Adaptive control method for hovering detection of binary asteroid

Abstract

The application discloses a binary asteroid hovering probe adaptive control method, and belongs to the technical field of deep space probe control. The bounded periodic orbit of the probe near the equilibrium point is obtained by selecting the orbit initial value, and the probe is kept near the nominal hovering orbit by the adaptive control, so that the fuel consumption of the probe during long-time hovering can be effectively reduced; the weight matrix is dynamically selected on the basis of the linear quadratic optimal control, and at the initial moment, the probe has a large position error from the nominal position, so that the controller outputs a large control force to make the probe reach the target position as soon as possible; when reaching the vicinity of the nominal hovering orbit, the controller only needs to provide a small control force to realize the orbit keeping motion of the probe, and further reduce the fuel consumption of the probe. The position error between the nominal hovering orbit near the equilibrium point and the state of the probe is fuzzified, and the adaptive ability of the probe is improved through the weight selection.

Description

TECHNICAL FIELD

[0001] The application relates to a binary asteroid hovering probe adaptive control method and belongs to the technical field of deep space probe control. BACKGROUND

[0002] Small asteroids have become the key targets of international deep space exploration in the 21st century because they contain important information about the origin of the solar system and the evolution of planets, and they may contain rich mineral resources and potential threats of impact on the earth. With the continuous development of deep space exploration in China, it is inevitable for the development of deep space exploration technology to carry out exploration of small asteroids with unique scientific value. Binary asteroid systems are a special form of many small asteroid groups, which means that two small asteroids rotate around their common center of mass, and the center of mass of the two asteroids revolves around the sun. Studies have shown that binary asteroid systems are a very common physical phenomenon in the solar system, with about 16% of near-earth asteroids and main belt asteroids belonging to binary asteroid systems. The exploration of binary asteroid systems composed of two small asteroids has a variety of unique scientific values that cannot be achieved by exploring a single small asteroid.

[0003] Similar to the restricted three-body problem, there are five equilibrium points near binary asteroids, and the probe is subjected to equal gravitational force and centrifugal force at the equilibrium points. For hovering exploration of any position in the small asteroid fixed coordinate system, the probe is expected to achieve long-time and low-consumption hovering at the equilibrium points. Due to the extremely complex dynamic environment of binary asteroids, the position of the probe does not remain unchanged at the equilibrium point without control, but moves around the equilibrium point or even gradually deviates from the equilibrium point. In addition, the probe is disturbed by solar radiation pressure near the binary asteroid, greatly increasing the difficulty of hovering control of the probe. SUMMARY

[0004] Due to the complex dynamic environment of binary asteroids and various disturbances in deep space environment, the probe will have the problem of excessive fuel consumption during long-time hovering. The purpose of the application is to provide a binary asteroid hovering probe adaptive control method, which sets the initial orbit value to optimize the nominal hovering orbit of the probe near the equilibrium point, dynamically selects the weight matrix on the basis of linear quadratic optimal control, meets the dynamic selection strategy of the weight matrix in different stages of the hovering orbit keeping process, makes the probe quickly approach the nominal hovering orbit and then keep on the nominal hovering orbit with small control force, and reduces the fuel consumption of the probe in the complex environment during long-time hovering through adaptive control.

[0005] The application is implemented by the following technical scheme.

[0006] The application discloses a kind of binary asteroid hovering detection self-adapting control method, establishes binary asteroid gravitational field model and detector motion equation.Binary asteroid system is established as sphere-ellipsoid model, using ellipsoid maximum half-length axis is normalized to distance, using spherical harmonic function respectively calculates the gravitational potential of two asteroids, and establishes the scalar equation of detector motion in binary asteroid vicinity in two asteroid coordinate system;L1 balance point is selected as hovering position to enable detector to simultaneously carry out close observation to two asteroids, ignore the high order term and disturbance of scalar equation of motion in binary asteroid vicinity, by setting orbit initial value, the analytical solution of detector motion in balance point vicinity is calculated, and the nominal hovering orbit of detector balance point vicinity is obtained.To reduce fuel consumption of detector in the process of orbit hovering, linear quadratic optimal control is used to optimize the output control force of detector, and the fuel consumption performance index represented by weight matrix Q and R is constructed;In different stages of hovering orbit maintaining process, the dynamic selection principle of weight matrix is determined based on linear quadratic optimal control, and for Q matrix, it is unit matrix, and R matrix is dynamically selected according to hovering stage: in the stage that detector approaches nominal orbit, the weight occupied by control matrix R is smaller, in the orbit maintaining stage, the weight occupied by control matrix R is larger;The position error between nominal hovering orbit in balance point vicinity and the state of detector is fuzzified, the fuzzy rule for determining the value of each element in spacecraft control matrix R is established, the fuzzy output of control matrix is de-fuzzified by using weighted average method, so that the value of each element in R matrix is dynamically selected according to the state error of detector, to meet the dynamic selection strategy of weight matrix in different stages of hovering orbit maintaining process, adapt to the requirements of hovering orbit maintaining process in different stages;According to the obtained dynamic control matrix R, the optimal output control force is calculated using linear quadratic optimal control, and the fuel consumption of detector in complex environment for a long time is reduced by adaptive control in different stages.

