CN114955007B - Method and device for rapidly planning relative movement time optimal track based on convex planning - Google Patents
Method and device for rapidly planning relative movement time optimal track based on convex planning Download PDFInfo
- Publication number
- CN114955007B CN114955007B CN202210515805.4A CN202210515805A CN114955007B CN 114955007 B CN114955007 B CN 114955007B CN 202210515805 A CN202210515805 A CN 202210515805A CN 114955007 B CN114955007 B CN 114955007B
- Authority
- CN
- China
- Prior art keywords
- time
- relative motion
- terminal error
- planning
- constraint
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 90
- 238000005457 optimization Methods 0.000 claims abstract description 76
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 34
- 230000006870 function Effects 0.000 claims description 55
- 206010048669 Terminal state Diseases 0.000 claims description 24
- 238000004364 calculation method Methods 0.000 claims description 21
- 238000004590 computer program Methods 0.000 claims description 14
- 239000011159 matrix material Substances 0.000 claims description 10
- 230000001133 acceleration Effects 0.000 claims description 7
- 230000007423 decrease Effects 0.000 claims description 7
- 230000005484 gravity Effects 0.000 claims description 6
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 238000010276 construction Methods 0.000 claims description 2
- 238000010586 diagram Methods 0.000 description 9
- 238000004088 simulation Methods 0.000 description 5
- 238000012546 transfer Methods 0.000 description 4
- 230000008859 change Effects 0.000 description 3
- 238000004458 analytical method Methods 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 230000001360 synchronised effect Effects 0.000 description 2
- 230000009466 transformation Effects 0.000 description 2
- 239000013598 vector Substances 0.000 description 2
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- PXFBZOLANLWPMH-UHFFFAOYSA-N 16-Epiaffinine Natural products C1C(C2=CC=CC=C2N2)=C2C(=O)CC2C(=CC)CN(C)C1C2CO PXFBZOLANLWPMH-UHFFFAOYSA-N 0.000 description 1
- 241000135164 Timea Species 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 239000000446 fuel Substances 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 239000004973 liquid crystal related substance Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000005312 nonlinear dynamic Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 238000004611 spectroscopical analysis Methods 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 230000003068 static effect Effects 0.000 description 1
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64G—COSMONAUTICS; VEHICLES OR EQUIPMENT THEREFOR
- B64G1/00—Cosmonautic vehicles
- B64G1/22—Parts of, or equipment specially adapted for fitting in or to, cosmonautic vehicles
- B64G1/24—Guiding or controlling apparatus, e.g. for attitude control
- B64G1/242—Orbits and trajectories
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/15—Vehicle, aircraft or watercraft design
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Remote Sensing (AREA)
- Aviation & Aerospace Engineering (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Chemical & Material Sciences (AREA)
- Combustion & Propulsion (AREA)
- Radar, Positioning & Navigation (AREA)
- Automation & Control Theory (AREA)
- Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)
Abstract
The application relates to a method, a device, computer equipment and a storage medium for fast planning of a relative motion time optimal track based on convex planning. The method comprises the following steps: establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions; setting a two-norm of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function; performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence; constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; and solving the double-layer optimization problem by using a hybrid optimization algorithm to obtain the shortest flight time. By adopting the method, the rapid track planning efficiency can be improved.
Description
Technical Field
The application relates to the field of spacecraft guidance and control, in particular to a method, a device, computer equipment and a storage medium for fast planning of a relative movement time optimal track based on convex planning.
Background
The relative motion track planning is a precondition and foundation for a spacecraft to implement a series of space operations such as approaching observation, on-orbit filling, formation flying and the like. The goal of time-optimal trajectory planning is to find the shortest time-of-flight trajectory from the initial state to the target state while meeting constraints of dynamics, control, etc. The shortest flight time has an important reference meaning to space mission design, and if a given flight time is less than the shortest flight time, there is no viable flight trajectory. For the relative motion trajectory planning problem, the processing is generally performed based on a strategy of a direct method or an indirect method. However, due to the complex nonlinear dynamics of the relative motion and various constraints, the first-order optimality requirement is often difficult to construct, limiting the further application of the indirect method. The direct method discretizes the control space and the state space, converts the optimal control problem into a nonlinear optimization problem, and mainly comprises a pseudo-spectrum method, a mixed integer linear programming algorithm and a quadratic programming algorithm, which are sensitive to initial values. In recent years, the convex planning algorithm is widely studied by students because of higher calculation efficiency, and is applied to the aspects of orbit transfer, multi-unmanned aerial vehicle collaborative planning, atmosphere capture track, spacecraft landing and the like, wherein the literature shows that the method has higher calculation efficiency compared with a pseudo-spectrometry. However, the objective function of the time-optimal problem is in a non-convex form and is difficult to solve directly with convex planning algorithms.
However, the traditional nonlinear optimization algorithm has low solving efficiency, and is difficult to meet the requirement of rapid trajectory planning.
Disclosure of Invention
Based on the foregoing, it is necessary to provide a method, an apparatus, a computer device and a storage medium for fast planning of a relative movement time optimal trajectory based on convex planning, which can improve the efficiency of fast trajectory planning.
A method for fast planning of a relative motion time optimal trajectory based on convex planning, the method comprising:
acquiring boundary conditions and constraint conditions in track planning;
establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions;
setting a two-norm of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function;
performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence;
Constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
And solving the double-layer optimization problem by using a hybrid optimization algorithm to obtain the shortest flight time.
In one embodiment, the establishing a time-optimal trajectory planning problem according to a spacecraft relative motion equation, boundary conditions and constraint conditions includes:
dispersing the spacecraft relative motion equation to obtain a discrete form relative motion equation in a relative motion coordinate system;
and establishing a time optimal track planning problem according to the discrete form relative motion equation, the boundary condition and the constraint condition.
