CN100428099C - Deep space detector soft landing autonomic obstruction evasion control method - Google Patents

Abstract

The present invention discloses a soft landing autonomic obstruction evasion control method for a deep space detector, which relates to a control method for a deep space detector. The present invention provides a soft landing autonomic obstruction evasion control method for a deep space detector aiming at the problems of low control precision and poor reliability existing in the existing deep space detector, wherein the current position r and the speed information x, y, z of the detector are measured by a self carrying navigation sensor, obstruction positions x 1, y 1 and the magnitude information z 1 of the obstruction are measured by a self carrying obstruction detection device, and the magnitude of control force p x, p y, p z, in three directions of a nozzle of the detector is obtained by calculation which is carried out by a controller of the detector using the formula and according to the measured information. With the action of control force p x, p y, p z, the detector can ensure safety landing along a descending track to a target planet surface. The present invention has the advantages of simple algorithm, minimum calculation amount, high control precision and high reliability, and can completely finish tasks in danger landform for the detector.

Description

Deep space detector soft landing autonomic obstruction evasion control method

Technical field

The present invention relates to a kind of control method, the control method that particularly a kind of deep space detection device can independently be evaded obstacle in the soft landing process to deep space probe.

Background technology

Increasing along with the interplanetary exploration task, the vital task and the problem of the following deep space scientific exploration of the detector safe soft landing on the celestial body surface having become.For the zone that scientific value is arranged being studied and being taken a sample, wish that detector can (rock, crater and abrupt slope) safe landing in the hazardous location.Success ratio, the survival rate of current planetary detection activity soft landing are still lower, and over more than 40 year, 30 mars exploration activities have several times been implemented in USSR (Union of Soviet Socialist Republics), the U.S., Japan and Europe altogether, and wherein about 2/3 ends in failure.In the survey of deep space task, owing to exist long communication delay between target celestial body and the ground base station, the process duration of celestial body of in addition landing is shorter relatively, adopts the traditional requirement that can't satisfy the obstacle avoidance real-time based on the navigational guidance control model of deep space net.For safety, drop to target celestial body surface exactly, following detector must have autonomous obstacle detection and the ability of evading.Detector soft landing autonomic obstacle avoidance is to obtain under the terrain information prerequisite of touch-down zone, detector motion track, translational velocity and the velocity of rotation of detector mobility satisfied in planning, promptly finish the navigation task of detector, thus with order give the detector attitude, control system is carried out motor-driven control.Detector soft landing autonomic obstacle avoidance comprises: parts such as detector motion trajectory planning, the control of detector obstacle avoidance.Up to the present, the detector with obstacle avoidance ability has only the Apollo series lunar orbiter of the U.S., and this series detector is owing to be manned, and the cosmonaut can participate in obstacle avoidance work directly, thereby greatly reduces the requirement to the detector capacity of will.Therefore, go back the detector that neither one is truly finished the soft landing autonomic obstacle avoidance at present.Because detector soft landing autonomic obstacle avoidance ability is the bottleneck of deep space probe viability, so deep space detector soft landing autonomic obstruction evasion control method is one of research direction of giving priority to of current various countries space flight scientific research department.

In the deep space detector soft landing autonomic obstruction evasion control method that has developed, formerly technology [1] is (referring to Andrew Johnson, Allan Klumpp, James Collier and Aron Wolf etal., LIDAR-based Hazard Avoidance for Safe Landing on Mars.Appearingas AAS 01-120 in the AAS/AIAA Space Flight Mechanics Meeting, SantaBarbara, CA, February 2001), the cover that U.S. NASA subordinate JPL laboratory and California Technical Research Center are developed jointly carries out obstacle detection based on scanning laser radar, evade algorithm.The obstacle avoidance control method that this cover algorithm proposes is to go out to land a little according to the complaint message advance planning, track is evaded in the detector current location and one of the velocity information planning that utilize navigational system to provide, and this track is finished two-point boundary value problem by the form of position quartic polynomial.In the decline process, produce control and make detector drop to target star catalogue face along this track.This control method is owing to having utilized polynomial form that analytical expression is arranged, therefore it has characteristics such as algorithm is simple, computing time is few, but because this control method is based on the open loop control theory, need too much outside precise information, but its many information that need can not accurately obtain, and this has caused the uncertainty of this control method control accuracy.

