CN112000132A - Spacecraft obstacle avoidance control method based on ellipsoid description - Google Patents

Spacecraft obstacle avoidance control method based on ellipsoid description Download PDF

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CN112000132A
CN112000132A CN202010650580.4A CN202010650580A CN112000132A CN 112000132 A CN112000132 A CN 112000132A CN 202010650580 A CN202010650580 A CN 202010650580A CN 112000132 A CN112000132 A CN 112000132A
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ellipsoid
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曹璐
冉德超
刘勇
王建
张飞
王凯
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National Defense Technology Innovation Institute PLA Academy of Military Science
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Abstract

The invention discloses a spacecraft obstacle avoidance control method based on ellipsoid description. The method is used for realizing autonomous obstacle avoidance of the target spacecraft and the tracking spacecraft, and comprises the following steps: establishing a coordinate system, establishing a relative kinetic equation, determining the shortest distance between an obstacle and a tracked spacecraft, establishing an artificial potential function, calculating attraction control force, calculating repulsion control force and calculating total control force. According to the spacecraft obstacle avoidance control method based on ellipsoid description, the shapes of the spacecraft and the obstacle are described by the ellipsoid, so that the modeling precision can be improved to improve the spacecraft control precision; meanwhile, the repulsion potential function is designed by using the Sigmoid function to generate the obstacle avoidance control force, the attraction potential function is designed by using the state dependence Riccati equation to generate the attraction control force, the integrated design of the corresponding controller is completed by using the terminal sliding mode control theory, the rapid obstacle avoidance control of the spacecraft can be realized, the control precision is high, the fuel consumption rate is low, and the method can be suitable for the on-orbit real-time operation of the spacecraft.

Description

Spacecraft obstacle avoidance control method based on ellipsoid description
Technical Field
The invention relates to the technical field of spacecraft motion control, in particular to a spacecraft obstacle avoidance control method based on ellipsoid description.
Background
In recent years, the number of on-orbit failure events of a spacecraft is increasing, in order to reduce the occurrence probability of the on-orbit failure events, prolong the working life of the spacecraft and improve the working performance, more and more on-orbit services are applied to the spacecraft, the close-range operation of the spacecraft is taken as a basic technology supporting the on-orbit services, and the close-range operation of the spacecraft needs to meet strict safety requirements.
Space environment is deteriorating with the increase of human space activity, and more space debris, space shuttle garbage and failed spacecrafts become fatal obstacles for space rendezvous and operation of spacecrafts. Therefore, when the spacecraft works in the space, the spacecraft needs to be strictly controlled to ensure that the spacecraft can avoid obstacles, and collision-free intersection and operation are realized.
At present, two methods are mainly adopted to realize obstacle avoidance control of a spacecraft; the method comprises the steps of describing an outer envelope of an obstacle by a sphere, converting a control problem of the spacecraft for avoiding the obstacle into an optimization problem of multipath constraint, and solving by adopting an optimal theory. For example, a hybrid linear programming theory is adopted to improve a predictive control algorithm, so that a spacecraft obstacle avoidance strategy for solving the problem of fuel consumption is obtained; on the basis, the nonlinear constraint of the autonomous rendezvous optimal control is solved based on a continuous quadratic programming method, a safe track with the optimal fuel is designed by considering a path planning algorithm, and the optimization target of the obstacle avoidance path is realized. And secondly, carrying out collision avoidance control design by utilizing an artificial potential function, carrying out outer envelope description on the obstacle by using a sphere, and carrying out minimum design on a target function by designing a cost function to realize autonomous obstacle avoidance control of the spacecraft.
The inventor finds that the prior art has at least the following problems:
the spacecraft collision avoidance control method based on the optimal theory cannot effectively guarantee the safety of a control result on an obstacle avoidance target, and the obstacle avoidance control design is carried out by adopting the optimal theory, so that the calculation complexity is high, and the spacecraft collision avoidance control method is not suitable for the on-orbit real-time operation of a spacecraft; although the calculated amount is small, the obstacle avoidance control method using the artificial potential function cannot adopt an optimization strategy, so that the energy consumption of the control strategy cannot be optimized, and the fuel consumption of the spacecraft is high; in addition, the existing method adopts a simple sphere to carry out outer envelope description on the obstacle, so that the description precision is poor, and the control error is large.
Disclosure of Invention
In order to solve the technical problems in the prior art, the invention provides an ellipsoid description-based spacecraft obstacle avoidance control method.