In one embodiment, the boundary conditions include an initial state constraint and a terminal state constraint; constraints include control saturation constraints; according to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem, wherein the method comprises the following steps:
The discrete form relative motion equation is x (i+1) =a dx(i)+Bd T (i), wherein i=1, … N, N is the discrete steps, T represents the thrust of the spacecraft, a d represents the state coefficient matrix, and B d represents the control coefficient matrix;
The initial state constraint is x (t 0)＝x0,m(t0)＝m0, where spacecraft mass I sp is vacuum specific impulse of the propeller, g 0 is sea level gravity acceleration;
the terminal state constraint is x (T f)＝xf. The saturation constraint is controlled to be T 2≤Tmax, wherein T max represents the maximum thrust of the spacecraft;
according to the discrete form relative motion equation, boundary condition and constraint condition, establishing a time optimal track planning problem as Where t 0 denotes an initial time and t f denotes a terminal time.
In one embodiment, setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function includes:
Setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem as min J 2＝||x(tf)-xf||2 according to the boundary condition, the constraint condition and the objective function, wherein when At this point, the minimum termination error J 2 decreases with increasing t f, whenWhen J 2 is always zero, x (t f) represents the actual terminal state, x f represents the desired terminal state,Representing the shortest time of flight.
In one embodiment, constructing the performance index using the terminal error and the control sequence includes:
constructing performance metrics using terminal errors and control sequences Wherein whenJ 3(tf) is greater than 0 whenWhen J 3(tf) =0, whenTime J 3(tf)＜0,Tmax represents the maximum thrust of the spacecraft.
In one embodiment, a hybrid optimization algorithm is used to solve a double-layer optimization problem to obtain a shortest flight time, including:
And (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time.
In one embodiment, the method of binary method is used to narrow the range of the solution space until the absolute function value of the upper and lower boundaries is smaller than the preset value, and then the calculation result is used as the initial value of newton method to solve, so as to obtain the shortest flight time, including:
and (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time, wherein the steps are as follows:
Step S1: let the upper and lower boundaries t 1b and t ub of the dichotomy equal to t LB and t UB respectively, solve the double-layer optimization problem by taking t 1b and t ub as the flight time respectively, obtain indexes J 3(t1b) and J 3(tub);tLB and t UB according to the calculation result to represent the upper and lower boundaries of the flight time;
Step S2: if the absolute values of J 3(t1b) and J 3(tub) are greater than the preset reference value Step S4 is performed. If not, executing step S5;
Step S3: let t 0＝(t1b+tub)/2 and calculate double-layer optimization problem with t 0 as flight time to obtain index J 3(t0), if J 3(t1b)·J3(t0) < 0, let t 1b＝t0, otherwise let t ub＝t0, repeat steps S1 to S3 until absolute values of J 3(t1b) and J 3(tub) are smaller than preset Let t 0＝t1b,t1＝tub, k=0; k represents the iteration number of newton's method;
Step S4: it is determined whether the absolute value of t 0-t1 is equal to or greater than ε and k < M. If yes, executing step S6, otherwise executing step S7; epsilon represents the algorithm precision requirement; m represents the maximum number of iterations;
Step S5: let t2＝t1-J3(t1)(t1-t0)/(J3(t1)-J3(t0)), solve the double-layer optimization problem with t 2 as the flight time, calculate J 3(t2);
step S6: causing t0＝t1,J3(t0)＝J3(t1),t1＝t2,J3(t1)＝J3(t2),k＝k+1, to perform step S5;
Step S7: judging whether the absolute value of t 0-t1 is smaller than epsilon; if yes, outputting t 1, otherwise, failing to calculate; t 1 represents the shortest time of flight.
A relative motion time optimal trajectory fast planning device based on convex planning, the device comprising:
The time optimal track planning problem construction module is used for acquiring boundary conditions and constraint conditions in track planning; establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions;
A minimum terminal error problem module is constructed and used for setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function;
The problem conversion module is used for carrying out convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence; constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
and the problem solving module is used for solving the double-layer optimization problem by utilizing a hybrid optimization algorithm to obtain the shortest flight time.
A computer device comprising a memory storing a computer program and a processor which when executing the computer program performs the steps of:
acquiring boundary conditions and constraint conditions in track planning;
establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions;
setting a two-norm of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function;
performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence;
Constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
And solving the double-layer optimization problem by using a hybrid optimization algorithm to obtain the shortest flight time.
A computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of:
acquiring boundary conditions and constraint conditions in track planning;
establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions;
setting a two-norm of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function;
performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence;
Constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
And solving the double-layer optimization problem by using a hybrid optimization algorithm to obtain the shortest flight time.
According to the method, the device, the computer equipment and the storage medium for quickly planning the relative motion time optimal track based on convex planning, the time optimal control problem is converted into the double-layer optimization problem, the minimum terminal error problem of the inner layer is solved through the mature convex planning algorithm, so that the calculation efficiency is improved, the terminal error and the control sequence are constructed into new performance indexes, the shortest time searching problem is converted into the problem of easily solving root hunting, and then the root hunting problem is quickly solved through the mixed optimization algorithm with higher calculation efficiency and robustness, so that the shortest flight time is obtained, and the track planning efficiency is greatly improved.