Formerly technology [2] is (referring to Edward C.Wong, Gurkirpal Singh and James P.Masciarelli et al., Autonomous Guidance and Control Design for HazardAvoidance and safe Landing on Mars.Appearing as 2002-4619 in theAIAA Atmospheric Flight Mechanics Conference and Exhibit), the obstacle avoidance control algolithm in the cover detector landing mission of U.S. NASA subordinate JPL laboratory and Johnson space center joint development.The obstacle avoidance control method of being utilized in this cover algorithm remains employing and selects the landing point in advance, detector current location and the velocity information of utilizing navigational system to provide are evaded track, and this track also is to finish two-point boundary value problem by polynomial form.This control method is to adopt the form of position cubic polynomial, and different with track of technology [1] advance planning formerly to be that this algorithm is convenient at set intervals carry out trajectory planning with navigation information, planning interlude inner control detector along on a planning track descend.This algorithm is outside having kept characteristics such as algorithm is simple, computing time is few, also has certain robustness, but this algorithm has only utilized the landing dot information when the planning descending trajectory, do not consider the information such as size, type of obstacle in the touchdown area, such evade track can not guarantee fully that detector does not bump with other obstacle in the process of evading.

Summary of the invention

Have at existing deep space probe that control accuracy is not high, the problem of poor reliability, the invention provides the deep space detector soft landing autonomic obstruction evasion control method that a kind of control accuracy and reliability are all higher and algorithm is simple, calculated amount is little, this control method is applied to the soft landing for deep space probe end, utilize terrain information and detector position, velocity information, it is that nozzle produces control that detector utilizes control signal driving topworks based on this control method, makes detector steadily drop to target celestial body surface safely.

A kind of deep space detector soft landing autonomic obstruction evasion control method, detector records detector current position r, speed by the navigation sensor that carries

Information records the position x of obstacle by the obstacle detecting device that carries _i, y _i, the big or small z of obstacle _iInformation, the controller of detector utilizes following formula (3), (2), (4) to calculate according to the above-mentioned information that records, and obtains system power P on three directions of detector nozzle _x, P _y, P _zSize, detector is subjected to P _x, P _y, P _zThe effect of control can guarantee its descending trajectory along safety target celestial body surface of landing;

Described formula is:

$P_x=-U_{x}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{x}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{x}m-k_x\stackrel{\·}{x}/2+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\σ}}^2}\right)}\frac{(x-x_i)}{{\mathrm{\σ}}^2}-p_1(x-x_i)---\left(3\right)$

$P_y=-U_{y}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{y}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{y}m-k_y\stackrel{\·}{y}/2+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\σ}}^2}\right)}\frac{(y-y_i)}{{\mathrm{\σ}}^2}-p_2(y-y_i)---\left(2\right)$

$P_z={-U}_{z}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{z}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{z}m-k_z\stackrel{.}{z}/2-p_3(z-z_i)---\left(4\right)$

In to target celestial body soft landing process, the kinetics equation of detector is:

$m\frac{{\mathrm{\δ}}^{2}r}{{\mathrm{\δt}}^2}=P+\mathrm{mU}-2m{\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}}-{\mathrm{m\ω}}_e\×({\mathrm{\ω}}_e\×r)---\left(5\right)$

In above-mentioned formula (3), (2), (4), (5): U is the celestial body gravitation acceleration; M is the deep space probe quality; ω _eBe the moving coordinate system angular velocity of rotation; R is the radius vector of detector barycenter in inertial coordinates system; k _x, k _y, k _zBe positive number, it is by the decision of Liapunov function value expectation decline rate; k ₁Be positive number, it be jeopardously the situation function with respect to the weight of energy function; σ is a positive number, and its numerical value is decided by the shape of situation jeopardously; p ₁, p ₂, p ₃Be positive number, it is the weight of location entries with respect to speed term; P is the control thrust vectoring that acts on the detector.

Technique effect of the present invention:

In order to verify technique effect of the present invention, below the control performance that utilizes described deep space detector soft landing autonomic obstruction evasion control method is carried out emulation testing, the emulation testing parameter is as shown in table 1.

The target touch-down zone landform of emulation testing as shown in Figure 1, Fig. 2, Fig. 3 have provided energy function value curved surface and dangerous potential function value curved surface in the Liapunov function respectively, Fig. 4 has provided Liapunov function value curved surface, Fig. 5, Fig. 6 have provided detector soft landing autonomic obstacle avoidance speed, position curve, and Fig. 7 evades the expression of track in the Liapunov function elevation map.