Therefore, the invention discloses an ellipsoid description-based spacecraft obstacle avoidance control method, which is used for realizing autonomous obstacle avoidance of a service spacecraft, wherein the service spacecraft comprises a target spacecraft and a tracking spacecraft, and the method comprises the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a relative kinetic equation: establishing a relative motion equation of the tracking spacecraft and the target spacecraft under an orbit coordinate system, determining a state vector of the tracking spacecraft, and acquiring a relative kinetic equation of the target spacecraft and the tracking spacecraft;
determining the shortest distance between the obstacle and the tracked spacecraft: describing the outer envelope of the obstacle and the tracking spacecraft by using an ellipsoid, determining a structural equation of the outer envelope ellipsoid of the obstacle and the tracking spacecraft, and determining the shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft based on the structural equation of the ellipsoid;
establishing an artificial potential function: establishing an artificial potential function comprising a gravitational potential function and a repulsive potential function based on a structural equation of an ellipsoid;
calculating an attraction control force: calculating and determining the attraction control force by using a state dependence Riccati equation and a terminal sliding film control theory;
calculating the repulsion control force: carrying out derivation processing on the repulsive force function, and calculating and determining repulsive control force;
and (3) calculating total control force: and calculating and determining the total control force acting on the tracking spacecraft according to the attraction control force and the repulsion control force.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, establishing a coordinate system includes:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, the equation of relative motion between the tracked spacecraft and the target spacecraft is as follows:
Figure BDA0002574799900000021
wherein r ═ x, y, z]TAnd
Figure BDA0002574799900000022
representing the relative position and relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft, x, y and z representing the coordinates of the tracking spacecraft in the x-direction, y-direction and z-direction of the orbital coordinate system, respectively,
Figure BDA0002574799900000031
and
Figure BDA0002574799900000032
respectively representing the relative velocity of the tracked spacecraft in the x-direction, the y-direction and the z-direction of the orbital coordinate system, u ═ u [ < u >x,uy，uz]TRepresenting the control acceleration, u, of the tracked spacecraftx、uyAnd uzRespectively represents the control acceleration of the tracking spacecraft in the x direction, the y direction and the z direction of an orbit coordinate system, mu is an earth gravity constant,
Figure BDA0002574799900000033
a and n are the orbit semi-major axis and the average angular velocity of the target spacecraft.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, the state vector of the tracked spacecraft is represented as:
Figure BDA0002574799900000034
the relative kinetic equation of the target spacecraft and the tracking spacecraft is as follows:
Figure BDA0002574799900000035
wherein A is a state transition matrix, B is a control matrix,
Figure BDA0002574799900000036
Figure BDA0002574799900000037
r represents the relative distance between the target spacecraft and the tracking spacecraft,mu is the gravitational constant, ω and
Figure BDA0002574799900000038
representing the angular velocity and angular acceleration of the target spacecraft, respectively.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, the structural equations of the obstacle and the outer envelope ellipsoid of the tracking spacecraft are as follows:
(l-li)TMi(l-li)＝1(i＝c,o)
wherein, when i is c, the structure equation of the outer envelope ellipsoid of the tracking spacecraft is corresponded, when i is o, the structure equation of the outer envelope ellipsoid of the obstacle is corresponded, l represents any point on the outer envelope ellipsoid of the following spacecraft or the obstacle, and l represents the maximum value of the outer envelope ellipsoid of the following spacecraft or the obstaclec＝[xc,yc,zc]TRepresenting the centroid of the ellipsoid of the outer envelope of the tracked spacecrafto＝[xo,yo,zo]TRepresenting the centroid of the outer envelope ellipsoid of the obstacle, MiRepresenting an ellipsoid space size influence matrix, assuming that three main axes of the ellipsoid are consistent with a reference coordinate system, the reference coordinate system is a main system for tracking the spacecraft, and the matrix MiIs denoted as Mi＝diag(ai,bi,ci)，ai、biAnd ciRespectively representing the semimajor axis size of the ellipsoid on its three major axes.
Further, in the spacecraft obstacle avoidance control method based on ellipsoid description, the shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft is calculated and determined by adopting a characteristic value method based on the structural equation of the ellipsoid.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, the gravitational potential function is in a quadratic function form, and the gravitational potential function is expressed as:
Figure BDA0002574799900000041
wherein phi isaRepresenting the gravitational potential function, r ═ x, y, z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TAnd the target position of the tracking spacecraft under the orbit coordinate system of the target spacecraft is shown, and M is a positive definite symmetric matrix.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, the repulsive force potential function is designed and generated by using a Sigmoid potential function, and the repulsive force potential function is expressed as:
Figure BDA0002574799900000042
wherein phi isrDenotes the repulsive potential function, dctAnd dotRespectively representing the distances from the centroids of the target spacecraft and the tracking spacecraft to the expected target position, d representing the shortest Euclidean distance between the obstacle and the spacecraft, dsRepresenting the minimum stopping distance of the tracked spacecraft, gamma representing the barrier influence range coefficient, e representing the natural logarithm, dsCalculated by the following formula;
Figure BDA0002574799900000043
amaxrepresenting the maximum acceleration, v, of the tracked spacecraftcoRepresenting relative parallel velocity, vcoCalculated by the following formula;
Figure BDA0002574799900000044
Figure BDA0002574799900000045
indicating the speed at which the spacecraft is being tracked,
Figure BDA0002574799900000046
which represents the velocity of the target spacecraft,
Figure BDA0002574799900000047
representing the euclidean distance of a point on the outer envelope of the obstacle,
Figure BDA0002574799900000048
representing the euclidean distance of a point on the outer envelope of the spacecraft.