Drawings
FIG. 1 is a flow chart of a method for fast planning of relative motion time optimal trajectories based on convex planning in one embodiment;
FIG. 2 is a schematic diagram of a relative coordinate system of a spacecraft in one embodiment;
FIG. 3 is a schematic diagram of a law of time variation of performance indicators in one embodiment;
FIG. 4 is a schematic diagram of a framework of a two-layer optimization problem in another embodiment;
FIG. 5 is a diagram showing the effects of a simulation experiment performed on the present invention in one embodiment;
FIG. 6 is a schematic diagram of a state change curve of a satellite relative transfer trajectory in one embodiment;
FIG. 7 is a schematic diagram of a thrust component variation of a satellite relative transfer trajectory in one embodiment;
FIG. 8 is a block diagram of a relative motion time optimal trajectory fast planning device based on convex planning in one embodiment;
fig. 9 is an internal structural diagram of a computer device in one embodiment.
Detailed Description
The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.
In one embodiment, as shown in fig. 2, a method for fast planning a relative motion time optimal trajectory based on convex planning is provided, which includes the following steps:
Step 102, obtaining boundary conditions and constraint conditions in track planning; and establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, the boundary conditions and the constraint conditions.
Boundary conditions include initial state constraints and terminal state constraints of the spacecraft; the constraint conditions comprise control saturation constraint, and a time optimal track planning problem can be established according to a spacecraft relative motion equation, boundary conditions and constraint conditions.
And 104, setting the two norms of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function.
Because the objective function of the time optimal control problem is not a convex form, the invention takes the terminal error of the spacecraft as the objective function, thereby constructing the minimum error problem which can be converted into a convex planning problem, and proving the thrust characteristics of the change rule of the optimal terminal error along with the time and the minimum error problem.
Step 106, performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence; constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem.
And solving the control sequence of the minimum terminal error problem by using a convex programming algorithm, and substituting the control sequence into a dynamic equation to obtain the actual terminal state of the spacecraft. And comparing actual and expected terminal states of the spacecraft to further obtain a terminal error of the spacecraft, and constructing a new performance index by utilizing the terminal error and the control sequence, so that the value of the performance index is zero if and only if the given flight time is equal to the shortest flight time. Based on the analysis, the time optimization problem can be converted into a double-layer optimization problem, wherein the inner layer is the minimum error problem, and the outer layer is the root finding problem.
And step 108, solving the double-layer optimization problem by using a hybrid optimization algorithm to obtain the shortest flight time.
The hybrid optimization algorithm is a method for reducing the range of a solution space by utilizing a dichotomy until the absolute function values of the upper boundary and the lower boundary are smaller than a preset value, and then solving the calculated result as an initial value of the Newton method, has the advantages of being high in dichotomy robustness and high in convergence speed of the Newton method, can quickly solve the root finding problem, and obtains the shortest flight time, so that the track planning efficiency is improved.
In the rapid planning method for the relative motion time optimal track based on convex planning, the time optimal control problem is converted into the double-layer optimization problem, the minimum terminal error problem of the inner layer is solved through the mature convex planning algorithm, so that the calculation efficiency is improved, the terminal error and the control sequence are constructed into new performance indexes, the shortest time search problem is converted into the root searching problem which is easy to solve, and then the root searching problem is rapidly solved through the mixed optimization algorithm with higher calculation efficiency and robustness, so that the shortest flight time is obtained, and the track planning efficiency is greatly improved.
In one embodiment, the establishing a time-optimal trajectory planning problem according to a spacecraft relative motion equation, boundary conditions and constraint conditions includes:
dispersing the spacecraft relative motion equation to obtain a discrete form relative motion equation in a relative motion coordinate system;
and establishing a time optimal track planning problem according to the discrete form relative motion equation, the boundary condition and the constraint condition.
In one embodiment, the boundary conditions include an initial state constraint and a terminal state constraint; constraints include control saturation constraints; according to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem, wherein the method comprises the following steps:
The discrete form relative motion equation is x (i+1) =a dx(i)+Bd T (i), wherein i=1, … N, N is the discrete steps, T represents the thrust of the spacecraft, a d represents the state coefficient matrix, and B d represents the control coefficient matrix;
The initial state constraint is x (t 0)＝x0,m(t0)＝m0, where spacecraft mass I sp is vacuum specific impulse of the propeller, and g0 is sea level gravity acceleration;
The terminal state constraint is x (T f)＝xf, controlling saturation constraints is T i 2≤Tmax.
According to the discrete form relative motion equation, boundary condition and constraint condition, establishing a time optimal track planning problem asWhere t 0 denotes an initial time and t f denotes a terminal time.
Spacecraft relative motion is typically described in terms of a relative coordinate system, as shown in fig. 2, with r d and r c representing position vectors of the tracking spacecraft and the reference spacecraft in the geocentric inertial system. The origin of the relative coordinate system is positioned at the center of mass of the reference spacecraft, the x-axis is consistent with the r c direction, the z-axis is consistent with the direction of the orbital moment of momentum, and the y-axis is determined by the right-hand rule.
The dynamics equation of satellites in the relative coordinate system can be expressed as
Where r= [ x, y, z ] T and v= [ v x,vy,vz]T ] represent relative positions and speeds of the tracking spacecraft, subscripts c and d represent the reference spacecraft and the tracking spacecraft, ω and ε are instantaneous angular speeds and angular accelerations of the reference spacecraft, t= [ T x,Ty,Tz]T and m are thrust and mass of the spacecraft, and μ is an gravitational constant. Assuming that the target spacecraft is located on a near circular orbit with an orbit radius much larger than the spacecraft relative distance, equation (1) can be reduced to
Scalar form of equation (2) is
Wherein n is the average orbital angular velocity of the reference spacecraft. Given a discrete time, deltat, equation (3) can be expressed in discrete form,
x(i+1)＝Adx(i)+BdT(i) (4)
Wherein x= [ r; v ] is a state vector, i=1, 2, … N is the number of discrete steps, a d and B d can be expressed as
Spacecraft mass variation following
Wherein I sp is the vacuum specific impulse of the propeller, and g 0＝9.80665m/s2 is the sea level gravity acceleration.