As can be seen from Figure 7, detector has arrived local minimum point along the direction that the Liapunov function value descends in emulation testing.As seen from Figure 5, when arriving safe landing point, detector speed is near null value.By above analysis, the soft landing autonomic obstacle avoidance control method that the present invention provides can well be finished the obstacle avoidance task of detector in dangerous landform.Simultaneously, deep space detector soft landing autonomic obstruction evasion control method of the present invention, its Liapunov function have promptly represented obstacle in the dangerous gesture that this point is produced, and have also represented detector to move required energy.Because described method is based on Liapunov second method first law and asks for control law, therefore this method is local progressive stable, this method has the advantage of not asking for the point that lands in advance simultaneously, arrive the point of safes in part but independently drive detector by control law, speed reaches zero simultaneously.This control method is owing to adopted exponential function form, and its differential has analytical form, makes this control method have the advantage that algorithm is simple, calculated amount is little, control accuracy is high, reliability is high.

Table 1 emulation testing condition

Description of drawings

Fig. 1 is the target touch-down zone landform synoptic diagram of emulation testing, Fig. 2 is a functional value curved surface synoptic diagram in the Liapunov function energy, Fig. 3 is a dangerous potential function value curved surface synoptic diagram in the Liapunov function, Fig. 4 is a Liapunov function value curved surface synoptic diagram, Fig. 5 is a detector soft landing autonomic obstacle avoidance rate curve synoptic diagram, Fig. 6 is a detector soft landing autonomic obstacle avoidance position curve synoptic diagram, and Fig. 7 evades the expression synoptic diagram of track in the Liapunov function elevation map.

Embodiment

Embodiment one: present embodiment is a kind of deep space detector soft landing autonomic obstruction evasion control method.At the autonomous soft landing end of deep space probe, based on the position of obstacle, the size information of obstacle, utilize this control method can be in dangerous touchdown area, finish the soft landing autonomic obstacle avoidance by regulating detector nozzle control size, thus make detector safety drop to target celestial body surface.From technical standpoint, this method belongs to a kind of nonlinear control method based on the Liapunov stability control theory.

Present embodiment has utilized the Liapunov stability control theory to carry out obstacle avoidance control, the dangerous gesture that on behalf of obstacle, its Liapunov function promptly produced at this point, represented detector to move required energy again, it is again detector position, function of speed simultaneously, in the time of can guaranteeing that by Liapunov second method first law detector arrives the landing point, its landing speed also reaches null value.

Concrete control method is that detector records detector current position r, speed by the navigation sensor that carries Information records the position x of obstacle by the obstacle detecting device that carries _i, y _i, the big or small z of obstacle _iInformation, the controller of detector utilizes following formula to calculate according to the above-mentioned information that records, and obtains control P on three directions of detector nozzle _x, P _y, P _zSize, detector is subjected to P _x, P _y, P _zThe effect of control can guarantee its descending trajectory along safety target celestial body surface of landing;

Described formula is:

$P_x=-U_{x}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{x}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{x}m-k_x\stackrel{\·}{x}/2+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\σ}}^2}\right)}\frac{(x-x_i)}{{\mathrm{\σ}}^2}-p_1(x-x_i)$

$P_y=-U_{y}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{y}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{y}m-k_y\stackrel{\·}{y}/2+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\σ}}^2}\right)}\frac{(y-y_i)}{{\mathrm{\σ}}^2}-p_2(y-y_i)$

$P_z=-U_{z}m+2{({\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}})}_{z}m+{({\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r))}_{z}m-k_z\stackrel{\·}{z}/2-p_3(z-z_i)$

Wherein: U is the celestial body gravitation acceleration; M is the deep space probe quality; ω _eBe the moving coordinate system angular velocity of rotation, r is the radius vector of detector barycenter in inertial coordinates system; k _x, k _y, k _zBe positive number, it is by the decision of Liapunov function value expectation decline rate; k ₁Be positive number, it be jeopardously the situation function with respect to the weight of energy function; σ is a positive number, and its numerical value is decided by the shape of situation jeopardously; p ₁, p ₂, p ₃Be positive number, it is the weight of location entries with respect to speed term.Described k _x, k _y, k _z, k ₁, σ, p ₁, p ₂, p ₃Concrete numerical value can determine according to prior art.