Further, in the above spacecraft obstacle avoidance control method based on ellipsoid description, a negative gradient derived from a repulsive force potential function to a relative position is a repulsive control force, and based on the repulsive force potential function, the repulsive control force is calculated and determined by the following formula;
Figure BDA0002574799900000051
wherein k isrIndicating a repulsive control force, krIs the coefficient of repulsion.
Further, in the spacecraft obstacle avoidance control method based on ellipsoid description, the total control force acting on the tracking spacecraft is calculated and determined through the following formula;
u(t)＝ua(t)+ur(t)
wherein u (t) represents the total control force acting on the tracking spacecraft at time t, ua(t) the attraction control force acting on the tracked spacecraft at time t, ur(t) represents the repulsive control force acting on the tracking spacecraft at time t.
The technical scheme of the invention has the following main advantages:
according to the spacecraft obstacle avoidance control method based on ellipsoid description, the shapes of the spacecraft and the obstacle are described by the ellipsoid, so that the modeling precision can be improved to improve the spacecraft control precision; meanwhile, the repulsive force potential function of the spacecraft is designed by using the Sigmoid function to generate the obstacle avoidance control force, the attractive force function of the spacecraft is designed by using the state dependence Riccati equation to generate the attractive control force, the integrated design of the corresponding controller is completed by using the terminal sliding mode control theory, the rapid obstacle avoidance control of the spacecraft can be realized, the control precision is high, the fuel consumption rate is low, and the method can be suitable for the on-orbit real-time operation of the spacecraft.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a spacecraft obstacle avoidance control method based on ellipsoid description according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a coordinate system according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the specific embodiments of the present invention and the accompanying drawings. It is to be understood that the described embodiments are merely a few embodiments of the invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme provided by the embodiment of the invention is described in detail below with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a spacecraft obstacle avoidance control method based on ellipsoid description, which is used for implementing autonomous obstacle avoidance of a service spacecraft, where the service spacecraft includes a target spacecraft and a tracking spacecraft, and the method includes the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a relative kinetic equation: establishing a relative motion equation of the tracking spacecraft and the target spacecraft under an orbit coordinate system, determining a state vector of the tracking spacecraft, and acquiring a relative kinetic equation of the target spacecraft and the tracking spacecraft;
determining the shortest distance between the obstacle and the tracked spacecraft: describing the outer envelope of the obstacle and the tracking spacecraft by using an ellipsoid, determining a structural equation of the outer envelope ellipsoid of the obstacle and the tracking spacecraft, and determining the shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft based on the structural equation of the ellipsoid;
establishing an artificial potential function: establishing an artificial potential function comprising a gravitational potential function and a repulsive potential function based on a structural equation of an ellipsoid;
calculating an attraction control force: calculating and determining the attraction control force by using a state dependence Riccati equation and a terminal sliding film control theory;
calculating the repulsion control force: carrying out derivation processing on the repulsive force function, and calculating and determining repulsive control force;
and (3) calculating total control force: and calculating and determining the total control force acting on the tracking spacecraft according to the attraction control force and the repulsion control force.
Specifically, each step in the spacecraft obstacle avoidance control method based on ellipsoid description provided in an embodiment of the present invention is specifically set forth below.
(1) Establishing a coordinate system
In the method for controlling obstacle avoidance for a spacecraft based on ellipsoid description according to an embodiment of the present invention, as shown in fig. 2, establishing a coordinate system includes:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
(2) Establishing a relative kinetic equation
The reference orbit of the target spacecraft is set to be any elliptical orbit, and because the motion in the orbit plane is separated from the motion of the vertical orbit plane, the relative motion model is analyzed and calculated by adopting a mode of researching the relative motion in the same orbit plane. Thus, the relative motion equation of the tracking spacecraft and the target spacecraft can be expressed as:
Figure BDA0002574799900000071
wherein r is [ x, y, z ]]TAnd
Figure BDA0002574799900000072
representing the relative position and relative velocity of the tracking spacecraft in an orbital coordinate system (LVLH) of the target spacecraft, x, y and z representing the coordinates of the tracking spacecraft in the x-direction, y-direction and z-direction of the orbital coordinate system, respectively,
Figure BDA0002574799900000073
and
Figure BDA0002574799900000074
respectively representing the relative velocity of the tracked spacecraft in the x-direction, the y-direction and the z-direction of the orbital coordinate system, u ═ u [ < u >x,uy，uz]TRepresenting the control acceleration of the tracking spacecraft, i.e. the control law of the controller of the tracking spacecraft, ux、uyAnd uzRespectively represents the control acceleration of the tracking spacecraft in the x direction, the y direction and the z direction of an orbit coordinate system, mu is an earth gravity constant,
Figure BDA0002574799900000075
a and n are the orbit semi-major axis and the average angular velocity of the target spacecraft.