[0007] The application discloses a kind of binary asteroid hovering detection self-adapting control method, including the following steps:

[0008] Step one, establish binary asteroid gravitational field model and detector motion equation.Binary asteroid system is established as sphere-ellipsoid model, using ellipsoid maximum half-length axis is normalized to distance, using spherical harmonic function respectively calculates the gravitational potential of two asteroids, and establishes the scalar equation of detector motion in binary asteroid vicinity in two asteroid coordinate system.

[0009] The binary asteroid system is established as a sphere-ellipsoid model, the primary star of the binary asteroid system is simplified as a sphere, and the secondary star is simplified as an ellipsoid, the masses of the primary star and the secondary star are M1 and M2 respectively, the mass ratio of the binary star system is defined as μ=M1 / (M1+M2), the semi-major axes of the ellipsoid are a, b and c respectively, wherein 0≤c≤b≤a, a fixed coordinate system of the binary star system is defined, the original center is the mass center of the binary star system, the x-axis direction is the direction from the mass center of the primary star to the mass center of the secondary star, the z-axis is the maximum inertia axis, and the y-axis direction is determined according to the right-hand rule. L , r L is the position vector of the spacecraft relative to the mass center of the system, and is normalized by using the maximum semi-major axis of the ellipsoid, so that r=r L / a=[x,y,z], l=l L / a, x, y and z are the normalized coordinates of the probe in the mass center coordinate system of the binary asteroid system.

[0010] The spherical harmonic method is used to calculate the gravitational field of the binary asteroid, and the gravitational potential function of the asteroid is approximated by spherical harmonic function expansion, as shown in formula (1)

[0011] U=U0+U1+U2+U3+U4+… (1)

[0012] U is the sum of the gravitational potential of each order of the asteroid calculated by the spherical harmonic method, U0, U1, U2, U3 and U4 are the zero-order, first-order, second-order, third-order and fourth-order gravitational potential of the asteroid in the spherical harmonic model, and the order and degree selected for the calculation of the asteroid gravitational potential function model are determined according to the required calculation accuracy and efficiency, preferably, a second-order quadratic spherical harmonic function model is used to calculate the gravitational field of the binary star system, in the present application, the high-order terms of the spherical harmonic function are ignored, and the second-order quadratic function model is used to calculate the gravitational potential of the asteroid as

[0013] U=U0+U1+U2 (2)

[0014]

[0015]

[0016]

[0017]

[0018] Wherein, δ is the latitude of the probe, and λ is the longitude of the probe.

[0019] When the mass center of the central gravitational body is taken as the origin of the coordinate system, the parameters in the second-order quadratic spherical harmonic function model are C 10 =C 11 =S 11 ​= 0, when the three axes of the central body-fixed coordinate system are along the principal axes of inertia of the central body, then the parameter C 21 = S 21 = S 22 = 0, thus in the above coordinate system, the celestial body's gravitational field calculated by the second-order quadratic spherical harmonic function model is simplified as

[0020]

[0021] In the Cartesian coordinate system The gravitational potential of the binary system is obtained as follows:

[0022]

[0023] where the parameters C 20 and C 22 are determined by the three principal axes of inertia of the celestial body, and have the following relationships

[0024]

[0025] The normalized results of the three semi-axes of the ellipsoid are α, β and γ, and the rotational inertia of the three coordinate axes is obtained as

[0026]

[0027] The second-order quadratic spherical harmonic function without integral elements is used to calculate the gravitational potential of the small celestial body, and the gravitational potential functions of the primary star and the secondary star are respectively

[0028]

[0029] In the combined coordinate system of the binary asteroid system, the scalar motion equation of the probe in the three-axis direction is

[0030]

[0031] where and are the first-order derivative and the second-order derivative of x, y and z, respectively, and ω represents the normalized angular velocity, and the calculation formula is

[0032]

[0033] Step 2, select the L1 equilibrium point as the hovering position to enable the probe to simultaneously observe the two small asteroids at close range, ignore the high-order terms and disturbances of the scalar equation of motion near the binary asteroid, set the initial orbit value, calculate the analytical solution of the probe motion near the equilibrium point, and obtain the nominal hovering orbit of the probe near the equilibrium point.

[0034] There are five equilibrium points in the asteroid binary system, including three collinear equilibrium points and two triangular equilibrium points, which make the dynamic equation and That is, the positions of the equilibrium points of the binary system are obtained, in which the L1 equilibrium point is located between the two stars, the L2 and L3 equilibrium points are located on both sides of the binary stars, and the L4 and L5 are non-collinear equilibrium points.