Ultimate principle of the present invention is as follows:

Liapunov second method first law:

The state equation of uniting of setting up departments is

$\stackrel{\·}{X}=f\left(X\right)$

Wherein f (0, t)=0.If exist the scalar function with continuous single order partial derivative be Liapunov function V (X t), and satisfies condition:

1, (X t) is positive definite to V

2,

Be negative definite

Then the equilibrium state at state space initial point place is consistent progressive stable.

Choose the Lyapunov function of positive definite, can represent hazard level under the current state with it, and distance land point the position relation or represent energy etc.The derivative that makes it is like this asked for control law for negative, can guarantee that the state of detector reaches the position of expectation.

In to target celestial body soft landing process, the kinetics equation of detector is:

$m\frac{{\mathrm{\δ}}^{2}r}{{\mathrm{\δt}}^2}=P+\mathrm{mU}-2m{\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}}-{\mathrm{m\ω}}_e\×({\mathrm{\ω}}_e\×r)$

Wherein: m is the deep space probe quality; R is the radius vector of detector barycenter in inertial coordinates system; P is the control thrust vectoring that acts on the detector; U is the celestial body gravitation acceleration; ω _eBe the moving coordinate system angular velocity of rotation.

Utilize the kinetics equation of detector can obtain system state equation to be:

$\stackrel{\·}{r}=v$

$\stackrel{\·}{v}=P/m+U-2{\mathrm{\ω}}_e\×\frac{\mathrm{\δr}}{\mathrm{\δt}}-{\mathrm{\ω}}_e\×({\mathrm{\ω}}_e\×r)---\left(1\right)$

Position, velocity information that the detector that the navigation sensor that this control method utilizes detector to carry provides is current, in the touchdown area that provides based on spaceborne obstacle detecting device, the position of obstacle, the size information of obstacle, the size of the nozzle control of control detector drive detector along the descending trajectory of the safety target celestial body surface of landing.

In application,, utilize the Lyapunov function method to ask for control law on X-axis, Y-axis and the Z-direction.The Lyapunov function that this invention utilizes is made up of two parts: 1, energy function, 2, situation function jeopardously.Below be the concrete manifestation of Lyapunov function:

1, energy function:

${\mathrm{\Φ}}_P(x,y,z,\stackrel{\·}{x},\stackrel{\·}{y},\stackrel{\·}{z})=\begin{array}{}\left[\begin{array}{cccccc}x-x_0& y-y_0& z-z_0& \stackrel{.}{x}& \stackrel{.}{y}& \stackrel{.}{z}\end{array}\right]\end{array}\left[\begin{array}{cccccc}{p}_1& 0& 0& 0& 0& 0\\ 0& p_2& 0& 0& 0& 0\\ 0& 0& p_3& 0& 0& 0\\ 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}x-x_0\\ y-y_0\\ z-z_0\\ \stackrel{\·}{x}\\ \stackrel{\·}{y}\\ \stackrel{\·}{z}\end{array}\right]$ Wherein, x, y, z have represented the current position on X-axis, Y-axis and Z-direction of detector, x ₀, y ₀, z ₀Obstacle avoidance zero hour is being carried out in representative, the position of detector on X-axis, Y-axis and Z-direction,

Represented the speed of detector on X-axis, Y-axis and Z-direction, above information provides by spaceborne navigation sensor, p ₁, p ₂, p ₃It is positive coefficient.This function is represented the distance between current location and the initial position, has represented the consumption of energy, and the energy that the big more representative of this function consumes is many more, otherwise few more.

2, jeopardously the situation function is:

${\mathrm{\Φ}}_s(x,y)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\σ}}^2}\right)}$

Wherein, x, y have represented the current position on X-axis and Y direction of detector, x _i, y _iRepresented the position of obstacle, z _iRepresented the height or the degree of depth of obstacle, above information provides by spaceborne obstacle detecting device, k ₁, σ is a positive number, i is the number of obstacle.This function has been represented near the dangerous terrain the touch-down zone, and the big more representative physical features of this function is dangerous more, otherwise safe more.

