CN106778012A - A kind of small feature loss attachment detection descending trajectory optimization method - Google Patents

Abstract

The present invention relates to a kind of small feature loss attachment detection descending trajectory optimization method, belong to field of aerospace.The present invention estimates the gravitational acceleration near target small feature loss using the humorous Gravitation Field Model of interior ball, using convex optimized algorithm solution optimal control problem.Small feature loss gravitational acceleration nearby is estimated using the humorous Gravitation Field Model of interior ball, has the advantages that computational efficiency is high.Optimal fuel control problem is solved using convex optimized algorithm, the derivation for avoiding indirect method is complicated, and association's state variable is difficult the problem of conjecture without physical significance, derive step relatively simple, the calculating time is saved, it is a kind of quick, high-precision Estimation Optimization method, and acquired results meet the constraint of initial and end state, Dynamic Constraints and control constraints.

Description

A kind of small feature loss attachment detection descending trajectory optimization method

Technical field

The present invention relates to a kind of small feature loss attachment detection descending trajectory optimization method, belong to field of aerospace.

Background technology

Small celestial body exploration understands solar system formation and evolution, origin of life and evolution and defends external celestial body as the mankind The important channel of shock, will be one of main contents of following survey of deep space activity, and attachment detection is people in following a period of time Class explores the major way of small feature loss.Decline stage is lander attachment small feature loss or completes the crucial rank that sampling returns to detection Can section, conclusive effect be played to safe and accurate reach the default target area with scientific exploration value, and this is under Depression of order section Trajectory Design, navigation and Guidance and control be proposed requirement very high.The decline process of small feature loss lander can be with It is converted into a track optimizing problem and the tracking control problem to nominal trajectory.The nominal trajectory of setting is required to peace Entirely, specified landing point is accurately arrived at, the multiple constraints such as whole story state constraint, path constraint, control constraints are met, while makes certain The important performance indications of item are optimized, such as burnup, time.Track optimizing method mainly includes direct based on parametric method Method and the indirect method based on Pang Te lia king minimal principles.Direct method need not derive the transversality condition of optimization problem, it is to avoid The association's state initial value for solving two-point boundary value problem is sensitive difficult, thus is widely used.Additionally, near for small feature loss Track optimizing problem, in addition it is also necessary to set up the Gravitation Field Model of gravitational acceleration near accurate description small feature loss.

In the small feature loss attachment detection descending trajectory optimization method for having developed, first technology [1] is (referring to Lantoine G,Braun R.Optimal trajectories for soft landing on asteroids.Space Systems Design Lab,Georgia Institute of Technology,Atlanta,GA,AE8900 MS Special Problems Report, Dec.2006.) gravitational acceleration near target small feature loss is solved using polyhedral model, with energy As optimizing index, big step-length optimization is carried out with direct method, so as to estimate to obtain association's state initial value of optimization problem, be then based on Pang Te lia kings principle carries out indirect method track optimizing calculating.Polyhedral model asks that gravitational acceleration efficiency is low, and optimized algorithm is numerous Trivial, time-consuming.

First technology [2] (referring to Ren, Y.and Shan, J., " Reliability-Based Soft Landing Trajectory Optimization near Asteroid with Uncertain Gravitational Field,” Journal of Guidance, Control, and Dynamics, Vol.38, No.9,2015, pp.1810-1820.), first The more specific energetic optimum problem of convergence region is built, then by adjusting homotopy coefficient, sequence is solved, most energetic optimum at last Problem is converted into fuel optimal problem, still needs to solve two-point boundary value problem using Homotopy, and optimization process is time-consuming more long.

The content of the invention

The invention aims to solve existing small feature loss attachment detection descending trajectory optimization method because drawing using polyhedron Force field model seeks gravitational acceleration inefficient；And track optimizing resolving is carried out using indirect method, because association's state initial value is difficult to estimate Solve difficult problem, there is provided a kind of small feature loss attachment detection descending trajectory optimization method.

A kind of small feature loss attachment detection descending trajectory optimization method, target small feature loss is estimated using the humorous Gravitation Field Model of interior ball Neighbouring gravitational acceleration, using convex optimized algorithm solution locus optimization method.

The convex optimized algorithm includes lax, linearisation, discretization and interior point method.