[0035] Selecting the L1 equilibrium point as the hovering position enables the probe to simultaneously observe the two asteroids at close range, ignoring high-order terms and disturbances. By selecting appropriate initial values of the orbit, the probe will move in the form of a bounded periodic orbit near the L1(x e ,0,0) equilibrium point, and the motion equation of the probe in the three-axis direction has the following form

[0036]

[0037] where ω z represents the orbital frequency of the probe in the z-axis direction, and the calculation formula is

[0038]

[0039] τ is a dimensionless time parameter, τ=nt, n=[G(M1+M2) / l 3 ] 1 / 2 , t is the time parameter, the unit is second, G is the gravitational constant, and other orbital parameters are

[0040]

[0041]

[0042] The calculation formula of the initial value of the orbit is as follows:

[0043]

[0044]

[0045]

[0046]

[0047] Step three, according to the scalar equation of the binary asteroid near motion obtained in step one, the dynamic equation of the probe in the controlled state is obtained; in order to reduce the fuel consumption of the probe in the process of hovering in the orbit, the output control force of the probe is optimized using linear quadratic optimal control, and a fuel consumption performance index represented by weight matrix Q and R is constructed; in different stages of the process of maintaining the hovering orbit, the dynamic selection principle of the weight matrix is determined on the basis of the linear quadratic optimal control. The dynamic selection strategy of the weight matrix suitable for different stages of the process of maintaining the hovering orbit is as follows: the Q matrix is taken as a unit matrix, and the R matrix is dynamically selected according to the hovering stage: in the stage of approaching the nominal orbit, the weight of the control matrix R is smaller, and in the stage of maintaining the orbit, the weight of the control matrix R is larger.

[0048] Due to the inaccuracy of the small asteroid gravity field model and other disturbances, any slight deviation in the orbit will make the probe deviate from the hovering orbit in an exponential form, so it is necessary to apply active control to the probe to keep it on the nominal hovering orbit.

[0049] According to the scalar equation of the binary asteroid near motion as shown in formula (12), the dynamic equation of the probe in the controlled state is

[0050]

[0051]

[0052] Where u = [u x ,u y ,u z ] is the size of the control force in the three-axis direction

[0053]

[0054] In order to reduce the fuel consumption of the probe in the process of hovering in the orbit, the optimal control force of the probe is calculated using linear quadratic optimal control, and the following performance index is designed

[0055]

[0056] The performance index is composed of two parts, where Q and R are weight matrices, and different sizes of Q and R matrices will produce different control effects. If the weight of the Q matrix is larger, the state of the binary asteroid hovering probe adaptive control system will converge faster, and the required control force will be larger, and vice versa. The weight of the R matrix is larger, the control required by the binary asteroid hovering probe adaptive control system to converge is reduced, and the convergence speed is slower.

[0057] There are different requirements for control force in different stages of the process of keeping the hovering orbit. At the initial moment, the probe has a large position error from the nominal position, and the controller needs to provide a large control force to make the probe reach the target position as soon as possible; when the probe reaches the vicinity of the nominal hovering orbit, the controller only needs to provide a small control force to realize the orbit keeping motion of the probe. In different stages of the process of keeping the hovering orbit, the weight matrix is dynamically selected on the basis of the linear quadratic optimal control to meet the different requirements for control force in different stages. The selection strategy is as follows: the Q matrix is taken as the unit matrix, and the R matrix is dynamically selected according to the hovering stage: in the stage of approaching the nominal orbit, the weight of the control matrix R is small, and in the orbit keeping stage, the weight of the control matrix R is large.

[0058] Step four, the position error between the nominal hovering orbit near the equilibrium point obtained in step two and the state of the probe is fuzzified, the fuzzy rules for determining the values of the elements of the spacecraft control matrix R are established, and the fuzzy output of the control matrix is de-fuzzified by using the weighted average method, so that the values of the elements of the R matrix are dynamically selected according to the state error of the probe, to meet the dynamic selection strategy of the weight matrix in different stages of the process of keeping the hovering orbit, and to adapt to the requirements of the process of keeping the hovering orbit in different stages.

[0059] Let the position error of the probe be The position error and the output result are divided into five fuzzy subsets, namely NB (negative big), NM (negative small), ZO (zero), PM (positive big) and PB (positive small). The commonly used triangle is used as the membership function to simplify the overall calculation amount. The expression of the triangular membership function is:

[0060]

[0061] Where i, j, k are dimensionless parameters.

[0062] The Q matrix is taken as the unit matrix, and the fuzzy rules are established to dynamically select the values of the elements of the R matrix.