Further, the state vector X of the tracking spacecraft may be represented as:
Figure BDA0002574799900000076
meanwhile, a matrix a is defined as a state transition matrix, a matrix B is defined as a control matrix, and the matrix B represents three mutually independent control quantities, and the state transition matrix a and the control matrix B are represented as:
Figure BDA0002574799900000077
Figure BDA0002574799900000078
combining the state vector X of the tracking spacecraft, the relative kinetic equation of the target spacecraft and the tracking spacecraft can be obtained as follows:
Figure BDA0002574799900000081
in formula 2, r represents the relative distance between the target spacecraft and the tracking spacecraft, ω and
Figure BDA0002574799900000082
representing angular velocity and angular acceleration, ω and
Figure BDA0002574799900000083
can be calculated according to the following formula;
Figure BDA0002574799900000084
Figure BDA0002574799900000085
in the formula, f represents the true perigee angle of the target spacecraft, and e represents the orbital eccentricity of the target spacecraft.
(3) Determining the shortest distance between an obstacle and a tracked spacecraft
And describing the outer envelope of the obstacle and the tracking spacecraft by using an ellipsoid, and establishing a structural equation of the ellipsoid of the outer envelope of the obstacle and the tracking spacecraft.
Specifically, the structural equation of the outer envelope ellipsoid can be expressed as:
(l-li)TMi(l-li)＝1(i＝c,o) (7)
in the formula, when i is c, the structural equation of the outer envelope ellipsoid of the tracked spacecraft is corresponded, when i is o, the structural equation of the outer envelope ellipsoid of the obstacle is corresponded, l represents any point on the outer envelope ellipsoid of the tracked spacecraft or the obstacle, and l represents the maximum value of the structural equation of the outer envelope ellipsoid of the tracked spacecraft or the obstaclec＝[xc,yc,zc]TRepresenting the centroid, x, of an ellipsoid of the outer envelope of the tracked spacecraftc、ycAnd zcRespectively representing the coordinates of the tracked spacecraft centroid in the x, y and z directions of the orbital coordinate system, lc＝r，lo＝[xo,yo,zo]TRepresenting the centroid, x, of the outer envelope ellipsoid of the obstacleo、yoAnd zoRespectively representing the coordinates of the center of mass of the obstacle in the x-direction, the y-direction and the z-direction of the orbital coordinate system, MiRepresenting an ellipsoid space size influence matrix, assuming that three main axes of the ellipsoid are consistent with a reference coordinate system, the reference coordinate system is a main system for tracking the spacecraft, and the matrix MiCan be represented as Mi＝diag(ai,bi,ci)，ai、biAnd ciRespectively representing the semimajor axis size of the ellipsoid on its three major axes.
Further, based on the determined structural equation of the outer envelope ellipsoid, a characteristic value method is adopted to calculate the shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft.
Specifically, the calculation of the shortest euclidean distance by using the eigenvalue method includes the following steps:
suppose that:
Figure BDA0002574799900000086
is a point on the outer envelope ellipsoid of the obstacle,
Figure BDA0002574799900000087
in order to track a point on the outer envelope ellipsoid of the spacecraft,
Figure BDA0002574799900000091
point and point
Figure BDA0002574799900000092
The distance between the points is the shortest Euclidean distance between the two ellipsoids.
According to Lagrange multiplier law, point
Figure BDA0002574799900000093
The coordinates of (c) can be determined by calculation of the following equation 8;
Figure BDA0002574799900000094
in the formula, λ1The lagrange multiplier is represented by a number of lagrange multipliers,
Figure BDA0002574799900000095
further, setting: matrix DcSatisfy the requirement of
Figure BDA0002574799900000096
I denotes an identity matrix, λ1Is a matrix DcMinimum eigenvalue, then point of
Figure BDA0002574799900000097
The coordinates of (a) can be determined by calculation of the following formula 9;
Figure BDA0002574799900000098
similarly, setting: matrix DoSatisfy the requirement of
Figure BDA0002574799900000099
Figure BDA00025747999000000910
Structural equation, λ, representing the outer envelope ellipsoid of an obstacle2Is a matrix DoMinimum eigenvalue, then point of
Figure BDA00025747999000000911
Can be determined by calculation of the following equation 10;
Figure BDA00025747999000000912
according to the obtained points
Figure BDA00025747999000000913
And point
Figure BDA00025747999000000914
The shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft can be calculated by using the following formula 11;
Figure BDA00025747999000000915
in the formula, d represents the shortest euclidean distance.
