An online trajectory planning method for the final stage of an elliptical target orbit-oriented launch vehicle

Abstract

The application discloses an online trajectory planning method for the final stage of a carrier rocket aiming at an elliptical target orbit and belongs to the field of carrier rocket trajectory and guidance, which comprises the following steps: step one, constructing the orbit entry terminal constraint and planning performance index aiming at the elliptical target orbit; step two, establishing the system dynamics constraint of the orbit entry of the final stage of the carrier rocket; step three, convex approximation is conducted on the planning orbit entry terminal constraint and performance index function; step four, state affine approximation and pseudo-spectrum discretization are conducted on the system dynamics constraint of step two; and step five, the optimal trajectory of the final stage entering the elliptical orbit is generated online through sequential convex iteration. The method of the application is suitable for the joint reconstruction of the final stage trajectory and the adaptive guidance of the carrier rocket launching the elliptical target orbit mission, can realize the online generation of the optimal trajectory with high precision and fast convergence, and is favorable for improving the reliability of the carrier rocket and enhancing the launch service fulfillment capability.

Description

Technical Field

[0001] This invention relates to the field of launch vehicle ballistics and guidance technology, and is applicable to the online generation of the final stage trajectory and adaptive guidance for launch vehicle missions launching elliptical targets. Specifically, it relates to an online trajectory planning method for the final stage of a launch vehicle oriented towards elliptical target trajectories. Background Technology

[0002] For the problem of online mission reconfiguration under non-fatal failures of the final stage of a launch vehicle, the similarity between the reconfigured trajectory and the original mission trajectory must be considered while ensuring payload survival. The terminal constraints of a launch vehicle mission are generally orbital elements, which are complex, especially for elliptical target orbits. The nonlinearity of the terminal element constraints with respect to flight position and velocity is high, placing high demands on the rapid online generation of high-precision optimal trajectories and the reconfiguration of the target trajectory. Summary of the Invention

[0003] The purpose of this invention is to provide an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit. The technical problem it solves is: when a non-fatal malfunction occurs during the final stage flight of a launch vehicle in an elliptical orbit mission, preventing the original target orbit from being reached, the optimal trajectory and the reconstructed trajectory are generated online through a sequential iterative algorithm. The method of this invention performs adaptive approximation processing on the online solution of orbit insertion terminal constraints, planning performance indicators, and system dynamic constraints, ensuring the similarity between the reconstructed trajectory and the original elliptical target orbit, while also considering the speed and convergence of online trajectory generation.

[0004] To achieve the above objectives, this invention provides an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit. Step 1 involves constructing the orbit insertion terminal constraints and planning performance indicators for the elliptical target orbit:

[0005] In the near-focal coordinate system of the original target orbit, with the eccentricity vector e = [e x ,e y ,e z ] T As an orbital insertion terminal constraint, it is specifically represented as follows:

[0006] e(r f ,v f ) = e o +ξ e (20)

[0007] Where, r f =[r xf ,r yf ,r zf ] T v is the terminal position state variable. f =[vxf ,v yf ,v zf ] T e is the terminal speed state variable. o =[e o ,0,0] T Given the known eccentricity of the original target orbit, ξ e =[ξ ex ,ξ ey ,ξ ez ] T The eccentricity is a virtual control variable;

[0008] The performance index is based on the highest perigee value, with a weighted penalty applied to the in-plane component of the orbital eccentricity vector. The performance index function is as follows:

[0009]

[0010] Where x = [r T ,v T ,p T ] T The state variable consists of position, velocity, and thrust direction vector, and the rate of change of the thrust direction is... To control the variable, w ex w ey Given the known virtual control penalty weights, 'a' is the semi-major axis of the orbit;

[0011] Step 2, establish system dynamic constraints for the launch vehicle's final stage to enter orbit:

[0012]

[0013] Where Γ is the current thrust amplitude and m is the current mass, both of which are known values ​​under the current state when the plan is started;

[0014] Step 3: Perform convex approximation on the planned orbit insertion terminal constraints and performance index functions:

[0015] The orbital termination constraint can be written as two sets of constraints, one in-plane and one out-of-plane, based on components. The in-plane constraint is then convexized. During the k-th (k>1) iteration of the sequential convexization process, the orbital termination constraint is processed into the following form:

[0016]

[0017] and

[0018]

[0019] in, This refers to the terminal state obtained from the previous iteration.