[0063]

[0064] The established control rules are shown in the table

[0065] Table 1 Fuzzy control rule table

[0066]

[0067] According to the fuzzy rules, the fuzzy output subsets of the R matrix are obtained, and the fuzzy output is de-fuzzied by using the weighted average method. For R 11 , R 22 , R 33 are calculated by the following formula

[0068]

[0069] R i For R 11 , R 22 , R 33 Actual output, R k For all non-zero open rules, mu (q k ) is the result of the action of all non-zero open rules.

[0070] Step five: based on the dynamic control matrix R obtained in step four, the optimal output control force is calculated according to the linear quadratic optimal control, the active control is applied to the probe according to the output control force, and the probe is kept on the nominal hovering orbit, and the fuel consumption of the probe in the complex environment is reduced through adaptive control at different stages.

[0071] According to the linear quadratic optimal control, the optimal control force is:

[0072] u(t)=-R -1 B T PX(t) (29)

[0073] Wherein, P matrix satisfies the condition: A T P+PA+Q-PBR -1 B T P=0.

[0074] Beneficial effects:

[0075] 1、The adaptive control method for double-body asteroid hovering probe disclosed by the application establishes a gravity field model and a dynamics model of asteroid double-star system, a group of bounded periodic orbits of the probe near the equilibrium point can be obtained by selecting appropriate initial orbit values, compared with the traditional fixed-point hovering mode, the nominal hovering orbit near the equilibrium point is more in line with the natural motion law of the probe, adaptive control is performed on the probe, the probe is kept near the nominal hovering orbit, fuel consumption of the probe during long-time hovering can be effectively reduced, secondly, the weight matrix is dynamically selected on the basis of linear quadratic optimal control, at the initial moment, the probe has a large position error from the nominal position, at this time, the controller outputs a large control force to make the probe reach the target position as soon as possible, when reaching the vicinity of the nominal hovering orbit, the controller only needs to provide a small control force to realize the orbit keeping motion of the probe, and further reduce the fuel consumption of the probe.

[0076] 2. The adaptive control method for hovering exploration of a two-body asteroid disclosed in the present invention fuzzifies the position error between the nominal hovering orbit and the state of the probe near the equilibrium point, establishes fuzzy rules for determining the values ​​of each element in the spacecraft control matrix R, and uses the weighted average method to defuzzify the fuzzy output of the control matrix. The values ​​of each element of the R matrix are dynamically selected according to the probe state error to meet the dynamic selection strategy of the weight matrix at different stages of the hovering orbit maintenance process, effectively improving the adaptive ability of the probe during the hovering process. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 Flowchart of the adaptive fuzzy control method for hovering detection of asteroid binary systems;

[0078] Figure 2 Schematic diagram of the centroid coordinate system of the binary star system model in step 1 of the embodiment of the present invention;

[0079] Figure 3 Schematic diagram of the nominal hovering trajectory of the probe near the L1 equilibrium point in step 2 of an embodiment of the present invention;

[0080] Figure 4 This is a diagram of the position error membership function in step 4 of an embodiment of the present invention;

[0081] Figure 5 This is a graph showing the hovering position error of the binary satellite system in step 5 of the embodiment of the present invention;

[0082] Figure 6 This is a graph of the acceleration of the dual-satellite system hovering control in step five of the embodiment of the present invention. DETAILED DESCRIPTION

[0083] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0084] Example 1:

[0085] Considering the solar light pressure disturbance that the probe receives during the hovering process, the binary star system 1999KW4 is selected as the hovering target object. The distance between the master star and the slave star is 2.54 km, and the total mass of the binary star is M1+M2=2.472×10 12 kg, mass ratio μ=0.9475, orbital period is 17.458h, the probe is hovered on the nominal hovering orbit near L1[1.7773;0;0]km, the initial position error is [-20;-40;-5]m, and the maximum acceleration output by the controller is 0.05m / s 2 .

[0086] like Figure 1As shown, the adaptive control method for a two-body asteroid hovering detection disclosed in this embodiment includes the following steps:

[0087] Step 1: Establish a gravitational field model for the binary asteroid and the probe's motion equations. The binary asteroid system is modeled as a sphere-ellipsoid. The distance is normalized using the ellipsoid's maximum semi-major axis. Spherical harmonics are used to calculate the gravitational potential of each asteroid. Finally, a scalar equation for the probe's motion near the binary asteroid is established in the combined coordinate system of the two asteroids.

[0088] like Figure 2 As shown, the binary asteroid system is established as a sphere-ellipsoid model. The primary star of the binary asteroid system is simplified into a sphere, and the secondary star is simplified into an ellipsoid. The masses of the primary star and the secondary star are M1 and M2 respectively. The mass ratio of the binary star system is defined as μ = M1 / (M1+M2). The semi-major axes of the ellipsoid are a, b, and c respectively, where 0≤c≤b≤a. The fixed coordinate system of the binary star system is defined, with the origin as the center of mass of the binary star system, the x-axis direction is the direction from the center of mass of the primary star to the center of mass of the secondary star, the z-axis is the axis of maximum inertia, and the y-axis direction is determined according to the right-hand rule. The relative distance between the primary star and the secondary star is defined as l L , r L is the position vector of the spacecraft relative to the center of mass of the system, normalized using the maximum semi-major axis of the ellipsoid to obtain r = r L / a=[x,y,z],l=l L / a, x, y, z are the normalized coordinates of the probe in the center-of-mass coordinate system of the binary asteroid system.