(4) Establishing an artificial potential function
The artificial potential function consists of two parts, including a gravitational potential function and a repulsive potential function, wherein the gravitational potential function is used for guiding the tracking spacecraft to move to a target position, the repulsive potential function is used for controlling the spacecraft to avoid an obstacle, and the mixed artificial potential function formed by superposing the gravitational potential function and the repulsive potential function can reflect the whole state space of the tracking spacecraft.
In one embodiment of the invention, the gravitational potential function can be expressed in a quadratic function form; in particular, the gravitational potential function phiaCan be expressed as:
Figure BDA0002574799900000101
wherein r is [ x, y, z ]]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TRepresenting the target position, x, of the tracking spacecraft in the orbital coordinate system of the target spacecraftf、yfAnd zfRespectively representing the target coordinates of the tracked spacecraft in the x direction, the y direction and the z direction of the orbit coordinate system, wherein M is a positive definite symmetric matrix.
Furthermore, the Sigmoid potential function can be used for describing the potential field of the obstacle with any shape, and meanwhile, the corresponding potential field model is analytic and continuous and differentiable in the first order, so that the continuous force generated in the action range can be ensured.
Therefore, in an embodiment of the invention, based on a structural equation of an ellipsoid, a repulsive force potential function caused by the generated barrier is designed by using a Sigmoid potential function.
Specifically, the potential field model general form of Sigmoid potential function is represented as:
Figure BDA0002574799900000102
in the formula, phirA potential field model representing Sigmoid potential function, N representing the number of surfaces constituting the obstacle, gamma representing the coefficient of the range of influence of the obstacle, e being the natural logarithm, SiA mathematical expression of a function representing the ith face of the obstacle.
Wherein when SiWhen the value is 0, the point falls on the curved surface of the obstacle, and the potential function value is 0.5; when S isiWhen the value is more than 0, the point is positioned in the curved surface of the obstacle, and the potential function value is a numerical value close to 1 and can be approximately equal to 1; when S isiIf the value is less than 0, the point is located outside the curved surface of the obstacle, and the potential function value is close to 0 and can be approximately equal to 0.
In an embodiment of the invention, according to the structural equation of the determined obstacle and the external envelope ellipsoid of the tracking spacecraft, the relative position relation S (r, r) between the obstacle and the centroid of the tracking spacecrafto) Can be expressed as:
S(r,ro)＝1-(r-ro)TMo(r-ro) (14)
in the formula, ro＝[xo,yo,zo]TRepresents the relative position of the centroid of the outer envelope ellipsoid of the obstacle under LVLH coordinate, and r is [ x, y, z ]]TRepresenting the relative position of the tracked spacecraft under LVLH, matrix Mo＝diag(ao,bo,co)，ao，boAnd coRespectively represents the semimajor axis sizes of the outer envelope ellipsoid of the obstacle on the three main axes.
Wherein, if S (r, r)o) If the mass center of the tracked spacecraft is larger than 0, the mass center of the tracked spacecraft is positioned in the envelope range of the envelope ellipsoid outside the obstacle; if S (r, r)o) When the mass center of the tracked spacecraft is 0, the mass center of the tracked spacecraft is located on the boundary line of the envelope range of the outer envelope ellipsoid of the obstacle; if S (r, r)o) If the mass center of the tracked spacecraft is less than 0, the mass center of the tracked spacecraft is positioned outside the envelope range of the envelope ellipsoid outside the obstacle.
And combining the general form of the potential field model of the Sigmoid potential function and the relative position relation expression between the obstacle and the centroid of the tracking spacecraft to obtain the repulsive potential function caused by the obstacle. In particular, the repulsive force potential function phi caused by an obstaclerCan be expressed as:
Figure BDA0002574799900000111
in the formula (d)ctAnd dotRespectively representing the distances from the centroids of the target spacecraft and the tracking spacecraft to the respective expected target positions, d representing the shortest Euclidean distance between the obstacle and the spacecraft, dsRepresenting the minimum stopping distance, d, of the tracked spacecraftsCan be determined by the calculation of equation 16;
Figure BDA0002574799900000112
in the formula, amaxRepresenting the maximum acceleration, v, of the tracked spacecraftcoRepresenting relative parallel velocity, vcoCan be determined by the calculation of equation 17;
Figure BDA0002574799900000113
in the formula (I), the compound is shown in the specification,
Figure BDA0002574799900000114
which represents the velocity of the target spacecraft,
Figure BDA0002574799900000115
indicating the speed at which the spacecraft is being tracked,
Figure BDA0002574799900000116
representing the euclidean distance of a point on the outer envelope of the obstacle,
Figure BDA0002574799900000117
representing the euclidean distance of a point on the outer envelope of the spacecraft.