A kind of small feature loss attachment detection descending trajectory optimization method, comprises the following steps：

Step one, the spherical harmonic coefficient by the humorous Gravitation Field Model of ball in Least Square Method：

Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should land with the target on small feature loss surface Point is tangent, and the centre of sphere is chosen and should ensure that lander descending trajectory is included inside Brillouin's ball.Appoint inside interior Brillouin's ball and take N_dataIt is individual, N is calculated by polyhedral model_dataThe gravitational acceleration of individual point, and 3N is constructed by the gravitational acceleration_data× 1 dimension MatrixThe humorous gravity model spherical harmonic coefficient of interior ball is asked for by least square method.

Wherein, n and m represent the order and power of Legnedre polynomial respectively,It is (a n²+ 2n) × 1 dimension Matrix,Contain spherical harmonic coefficient in the required each rank for taking

The matrix that the derivative for being gravitational acceleration on interior spherical harmonic coefficient is constituted, dimension is (n²+2n)× 3N_data.W is a 3N_dataDimension unit matrix；

Step 2, construction small feature loss attachment detection descending trajectory optimization method：

It is connected under coordinate system in small feature loss, lander meets following kinetics equation

Wherein, r=[x, y, z]^TWithThe position vector and speed of lander under respectively connected coordinate system Vector；ω=[0,0, ω]^TIt is small feature loss spin angle velocity vector；T=[T_x,T_y,T_z]^TIt is lander thrust vectoring；m_eFor The quality of land device；I_spIt is engine/motor specific impulse；g_e=9.807 is normal gravity constant； It is gravitational acceleration vector, is calculated by below equation：

Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball, δ in step one_0,m For Kronecker delta (Ke Laoneike) function (as m=0, δ_0,m=1).Interior ball required by step one Humorous coefficient；It is the humorous Gravitation Field Model basic function of interior ball in step one, meets following recurrence relation.

Lander meets following boundary condition

Wherein, r₀, v₀And m₀The respectively position of original position lander, speed and quality.t_fIt is terminal time, r_fFor Target landing point, v_fFor terminal velocity is constrained, for soft landing problem, v_f=0.

Lander thrust vectoring meets following constraints

0≤||T||≤T_max (7)

Fuel optimal performance index is expressed as follows

Formula (3), (6), (7), (8) constitute descending trajectory optimization method；

Step 3, in the descending trajectory optimization method obtained by step 2 introduce slack variable Γ, to the descending trajectory Optimization method is relaxed：

It is introduced into slack variable Γ and substitutes | | T | | in descending trajectory optimization method, then the track optimizing equation after relaxing is：

Step 4, to step 3 gained equation linearization process：

Define new variables as follows

By in the optimization method of above variable substitution step 3, the optimization method for being linearized is

Wherein,T represents time variable.

Step 5, sliding-model control is carried out to the optimization method obtained by step 4：

By time interval [0, t_f] N parts is divided into, obtainOptimization method to step 4 is carried out at discretization Reason, after discretization, track optimizing equation is converted to parameter optimization equation, and the expression formula of parameter optimization equation is as follows：

Wherein, M=[I₆,0_6×1], t_kRepresent k-th timing node, u_kAnd σ_kT is represented respectively_kThe value of moment u and σ.

Step 6, solution is iterated to the parameter optimization equation in step 5 using interior point method, specific solution procedure is such as Under：

1) it is a constant value ▽ V to make gravitational acceleration₀, using the parameter optimization equation in interior point method solution procedure five, obtain One track；

2) using step 1) obtained by track as reference locus, calculate in reference locus each node (i.e. k=0 ..., N in the) gravitational acceleration at place, and the parameter optimization equation brought into step 5, solved using interior point method, obtained one newly Track, reference locus of the new track that will be obtained as next iteration；

3) when the track convergence for obtaining, then optimal solution is obtained, that is, obtains detecting optimal descending trajectory.

Sliding-model control method described in step 5 uses explicit fourth order Runge-Kutta integral formula method；

Beneficial effect

A kind of small feature loss attachment detection descending trajectory optimization method given by the present invention, using the humorous Gravitation Field Model of interior ball Estimate small feature loss gravitational acceleration nearby, have the advantages that computational efficiency is high.Optimal fuel control is solved using convex optimized algorithm Problem, it is to avoid the derivation of indirect method is complicated, and association's state variable is difficult the problem of conjecture without physical significance, derives step more Simplicity, has saved the calculating time, is a kind of quick, high-precision Estimation Optimization method, and acquired results meet initial and end State constraint, Dynamic Constraints and control constraints.