[0089] The gravitational field of the binary asteroid is calculated using the spherical harmonic method. The gravitational potential function of the asteroid is approximated by the spherical harmonic function expansion, as shown in formula (1):

[0090] U=U0+U1+U2+U3+U4+… (30)

[0091] U is the sum of the gravitational potentials of the asteroids of various orders calculated by the spherical harmonic method. U0, U1, U2, U3, and U4 are the zero-order, first-order, second-order, third-order, and fourth-order gravitational potentials of the asteroids under the spherical harmonic model, respectively. The order and number of times the asteroid gravitational potential function model is used for calculation are determined according to the required calculation accuracy and efficiency. Preferably, a second-order quadratic spherical harmonic function model is used to calculate the gravitational field of the binary system. In the present invention, the high-order terms of the spherical harmonic function are ignored, and the second-order quadratic function model is used to calculate the asteroid gravitational potential:

[0092] U=U0+U1+U2 (31)

[0093] in

[0094]

[0095]

[0096]

[0097] where δ is the latitude of the probe, and λ is the longitude of the probe.

[0098] When the center of mass of the central gravitating body is taken as the origin of the coordinate system, the parameter value of the second-order quadratic spherical harmonic function model is C 10 = C 11 = S 11 = 0, when the three axes of the fixed coordinate system of the central gravitating body are along the directions of the principal axes of inertia of the central body, then the parameter C 21 = S 21 = S 22 = 0, therefore, in the above coordinate system, the celestial gravitational field calculated by the second-order quadratic spherical harmonic function model is simplified as

[0099]

[0100] In the Cartesian coordinate system The form of the gravitational potential of the binary star system is obtained as follows:

[0101]

[0102] where the parameters C 20 and C 22 of the second-order quadratic spherical harmonic function model are determined by the three principal axes of inertia of the celestial body, and have the following relationships

[0103]

[0104] The normalized results of the three semi-axes of the ellipsoid are α, β and γ, respectively, and the rotational inertia of each coordinate axis is obtained as

[0105]

[0106] The second-order quadratic spherical harmonic function without integral elements is used to calculate the gravitational potential of the small celestial body, and the gravitational potential functions of the primary star and the secondary star are respectively

[0107]

[0108]

[0109] In the combined coordinate system of the binary asteroid system, the scalar motion equation of the probe in the three-axis direction is

[0110]

[0111] where and First and second derivatives of x, y, z, respectively, and ω represents the normalized angular velocity of the system, and the calculation formula is

[0112]

[0113] Step two, select L1 equilibrium point as hovering position to enable the probe to simultaneously observe two small asteroids at close range, ignore high order terms and disturbances of the scalar equation of motion near the binary asteroid system, set the initial value of the orbit, calculate the analytical solution of the probe motion near the equilibrium point, and obtain the nominal hovering orbit of the probe near the equilibrium point.

[0114] There are five equilibrium points in the binary asteroid system, including three collinear equilibrium points and two triangular equilibrium points, let And That is, the position of the equilibrium point of the binary star system is obtained, where the L1 equilibrium point is located between the two stars, the L2 and L3 equilibrium points are located on both sides of the binary stars, and the L4 and L5 are non-collinear equilibrium points.

[0115] Select L1 equilibrium point as hovering position to enable the probe to simultaneously observe two small asteroids at close range, ignore high order terms and disturbances, and by selecting appropriate initial values of the orbit, the probe will move in the form of a bounded periodic orbit near the L1(x e ,0,0) equilibrium point, and the motion equation of the probe in the three-axis direction has the following form

[0116]

[0117] Where ω z represents the orbital frequency of the probe in the z-axis direction, and the calculation formula is

[0118]

[0119] τ is a dimensionless time parameter, τ = nt, n = [G(M1+M2) / l 3 ] 1 / 2 , t is the time parameter, unit: second, G is the gravitational constant, and other orbital parameters are

[0120]

[0121]

[0122] The calculation formula of the initial value of the orbit is as follows:

[0123]

[0124]

[0125]

[0126]

[0127] Step three, according to the scalar equation of the binary asteroid near motion obtained in step one, the dynamic equation of the probe in the controlled state is obtained; in order to reduce the fuel consumption of the probe in the process of hovering in the orbit, the optimal control force of the probe is optimized by using linear quadratic optimal control, and a fuel consumption performance index represented by weight matrix Q and R is constructed; in different stages of the process of maintaining the hovering orbit, the dynamic selection principle of the weight matrix is determined on the basis of the linear quadratic optimal control. The dynamic selection strategy of the weight matrix suitable for different stages of the process of maintaining the hovering orbit is as follows: the Q matrix is taken as a unit matrix, and the R matrix is dynamically selected according to the hovering stage: in the stage of approaching the nominal orbit, the weight of the control matrix R is smaller, and in the stage of maintaining the orbit, the weight of the control matrix R is larger.