The Lyapunov function of then choosing is:

Φ＝Φ _P+Φ _S

By Φ _PAnd Φ _SAs can be known:

Φ＞0

Being known by Liapunov second theorem ought $\stackrel{.}{\mathrm{\&Phi;}}<0$ The time, then system will converge on equilibrium point.

So order

$\stackrel{\&CenterDot;}{\mathrm{\&Phi;}}=-k_x{\stackrel{\&CenterDot;}{x}}^2-k_y{\stackrel{\&CenterDot;}{y}}^2-k_z{\stackrel{\&CenterDot;}{z}}^2$

K wherein _x, k _y, k _zIt is positive number.Coupling system state equation (1) can be asked for control P.

Derivation above utilizing can controlled power P expression formula be:

$P_x=-U_{x}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{x}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{x}m-k_x\stackrel{\&CenterDot;}{x}/2+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\&sigma;}}^2}\right)}\frac{(x-x_i)}{{\mathrm{\&sigma;}}^2}-p_1(x-x_i)$

$P_y=-U_{y}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{y}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{y}m-k_y\stackrel{\&CenterDot;}{y}/2+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\&sigma;}}^2}\right)}\frac{(y-y_i)}{{\mathrm{\&sigma;}}^2}-p_2(y-y_i)---\left(2\right)$

$P_z=-U_{z}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{z}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{z}m-k_z\stackrel{\&CenterDot;}{z}/2-p_3(z-z_i)$

X, y, z have represented the current position on X-axis, Y-axis and Z-direction of detector,

Represented the speed of detector on X-axis, Y-axis and Z-direction, x _i, y _iRepresented the position of obstacle, z _iRepresented the height or the degree of depth of obstacle, these information have been brought into the size that gets final product controlled power P in the formula (2).

Claims (1)

1. a deep space detector soft landing autonomic obstruction evasion control method is characterized in that detector records detector current position r, speed by the navigation sensor that carries

Information records the position x of obstacle by the obstacle detecting device that carries _i, y _i, the big or small z of obstacle _iInformation, the controller of detector utilizes following formula (3), (2), (4) to calculate according to the above-mentioned information that records, and obtains control P on three directions of detector nozzle _x, P _y, P _zSize, detector is subjected to P _x, P _y, P _zThe effect of control can guarantee its descending trajectory along safety target celestial body surface of landing;

Described formula is:

$P_x=-U_{x}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{x}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{x}m-k_x\stackrel{\&CenterDot;}{x}/2+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\&sigma;}}^2}\right)}\frac{(x-x_i)}{{\mathrm{\&sigma;}}^2}-p_1(x-x_i)---\left(3\right)$

$P_y=-U_{y}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{y}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{y}m-k_y\stackrel{\&CenterDot;}{y}/2+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{k}_1\left|z_i\right|e^{\left(\frac{{(x-x_i)}^2+{(y-y_i)}^2}{{\mathrm{\&sigma;}}^2}\right)}\frac{(y-y_i)}{{\mathrm{\&sigma;}}^2}-p_2(y-y_i)---\left(2\right)$

$P_z=-U_{z}m+2{({\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}})}_{z}m+{({\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r))}_{z}m-k_z\stackrel{\&CenterDot;}{z}/2-p_3(z-z_i)---\left(4\right)$

In to target celestial body soft landing process, the kinetics equation of detector is:

$m\frac{{\mathrm{\&delta;}}^{2}r}{\mathrm{\&delta;}{t}^2}=P+\mathrm{mU}-2m{\mathrm{\&omega;}}_e\&times;\frac{\mathrm{\&delta;r}}{\mathrm{\&delta;t}}-m{\mathrm{\&omega;}}_e\&times;({\mathrm{\&omega;}}_e\&times;r)---\left(5\right)$

In above-mentioned formula (3), (2), (4), (5): U is the celestial body gravitation acceleration; M is the deep space probe quality; ω _eBe the moving coordinate system angular velocity of rotation; R is the radius vector of detector barycenter in inertial coordinates system; k _x, k _y, k _zBe positive number, it is by the decision of Liapunov function value expectation decline rate; k ₁Be positive number, it be jeopardously the situation function with respect to the weight of energy function; σ is a positive number, and its numerical value is decided by the shape of situation jeopardously; p ₁, p ₂, p ₃Be positive number, it is the weight of location entries with respect to speed term; P is the control thrust vectoring that acts on the detector.

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