Brief description of the drawings

Fig. 1 is the flow chart of the inventive method；

Fig. 2 is simulation result schematic diagram, is most had track by four iteration altogether；Wherein (a) is the connected seat of small feature loss The lower lander track along the x-axis direction of mark system, (b) is track schematic diagram along the y-axis direction, and (c) is that track is illustrated along the z-axis direction Figure, (d) is the big logotype of thrust.

Specific embodiment

The invention will be further described with embodiment below in conjunction with the accompanying drawings.

Embodiment 1

A kind of small feature loss attachment detection descending trajectory optimization method, comprises the following steps：

Step one, the spherical harmonic coefficient by the humorous Gravitation Field Model of ball in Least Square Method：

Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should land with the target on small feature loss surface Point is tangent, and the centre of sphere is chosen and should ensure that lander descending trajectory is included inside Brillouin's ball.Appoint inside interior Brillouin's ball and take N_dataIt is individual, N is calculated by polyhedral model_dataThe gravitational acceleration of individual point, and 3N is constructed by the gravitational acceleration_data× 1 dimension MatrixThe humorous gravity model spherical harmonic coefficient of interior ball is asked for by least square method.

Wherein, n and m represent the order and power of Legnedre polynomial respectively,It is (a n²+ 2n) × 1 dimension Matrix,Contain spherical harmonic coefficient in the required each rank for taking

The matrix that the derivative for being gravitational acceleration on interior spherical harmonic coefficient is constituted, dimension is (n²+2n)× 3N_data.W is a 3N_dataDimension unit matrix；

Step 2, construction small feature loss attachment detection descending trajectory optimization method：

It is connected under coordinate system in small feature loss, lander meets following kinetics equation

Wherein, r=[x, y, z]^TWithThe position vector and speed of lander under respectively connected coordinate system Vector；ω=[0,0, ω]^TIt is small feature loss spin angle velocity vector；T=[T_x,T_y,T_z]^TIt is lander thrust vectoring；m_eFor The quality of land device；I_spIt is engine/motor specific impulse；g_e=9.807 is normal gravity constant； It is gravitational acceleration vector, is calculated by below equation：

Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball, δ in step one_0,m For (Ke Laoneike) Kronecker delta functions (as m=0, δ_0,m=1).Interior ball required by step one Humorous coefficient；It is the humorous Gravitation Field Model basic function of interior ball in step one, meets following recurrence relation.

Lander meets following boundary condition

Wherein, r₀, v₀And m₀The respectively position of original position lander, speed and quality.t_fIt is terminal time, r_fFor Target landing point, v_fFor terminal velocity is constrained, for soft landing problem, v_f=0.

Lander thrust vectoring meets following constraints

0≤||T||≤T_max (19)

Fuel optimal performance index is expressed as follows

Formula (15), (18), (19), (20) constitute descending trajectory optimization method；

Step 3, in the descending trajectory optimization method obtained by step 2 introduce slack variable Γ, to the descending trajectory Optimization method is relaxed：

It is introduced into slack variable Γ and substitutes | | T | | in descending trajectory optimization method, then the track optimizing equation after relaxing is：

Step 4, to step 3 gained equation linearization process：

Define new variables as follows

By in the optimization method of above variable substitution step 3, the optimization method for being linearized is

Wherein,T represents time variable.

Step 5, sliding-model control is carried out to the optimization method obtained by step 4：

By time interval [0, t_f] N parts being divided into, can obtainBy explicit fourth order Runge-Kutta integral formula, Optimization method to step 4 carries out discretization

Wherein,r_k, v_kAnd p_kRepresent r, v and p in timing node t respectively_kThe value at place, U_kAnd ▽ V_kRepresent state variable, control input and gravitational acceleration in timing node t respectively_kThe value at place.

u_kAnd σ_kT is represented respectively_kThe value of moment u and σ.After discretization, track optimizing equation is converted to a ginseng Number optimization method, its expression formula is as follows：

Wherein, M=[I₆,0_6×1]。

Step 6, solution is iterated to the parameter optimization equation in step 5 using interior point method, specific solution procedure is such as Under：

1) it is a constant value ▽ V to make gravitational acceleration₀, using the parameter optimization equation in interior point method solution procedure five, obtain One track；

2) using step 1) obtained by track as reference locus, calculate in reference locus each node (i.e. k=0 ..., N in the) gravitational acceleration at place, and the parameter optimization equation brought into step 5, solved using interior point method, obtained one newly Track, reference locus of the new track that will be obtained as next iteration；

3) when the track convergence for obtaining, then optimal solution is obtained, that is, obtains detecting optimal descending trajectory.