[0128] Due to the inaccuracy of the small asteroid gravity field model and other disturbances, any slight deviation in the orbit entry will make the probe deviate from the hovering orbit in an exponential form, so it is necessary to apply active control to the probe to keep it on the nominal hovering orbit.

[0129] According to the scalar equation of the binary asteroid near motion as shown in formula (12), the dynamic equation of the probe in the controlled state is

[0130]

[0131]

[0132] Where u = [u x ,u y ,u z ] is the size of the control force in the three-axis direction

[0133]

[0134] In order to reduce the fuel consumption of the probe in the process of hovering in the orbit, the optimal control force of the probe is calculated by using linear quadratic optimal control, and the following performance index is designed

[0135]

[0136] The performance index is composed of two parts, where Q and R are weight matrices, and different sizes of Q and R matrices will produce different control effects. If the weight of the Q matrix is larger, the state of the binary asteroid hovering probe adaptive control system will converge faster, and the required control force will be larger, and vice versa. The weight of the R matrix is larger, the control required for the convergence of the binary asteroid hovering probe adaptive control system is reduced, and the convergence speed is slower.

[0137] In different stages of the process of keeping the hovering orbit, the requirements of control force are different. At the initial moment, the probe has a large position error from the nominal position, and the controller needs to provide a large control force to make the probe reach the target position as soon as possible; when the probe reaches the vicinity of the nominal hovering orbit, the controller only needs to provide a small control force to realize the orbit keeping motion of the probe. In different stages of the process of keeping the hovering orbit, in order to meet the requirements of control force in different stages, the weight matrix is dynamically selected on the basis of linear quadratic optimal control, and the selection strategy is as follows: the Q matrix is taken as the unit matrix, and the R matrix is dynamically selected according to the hovering stage: in the stage of the probe approaching the nominal orbit, the weight of the control matrix R is small, and in the orbit keeping stage, the weight of the control matrix R is large.

[0138] Step four, the position error between the nominal hovering orbit near the equilibrium point obtained in step two and the state of the probe is fuzzified, the fuzzy rules for determining the values of each element of the spacecraft control matrix R are established, and the fuzzy output of the control matrix is de-fuzzified by using the weighted average method, so that the values of each element of the R matrix are dynamically selected according to the state error of the probe, to meet the dynamic selection strategy of the weight matrix in different stages of the process of keeping the hovering orbit, and to adapt to the requirements of the process of keeping the hovering orbit in different stages.

[0139] Let the position error of the probe be The position error and the output result are divided into five fuzzy subsets, namely NB (negative big), NM (negative small), ZO (zero), PM (positive big) and PB (positive small), as shown in Figure 4 The commonly used triangle is used as the membership function to simplify the overall calculation amount, and the expression of the triangular membership function is:

[0140]

[0141] Where i, j, k are dimensionless parameters.

[0142] The Q matrix is taken as the unit matrix, and the fuzzy rules are established to dynamically select the values of each element of the R matrix.

[0143]

[0144] The established control rules are shown in the table

[0145] Table 2 Fuzzy control rule table

[0146]

[0147] According to the fuzzy rules, the fuzzy output subsets of the R matrix are obtained, and the fuzzy output is de-fuzzied by using the weighted average method. For R 11 , R 22、R 33 All are calculated by the following formula

[0148]

[0149] R i R 11 、R 22 、R 33 Actual output, R k For all non-zero openness rules, μ(q k ) is the result of all non-zero openness rules.

[0150] Step 5: Based on the dynamic control matrix R obtained in step 4, the optimal output control force is calculated according to the linear quadratic optimal control. Active control is applied to the probe according to the output control force to keep the probe on the nominal hovering orbit. Adaptive control is used at different stages to reduce the fuel consumption of the probe during long-term hovering in complex environments.

[0151] According to linear quadratic optimal control, the optimal control force is:

[0152] u(t)=-R -1 B T PX(t) (58)

[0153] Among them, the P matrix meets the conditions: A T P+PA+Q-PBR -1 B T P = 0. Figure 5 As shown in , the position error of the probe relative to the nominal hovering trajectory gradually approaches zero; Figure 6 As shown in the figure, at the initial moment, due to the large proportion of the control matrix R, the detector outputs a large control force to make the detector track the nominal orbit as quickly as possible. After 100 seconds, as the position error gradually decreases, the output control force gradually decreases.