The relative motion process of the spacecraft needs to satisfy the initial state constraint of the formula (8) and the terminal state constraint of the formula (9), and the control saturation constraint of the formula (10).
x(t0)＝x0,m(t0)＝m0 (8)
x(tf)＝xf (9)
In the formula of 2≤Tmax (10), T max is the maximum thrust of the spacecraft, and T 0 is the initial time and is usually set to zero. t f is the desired termination time, x 0、m0 and x f are the given spacecraft initial state, initial mass and desired termination state, respectively. Thus, the time-optimal trajectory planning problem can be summarized as
Satisfying constraints (4), (7) to (10).
When T < T f, the optimal thrust amplitude of the time-optimal trajectory planning problem is always T *||2＝Tmax,||T*||2≤Tmax, it is only possible to find a terminal synergy value λ v(tf at t=t f and speed=0.
In one embodiment, setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function includes:
Setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem as min J 2＝||x(tf)-xf||2 according to the boundary condition, the constraint condition and the objective function, wherein when At this point, the minimum termination error J 2 decreases with increasing t f, whenWhen J 2 is always zero, x (t f) represents the actual terminal state, x f represents the desired terminal state,Representing the shortest time of flight.
The objective function of the time-optimal trajectory planning problem is in a non-convex form and is difficult to directly solve by a convex planning algorithm. The invention aims at the terminal error between the actual state and the expected state, constructs the minimum terminal error problem under the given flight time t f, and meets the constraints (4), (7) to (10).
Notably, the objective function and inequality constraints of the minimum terminal error problem are convex functions, and the equality constraints can be expressed in affine form and thus can be translated into convex planning problems.
At the same time, whenAt this point, the minimum termination error J 2 decreases with increasing t f, whenSince J 2 is always zero, the shortest flight time is the inflection point at which J 2 =0 is established. When (when)And when the minimum terminal error problem occurs, the amplitude of the optimal thrust is always the maximum value.
In one embodiment, constructing the performance index using the terminal error and the control sequence includes:
constructing performance metrics using terminal errors and control sequences Wherein whenJ 3(tf) is greater than 0 whenWhen J 3(tf) =0, whenTime J 3(tf)＜0,Tmax represents the maximum thrust of the spacecraft, as shown in fig. 3.
Notably, J 2 represents the optimization objective of convex planning, while J 3 is just one performance index constructed based on thrust and terminal errors for searching for the shortest time of flight. Through the analysis, the initial time optimal problem is converted into a double-layer optimal problem, and the inner layer is a convex planning problem, namely, a minimum terminal error problem of a given flight time. The outer layer is the root finding problem, and the flight time t f corresponding to the performance index J 3(tf) =0 is the shortest flight timeAs shown in fig. 4.
In one embodiment, a hybrid optimization algorithm is used to solve a double-layer optimization problem to obtain a shortest flight time, including:
And (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time.
In one embodiment, the method of binary method is used to narrow the range of the solution space until the absolute function value of the upper and lower boundaries is smaller than the preset value, and then the calculation result is used as the initial value of newton method to solve, so as to obtain the shortest flight time, including:
and (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time, wherein the steps are as follows:
Step S1: let the upper and lower boundaries t 1b and t ub of the dichotomy equal to t LB and t UB respectively, solve the double-layer optimization problem by taking t 1b and t ub as the flight time respectively, obtain indexes J 3(t1b) and J 3(tub);tLB and t UB according to the calculation result to represent the upper and lower boundaries of the flight time;
Step S2: if the absolute values of J 3(t1b) and J 3(tub) are greater than the preset reference value Step S4 is performed. If not, executing step S5;
Step S3: let t 0＝(t1b+tub)/2 and calculate double-layer optimization problem with t 0 as flight time to obtain index J 3(t0), if J 3(t1b)·J3(t0) < 0, let t 1b＝t0, otherwise let t ub＝t0, repeat steps S1 to S3 until absolute values of J 3(t1b) and J 3(tub) are smaller than preset Let t 0＝t1b,t1＝tub, k=0; k represents the iteration number of newton's method;
Step S4: it is determined whether the absolute value of t 0-t1 is equal to or greater than ε and k < M. If yes, executing step S6, otherwise executing step S7; epsilon represents the algorithm precision requirement; m represents the maximum number of iterations;
Step S5: let t2＝t1-J3(t1)(t1-t0)/(J3(t1)-J3(t0)), solve the double-layer optimization problem with t 2 as the flight time, calculate J 3(t2);
step S6: causing t0＝t1,J3(t0)＝J3(t1),t1＝t2,J3(t1)＝J3(t2),k＝k+1, to perform step S5;
Step S7: judging whether the absolute value of t 0-t1 is smaller than epsilon; if yes, outputting t 1, otherwise, failing to calculate; t 1 represents the shortest time of flight.
Aiming at the problem of outer layer root finding in a double-layer optimization framework, the invention provides a hybrid optimization algorithm by combining the advantages of Newton method and dichotomy. The method comprises the steps of firstly reducing the range of a solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and then solving a calculation result as an initial value of the Newton method. The Newton method is provided with a high-quality initial value through the dichotomy, and the hybrid optimization algorithm has the advantages of being high in dichotomy robustness and Newton method convergence rate, and the shortest flight time can be accurately and rapidly calculated, so that the track planning efficiency is improved.
In one embodiment, the performance of the present invention is verified by a numerical simulation method.