(5) Calculating attraction control force
In one embodiment of the invention, the attraction control force is calculated and determined by using a state-dependent Riccati equation and a terminal sliding film control theory.
Specifically, the process of determining the attraction control force by using the state-dependent ricattes equation and the terminal synovial membrane control theory calculation is as follows:
the method comprises the steps of designing an optimal controller of a tracking spacecraft by adopting a State Dependent Riccati Equation (SDRE) suitable for a nonlinear system, and selecting an optimized performance index function according to an optimization control theory.
In an embodiment of the present invention, the selected optimized performance index function J may be:
Figure BDA0002574799900000121
wherein X denotes a state vector of the tracking spacecraft, Q denotes a weighting matrix, R denotes a semi-positive definite symmetric matrix, and u ═ u [ [ u ] ]x,uy，uz]TAnd the control law of a controller of the tracking spacecraft is shown, and Q and R are selected according to actual requirements.
According to the minimum value principle of the formula 18, an optimal controller u can be obtained*(X)：
u*(X)＝-R(X)-1B(X)TP(X)X(t) (19)
Wherein, R (X) represents a time-varying controlled variable weighting matrix, B (X) represents a state matrix before the controlled variable of the kinetic equation, X (t) represents a state vector at the time t, and P (X) is a positive definite matrix and satisfies the equation shown in the formula 20;
P(X)A(X)+A(X)P(X)+Q(X)-P(X)B(X)R(X)-1B(X)TP(X)＝0 (20)
in the formula, a (x) represents a state matrix before a state vector of a kinetic equation, and q (x) represents a weighting matrix of the state vector.
Further, by designing an integral synovial membrane controller in combination with the optimal controller shown in formula 19, an integral synovial membrane surface S can be obtained1(X,t)：
Figure BDA0002574799900000122
Wherein G is BTB denotes a control matrix, X (0) denotes an initial value of the state vector, and X (τ) denotes the state vector at time τ.
Based on the determined integral slide film surface, an equivalent controller can be obtained by using a formula 22 according to a terminal slide film control theory;
ueq(t)＝-R(X)-1B(X)TP(X)X(t) (22)
in the formula ueq(t) represents an equivalent controller.
In order to overcome the influence of external disturbance, the state variable of the tracked spacecraft needs to be gradually converged on a sliding film surface, in one embodiment of the invention, switching control is designed by combining an equivalent controller, specifically as shown in a formula 23;
usw(t)＝-(GB)-1ηsgn(S1)α (23)
in the formula usw(t) represents a switching control amount, > 0, η represents a switching function parameter, sgn (S)1)α＝[|S11|αsgn(S11),|S12|αsgn(S12),|S13|αsgn(S13)]T，S1＝[S11 S12 S13]TDenotes the slide face, S11、S12And S13Represents the synovial surface component, sgn (·) represents the sign function, and α represents the exponential parameter.
Based on the above-described design results of the optimum controller and the synovial controller, the attraction control force can be determined by calculation of the following equation 24;
ua(t)＝ueq(t)+usw(t) (24)
in the formula ua(t) represents an attraction control force, ueq(t) denotes an equivalent controller, usw(t) represents a switching control amount.
(6) Calculating a repulsive control force
Further, since the repulsion control force is used for controlling the spacecraft to avoid the obstacle, in the spacecraft obstacle avoidance control method based on the ellipsoid description provided in the embodiment of the present invention, based on the determined repulsion potential function caused by the obstacle, a negative gradient of the repulsion potential function derived from the relative position is defined as the corresponding repulsion control force, which is the obstacle avoidance control force, and the repulsion control force can be determined by calculation according to the following formula 25;
Figure BDA0002574799900000131
in the formula ur(t) denotes a repulsive control force, krIs the coefficient of repulsion.
(7) Calculating total control force
Further, on the basis of the above calculation and analysis, in an embodiment of the present invention, the total control force acting on the tracking spacecraft can be determined by the following formula 26;
u(t)＝ua(t)+ur(t)＝ueq(t)+usw(t)+ur(t) (26)
wherein u (t) represents the total control force acting on the tracked spacecraft at time t, ua(t) the attraction control force acting on the tracked spacecraft at time t, ur(t) represents the repulsive control force acting on the tracking spacecraft at time t.