[0154] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for adaptive control of hovering probe of a binary asteroid, characterized in that: Comprising the following steps, Step one, establish the binary asteroid gravity field model and the probe motion equation; the binary asteroid system is established as a sphere-ellipsoid model, the maximum semi-major axis of the ellipsoid is used for distance normalization, the spherical harmonic function is used to calculate the gravity potential of the two asteroids respectively, and the scalar equation of the probe motion near the binary asteroid is established in the combined coordinate system of the two asteroids; Step two, select L1 balance point as the hovering position to enable the probe to simultaneously observe the two asteroids at close range, ignore the high-order terms and disturbances of the scalar equation of the motion near the binary asteroid, set the initial orbit value, calculate the analytical solution of the probe motion near the balance point, and obtain the nominal hovering orbit of the probe near the balance point; Step three, obtain the dynamic equation of the probe in the controlled state according to the scalar equation of the motion near the binary asteroid obtained in step one; in order to reduce the fuel consumption of the probe during the hovering process on the orbit, the output control force of the probe is optimized using linear quadratic optimal control, and a fuel consumption performance index represented by weight matrix Q and R is constructed; in different stages of the hovering orbit maintaining process, the weight matrix dynamic selection principle is determined on the basis of linear quadratic optimal control; the weight matrix dynamic selection strategy suitable for different stages of the hovering orbit maintaining process is as follows: the Q matrix is taken as a unit matrix during dynamic selection, and the R matrix is dynamically selected according to the hovering stage: during the approach of the probe to the nominal orbit, the weight of the control matrix R is small, and during the orbit maintaining stage, the weight of the control matrix R is large; Step four, fuzzy processing is performed on the position error between the nominal hovering orbit near the balance point obtained in step two and the state of the probe, fuzzy rules for determining the values of each element in the spacecraft control matrix R are established, and the fuzzy output of the control matrix is de-fuzzied by using the weighted average method, so that the values of each element in the R matrix are dynamically selected according to the state error of the probe, so as to meet the weight matrix dynamic selection strategy in different stages of the hovering orbit maintaining process and adapt to the requirements of the hovering orbit maintaining process in different stages; Step five: based on the dynamic control matrix R obtained in step four, the optimal output control force is calculated according to the linear quadratic optimal control, and the probe is subjected to active control according to the output control force to keep the probe on the nominal hovering orbit. In different stages, the fuel consumption of the probe in the complex environment is reduced through adaptive control during long-time hovering.

2. The adaptive control method for hovering around a binary asteroid as claimed in claim 1, wherein: The implementation method of step one is, The binary asteroid system is established as a sphere-ellipsoid model, the primary star of the binary asteroid system is simplified as a sphere, and the secondary star is simplified as an ellipsoid. The masses of the primary star and the secondary star are M1 and M2 respectively, the mass ratio of the binary star system is defined as μ=M1 / (M1+M2), the semi-major axes of the ellipsoid are a, b and c respectively, wherein 0≤c≤b≤a, a fixed coordinate system of the binary star system is defined, the original center is the mass center of the binary star system, the x-axis direction is the direction from the mass center of the primary star to the mass center of the secondary star, the z-axis is the maximum inertia axis, and the y-axis direction is determined according to the right-hand rule; the relative distance between the primary star and the secondary star is defined as l L , and L r is the position vector of the spacecraft relative to the mass center of the system, and is normalized using the maximum semi-major axis of the ellipsoid to obtain r=r L / a=[x,y,z], l=l L / a, x, y and z are the normalized coordinates of the probe in the mass center coordinate system of the binary asteroid system. The spherical harmonic method is used to calculate the gravity field of the binary asteroid, and the gravity potential function of the asteroid is approximated by the spherical harmonic function expansion, as shown in formula (1) U = U0 + U1 + U2 + U3 + U4 + … (1) U is the sum of the gravity potential of each order of the asteroid calculated by the spherical harmonic method, U0, U1, U2, U3, U4 are the zero-order, first-order, second-order, third-order and fourth-order gravity potential of the asteroid under the spherical harmonic model, and the order and degree selected for the calculation of the asteroid gravity potential function model are determined according to the required calculation accuracy and efficiency.