The reference spacecraft was operated on a nearly circular orbit 500km high with an initial mass of 1000kg for the satellites. The maximum thrust of the engine is 50N, the maximum I sp is 200s, and the simulation process is discretized into 100 steps. The upper and lower boundary values of the time of flight are 100s and 3000s respectively,The convex optimization problem is based on the convex optimization toolbox CVX solution, and SDPT3 is selected as a solver. The simulation computer is equipped with 3.0GHz Intel Core i7 processors and a 16Gb cache.
Assuming that the satellite maneuvers from one initial elliptical orbit around the fly to another elliptical orbit around the earth, the satellite may fly around the target without taking into account the effects of various perturbation factors and without consuming additional fuel.
The initial state and the final state of the satellite are
X0＝[1×103m,1×104m,0m,0m/s,-2.21m/s,2.21m/s]T；
Xf＝[866.03m,-1×103m,0m,-0.55m/s,-1.92m/s,0m/s]T；
Firstly, in order to verify the correctness of the theoretical derivation, the minimum terminal error problem is solved by the given flight time. Sampling every 10s between the lower boundaries in time, the simulation results are shown in fig. 5, where J 31 is the terminal error, J 32 is used to measure the difference between the thrust curve and the maximum thrust, and J 3 is the sum of J 31 and J 32. As can be seen from FIG. 5, whenWhen the optimum terminal error J 31 is greater than zero and decreases with time, whenThe optimum termination error J 31 is equal to zero. When (when)The thrust amplitude remains at T max whenThe thrust amplitude is less than T max, so index J 32 is zero in the first portion and non-zero in the second portion.
Then, the double-layer optimization method provided by the invention is utilized to solve the time optimal track planning problem, wherein the state and thrust change curves are shown in fig. 6-7. As can be seen from fig. 6, the method proposed by the present invention can successfully generate the satellite relative transfer trajectories. As shown in fig. 7, although the thrust component varies with time, the thrust magnitude remains at T max.
In order to evaluate the performance of the proposed hybrid optimization algorithm, the time-optimal problem with the same configuration is solved by adopting the traditional dichotomy, newton method and sequential quadratic programming method. The SQP method may be implemented by directly calling the nonlinear programming function Fmincon in the Matlab optimization tool box. Notably, the first three methods are based on convex programming to optimize the control sequence, which itself is used only to search for the shortest time of flight, whereas the SQP method directly optimizes the control sequence and the minimum time of flight simultaneously. Since the calculation efficiency and convergence speed of the SQP method and the conventional newton method are greatly affected by the initial value, both methods are performed 10 times with random initial values, and the comparison of performance indexes of the different methods is shown in table 1.
Table 1 comparison of different algorithm performances
As can be seen directly from table 1, the minimum flight times obtained for the four methods described above are substantially the same, verifying the effectiveness of the hybrid methods herein. For the calculation time criteria in table 1, although the calculation time criteria are affected by various factors such as computer configuration and program integration level, the calculation time of the first three methods is about two orders of magnitude less than that of the SQP method, which proves that the convex planning method is absolutely superior to the nonlinear optimization method in terms of calculation efficiency. The dichotomy takes about twice as much time as the mixing method, while the newton method takes slightly less time than the mixing method. It should be added that the conventional newton method can only converge half in 10 repeated calculations. Thus, the hybrid optimization algorithm presented herein has advantages in terms of both computational efficiency and robustness.
It should be understood that, although the steps in the flowchart of fig. 1 are shown in sequence as indicated by the arrows, the steps are not necessarily performed in sequence as indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in fig. 1 may include multiple sub-steps or stages that are not necessarily performed at the same time, but may be performed at different times, nor do the order in which the sub-steps or stages are performed necessarily performed in sequence, but may be performed alternately or alternately with at least a portion of other steps or sub-steps of other steps.
In one embodiment, as shown in fig. 8, there is provided a rapid planning apparatus for a relative movement time optimal trajectory based on convex planning, including: a time optimal trajectory planning problem building module 802, a build minimum terminal error problem module 804, a problem transformation module 806, and a problem solving module 808, wherein:
a time optimal trajectory planning problem building module 802, configured to obtain boundary conditions and constraint conditions in trajectory planning; establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, boundary conditions and constraint conditions;
A minimum terminal error problem constructing module 804, configured to set a two-norm of a terminal error as an objective function of a minimum terminal error problem, and construct the minimum terminal error problem according to a boundary condition, a constraint condition and the objective function;
The problem conversion module 806 is configured to perform convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence; constructing performance indexes by using the terminal errors and the control sequences, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance indexes; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
And a problem solving module 808, configured to solve the double-layer optimization problem by using a hybrid optimization algorithm, so as to obtain the shortest flight time.
In one embodiment, the time-optimal trajectory planning problem building module 802 is further configured to build a time-optimal trajectory planning problem according to the spacecraft relative motion equation, the boundary condition, and the constraint condition, including:
dispersing the spacecraft relative motion equation to obtain a discrete form relative motion equation in a relative motion coordinate system;
and establishing a time optimal track planning problem according to the discrete form relative motion equation, the boundary condition and the constraint condition.
In one embodiment, the boundary conditions include an initial state constraint and a terminal state constraint; constraints include control saturation constraints; the time-optimal trajectory planning problem building module 802 is further configured to build a time-optimal trajectory planning problem according to the discrete form relative motion equation, the boundary condition, and the constraint condition, including:
The discrete form relative motion equation is x (i+1) =a dx(i)+Bd T (i), wherein i represents the number of discrete steps, T represents the thrust of the spacecraft, a d represents the state coefficient matrix, and B d represents the control coefficient matrix;
The initial state constraint is x (t 0)＝x0,m(t0)＝m0, where spacecraft mass I sp is vacuum specific impulse of the propeller, and g0 is sea level gravity acceleration;
the terminal state constraint is x (T f)＝xf. The saturation constraint is controlled to be T 2≤Tmax, wherein T max represents the maximum thrust of the spacecraft;
according to the discrete form relative motion equation, boundary condition and constraint condition, establishing a time optimal track planning problem as Where t 0 denotes an initial time and t f denotes a terminal time.