Fig. 2 is the emulation schematic diagram carried out on small feature loss 216Kleopatra.The initial position of lander for [- 150108,6010, -1034] m, target location is [- 112600,6340, -12520] m.Using small feature loss proposed by the invention Attachment detection descending trajectory optimization method, altogether by four iteration, obtains final burnup optimal trajectory.As shown in Figure 2, optimize Result meets every constraints, and lander is with zero velocity soft landing in default landing point, and whole calculating process is time-consuming 11.4 seconds, Optimize simultaneously the controling power for obtaining all the time setting the motor power upper limit within.

Claims (4)

1. a kind of small feature loss attachment detects descending trajectory optimization method, it is characterised in that：Estimated using the humorous Gravitation Field Model of interior ball Gravitational acceleration near target small feature loss, using convex optimized algorithm solution locus optimization method, finally realizes that descending trajectory optimizes.

2. a kind of small feature loss attachment as claimed in claim 1 detects descending trajectory optimization method, it is characterised in that：It is described convex excellent Changing algorithm includes lax, linearisation, discretization and interior point method.

3. a kind of small feature loss attachment as claimed in claim 1 detects descending trajectory optimization method, it is characterised in that：It is specific detailed Step is as follows：

Step one, the spherical harmonic coefficient by the humorous Gravitation Field Model of ball in Least Square Method：

Brillouin's ball in small feature loss external structure, constructing interior Brillouin's ball should be with the target landing point phase on small feature loss surface Cut, the centre of sphere is chosen and should ensure that lander descending trajectory is included inside Brillouin's ball；Appoint inside interior Brillouin's ball and take N_data It is individual, N is calculated by polyhedral model_dataThe gravitational acceleration of individual point, and 3N is constructed by the gravitational acceleration_data× 1 dimension matrixThe humorous gravity model spherical harmonic coefficient of interior ball is asked for by least square method；

$\[{\tilde{C}}_{n,m}^i\]=\left({\[Q_{n,m}^i\]}^{T}W{\[Q_{n,m}^i\]}^{-1}\right)\left\{{\[Q_{n,m}^i\]}^{T}W\left(\frac{\∂V}{\∂r}\right)\right\}---\left(1\right)$

Wherein, n and m represent the order and power of Legnedre polynomial respectively,It is (a n²+ 2n) × 1 matrix tieed up,Contain spherical harmonic coefficient in the required each rank for taking

$\[{\tilde{C}}_{n,m}^i\]=\[C_{1,0}^i,C_{1,1}^i,S_{1,1}^i,C_{2,0}^i,C_{2,1}^i,S_{2,1}^i,C_{2,2}^i,S_{2,2}^i,C_{3,0}^i,...\]---\left(2\right)$

The matrix that the derivative for being gravitational acceleration on interior spherical harmonic coefficient is constituted, dimension is (n²+2n)×3N_data；W is One 3N_dataDimension unit matrix；

Step 2, construction small feature loss attachment detection descending trajectory optimization method：

It is connected under coordinate system in small feature loss, lander meets following kinetics equation

$\left\{\begin{array}{c}\stackrel{\·}{r}=v\\ \stackrel{\·}{v}=-2\mathrm{\ω}\×v-\mathrm{\ω}\×(\mathrm{\ω}\×r)+\▿V+\frac{T}{m}\\ \stackrel{\·}{m}=-\frac{\left|\right|T\left|\right|}{I_{sp}{g}_e}\end{array}\right.---\left(3\right)$

