CN113885571B - Circular track guidance method without zero crossing during overload - Google Patents
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Abstract
The invention relates to a circular track guidance method with overload zero crossing, which comprises the following steps of: establishing a target dynamics equation based on a dynamics theory, and calculating a target reachable domain according to the target dynamics equation; step 2: establishing a BTT missile dynamics equation according to the target reachable domain range obtained in the step 1, calculating an envelope circle of the reachable domain, calculating a central angle corresponding to a track of the missile flying along the envelope circle, calculating the missile flight time, and iteratively calculating the target reachable domain and the envelope circle according to the missile flight time to obtain a guided circle track and a maneuvering overload of the missile; step 3: and if the guidance track is calculated for the first time during launching, calculating a guidance stability criterion according to the missile flight time obtained in the step 2, and adjusting the missile launching direction. The invention has the advantages of good real-time performance and stable algorithm, and can effectively avoid the singular state of the BTT missile attitude calculation, thereby improving the control performance of the missile.
Description
Technical Field
The invention belongs to the technical field of missile guidance in aerospace technology, and particularly provides a circular track guidance method with overload zero crossing.
Background
Missiles are an important means of performing military strikes. With the development of military weapons, the target hitting mobility is stronger and higher requirements are put on the performance of missiles. Compared with STT missiles, BTT missiles have obvious advantages in the aspects of aerodynamic efficiency, maneuverability, control performance and the like by adopting a banked turning mode. In order to fully exert the power of the BTT missile, the guidance law suitable for the BBT missile needs to be designed.
Xi Yong et al state ([ 1] Xi Yong, chen Guangshan, peng Jiping, etc.. A nonsingular roll instruction generation algorithm for BTT missiles, CN108801081A [ P ]. 2018.) when the control mode of a BTT missile solves a gesture instruction due to the existence of disturbance in the flight, the overload of a longitudinal channel is a singular point at zero, which can seriously affect the stability of the missile. So, to avoid the problem of singular points, the overload zero crossing should be avoided as much as possible. Conventional proportional guidance laws are easy to implement, but do not guarantee overload but zero-crossing. Therefore, it is critical to design a new guidance algorithm that is not zero crossing of overload.
Disclosure of Invention
The invention solves the problem that the traditional guidance law cannot ensure the zero crossing of overload, provides the circular track guidance method with the zero crossing of overload, has the advantages of good instantaneity and stable algorithm, can effectively avoid the singular calculation of the gesture of the BTT missile, and further improves the control performance of the missile.
The invention provides a circular track guidance method with overload zero crossing, which is characterized by comprising the following steps of:
step 1: establishing a target dynamics equation based on a dynamics theory, and calculating a target reachable domain according to the target dynamics equation;
Step 2: and (3) updating and calculating the guidance track at each moment of missile flight according to the target reachable domain range obtained in the step (1). Firstly, establishing a BTT missile dynamics equation, calculating an envelope circle of a reachable domain, calculating a central angle corresponding to a track of the missile flying along the envelope circle, and calculating the missile flight time. And iteratively calculating a target reachable domain and an envelope circle according to the missile flight time to obtain a guided circle track and a missile maneuvering overload.
Step 3: if the guidance track is updated and calculated for the first time, calculating a guidance stability criterion according to the missile flight time obtained in the step 2, and adjusting the missile launching direction;
In the step 1: the target kinetic equation is established as follows:
taking two-dimensional conditions into consideration, establishing a ground surface fixed coordinate system by taking a missile launching position as an origin, wherein an x axis and a y axis are respectively the x direction and the y direction of a horizontal plane;
Definition vector r t＝[rtx,rty represents the location of the target; wherein, two components r tx,rty of r t represent the position components of the target on the x and y axes, respectively; r t0＝[rtx0,rty0 represents the initial time value of the position r t, and r tx0,rty0 represents the initial components of the position of the target on the x and y axes, respectively. Setting the speed scalar value to v t;vt0 to represent an initial time value of the speed v t; let the velocity direction and the positive x-axis direction have an angle of θ t,θt0 represent the initial time value of the angle θ t. Defining a tt as a target tangential acceleration, a tn as a target normal acceleration, and defining scalar values of the target tangential and normal accelerations as:
btt＝±||att||
btn＝±||atn|| (1)
wherein, the term "two norms" means a vector. The right side of the equation takes the "+" sign when the target is accelerating or steering to the left, and the "-" sign otherwise. b tt and b tn satisfy the constraint:
bttmin≤btt≤bttmax
btnmin≤btn≤btnmax (2)
Wherein b ttmin and b ttmax are the target minimum tangential acceleration and the target maximum tangential acceleration, respectively, specifying that the acceleration takes a "+" sign. b tnmax and b tnmin are the target maximum normal acceleration and the target minimum normal acceleration, respectively, and are given a "+" sign when steering left.