In one embodiment, the minimum terminal error problem constructing module 804 is further configured to set a two-norm of a terminal error as an objective function of a minimum terminal error problem, and construct the minimum terminal error problem according to a boundary condition, a constraint condition, and the objective function, including:
Setting the two norms of the terminal error as the objective function of the minimum terminal error problem, and constructing the minimum terminal error problem as min J 2＝||x(tf)-xf||2 according to the boundary condition, the constraint condition and the objective function, wherein when At this point, the minimum termination error J 2 decreases with increasing t f, whenAt this time, J 2 is always zero, x (t f) represents the actual terminal state, and x f represents the desired terminal state.
In one embodiment, the problem transformation module 806 is further configured to construct a performance index using the terminal error and the control sequence, including:
constructing performance metrics using terminal errors and control sequences Wherein whenJ 3(tf) is greater than 0 whenWhen J 3(tf) =0, whenTime J 3(tf) < 0.
In one embodiment, the problem solving module 808 is further configured to solve the two-layer optimization problem using a hybrid optimization algorithm, which obtains a shortest flight time, including:
And (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time.
In one embodiment, the problem solving module 808 is further configured to narrow the range of the solution space by using a dichotomy until the absolute function values of the upper and lower boundaries are smaller than a preset value, and then solve the calculation result as an initial value of newton method, so as to obtain the shortest flight time, including:
and (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time, wherein the steps are as follows:
Step S1: let the upper and lower boundaries t 1b and t ub of the dichotomy equal to t LB and t UB respectively, solve the double-layer optimization problem by taking t 1b and t ub as the flight time respectively, obtain indexes J 3(t1b) and J 3(tub);tLB and t UB according to the calculation result to represent the upper and lower boundaries of the flight time;
Step S2: if the absolute values of J 3(t1b) and J 3(tub) are greater than the preset value Step S4 is performed. If not, executing step S5;
Step S3: let t 0＝(t1b+tub)/2 and calculate double-layer optimization problem with t 0 as flight time to obtain index J 3(t0), if J 3(t1b)·J3(t0) < 0, let t 1b＝t0, otherwise let t ub＝t0, repeat steps S1 to S3 until absolute values of J 3(t1b) and J 3(tub) are smaller than preset Let t 0＝t1b,t1＝tub, k=0; k represents the iteration number of newton's method;
Step S4: it is determined whether the absolute value of t 0-t1 is equal to or greater than ε and k < M. If yes, executing step S6, otherwise executing step S7; epsilon represents the algorithm precision requirement; m represents the maximum number of iterations;
Step S5: let t2＝t1-J3(t1)(t1-t0)/(J3(t1)-J3(t0)), solve the double-layer optimization problem with t 2 as the flight time, calculate J 3(t2);
step S6: causing t0＝t1,J3(t0)＝J3(t1),t1＝t2,J3(t1)＝J3(t2),k＝k+1, to perform step S5;
Step S7: judging whether the absolute value of t 0-t1 is smaller than epsilon; if yes, outputting t 1, otherwise, failing to calculate; t 1 represents the shortest time of flight.
For the specific limitation of the device for fast planning the optimal trajectory of the relative movement time based on the convex programming, reference may be made to the limitation of the method for fast planning the optimal trajectory of the relative movement time based on the convex programming hereinabove, and the description thereof will not be repeated here. The modules in the rapid planning device for the relative motion time optimal track based on convex planning can be fully or partially realized by software, hardware and a combination thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.
In one embodiment, a computer device is provided, which may be a terminal, and the internal structure thereof may be as shown in fig. 9. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface of the computer device is used for communicating with an external terminal through a network connection. The computer program, when executed by the processor, implements a method for fast planning of a relative movement time optimal trajectory based on convex planning. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.
It will be appreciated by persons skilled in the art that the architecture shown in fig. 9 is merely a block diagram of some of the architecture relevant to the present inventive arrangements and is not limiting as to the computer device to which the present inventive arrangements are applicable, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.
In an embodiment a computer device is provided comprising a memory storing a computer program and a processor implementing the steps of the method of the above embodiments when the computer program is executed.
In one embodiment, a computer storage medium is provided, on which a computer program is stored which, when executed by a processor, implements the steps of the method of the above embodiments.
Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in embodiments provided herein may include non-volatile and/or volatile memory. The nonvolatile memory can include Read Only Memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (SYNCHLINK) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), among others.
The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.