Wherein, r=[x, y, z]^TWithThe position vector and speed arrow of lander under respectively connected coordinate system Amount；ω=[0,0, ω]^TIt is small feature loss spin angle velocity vector；T=[T_x,T_y,T_z]^TIt is lander thrust vectoring；m_eTo land The quality of device；I_spIt is engine/motor specific impulse；g_e=9.807 is normal gravity constant；For Gravitational acceleration vector, is calculated by below equation：

$\begin{array}{c}\frac{\∂V}{\∂x}=\frac{GM}{{\left(R\right)}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\left[\begin{array}{c}{C}_{n,m}^i\\ S_{n,m}^i\end{array}\right]\·\[-\frac{1}{2}(1+{\mathrm{\δ}}_{0,m})b_{n-1,m+1}^i+\frac{1}{2}\frac{(n+m)!}{(n+m-2)!}{b}_{n-1,m-1}^i\]\\ \frac{\∂V}{\∂y}=\frac{GM}{{\left(R\right)}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\left[\begin{array}{c}{S}_{n,m}^i\\ -C_{n,m}^i\end{array}\right]\·\[\frac{1}{2}(1+{\mathrm{\δ}}_{0,m})b_{n-1,m+1}^i+\frac{1}{2}\frac{(n+m)!}{(n+m-2)!}{b}_{n-1,m-1}^i\]\\ \frac{\∂V}{\∂z}=\frac{GM}{{\left(R\right)}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}\underset{m=0}{\overset{n}{\Σ}}\left[\begin{array}{c}{C}_{n,m}^i\\ S_{n,m}^i\end{array}\right]\·\[(n+m)b_{n-1,m}^i\]\end{array}---\left(16\right)$

Wherein, G is universal gravitational constant, and M is target small feature loss quality, and R is interior Brillouin's radius of a ball, δ in step one_0,mFor Kronecker delta (Ke Laoneike) function (as m=0, δ_0,m=1)；Interior ball required by step one is humorous Coefficient；It is the humorous Gravitation Field Model basic function of interior ball in step one, meets following recurrence relation；

$\left\{\begin{array}{c}{b}_{0,0}^i=\left[\begin{array}{c}1\\ 0\end{array}\right]\\ b_{n,n}^i=(2n-1)\left[\begin{array}{cc}x/R& -y/R\\ y/R& x/R\end{array}\right]b_{n-1,n-1}^i\\ b_{n,m}^i=\frac{2n-1}{n-m}\frac{z}{R^i}{b}_{n-1,m}^i-\frac{n+m-1}{n-m}{\left(\frac{\sqrt{x^2+y^2+z^2}}{R}\right)}^2{b}_{n-2,m}^i\\ b_{n,n-1}^i=(2n-1)\frac{z}{R}{b}_{n-1,n-1}^i\end{array}\right.---\left(5\right)$

Lander meets following boundary condition

$\begin{array}{c}r\left(0\right)=r_0,v\left(t_0\right)=v_0,m_e\left(0\right)=m_0\\ r\left(t_f\right)=r_f,v\left(t_f\right)=v_f\end{array}---\left(6\right)$

Wherein, r₀, v₀And m₀The respectively position of original position lander, speed and quality；t_fIt is terminal time, r_fIt is target Landing point, v_fFor terminal velocity is constrained, for soft landing problem, v_f=0；

Lander thrust vectoring meets following constraints

0≤||T||≤T_max (7)

Fuel optimal performance index is expressed as follows

$J={\∫}_0^{t_f}\left|\right|T\left|\right|dt---\left(8\right)$

Formula (3), (6), (7), (8) constitute descending trajectory optimization method；

Step 3, in the descending trajectory optimization method obtained by step 2 introduce slack variable Γ, to the descending trajectory optimize Equation is relaxed：

It is introduced into slack variable Γ and substitutes | | T | | in descending trajectory optimization method, then the track optimizing equation after relaxing is：

$\begin{array}{c}\begin{array}{cc}\min & {\∫}_0^{t_f}\mathrm{\Γ}dt\end{array}\\ \begin{array}{ccc}subjecto& \stackrel{\·}{m}=-\frac{\mathrm{\Γ}}{I_{sp}{g}_e}& \stackrel{\·}{r}=v\end{array}\\ \stackrel{\·}{v}=-2\mathrm{\ω}\×v-\mathrm{\ω}\×(\mathrm{\ω}\×r)+\▿V+\frac{T}{m}\\ \begin{array}{ccc}r\left(0\right)=r_0& v\left(0\right)=v_0& m\left(0\right)=m_0\end{array}\\ \begin{array}{cc}r\left(t_f\right)=r_f& v\left(t_f\right)=0\end{array}\\ \begin{array}{cc}0\≤\mathrm{\Γ}\≤T_{\max }& \sqrt{T_x^2+T_y^2+T_z^2}\≤\mathrm{\Γ}\end{array}\end{array}---\left(9\right)$

