi is more than or equal to 0. Selecting d and
as a parameter of the cost value, the distance to the target point can be shortened quickly, and a rugged terrain can be avoided to a certain extent by reducing psi.
Taking the current position of the detector as a principal point rHCalculating the cost value J of the main point of the detector by substituting formula (1)H。
Step 2: and selecting a corresponding number of sample points meeting the requirement in the principal point generated sample space sigma, repeatedly generating a sample space for the new sample points, selecting a next layer of sample points in the new space, and repeating the process until M layers of sample points are generated.
Sigma is given in the form of
Wherein D is a search radius; z is a height coordinate under a surface coordinate system; d' is the search radius at height z; theta is the search azimuth angle and satisfies the normal distribution theta-N (0, sigma)2) And sigma is a normal distribution standard deviation; points in the search space should fall on the small celestial body, so there are [ D 'cos θ D' sin θ z]T∈surface。
As shown in fig. 2, the surface coordinate system is established as follows: the origin s is the starting point of the detector, and T is the vector of the starting point of the single bounce pointing to the target point. g is the gravity acceleration vector at the starting point. The sn axis is the vector in the plane of T-g, perpendicular to the vector T and pointing outside the celestial object. The sk axis and the st axis and the sn axis form a right-hand system.
Generating a sample space under the surface coordinate system, and randomly selecting L sample points in the sample space to form a first layer of prediction points, wherein each point r1,iShould satisfy, r1,i∈{∑|J1,i<JH,i＝1,...,L}，J1,iIs a is and r1,iCorresponding cost values, where 1 represents a first layer sample space and i represents a first layer sample point order; establishing a surface coordinate system of the first layer of predicted points, and further generating respective sample spaces sigma of the first layer of predicted points1,iAnd in the sample space ∑1,iRandomly selecting L sample points to form a second layer of prediction points, wherein each point satisfies r2,i,j∈{∑1,i|J2,i,j<J1,i,j＝1,...,N}，J2,i,jIs a is and r2,i,jCorresponding cost values, where 2 represents the second layer sample space and j represents the second layer sample point order. And repeating the generation of the sample space and the selection of the sample points until M layers of prediction points are generated.
And step 3: computing a weighted cost value J for the first layer sample pointsDiAnd selecting the optimal prediction point.
Wherein w is a weight coefficient of each layer cost value.
Selecting the first layer of predicted points
The smallest intermediate landing site that acts as a bounce.
And 4, step 4: obtaining an initial speed required by transfer by using a simplified dynamic model, wherein the transfer refers to the bounce from a current principal point to an intermediate landing point; and controlling the detector to complete corresponding bouncing movement by using the pulse motor.
The detector has a small movement distance in single bounce, so that the influence caused by the change of a gravitational field can be ignored, namely the gravitational force borne by the detector in single bounce is a constant value, and the single bounce of the detector can be regarded as oblique throwing movement under a surface coordinate system. gtAnd gnThe component of the gravitational acceleration g on the st axis and the sn axis. Given the time t required for a single bouncepThe components of the initial velocity vector v of the detector along the st axis and the sn axis under the surface coordinate system can be calculated
The trajectory and velocity of the detector are time-varying as follows
Wherein x ist，xnRespectively representing the components of the coordinate along the st axis and the sn axis along the time change in the process of transferring the detector under the surface system; v. oft，vnThe components of the speed along the st axis and the sn axis along the time change in the process of transferring the surface system lower detector are respectively; t is the time of detector transfer.
And according to the obtained initial speed, utilizing the pulse engine to realize the bouncing movement between the main point and the predicted intermediate landing point.
And 5: and (4) when the landing point of the bouncing movement in the step (4) does not reach the target point, repeating the planning control process from the step (1) to the step (4), and when the detector is transferred to the target point through the bouncing for multiple times, finishing the control of the detector on the surface of the small celestial body.
In the simulation, the detector bounces for 9 times in total, and the coordinates of the bounced middle landing point under the small celestial body fixed coordinate system are shown in the table
TABLE 1 intermediate landing Point coordinates
| Sequence number of intermediate landing point | Middle landing point coordinate (m) |
| 1 | [-166.84；6084.44；1586.45] |
| 2 | [-494.41；6586.89；-1601.95] |
| 3 | [-934.54；6993.96；-1577.78] |
| 4 | [-1385.94；7387.34；-1539.09] |
| 5 | [-1833.37；7786.49；-1560.95] |
| 6 | [-2378.41；8037.34；-1557.58] |
| 7 | [-2953.99；8204.78；-1531.73] |
| 8 | [-3551.69；8159.43；-1505.35] |
| 9 | [-4134.89；8039.60；-1431.06] |
| 10 | [-4530.08；7874.17；-1361.66] |
The obtained detector bounce track is shown in fig. 3(a), the change of the three-axis position of the detector along with time is shown in fig. 3(b) under the small celestial body fixed coordinate system, and the change of the three-axis speed of the detector along with time is shown in fig. 3(c) under the small celestial body fixed coordinate system.