Establishing a target kinetic equation:
in the step 1: the calculation target reachable domain is as follows:
Given a certain time t=t 0, the values of b tt and b tn are respectively combined according to the following table and substituted into the equation set (3), six boundary points of the reachable domain are calculated, the position vector r i＝[rix,riy],i＝1,2,...,6,rix,riy of the boundary points represents initial components of the i boundary points on the x axis and the y axis, and the six points are connected end to obtain the reachable domain.
TABLE 1 reachable Domain boundary Point calculation
In the step 2: the missile dynamics equation is established as follows:
Defining a vector r B＝[rBx,rBy to represent the position of the missile, wherein two components r Bx,rBy of r B represent the position components of the missile position on the x and y axes respectively; r B0＝[rBx0,rBy0 represents the initial time value of the position r B, and the two components r Bx0,rBy0 of r B0 represent the position components of the initial time position of the missile on the x and y axes respectively. Let the missile speed scalar value be v B. Let the missile velocity direction and the positive x-axis direction form an angle theta B;θB0 to represent the initial time value of the angle theta B. Let a Bn be the missile normal acceleration vector. Definition:
bBn＝±||aBn|| (4)
When the missile turns leftwards, the right side of the equation takes the "+" sign, and conversely takes the "-" sign. The constraint is satisfied by the ||a Bn |:
0＜||aBn||≤aBmax (5)
Wherein a Bmax is the maximum normal acceleration of the missile.
The missile dynamics equation is:
in the step 2: the envelope circle is calculated as follows:
Setting the circle center of the enveloping circle as O'; position vector r O′＝[rO′x,rO′y ], wherein the two components r O′x,rO′y of r O′ represent the position components of the missile position on the x and y axes, respectively; the radius is R O′.
Let the radius R i of a circle with the missile centroid and boundary point i, and tangent to the missile velocity direction, i=1, 2,..6. R i is obtained by calculating the following formula:
Ri＝|ρi|，i＝1，2，...，6 (7)
Where ρ i is a parameter for determining the direction of the missile steering, ρ i is positive for the missile steering to the left.
Let the radius of the circle with the sequence i=k be the largest, k e {1, 2..6 }. The following formula is calculated to give R O′ and R O′:
rO′x＝rBx-ρk sinθB
rO′y＝rBy+ρk cosθB
RO′＝Rk (8)
In the step 2: the corresponding central angle of the circular track is calculated as follows:
Assuming that the central angle corresponding to the missile flight circle track is alpha B, calculating the following formula to obtain alpha B:
Wherein, α' B is the included angle between the line connecting the object and the origin of the coordinate system and the x-axis, ρ k is given by the formula (7).
In the step 2: iterative calculation of the circle guide track and corresponding overload is as follows:
Calculating the distance S required by the missile to hit the target along the enveloping circle:
S＝αBRO′ (10)
calculating the time required for the missile to hit the target:
and (3) re-calculating a target reachable domain by taking t f as an iteration initial value, re-calculating an envelope circle and t f, iterating the iterative calculation until the precision requirement is met, taking the final envelope circle as a guidance circle track, and taking t f as the iteration initial value in the next circle track calculation.
The missile overload is calculated by calculating the following steps:
Where n is positive indicating that the missile is turning left. ρ k is given by equation (9).
In the step 3: the guidance stability is determined as follows:
And judging the guidance stability when the missile launches to perform first guidance track calculation. Let the target acceleration a t satisfy the constraint:
||at||≤atmax (13)
Where a tmax is the maximum value of the target acceleration magnitude. Let t f＝tf0 be the beginning of the circular trajectory guidance and t f＝tf1 be the end of the guidance. Wherein t f0 is calculated by missile launching calculation step 2. The following is calculated to obtain the magnitude of the missile normal acceleration (a Bn2) at the end of guidance:
Calculating whether the stability criterion is satisfied by the A Bn2:
0＜||aBn2||≤aBnmax (15)
if so, the missile performance meets the guidance requirement, and the guidance can be stabilized. If not, the missile launching position and direction are adjusted until the criterion is met.
Compared with the prior art, the invention has the advantages that:
(1) The invention gives the reachable domain range of the hit target based on the dynamics theory and the differential algebra principle, obtains the guided circle track of the missile based on the iterative algorithm, and gives the analysis criterion of the guided stability based on the dynamics characteristics of the target and the missile. Compared with the traditional proportional guidance law, the invention can ensure that the overload of the guided whole-course missile does not cross zero, can effectively prevent singular points from appearing when the BTT missile calculates the gesture instruction, and improves the control stability of the BTT missile.