Step 4, to step 3 gained equation linearization process：

Define new variables as follows

$\begin{array}{ccc}\mathrm{\σ}\stackrel{\mathrm{\Δ}}{=}\frac{\mathrm{\Γ}}{m}& u\stackrel{\mathrm{\Δ}}{=}\frac{T}{m}& p\stackrel{\mathrm{\Δ}}{=}lnm\end{array}---\left(10\right)$

By in the optimization method of above variable substitution step 3, the optimization method for being linearized is

$\begin{array}{c}\begin{array}{cc}\min & J={\∫}_0^{t_f}\mathrm{\σ}dt\end{array}\\ \begin{array}{ccc}subjecto& \stackrel{\·}{p}=-\frac{\mathrm{\σ}}{I_{sp}{g}_e}& \stackrel{\·}{r}=v\end{array}\\ \stackrel{\·}{v}=-2\mathrm{\ω}\×v-\mathrm{\ω}\×(\mathrm{\ω}\×r)+\▿V+u\\ \begin{array}{ccc}r\left(0\right)=r_0& v\left(0\right)=v_0& p\left(0\right)=\ln m_0\end{array}\\ \begin{array}{cc}r\left(t_f\right)=r_f& v\left(t_f\right)=0\end{array}\\ \begin{array}{cc}\left|\right|u\left|\right|\≤\mathrm{\σ}& 0\≤\mathrm{\σ}\≤T_{\max }{e}^{-p_0}\[1-(p-p_0)\]\end{array}\end{array}---\left(11\right)$

Wherein,T represents time variable；

Step 5, sliding-model control is carried out to the optimization method obtained by step 4：

By time interval [0, t_f] N parts is divided into, obtainOptimization method to step 4 carries out sliding-model control, warp Cross after discretization, track optimizing equation is converted to parameter optimization equation, the expression formula of parameter optimization equation is as follows：

$\begin{array}{c}\min \underset{u_k,{\mathrm{\σ}}_k}{J}=\underset{k=0}{\overset{N}{\Σ}}{\mathrm{\σ}}_k\\ subjectto\left\{\begin{array}{c}{X}_0={\[r_0^T,v_0^T,p_0\]}^T\\ {\mathrm{MX}}_N={\[r_f^T,0_{1\×3}\]}^T\\ \begin{array}{cc}\left|\right|u_k\left|\right|\≤{\mathrm{\σ}}_k& k=0,\mathrm{...},N\end{array}\\ \begin{array}{cc}0\≤{\mathrm{\σ}}_k\≤T_{\max }{e}^{-p_0\left(t_k\right)}\[1-(p_k-p_0(t_k\left)\right)\]& k=0,\mathrm{...},N\end{array}\end{array}\right.\end{array}---\left(12\right)$

Wherein, M=[I₆,0_6×1], t_kRepresent k-th timing node, u_kAnd σ_kT is represented respectively_kThe value of moment u and σ；

Step 6, solution is iterated to the parameter optimization equation in step 5 using interior point method, specific solution procedure is as follows：

1) it is a constant value ▽ V to make gravitational acceleration₀, using the parameter optimization equation in interior point method solution procedure five, obtain a rail Mark；

2) using step 1) obtained by track as reference locus, calculate each node (i.e. k=0 ..., N) place in reference locus Gravitational acceleration, and in the parameter optimization equation brought into step 5, solved using interior point method, obtain a new rail Mark, reference locus of the new track that will be obtained as next iteration；

3) when the track convergence for obtaining, then optimal solution is obtained, that is, obtains detecting optimal descending trajectory.

4. a kind of small feature loss attachment as claimed in claim 3 detects descending trajectory optimization method, it is characterised in that：Step 5 institute Sliding-model control method is stated using explicit fourth order Runge-Kutta integral formula method.