Therefore, the ellipsoid description-based spacecraft obstacle avoidance control method provided by the embodiment of the invention adopts the ellipsoid to describe the shapes of the spacecraft and the obstacle, and can improve the modeling precision so as to improve the spacecraft control precision; meanwhile, the repulsive force potential function of the spacecraft is designed by using the Sigmoid function to generate the obstacle avoidance control force, the attractive force function of the spacecraft is designed by using the state dependence Riccati equation to generate the attractive control force, the integrated design of the corresponding controller is completed by using the terminal sliding mode control theory, the rapid obstacle avoidance control of the spacecraft can be realized, the control precision is high, the fuel consumption rate is low, and the method can be suitable for the on-orbit real-time operation of the spacecraft.
It is noted that, in this document, relational terms such as "first" and "second," and the like, may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. In addition, "front", "rear", "left", "right", "upper" and "lower" in this document are referred to the placement states shown in the drawings.
Finally, it should be noted that: the above examples are only for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. A spacecraft obstacle avoidance control method based on ellipsoid description is characterized in that the method is used for realizing autonomous obstacle avoidance of a service spacecraft, the service spacecraft comprises a target spacecraft and a tracking spacecraft, and the method comprises the following steps:
establishing a coordinate system: establishing an epoch J2000 earth inertia coordinate system, and establishing an orbit coordinate system of the target spacecraft on the basis of the earth inertia coordinate system;
establishing a relative kinetic equation: establishing a relative motion equation of the tracking spacecraft and the target spacecraft under an orbit coordinate system, determining a state vector of the tracking spacecraft, and acquiring a relative kinetic equation of the target spacecraft and the tracking spacecraft;
determining the shortest distance between the obstacle and the tracked spacecraft: describing the outer envelope of the obstacle and the tracking spacecraft by using an ellipsoid, determining a structural equation of the outer envelope ellipsoid of the obstacle and the tracking spacecraft, and determining the shortest Euclidean distance between the outer envelope ellipsoid of the obstacle and the outer envelope ellipsoid of the tracking spacecraft based on the structural equation of the ellipsoid;
establishing an artificial potential function: establishing an artificial potential function comprising a gravitational potential function and a repulsive potential function based on a structural equation of an ellipsoid;
calculating an attraction control force: calculating and determining the attraction control force by using a state dependence Riccati equation and a terminal sliding film control theory;
calculating the repulsion control force: carrying out derivation processing on the repulsive force function, and calculating and determining repulsive control force;
and (3) calculating total control force: and calculating and determining the total control force acting on the tracking spacecraft according to the attraction control force and the repulsion control force.
2. The spacecraft obstacle avoidance control method based on ellipsoid description of claim 1, wherein establishing a coordinate system comprises:
by using O-XIYIZIRepresenting epoch J2000 earth inertial coordinate system with earth center as origin of coordinates, XIThe axis points to epoch J2000 spring minute point, the earth equator plane is the basic plane, ZIAxial direction to the Earth's North Pole, YIAxis and XIAxis, ZIThe axes form a right-hand rectangular coordinate system;
the orbit coordinate system of the target spacecraft is represented by o-xyz, the centroid of the target spacecraft is a coordinate origin, the x axis points to the centroid of the target spacecraft from the earth geocentric, the y axis is perpendicular to the x axis in the orbit plane of the target spacecraft and points to the speed direction of the target spacecraft, the z axis is perpendicular to the orbit plane of the target spacecraft, and the z axis, the x axis and the y axis form a right-hand rectangular coordinate system.
3. The spacecraft close-range safe operation control method based on the equal collision probability line method according to any one of claims 1 to 2, characterized in that the relative motion equation of the tracking spacecraft and the target spacecraft is as follows:
Figure FDA0002574799890000011
wherein r ═ x, y, z]TAnd
Figure FDA0002574799890000012
representing the relative position and relative velocity of the tracking spacecraft in the orbital coordinate system of the target spacecraft, x, y and z representing the coordinates of the tracking spacecraft in the x-direction, y-direction and z-direction of the orbital coordinate system, respectively,
Figure FDA0002574799890000021
and
Figure FDA0002574799890000022
respectively representing the relative velocity of the tracked spacecraft in the x-direction, the y-direction and the z-direction of the orbital coordinate system, u ═ u [ < u >x,uy，uz]TRepresenting the control acceleration, u, of the tracked spacecraftx、uyAnd uzRespectively represents the control acceleration of the tracking spacecraft in the x direction, the y direction and the z direction of an orbit coordinate system, mu is an earth gravity constant,
Figure FDA0002574799890000023
a and n are the orbit semi-major axis and the average angular velocity of the target spacecraft.
4. The ellipsoid description-based spacecraft obstacle avoidance control method according to any one of claims 1 to 3, wherein a state vector of a tracked spacecraft is represented as:
Figure FDA0002574799890000024
the relative kinetic equation of the target spacecraft and the tracking spacecraft is as follows:
Figure FDA0002574799890000025
wherein A is a state transition matrix, B is a control matrix,
Figure FDA0002574799890000026
Figure FDA0002574799890000027
r represents the relative distance between the target spacecraft and the tracking spacecraft, μ is the Earth's gravitational constant, ω and
Figure FDA0002574799890000028
representing the angular velocity and angular acceleration of the target spacecraft, respectively.