[0020]

[0021]

[0022] The performance index function convexes in the k-th iteration as a combination of the linear index and the cone constraint, namely:

[0023]

[0024] and

[0025]

[0026] Where, ρ ex ρ ey These are slack variables;

[0027] Step 4: Perform state affine approximation and pseudospectral discretization on the system dynamic constraints of Step 2:

[0028] Select N Radau pseudospectral collocation points τ1,τ2,...,τ N , where τ1=-1, τ N <+1, the discrete point is all collocation points plus τ N+1 =+1, and correspondingly, the affine discrete system dynamics constraints at each collocation point are:

[0029]

[0030] in,

[0031]

[0032] Step 5: Generate the optimal trajectory for the final stage to enter the elliptical orbit online through sequential convexity iteration:

[0033] Using the nominal trajectory at the start of the planning process as the initial conjecture x (0) (τ j ), (j=1,…,N+1), the convex subproblem consisting of linear orbital terminal constraints (23) and (24), linear index function (27), virtual control cone constraint (28), and affine discrete dynamics constraint (29) is solved iteratively by an embedded customized sequence convexity algorithm.

[0034] Given a radius of convergence Below, when the solutions of two consecutive iterations satisfy At that time, the optimal trajectory x for the final stage of the launch vehicle to enter the elliptical orbit is obtained. opt =x (k) Optimal control u opt =u (k)And the corresponding reconstructed target orbit parameters calculated according to formulas (2) and (4). and

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] This invention discloses an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit. In cases where a non-fatal malfunction occurs during the final stage flight of a launch vehicle in an elliptical orbit mission, preventing the remaining capacity from entering the original target orbit, the method generates a high-precision optimal trajectory online through sequential convexity iteration. Simultaneously, it reconstructs a new orbital element that is as similar as possible to the original target orbit, which can further enhance the flight adaptability and launch service reliability of the launch vehicle and effectively improve the intelligence level of space transportation. Attached Figure Description

[0037] The following embodiments and accompanying drawings illustrate an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit.

[0038] Figures 1-3 The following are, in order, the curves showing the changes of the x-position component, y-position component, and z-position component of the trajectory generated by the method of this invention in the geocentric launch inertial coordinate system over time;

[0039] Figures 4-6 The following are, in order, the time-varying curves of the Vx, Vy, and Vz velocity components of the trajectory generated by the method of this invention in the geocentric launch inertial coordinate system.

[0040] Among them, "nominal trajectory" is the theoretical flight trajectory, "GPOPS optimization result" is the trajectory obtained offline using nonlinear programming after the fault, and "convex optimization result" is the optimal trajectory generated online using the method of this invention after the fault.

[0041] Figure 7 This is a flowchart of the method of the present invention. Detailed Implementation

[0042] The following provides a more detailed description of an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit.

[0043] This invention discloses an online trajectory planning method for the final stage of a launch vehicle oriented towards an elliptical target orbit. The specific implementation steps are as follows:

[0044] Step 1: Construct orbit insertion terminal constraints and planning performance indicators for an elliptical target orbit:

[0045] In the near-focal coordinate system of the original target orbit, with the eccentricity vector e = [e x ,e y ,ez ] T As an orbital insertion terminal constraint, it is specifically represented as follows:

[0046] e(r f ,v f ) = e o +ξ e (31)

[0047] Where, r f =[r xf ,r yf ,r zf ] T v is the terminal position state variable. f =[v xf ,v yf ,v zf ] T e is the terminal speed state variable. o =[e o ,0,0] T Given the known eccentricity of the original target orbit, ξ e =[ξ ex ,ξ ey ,ξ ez ] T The eccentricity is a virtual control variable;