The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (6)
1. The method for rapidly planning the relative movement time optimal track based on convex planning is characterized by comprising the following steps:
acquiring boundary conditions and constraint conditions in track planning;
Establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, the boundary condition and the constraint condition;
Setting a two-norm of a terminal error as an objective function of a minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function;
Performing convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence;
Constructing a performance index by utilizing the terminal error and the control sequence, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance index; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem;
solving the double-layer optimization problem by utilizing a hybrid optimization algorithm to obtain the shortest flight time;
According to the spacecraft relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem, wherein the method comprises the following steps:
dispersing the spacecraft relative motion equation to obtain a discrete form relative motion equation in a relative motion coordinate system;
establishing a time optimal track planning problem according to the discrete form relative motion equation, the boundary condition and the constraint condition;
the boundary conditions comprise initial state constraints and terminal state constraints; the constraint conditions include controlling saturation constraints; according to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem, wherein the method comprises the following steps:
The discrete form relative motion equation is x (i+1) =a dx(i)+Bd T (i), wherein i=1, … N, N is the discrete step number, T represents the thrust of the spacecraft, a d represents the state coefficient matrix, and B d represents the control coefficient matrix;
The initial state constraint is x (t 0)＝x0,m(t0)＝m0, wherein spacecraft mass I sp is vacuum specific impulse of the propeller, g 0 is sea level gravity acceleration;
The terminal state constraint is x (T f)＝xf; the control saturation constraint is ||t| 2≤Tmax, wherein T max represents the maximum thrust of the spacecraft;
According to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem as Wherein t 0 represents an initial time, and t f represents a terminal time;
Setting the two norms of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function, wherein the method comprises the following steps:
Setting the two norms of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem as min J 2＝||x(tf)-xf||2 according to the boundary condition, the constraint condition and the objective function when At this point, the minimum termination error J 2 decreases with increasing t f, whenWhen J 2 is always zero, x (t f) represents the actual terminal state, x f represents the desired terminal state,Representing the shortest time of flight;
Constructing a performance index using the terminal error and the control sequence, comprising:
Constructing performance index using the terminal error and control sequence Wherein whenJ 3(tf) is greater than 0 whenWhen J 3(tf) =0, whenTime J 3(tf)＜0,Tmax represents the maximum thrust of the spacecraft.
2. The method of claim 1, wherein solving the bi-layer optimization problem using a hybrid optimization algorithm results in a minimum time of flight comprising:
And (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time.
3. The method of claim 2, wherein the narrowing of the solution space by the dichotomy until the absolute function value of the upper and lower boundaries is smaller than a preset value, and solving the calculation result as an initial value of newton's method to obtain the shortest flight time comprises:
and (3) reducing the range of the solution space by using a dichotomy until the absolute function value of the upper boundary and the lower boundary is smaller than a preset value, and solving the calculated result as an initial value of the Newton method to obtain the shortest flight time, wherein the steps are as follows:
Step S1: making the upper and lower boundaries t 1b and t ub of the dichotomy equal to t LB and t UB respectively, solving a double-layer optimization problem by taking t 1b and t ub as flight time respectively, and obtaining indexes J 3(t1b) and J 3(tub according to a calculation result; the t LB and t UB represent the upper and lower boundaries of time of flight;
Step S2: if the absolute values of J 3(t1b) and J 3(tub) are greater than the preset reference value Executing the step S4, if not, executing the step S5;
Step S3: let t 0＝(t1b+tub)/2 and calculate double-layer optimization problem with t 0 as flight time to obtain index J 3(t0), if J 3(t1b)·J3(t0) < 0, let t 1b＝t0, otherwise let t ub＝t0, repeat steps S1 to S3 until absolute values of J 3(t1b) and J 3(tub) are smaller than preset Let t 0＝t1b,t1＝tub, k=0; k represents the iteration number of newton's method;
Step S4: judging whether the absolute value of t 0-t1 is larger than or equal to epsilon and k is smaller than M, if yes, executing step S6, otherwise, executing step S7; the epsilon represents the algorithm precision requirement; the M represents the maximum iteration number;
Step S5: let t2＝t1-J3(t1)(t1-t0)/(J3(t1)-J3(t0)), solve the double-layer optimization problem with t 2 as the flight time, calculate J 3(t2);
step S6: causing t0＝t1,J3(t0)＝J3(t1),t1＝t2,J3(t1)＝J3(t2),k＝k+1, to perform step S5;
Step S7: judging whether the absolute value of t 0-t1 is smaller than epsilon; if yes, outputting t 1, otherwise, failing to calculate; the t 1 represents the shortest time of flight.
4. A convex programming-based rapid planning apparatus for a relative movement time optimal trajectory, for implementing the convex programming-based rapid planning method for a relative movement time optimal trajectory according to claim 1, characterized in that the apparatus comprises:
The time optimal track planning problem construction module is used for acquiring boundary conditions and constraint conditions in track planning; establishing a spacecraft relative motion equation under a relative motion coordinate system, and establishing a time optimal track planning problem according to the spacecraft relative motion equation, the boundary condition and the constraint condition, wherein the method comprises the following steps: dispersing the spacecraft relative motion equation to obtain a discrete form relative motion equation in a relative motion coordinate system; establishing a time optimal track planning problem according to the discrete form relative motion equation, the boundary condition and the constraint condition, wherein the boundary condition comprises an initial state constraint and a terminal state constraint; the constraint conditions include controlling saturation constraints; according to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem, wherein the method comprises the following steps: the discrete form relative motion equation is x (i+1) =a dx(i)+Bd T (i), wherein i=1, … N, N is the discrete step number, T represents the thrust of the spacecraft, a d represents the state coefficient matrix, and B d represents the control coefficient matrix;
The initial state constraint is x (t 0)＝x0,m(t0)＝m0, wherein spacecraft mass I sp is vacuum specific impulse of the propeller, g 0 is sea level gravity acceleration;
The terminal state constraint is x (T f)＝xf; the control saturation constraint is ||t| 2≤Tmax, wherein T max represents the maximum thrust of the spacecraft;
According to the discrete form relative motion equation, the boundary condition and the constraint condition, establishing a time optimal track planning problem as Wherein t 0 represents an initial time, and t f represents a terminal time;
the minimum terminal error problem constructing module is configured to set a two-norm of a terminal error as an objective function of a minimum terminal error problem, and construct the minimum terminal error problem according to the boundary condition, the constraint condition and the objective function, and includes:
Setting the two norms of the terminal error as an objective function of the minimum terminal error problem, and constructing the minimum terminal error problem as min J 2＝||x(tf)-xf||2 according to the boundary condition, the constraint condition and the objective function when At this point, the minimum termination error J 2 decreases with increasing t f, whenWhen J 2 is always zero, x (t f) represents the actual terminal state, x f represents the desired terminal state,Representing the shortest time of flight;
the problem conversion module is used for carrying out convex planning on the minimum terminal error problem to obtain a terminal error and a control sequence; constructing a performance index by utilizing the terminal error and the control sequence, and converting the time optimal track planning problem into a double-layer optimization problem according to the performance index; the inner layer of the double-layer optimization problem is the minimum terminal error problem, and the outer layer is the root finding problem; constructing a performance index using the terminal error and the control sequence, comprising:
Constructing performance index using the terminal error and control sequence Wherein whenJ 3(tf) is greater than 0 whenWhen J 3(tf) =0, whenTime J 3(tf)＜0,Tmax represents the maximum thrust of the spacecraft;
And the problem solving module is used for solving the double-layer optimization problem by utilizing a hybrid optimization algorithm to obtain the shortest flight time.
5. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1 to 3 when the computer program is executed.
6. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 3.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210515805.4A CN114955007B (en) | 2022-05-12 | 2022-05-12 | Method and device for rapidly planning relative movement time optimal track based on convex planning |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210515805.4A CN114955007B (en) | 2022-05-12 | 2022-05-12 | Method and device for rapidly planning relative movement time optimal track based on convex planning |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN114955007A CN114955007A (en) | 2022-08-30 |
| CN114955007B true CN114955007B (en) | 2024-07-26 |
Family
ID=82981243
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210515805.4A Active CN114955007B (en) | 2022-05-12 | 2022-05-12 | Method and device for rapidly planning relative movement time optimal track based on convex planning |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114955007B (en) |
Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111444603A (en) * | 2020-01-17 | 2020-07-24 | 北京理工大学 | Method for rapidly planning shortest time off-orbit trajectory of recoverable spacecraft |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8489260B2 (en) * | 2008-12-16 | 2013-07-16 | California Institute Of Technology | Method and apparatus for powered descent guidance |
| CN111562797B (en) * | 2020-07-06 | 2021-07-30 | 北京理工大学 | Unmanned aerial vehicle flight time optimal real-time trajectory optimization method capable of ensuring convergence |
| CN112318505B (en) * | 2020-10-28 | 2021-11-16 | 江南大学 | Mobile robot batch length-variable iterative learning optimization control method |
| CN113341731B (en) * | 2021-06-29 | 2023-03-24 | 西北工业大学 | Space robot trajectory planning method based on sequence convex optimization |
| CN113467498B (en) * | 2021-07-14 | 2022-07-01 | 西北工业大学 | Carrier rocket ascending section trajectory planning method based on Bezier-convex optimization |
-
2022
- 2022-05-12 CN CN202210515805.4A patent/CN114955007B/en active Active
Patent Citations (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111444603A (en) * | 2020-01-17 | 2020-07-24 | 北京理工大学 | Method for rapidly planning shortest time off-orbit trajectory of recoverable spacecraft |
Also Published As
| Publication number | Publication date |
|---|---|
| CN114955007A (en) | 2022-08-30 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Tang et al. | Fuel-optimal low-thrust trajectory optimization using indirect method and successive convex programming | |
| Petersen et al. | Constrained quadratic programming techniques for control allocation | |
| Lu et al. | Finite‐time fault‐tolerant control for rigid spacecraft with actuator saturations | |
| CN112394645B (en) | Neural network backstepping sliding mode control method and system for spacecraft attitude tracking | |
| Yoon et al. | Adaptive spacecraft attitude tracking control with actuator uncertainties | |
| Hu et al. | Analytical solution for nonlinear three-dimensional guidance with impact angle and field-of-view constraints | |
| US11958635B2 (en) | Linear programming problem solving system, solution candidate calculation device, optimal solution calculation device, thruster control device for spacecraft, flying object control device, and linear programming problem solving method | |
| Wang et al. | Neural network‐based multivariable fixed‐time terminal sliding mode control for re‐entry vehicles | |
| Li et al. | Multistage linear gauss pseudospectral method for piecewise continuous nonlinear optimal control problems | |
| Li et al. | Adaptive sliding mode control for spacecraft rendezvous with unknown system parameters and input saturation | |
| Xiao et al. | Two‐stage robust extended Kalman filter in autonomous navigation for the powered descent phase of Mars EDL | |
| Hu et al. | Robust model predictive control for hypersonic vehicle with state‐dependent input constraints and parameter uncertainty | |
| CN114955007B (en) | Method and device for rapidly planning relative movement time optimal track based on convex planning | |
| Mu et al. | Control allocation design of reaction control system for reusable launch vehicle | |
| Cui et al. | Finite‐time trajectory tracking control for autonomous airships with uncertainties and external disturbances | |
| CN113093776A (en) | Method and device for determining off-orbit parameters of spacecraft | |
| Gao et al. | Backstepping sliding mode control for combined spacecraft with nonlinear disturbance observer | |
| Lee et al. | Optimal Trajectory Generation for Mars Atmospheric Entry Guidance using Parameter Optimization | |
| Zhang et al. | A three-stage sequential convex programming approach for trajectory optimization | |
| He et al. | Compound control methodology for a robust missile autopilot design | |
| Wan et al. | Robust Tracking Control for Rendezvous in Near‐Circular Orbits | |
| CN114415705B (en) | Liquid rocket attitude control implementation method, implementation system and storage medium | |
| CN118295238B (en) | Online robust tracking method, device and equipment for aircraft track | |
| CN111781939B (en) | Attitude control method and system based on three-ultrasonic mutual constraint and coupling of spacecraft | |
| Darling et al. | Modified state observer for atmospheric reentry uncertainty estimation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |