Large-range autonomous orbit transfer control method based on Lambert
By adopting a large-scale autonomous track transfer control method based on Lambert in ultra-long-distance rail change, combined with multi-pulse rail change, the problem of low rail change accuracy is solved, and efficient and accurate track transfer is achieved.
Patent Information
- Application Number
- CN202510064087.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-15
- Publication Date
- 2025-05-23
AI Technical Summary
In the ultra-long-distance rail change, the existing technology has problems such as long single jet time, large arc segment losses, increased orbital recursive errors and low rail change placement accuracy.
The large-scale autonomous orbit transfer control method based on Lambert is adopted to predict the current orbit through orbit recursive algorithm, and the velocity increment is calculated using the Lambert rail change method and the jet is performed, and the residual deviation is controlled in combination with multi-pulse rail change.
The rail change at any time and position is achieved without hesitation of fuel consumption. By correcting the jet time and recalculating the control speed increase, the accuracy and efficiency of the rail change are improved.
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Figure CN120024514A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a Lambert large-range autonomous orbit transfer control method, belonging to the technical field of satellite guidance, navigation and control. Background Art
[0002] For the actual on-orbit application scenario of ultra-long-distance orbit transfer in the near geostationary orbit, considering the constraint conditions of detection loads such as radar on the action distance and the relative velocity with the detection target, the traditional orbit transfer strategy based on Hohmann transfer has deficiencies such as long time consumption and poor flexibility due to the need to ignite at specific orbit positions, and it is difficult to meet the on-orbit requirements of rapid transfer. Although Lambert orbit transfer can achieve position transfer within any time, due to the poor accuracy of orbit recursion for the arrival time under ultra-long-distance orbit transfer, it leads to a large deviation in the calculation of velocity increment and an inaccurate starting control moment, and still results in poor control accuracy of the arrival position. Summary of the Invention
[0003] The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, providing a Lambert large-range autonomous orbit transfer control method, which solves the problems that ultra-long-distance orbit transfer is bound to cause a long single jet time, a large loss of arc segment, an increase in orbit recursion error in ultra-long-time orbit transfer, and low orbit transfer arrival accuracy.
[0004] The technical solution of the present invention is: a Lambert large-range autonomous orbit transfer control method, including:
[0005] Step 1: Using the orbit recursion algorithm, predict the current orbit to the transfer start time T 0 , taking the target orbit at the transfer end time T 1 as the desired orbit, calculating the two velocity increments in the main star orbit system based on the Lambert orbit transfer method, and using the first velocity increment to perform the first jet;
[0006] Step 2: Set the correction time T 2 and the main star recursion orbit at this time, calculate the correction amount and verify its rationality; if it is reasonable, then perform jet according to the correction amount and enter Step 3, otherwise directly enter Step 3;
[0007] Step 3: Recalculate the second velocity increment obtained in Step 1 before the transfer end time T 1 and perform the last jet to correct the velocity deviation at the end point;
[0008] Step 4: After correcting the velocity deviation, calculate the residual deviation between the Lambert transfer and the desired orbit, and control the residual deviation within the threshold range based on multi-pulse orbit transfer within the specified correction duration ΔT m .
[0009] In the step 1, two velocity increments in the primary star orbit system are calculated based on the Lambert orbit change method, including:
[0010] First, the expected speed after Lambert's orbit change is calculated based on the Lambert orbit change method:
[0011]
[0012] Where: V x 、V y 、V z They are the three-axis components of the expected velocity in the inertial system after Lambert orbit change, K v is the transfer start time T 0 The expected flight velocity amplitude in the inertial system; i s ,Ω s ,ω s They are respectively 0 and the end time T 1 The inertial position vector R 0 and R 1 The inclination of the transfer orbit, the right ascension of the ascending node and the argument of perigee are determined jointly; s and E s are the transfer orbit eccentricity and T obtained by Lambert's orbit transfer method respectively. 0 The expectation of the moment is close to the point angle;
[0013] Let V 0 T 0 The velocity vector of the inertial system of the host star at the time, then the first velocity increment in the inertial system is:
[0014] ΔV 0 =[V x V y V z ] T -V 0
[0015] The velocity increment in the orbital system is in the form of ΔV 0_o =A oi_0 ΔV 0 , where A oi_0 T 0 The transformation matrix from the inertial system to the orbital system at the moment is given by T 0 The right ascension of the orbital node at the time 0 , orbital inclination i 0 and latitude argument u 0 Calculate;
[0016] Similarly, calculate the transfer end time T 1 The expected flight velocity amplitude K in the inertial systemv1 , and then get the expected three-axis velocity components V of the last jet of Lambert orbit change in the inertial system x1 、V y1 、V z1 , the second velocity increment ΔV in the inertial system 1 =V 1 -[V x1 V y1 V z1 ] T , and the corresponding orbital velocity increment form ΔV 1_o .
[0017] Considering the influence of limited thrust on the timing of jet, the first jet time T 0 ′=T 0 -M||ΔV 0 || / 2F; where M is the mass of the satellite, F is the resultant force in the main thrust direction of the satellite system, and ||·|| represents the modulus of ·.
[0018] Said where a s is the semi-major axis of the transfer orbit obtained by Lambert's orbit transfer method; μ is the gravitational constant of the central celestial body; R 0 is time T 0 The inertial position vector of .
[0019] In the step 2, the correction time T is set 2 Recursively calculate the orbit of the primary star at that moment, calculate the correction value and verify its rationality, including:
[0020] T 2 The recursive orbit of the main star at time T 1 The expected trajectory at time and the transfer time T 1 -T 2 As the input of Lambert's track change algorithm, calculate T 2 The velocity increment ΔV applied at the moment 2 , and make the following judgment: If ΔV 2 Less than the first track change speed increment modulus ||ΔV 0 || 20% is considered reasonable, then in T 2 Execute the jet; otherwise, it is considered that the calculation deviation of the correction amount is too large and unreasonable.
[0021] In step 3, at the end time T of the transfer, 1 Recalculate the second velocity increment obtained in step 1 before, including:
[0022] Based on the orbit recursion algorithm, the transfer end time T is obtained 1 The transition orbit position velocity Rf and V f ; The speed increment of the last pulse control is:
[0023] ΔV 1 =V 1 -V f
[0024] Where V 1 Indicates T 1 The expected speed at the moment, at the same time, the velocity increment form ΔV in the orbital system is obtained 1_o =A oi_1 ΔV 1 , A oi_1 T 1 The transformation matrix from the inertial system to the orbital system at the moment is given by T 1 The right ascension of the orbital node at the time 1 , orbital inclination i 1 and latitude argument u 1 Calculate.
[0025] Considering the influence of limited thrust on the jet timing, the last jet timing is:
[0026] T 1 ′=T 1 -M||ΔV 1 || / 2F.
[0027] The residual deviation from the desired orbit refers to the relative position velocity of the primary orbit relative to the desired orbit; based on the multi-pulse orbit change at the specified time ΔT m Controlling the residual deviation within the threshold range means using the residual deviation as the input of the CW track change, transferring the target position speed to 0, and realizing precise control of the track after the Lambert track change through two speed increments in the track system.
[0028] The specified time ΔT m =T m1 -T m0 ; T m0 The expected velocity vector V at time m ' 0 and T m1 The predicted velocity vector V at time m ' 1 They are:
[0029]
[0030] Among them, V m ' 0 and R m0 T m0 The expected velocity vector and current position vector at the moment, V m '1 It is T m1 The predicted velocity vector at time φ 11 ,φ 12 ,φ 21 ,φ 22 From T m0 to T m1 The block matrix in the state transfer matrix Φ is
[0031] The two velocity increments of the orbital system are:
[0032]
[0033] Where: ΔV m0 and ΔV m1 They are the two velocity increments in the multi-pulse orbit change system, V m0 It is T m0 The current velocity vector at the moment.
[0034] The beneficial effects of the present invention are:
[0035] 1) The Lambert orbit change method is applied to achieve orbit change at any specified time and position without sacrificing fuel consumption. The center point deviation caused by limited thrust is considered and the jet timing of the two orbit changes is corrected. It can be used as a rough control method for high-maneuverability and long-distance orbit change.
[0036] 2) During the transfer process, the control speed increment from the current moment to the end of the transfer is recalculated and verified, thereby realizing the mid-course correction of the control deviation caused by the perturbation and execution error;
[0037] 3) After the coarse control is in place, a multi-pulse control method based on CW track change is applied to achieve a secondary correction of the terminal position velocity error and control the residual control relative to the desired track to within the threshold range.
[0038] Since then, high-precision and large-range autonomous orbit transfer has been achieved through the combination of Lambert + multi-pulse orbit change. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 This is a schematic diagram of the control process of large-scale autonomous orbit transfer based on Lambert;
[0040] Figure 2 This is the data flow diagram for the large-scale autonomous orbit transfer control based on Lambert. DETAILED DESCRIPTION
[0041] Step 1: Calculate and execute the first orbit change amount based on the Lambert orbit change algorithm, and set the theoretical first velocity increment jet execution time as T0 ,like Figure 1 The specific calculation method is as follows:
[0042] Considering that task initiation is often earlier than the transfer start time T 0 , let’s define the task initiation time as T before , transfer start time T 0 , end time T 1 All of them are derived from the ground parameters. before Target orbit at the moment before Prediction to end time T 1 , as the expected orbit of the Lambert orbit change algorithm Orbit c1 Similarly, T before The orbit of the main star at time T is recursively transferred to the starting time T 0 , as the initial orbit of the Lambert orbit algorithm Orbit c0 ; Transfer time is T 1 -T 0 The input and output of Lambert's track change are as follows: Figure 2 As shown in the "Calculation and Execution of the First Track Change Amount" section. Since most Lambert algorithms only have numerical solutions, it often takes multiple iterations to approximate the true solution. Considering the hardware computing power, calculation time should be reserved.
[0043] The direct output of the Lambert algorithm is the semi-major axis, eccentricity and time T of the transfer orbit. 0 The expected true anomaly angle (denoted as a s 、e s and f s ). According to the position vector R at the start and end time 0 and R 1 , we can get the transfer orbital angular momentum as
[0044] H s =R 0 ×R 1
[0045] Here, × represents the cross product of two vectors.
[0046] The diagonal momentum is normalized,
[0047] H s =H s / ||H s ||
[0048] If T 0 When the true anomaly is greater than 180°, H s Need to be negated.
[0049] Furthermore, the orbital inclination, right ascension of the ascending node, argument of latitude, and argument of perigee of the transfer orbit are respectively
[0050]
[0051] true anomaly f s and eccentric anomaly E s The conversion formula is:
[0052]
[0053] The expected flight velocity vector in the inertial system after Lambert orbit transfer is:
[0054]
[0055] Where: is the magnitude of the expected flight velocity at the start time T 0 of the transfer in the inertial system, and μ is the gravitational constant of the central body.
[0056] Then the first impulse control velocity increment is:
[0057] ΔV 0 = [V x V y V z T - V 0
[0058] Convert it to the primary star orbit system at time T 0 :
[0059] ΔV 0_o = A oi_0 ΔV 0
[0060] Where: A oi_0 is the conversion matrix from the inertial system to the orbit system at time T 0 , and there is
[0061]
[0062] Considering the influence of finite thrust on the jet timing, taking the theoretical jet time T 0 as the midpoint, the corrected first orbit transfer time is calculated as:
[0063] T′ 0 = T 0 - M||ΔV 0 || / 2F
[0064] Where: M is the satellite mass, and F is the resultant force in the direction of the main thrust in the satellite's body system.
[0065] In order to avoid interference and fuel waste caused by the coupling of attitude and orbit when multiple axes are jetting at the same time, the main thrust direction of the main satellite system is adjusted to ΔV by attitude maneuvers. 0 The directions coincide. Taking the X-axis as the main thrust direction as an example, the three-axis attitude offset angles from the ground attitude to the trajectory change velocity vector direction are:
[0066]
[0067] Step 2: Let the mid-course correction time be T 2 ,like Figure 1 As shown. Update the corrected jet ΔV based on Lambert trajectory change 2_o And the recursive orbit of the main star at that time c2 , calculate the correction amount and verify its rationality. The specific implementation method is as follows;
[0068] The modified track change amount during the transfer process is calculated based on the Lambert track change algorithm. The input includes T 2 The recursive orbit of the main star at time (obtained by the orbit recursive algorithm), T 1 The expected trajectory at time and the transfer time T 1 -T 2 , the calculation method is similar to step 1.
[0069] The speed increment ΔV output by the algorithm 2 Make a judgment: less than the first track change speed increment ||ΔV 0 || 20% is considered effective at T 2 Otherwise, the correction calculation deviation is considered too large, and the jet is not executed. The correction is executed directly without attitude maneuvers. Figure 2 As shown in the "Calculation and Execution of Corrected Track Change Amount" section.
[0070] Step 3: Let the jet execution time of the theoretical last velocity increment be T 1 ,like Figure 1 As shown. 1 The recursive orbit and expected orbit of the primary star at time T are taken as input, and at the end time T 1 Recalculate the second velocity increment ΔV calculated in step 1 before 1_o The last jet is executed and the input and output of the last velocity increment calculation are as follows: Figure 2 The speed increment ΔV is shown in the "Calculation and execution of the last track change" section. 1 =V 1 -V f , where V 1 T is calculated based on the expected trajectory 1 Expected speed at the moment.
[0071] By analogy with the previous section, we can get the velocity increment form ΔV in the orbital system: 1_o , the corrected last track change time T 1 and attitude maneuver offset angle θ 1 and No more details.
[0072] Step 4: After correcting the speed deviation, calculate the position speed residual deviation after Lambert transfer and specify the correction time ΔT m , calculate the multi-pulse trajectory change at T m0 and T m1 Two precise jet control ΔV at time m0 and ΔV m1 ,like Figure 1 The specific calculation process is as follows:
[0073] The input of multi-pulse orbit change is defined as the relative velocity of the main satellite orbit relative to the desired orbit, and the desired velocity is set to 0. Based on CW orbit change, two pulses are used to achieve precise orbit control after Lambert orbit change, such as Figure 2 As shown in the section "Terminal position velocity correction based on multi-pulse track change".
[0074] According to the orbital angular velocity n and the transfer time ΔT m =T m1 -T m0 Calculate from T m0 to T m1 The position-speed transfer relationship is:
[0075]
[0076] make Indicates that from T m0 to T m1 The state transfer matrix of
[0077]
[0078] According to T m0 The velocity vector R m0 、V m0 and the target position vector 0, calculate T m0 The expected velocity vector V at time m ' 0 and T m1 The predicted velocity vector V at time m ' 1 :
[0079]
[0080] The two velocity increments in the orbital system are:
[0081]
[0082] The orbit recursion correlation algorithm and Lambert orbit change and CW orbit change algorithms mentioned in the present invention are well-known contents and will not be elaborated in detail.
Claims
1. A Lambert-based large-scale autonomous orbit transfer control method, characterized in that: include: Step 1: Use the orbit recursion algorithm to predict the current orbit to the transfer start time T0, take the target orbit at the transfer end time T1 as the expected orbit, calculate two velocity increments in the primary star orbit system based on the Lambert orbit change method, and use the first velocity increment to perform the first jet; Step 2: Set the correction time T2 and the recursive orbit of the primary star at that time, calculate the correction amount and verify its rationality; If it is reasonable, the injection is performed according to the correction amount and then the process goes to step 3; otherwise, the process goes directly to step 3; Step 3: before the transfer end time T1, recalculate the second speed increment obtained in step 1 and perform the last jet to correct the speed deviation at the end point; Step 4: After correcting the speed deviation, calculate the residual deviation from the desired orbit after Lambert transfer, based on the multi-pulse orbit change at the specified correction time ΔT m The residual deviation is controlled within the threshold range.
2. A Lambert-based large-scale autonomous orbit transfer control method as claimed in claim 1, characterized in that: In the step 1, two velocity increments in the primary star orbit system are calculated based on the Lambert orbit change method, including: First, the expected speed after Lambert's orbit change is calculated based on the Lambert orbit change method: Where: V x 、V y 、V z They are the three-axis components of the expected velocity in the inertial system after Lambert orbit change, K v is the expected flight velocity amplitude in the inertial system at the transfer start time T0; i s ,Ω s ,ω s are the transfer orbit inclination, ascending node right ascension and perigee argument determined by the inertial system position vectors R0 and R1 at time T0 and end time T1 respectively; s and E s are the transfer orbit eccentricity and the expected anomaly angle at time T0 obtained by the Lambert orbit transfer method respectively; Let V0 be the velocity vector of the host star inertial system at time T0, then the first velocity increment in the inertial system is: ΔV0=[V x V y V z ] T -V0 The velocity increment in the orbital system is in the form of ΔV 0_o =A oi_0 ΔV0, where A oi_0 is the conversion matrix from the inertial system to the orbital system at time T0, which is calculated from the right ascension Ω0 of the orbital ascending node, the orbital inclination i0 and the latitude argument u0 at time T0; Similarly, calculate the expected flight speed amplitude K in the inertial system at the end of the transfer time T1 v1 , and then get the expected three-axis velocity components V of the last jet of Lambert orbit change in the inertial system x1 、V y1 、V z1 , the second velocity increment in the inertial system ΔV1=V1-[V x1 V y1 V z1 ] T , and the corresponding orbital velocity increment form ΔV 1_o .
3. A Lambert-based large-scale autonomous orbit transfer control method as claimed in claim 2, characterized in that: Considering the influence of limited thrust on the timing of injection, the first injection time T0′=T0-M||ΔV||0 / 2F; where M is the satellite mass, F is the resultant force in the main thrust direction of the satellite system, and ||·|| represents the modulus of ·.
4. The Lambert-based large-scale autonomous orbit transfer control method according to claim 2, characterized in that: Said where a s is the semi-major axis of the transfer orbit obtained by Lambert's orbit transfer method; μ is the gravitational constant of the central celestial body; R0 is the inertial system position vector at time T0.
5. The Lambert-based large-scale autonomous orbit transfer control method according to claim 3, characterized in that: In step 2, the correction time T2 and the recursive orbit of the primary star at that time are set, and the correction amount is calculated and its rationality is verified, including: The recursive orbit of the primary star at time T2, the expected orbit at time T1, and the transfer time T1-T2 are used as the input of the Lambert orbit change algorithm, and the velocity increment ΔV2 applied at time T2 is calculated, and the following judgment is made: if ΔV2 is less than 20% of the modulus of the first orbit change velocity increment ||ΔV0||, it is considered reasonable, and the jet is executed at T2; otherwise, it is considered that the calculation deviation of the correction amount is too large and it is considered unreasonable.
6. A Lambert-based large-scale autonomous orbit transfer control method as claimed in claim 2, characterized in that: In the step 3, the second speed increment obtained in the step 1 is recalculated before the transfer end time T1, including: Based on the orbit recursion algorithm, the transition orbit position speed R at the transfer end time T1 is obtained f and V f ; The speed increment of the last pulse control is: ΔV1=V1-V f Where V1 represents the expected velocity at time T1, and at the same time, the velocity increment form ΔV in the orbital system is obtained 1_o =A oi_1 ΔV1, A oi_1 It is the conversion matrix from the inertial system to the orbital system at time T1, which is calculated by the right ascension Ω1 of the orbital ascending node, the orbital inclination i1 and the latitude argument u1 at time T1.
7. A Lambert-based large-scale autonomous orbit transfer control method as claimed in claim 6, characterized in that: Considering the influence of limited thrust on the jet timing, the last jet timing is: T1′=T1-M||ΔV1|| / 2F.
8. The Lambert-based large-scale autonomous orbit transfer control method according to claim 1, characterized in that: The residual deviation from the desired orbit refers to the relative position velocity of the primary orbit relative to the desired orbit; based on the multi-pulse orbit change at the specified time ΔT m Controlling the residual deviation within the threshold range means using the residual deviation as the input of the CW track change, transferring the target position speed to 0, and realizing precise control of the track after the Lambert track change through two speed increments in the track system.
9. A Lambert-based large-scale autonomous orbit transfer control method as claimed in claim 8, characterized in that: The specified time ΔT m =T m1 -T m0 ; T m0 The expected velocity vector V at time m ′0 and T m1 The predicted velocity vector V at time m ′1 are respectively: Among them, V m ′0 and R m0 T m0 The expected velocity vector and current position vector at the moment, V m ′1 is T m1 The predicted velocity vector at time φ 11 ,φ 12 ,φ 21 ,φ 22 From T m0 to T m1 The block matrix in the state transfer matrix Φ is 10. The Lambert-based large-scale autonomous orbit transfer control method according to claim 9, characterized in that: The two velocity increments of the orbital system are: Where: ΔV m0 and ΔV m1 They are the two velocity increments in the multi-pulse orbit change system, V m0 It is T m0 The current velocity vector at the moment.