[0048] The performance index is based on the highest perigee value, with a weighted penalty applied to the in-plane component of the orbital eccentricity vector. The performance index function is as follows:

[0049]

[0050] Where x = [r T ,v T ,p T ] T The state variable consists of position, velocity, and thrust direction vector, and the rate of change of the thrust direction is... To control the variable, w ex w ey Given the known virtual control penalty weights, 'a' is the semi-major axis of the orbit;

[0051] Step 2, establish system dynamic constraints for the launch vehicle's final stage to enter orbit:

[0052]

[0053] Where Γ is the current thrust amplitude and m is the current mass, both of which are known values ​​under the current state when the plan is started;

[0054] Step 3: Perform convex approximation on the planned orbit insertion terminal constraints and performance index functions:

[0055] The orbital termination constraint can be written as two sets of constraints, one in-plane and one out-of-plane, based on components. The in-plane constraint is then convexized. During the k-th (k>1) iteration of the sequential convexization process, the orbital termination constraint is processed into the following form:

[0056]

[0057] and

[0058]

[0059] in, This refers to the terminal state obtained from the previous iteration.

[0060]

[0061]

[0062] The performance index function convexes in the k-th iteration as a combination of the linear index and the cone constraint, namely:

[0063]

[0064] and

[0065]

[0066] Where, ρ ex ρ ey These are slack variables;

[0067] Step 4: Perform state affine approximation and pseudospectral discretization on the system dynamic constraints of Step 2:

[0068] Select N Radau pseudospectral collocation points τ1,τ2,…,τ N , where τ1=-1, τ N <+1, the discrete point is all collocation points plus τ N+1 =+1, and correspondingly, the affine discrete system dynamics constraints at each collocation point are:

[0069]

[0070] in,

[0071]

[0072] Step 5: Generate the optimal trajectory for the final stage to enter the elliptical orbit online through sequential convexity iteration:

[0073] Using the nominal trajectory at the start of the planning process as the initial conjecture x (0) (τ j), (j=1,…,N+1), the convex subproblem consisting of linear orbital terminal constraints (34) and (35), linear index function (38), virtual control cone constraint (39), and affine discrete dynamics constraint (40) is solved iteratively by an embedded customized sequence convexity algorithm.

[0074] Given a radius of convergence Below, when the solutions of two consecutive iterations satisfy At that time, the optimal trajectory x for the final stage of the launch vehicle to enter the elliptical orbit is obtained. opt =x (k) Optimal control u opt =u (k) And the corresponding reconstructed target orbit parameters calculated according to formulas (2) and (4). and

[0075] In this embodiment, the method of the present invention is applied to an elliptical orbit launch mission for a certain type of launch vehicle. Assuming a non-fatal failure in the final stage, the method of the present invention is used for online trajectory generation and target orbit reconstruction. With the same number of discrete points and computational resources, the trajectory accuracy obtained by the method of the present invention is comparable to that obtained by nonlinear programming using the GPOPS toolkit. However, the average computation time of the method of the present invention is 0.43 seconds, while the average computation time of the GPOPS toolkit is 3.83 seconds. The method of the present invention can improve the solution speed by nearly an order of magnitude while maintaining solution accuracy, significantly improving the convergence performance of trajectory planning and possessing optimal online trajectory generation capabilities.

[0076] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make possible variations and modifications to the technical solutions of the present invention using the disclosed methods and techniques without departing from the spirit and scope of the invention. Therefore, any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the invention, are all within the protection scope of the present invention. Content not described in detail in this specification is common knowledge to those skilled in the art.