5. The spacecraft obstacle avoidance control method based on ellipsoid description of any one of claims 1 to 4, wherein the structural equations of the obstacles and the outer envelope ellipsoid of the tracking spacecraft are as follows:
(l-li)TMi(l-li)＝1(i＝c,o)
wherein, when i is c, the structure equation of the outer envelope ellipsoid of the tracking spacecraft is corresponded, when i is o, the structure equation of the outer envelope ellipsoid of the obstacle is corresponded, l represents any point on the outer envelope ellipsoid of the following spacecraft or the obstacle, and l represents the maximum value of the outer envelope ellipsoid of the following spacecraft or the obstaclec＝[xc,yc,zc]TRepresenting the centroid, x, of an ellipsoid of the outer envelope of the tracked spacecraftc、ycAnd zcRespectively representing the coordinates of the tracked spacecraft centroid in the x, y and z directions of the orbital coordinate system, lo＝[xo,yo,zo]TRepresenting the centroid, x, of the outer envelope ellipsoid of the obstacleo、yoAnd zoRespectively representing the coordinates of the center of mass of the obstacle in the x-direction, the y-direction and the z-direction of the orbital coordinate system, MiRepresenting an ellipsoid space size influence matrix, assuming that three main axes of the ellipsoid are consistent with a reference coordinate system, the reference coordinate system is a main system for tracking the spacecraft, and the matrix MiIs denoted as Mi＝diag(ai,bi,ci)，ai、biAnd ciRespectively representing the semimajor axis size of the ellipsoid on its three major axes.
6. The spacecraft obstacle avoidance control method based on ellipsoid description of any one of claims 1 to 5, wherein a shortest Euclidean distance between an obstacle outer envelope ellipsoid and a tracking spacecraft outer envelope ellipsoid is calculated and determined by adopting a characteristic value method based on a structural equation of the ellipsoid.
7. The spacecraft obstacle avoidance control method based on ellipsoid description of any one of claims 1 to 6, wherein a gravitational potential function is in a quadratic function form, and the gravitational potential function is expressed as:
Figure FDA0002574799890000031
wherein phi isaRepresenting the gravitational potential function, r ═ x, y, z]TRepresenting the relative position of the tracking spacecraft in the orbital coordinate system of the target spacecraft, rf＝[xf,yf,zf]TAnd the target position of the tracking spacecraft under the orbit coordinate system of the target spacecraft is shown, and M is a positive definite symmetric matrix.
8. The spacecraft obstacle avoidance control method based on ellipsoid description of any one of claims 1 to 7, wherein a repulsive force potential function is designed and generated by using a Sigmoid potential function, and the repulsive force potential function is expressed as:
Figure FDA0002574799890000032
wherein phi isrDenotes the repulsive potential function, dctAnd dotRespectively representing the distances from the centroids of the target spacecraft and the tracking spacecraft to the expected target position, d representing the shortest Euclidean distance between the obstacle and the spacecraft, dsRepresenting the minimum stopping distance of the tracked spacecraft, gamma representing the barrier influence range coefficient, e representing the natural logarithm, dsCalculated by the following formula;
Figure FDA0002574799890000033
amaxrepresenting the maximum acceleration, v, of the tracked spacecraftcoRepresenting relative parallel velocity, vcoCalculated by the following formula;
Figure FDA0002574799890000034
Figure FDA0002574799890000035
which represents the velocity of the target spacecraft,
Figure FDA0002574799890000036
indicating the speed at which the spacecraft is being tracked,
Figure FDA0002574799890000037
representing the euclidean distance of a point on the outer envelope of the obstacle,
Figure FDA0002574799890000041
representing the euclidean distance of a point on the outer envelope of the spacecraft.
9. The spacecraft obstacle avoidance control method based on the ellipsoid description according to any one of claims 1 to 8, wherein a negative gradient of a repulsion potential function derived from a relative position is a repulsion control force, and the repulsion control force is calculated and determined by the following formula based on the repulsion potential function;
Figure FDA0002574799890000042
wherein k isrIndicating a repulsive control force, krIs the coefficient of repulsion.
10. The spacecraft obstacle avoidance control method based on the ellipsoid description according to any one of claims 1 to 9, wherein the total control force acting on the tracking spacecraft is calculated and determined by the following formula;
u(t)＝ua(t)+ur(t)
wherein u (t) represents the total control force acting on the tracking spacecraft at time t, ua(t) attraction control acting on the tracked spacecraft at time tBraking force ur(t) represents the repulsive control force acting on the tracking spacecraft at time t.
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