3. The adaptive control method for hovering around a binary asteroid as claimed in claim 2, wherein: The second-order quadratic spherical harmonic function model is used to calculate the gravity field of the binary star system, the high-order terms of the spherical harmonic function are ignored, and the second-order quadratic function model is used to calculate the gravity potential of the asteroid as U = U0 + U1 + U2 (2) where where: δ is the latitude of the probe, λ is the longitude of the probe; When the center of mass of the central gravitating body is taken as the origin of the coordinate system, the parameter value in the second-order quadratic spherical harmonic function model is C 10 = C 11 = S 11 = 0, when the three axes of the coordinate system fixed to the central gravitating body are along the directions of the principal axes of inertia of the central body, the parameter C 21 = S 21 = S 22 = 0, therefore in the above coordinate system, the celestial body gravitational field calculated by the second-order quadratic spherical harmonic function model is simplified to In the Cartesian coordinate system The gravitational potential of the binary system is obtained as where C 20 and C 22 are determined by the three principal axes of inertia of the celestial body, with the following relationships The normalized results of the three semi-axes of the ellipsoid are α, β and γ, and the rotational inertia of the three coordinate axes is obtained The gravitational potential functions of the primary star and the secondary star are In the barycentric coordinate system of the binary asteroid system, the scalar motion equations of the probe in the three-axis directions are where and are the first and second derivatives of x, y, z, respectively, and ω is the normalized angular velocity of the system, calculated as 4. The adaptive control method for hovering around a binary asteroid as claimed in claim 2 or 3, wherein: Step two is implemented by There are five equilibrium points in the asteroid binary system, including three collinear equilibrium points and two triangular equilibrium points, which make the dynamic equation of and That is, the positions of the equilibrium points of the binary system are obtained, wherein the L1 equilibrium point is located between the two stars, the L2 and L3 equilibrium points are located on the two sides of the binary stars, and the L4 and L5 are non-collinear equilibrium points. The selection of L1 equilibrium point as hovering position enables the probe to observe two small asteroids at the same time, ignoring high order terms and disturbances. By selecting appropriate initial values of orbit, the probe will move in the form of bounded periodic orbit near L1(x e ,0,0) equilibrium point. The motion equation of the probe in three-axis direction has the following form where ω z represents the orbital frequency of the detector in the z-axis direction, and the calculation formula is t is the time parameter in seconds, G is the gravitational constant, and the other orbital parameters are 3 ] 1 / 2 , t is the time parameter in seconds, G is the gravitational constant, and the other orbital parameters are The calculation formula of the initial value of the orbit is as follows:

5. The adaptive control method for hovering around a binary asteroid as claimed in claim 4, wherein: Step three is implemented by According to the scalar equation of motion near the binary asteroid as shown in formula (12), the dynamics equation of the probe in the controlled state is where u = [u x ,u y ,u z ] is the magnitude of the control force in the three-axis direction In order to reduce the fuel consumption of the probe during the orbit hovering process, the optimal control force of the probe is calculated using linear quadratic optimal control, and the following performance index is designed The performance index is composed of two parts, where Q and R are weight matrices, and different sizes of Q and R matrices will produce different control effects. If the weight of the Q matrix is larger, the state of the binary asteroid hovering probe adaptive control system will converge at a faster speed, and the required control force is larger. On the contrary, if the weight of the R matrix is larger, the control required by the binary asteroid hovering probe adaptive control system to converge is reduced, and the convergence speed is slower. During the different stages of the hovering orbit keeping process, the control force requirements are different. At the initial moment, the probe has a large position error from the nominal position, and at this time the controller needs to provide a large control force to make the probe reach the target position as soon as possible. When reaching the vicinity of the nominal hovering orbit, the controller only needs to provide a small control force to realize the orbit keeping motion of the probe. In order to meet the different requirements of the control force at different stages of the hovering orbit keeping process, the weight matrix is dynamically selected on the basis of the linear quadratic optimal control, and the selection strategy is as follows: the Q matrix is taken as the unit matrix, and the R matrix is dynamically selected according to the hovering stage: when the probe approaches the nominal orbit, the weight of the control matrix R is small, and when the orbit is kept, the weight of the control matrix R is large.

6. The adaptive control method for hovering around a binary asteroid as claimed in claim 5, wherein: Step four is implemented by The position error of the detector is The position error and output result are divided into five fuzzy subsets, namely, negative big NB, negative small NM, zero ZO, positive big PM and positive small PB. Common triangles are used as membership functions to simplify the overall calculation amount. The expression of the triangular membership function is: Where i, j, k are dimensionless parameters. The Q matrix is taken as the unit matrix, and the R matrix is dynamically selected according to the state error of the probe by establishing fuzzy rules. The established control rules are shown in Table 1 Table 1 Fuzzy control rule table The fuzzy output subset of the R matrix is obtained according to the fuzzy rule, and the fuzzy output is defuzzified using a weighted average method. For R 11 , R 22 , and R 33 are calculated by the following formula R i R 11 、R 22 、R 33 Actual output, R k For all non-zero openness rules, μ(q k ) is the result of all non-zero openness rules.

7. The adaptive control method for hovering around a binary asteroid as claimed in claim 6, wherein: In step five, According to the linear quadratic optimal control, the size of the optimal control force is: u(t) = -R -1 B T PX(t) (29) where the P matrix satisfies the condition: A T P+PA+Q-PBR -1 B T P = 0.

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