Claims

1. A method for online trajectory planning of the final stage of a launch vehicle for elliptical target orbits, characterized in that, The steps include the following: Step 1: Constructing orbit insertion terminal constraints and planning performance indicators for an elliptical target orbit; Step 2: Establish system dynamic constraints for the launch vehicle's final stage to enter orbit; Step 3: Perform convex approximation on the planned orbit insertion terminal constraints and performance index functions; Step 4: Perform state affine approximation and pseudospectral discretization on the system dynamic constraints of Step 2; Step 5: Generate the optimal trajectory for the final stage to enter the elliptical orbit online through sequential convexity iteration; In step one, the orbit insertion terminal constraints and planning performance indicators for an elliptical target orbit are constructed: For the mission of launching a launch vehicle into an elliptical target orbit, relevant variables are described in the near-focal coordinate system of the original target orbit. The reconstructed orbit should be as close as possible to the original orbit, using the eccentricity vector... As an orbital insertion terminal constraint, this vector can simultaneously constrain the magnitude of eccentricity, the argument of perigee, and the orientation of the orbital plane, as specifically represented below: （1） in, For terminal location state variables, For terminal speed state variables, Given the known eccentricity of the original target orbit, Let eccentricity be the virtual control variable. The constraint relationship between eccentricity and state variables is as follows: （2） in, The gravitational constant of Earth; To ensure the survivability of the reconstructed orbit, the highest perigee is used as the performance index. Furthermore, a weighted penalty is applied to the in-plane component of the orbit eccentricity vector within the index to guarantee the similarity between the reconstructed orbit and the original target orbit. Therefore, the performance index function can be expressed as: （3） in, For a trajectory planning problem, the state variables are the position, velocity, and thrust direction vectors; the rate of change of the thrust direction is also considered. As a control variable in the trajectory planning problem; , The penalty weights are known virtual control variables; Let be the semi-major axis of the track, and its calculation formula is as follows: （4）; In step two, the system dynamic constraints for the launch vehicle's final stage orbital insertion are established: （5） in, This represents the current thrust amplitude. For the current quality, all values ​​are known under the current state at the start of the planning process; constraint formula (5) can be written as follows regarding the control variables. Affine form: （6） in, （7）; In step three, the planned orbital insertion terminal constraints and performance index functions are approximated using convexity: Considering that the reconstructed orbit and the original target orbit should be as coplanar as possible, the orbit insertion terminal constraint formula (1) can be written as two sets of constraints in the orbital plane and out of the plane, namely: （8） and （9） Constraint formula (9) is a linear equality constraint with respect to the state variables, and constraint formula (8) is non-convex with respect to the state variables. The following function is defined with respect to the terminal state: （10） Accordingly, constraint formula (8) can be written as: （11） During the k-th solution process through sequential convexity iteration, where k > 1, the state obtained in the previous iteration is... The constraint formula (11) is approximated by a first-order Taylor expansion, i.e.: （12） The above constraint formula (12) is the convex approximation of the terminal orbital insertion constraint formula (8) with respect to the state variables and virtual control variables, where （13） For the planning performance index function (3), the state obtained in the previous iteration is also... A first-order Taylor expansion approximation is performed in the vicinity. Since the constant term of the expansion has no effect on the convergence of the performance index, the... The performance metric for the next iteration can be convexified into a combination of the following linear metric and cone constraint: （14） and （15） in, , These are slack variables; Thus, the orbital termination constraint formula (1) and performance index function (3) of the planning problem are approximated by convexity as linear constraint formula (12), linear function (14), and cone constraint formula (15); In step four, the system dynamic constraints from step two are subjected to state affine approximation and pseudospectral discretization: the system dynamic constraint formula (5) contains only one non-convex term. The first step is to perform the sequence iteration. In this solution process, the position state obtained from the previous solution is used. The constraint formula (5) can be approximated as the following state-control affine form: （16） Wherein, the state transition matrix The calculation formula is: （17） Next, pseudospectral discretization of the dynamic constraints is performed, and [the following is selected]... Radau point ,in , Discrete points are all collocation points plus Accordingly, the dynamic constraint formula (16) for the affine approximation system at each collocation point can be discretely expressed as: （18） in, （19）。

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