And then, the control of the bounce of the deep space probe on the surface of the small celestial body is completed.
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 planning method for the safe bounce movement track of the surface of the small celestial body is characterized by comprising the following steps of: the method comprises the following steps:
step 1: taking the current position of the detector as a principal point rHCalculating the cost value J of the detector principal pointH；
The cost value J is defined as follows
Wherein the content of the first and second substances,
is the current and target point vectors r of the detectortThe included angle between them; d is the distance of the detector relative to the target point; psi is a weighting coefficient of the distance, and the value phi meets the condition that psi is more than or equal to 0; selecting d and
as a parameter of the cost value, the distance between the target point and the ground can be shortened rapidly, and rugged terrain can be avoided to a certain extent by reducing psi;
taking the current position of the detector as a principal point rHCalculating the cost value J of the main point of the detector by substituting formula (1)H；
Step 2: selecting a corresponding number of sample points meeting the requirement from the principal point generated sample space sigma, repeatedly generating a sample space for a new sample point, selecting a next layer of sample points from the new space, and repeating the process until M layers of sample points are generated;
sigma is given in the form of
Wherein D is a search radius; z is a height coordinate under a surface coordinate system; d' is the search radius at height z; theta is the search azimuth angle and satisfies the normal distribution theta-N (0, sigma)2) And sigma is a normal distribution standard deviation; points in the search space should fall on the small celestial body, so there are [ D 'cos θ D' sin θ z]T∈surface；
As shown in fig. 2, the surface coordinate system is established as follows: the origin s is a detector starting point, and T is a vector pointing to a target point from the starting point of single bounce; g is a gravity acceleration vector at a starting point; the sn axis is a vector which is perpendicular to the vector T in the plane of the T-g and points to the outer side of the small celestial body; the sk axis, the st axis and the sn axis form a right-hand system;
generating a sample space under the surface coordinate system, and randomly selecting L sample points in the sample space to form a first layer of prediction points, wherein each point r1,iShould satisfy, r1,i∈{∑|J1,i<JH,i＝1,...,L}，J1,iIs a is and r1,iCorresponding cost values, where 1 represents a first layer sample space and i represents a first layer sample point order; establishing a surface coordinate system of the first layer of predicted points, and further generating respective sample spaces sigma of the first layer of predicted points1,iAnd in the sample space ∑1,iRandomly selecting L sample points to form a second layer of prediction points, wherein each point satisfies r2,i,j∈{∑1,i|J2,i,j<J1,i,j＝1,...,N}，J2,i,jIs a is and r2,i,jCorresponding cost values, where 2 represents the second layer sample space and j represents the second layer sample point order; repeating the generation of the sample space and the selection of the sample points until M layers of prediction points are generated;
and step 3: computing weighted cost values for first layer sample points
Selecting an optimal prediction point;
Wherein, w is the weight coefficient of each layer cost value;
predicting the first layer in the point
The smallest intermediate landing site that is a bounce;
and 4, step 4: obtaining an initial speed required by transfer by using a simplified dynamic model, wherein the transfer refers to the bounce from a current principal point to an intermediate landing point; controlling the detector to complete corresponding bouncing movement by using a pulse engine;
the detector has a small movement distance in single bounce, so that the influence caused by the change of a gravitational field can be ignored, namely the gravitation borne by the detector in single bounce is a constant value, and the single bounce of the detector can be regarded as oblique throwing movement under a surface coordinate system; gtAnd gnThe components of the gravity acceleration vector g on the st axis and the sn axis; given the time t required for a single bouncepThe components of the initial velocity vector v of the detector along the st axis and the sn axis under the surface coordinate system can be calculated
The trajectory and velocity of the detector are time-varying as follows
Wherein x ist，xnRespectively representing the components of the coordinate along the st axis and the sn axis along the time change in the process of transferring the detector under the surface system; v. oft，vnThe components of the speed along the st axis and the sn axis along the time change in the process of transferring the surface system lower detector are respectively; t is the time of detector transfer;
according to the obtained initial speed, a pulse engine is utilized to realize bouncing movement between the main point and the predicted middle landing point;
and 5: when the landing point of the bouncing movement in the step (4) does not reach the target point, the planning control process from the step (1) to the step (4) is repeated, and when the detector is transferred to the target point through the bouncing for multiple times, the control of the detector for bouncing on the surface of the small celestial body is completed;
and (3) predicting a plurality of future landing sites of the detector according to the M layers of predicted points obtained in the step (2), and filtering out the locally optimal intermediate landing sites by using the multi-step predicted landing site information so as to find out the globally optimal intermediate landing sites.
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