(2) The method provided by the invention is used for deducing the reachable domain range of the hit target based on semi-analytic, obtaining the guided circle track through iterative calculation, providing the guided stability criterion, realizing good real-time performance and stability judgment, and having important theoretical significance for improving the reliability and control stability of the missile.
(3) The circular track guidance method with the overload zero crossing can be widely applied to various task scenes of the BTT missile, and has important theoretical reference value for the accurate guidance and control of the BTT missile.
Drawings
FIG. 1 is a flow chart of an implementation of the method of the present invention;
FIG. 2 is a schematic diagram of a target reachable domain in an embodiment of the invention;
FIG. 3 is a schematic diagram of a target reachable domain and a guided circle trajectory in an embodiment of the invention;
FIG. 4 is a schematic diagram of missile overload variation in accordance with an embodiment of the present invention;
FIG. 5 is a schematic diagram of the change in distance between a missile and a target in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings and examples.
As shown in fig. 1, the circular track guidance method with overload zero crossing comprises the following steps:
1) Calculating a target reachable domain;
1-1) establishing a target kinetic equation;
taking two-dimensional conditions into consideration, establishing a ground surface fixed coordinate system by taking a missile launching position as an origin, wherein an x axis and a y axis are respectively the x direction and the y direction of a horizontal plane;
Definition vector r t＝[rtx,rty represents the location of the target; wherein, two components r tx,rty of r t represent the position components of the target on the x and y axes, respectively; r t0＝[rtx0,rty0 represents the initial time value of the position r t, and r tx0,rty0 represents the initial components of the position of the target on the x and y axes, respectively. Setting the speed scalar value to v t;vt0 to represent an initial time value of the speed v t; let the velocity direction and the positive x-axis direction have an angle of θ t,θt0 represent the initial time value of the angle θ t.
Let a t be the acceleration vector, decompose the acceleration vector to tangential and normal to the velocity:
at＝att+atn (1)
Wherein a tt is tangential acceleration, a tn is normal acceleration, and scalar values defining target tangential and normal acceleration are respectively:
btt＝±||att||
btn＝±||atn|| (2)
wherein, the term "two norms" means a vector. The right side of the equation takes the "+" sign when the target is accelerating or steering to the left, and the "-" sign otherwise.
The target kinetic equation is written as:
Approximation of equation set (3), the post-decoupling integral is expressed by:
Wherein b tt and b tn satisfy the constraint:
bttmin≤btt≤bttmax
btnmin≤btn≤btnmax (5)
Wherein b ttmin and b ttmax are the target minimum tangential acceleration and the target maximum tangential acceleration, respectively, specifying that the acceleration takes a "+" sign. b tnmax and b tnmin are the target maximum normal acceleration and the target minimum normal acceleration, respectively, and are given a "+" sign when steering left.
1-2) Computing target reachability fields
Given a certain time t 0, calculating the range of the region (reachable domain) which can be reached by the target in t 0, respectively combining the values of b tt and b tn according to the following table, substituting the values into the equation set (4), and calculating six boundary points of the reachable domain, wherein the position vector of the boundary points is r i＝[rix,riy],i＝1,2,...,6,rix,riy and respectively represents the initial components of the positions of the ith boundary point on the x and y axes. As shown in fig. 2: the region surrounded by six points end to end is the target reachable domain.
TABLE 2 reachable Domain boundary Point calculation
2) Calculating a circle guidance track;
2-1) establishing a BTT missile dynamics equation;
Defining a vector r B＝[rBx,rBy to represent the position of the missile, wherein two components r Bx,rBy of r B represent the position components of the missile on the x and y axes respectively; r B0＝[rBx0,rBy0 represents the initial time value of the position r B, and the two components r Bx0,rBy0 of r B0 represent the position components of the initial time position of the missile on the x and y axes respectively. The missile moves at a nearly uniform speed, and the speed scalar value is v B. Let the velocity direction and the positive x-axis direction have an angle of θ B;θB0 represent the initial time value of the angle θ B.
Let a Bn be the missile normal acceleration vector. Definition:
bBn＝±||aBn|| (6)
When the missile turns leftwards, the right side of the equation takes the "+" sign, and conversely takes the "-" sign. The constraint is satisfied by the ||a Bn |:
0＜||aBn||≤aBmax (7)
Wherein a Bmax is the maximum normal acceleration of the missile.
The missile dynamics equation can be written as:
2-2) calculating an envelope circle;
The circle which is tangent to the missile speed direction and passes through the missile mass center is solved, so that the circle exactly envelops the target reachable domain. Setting the circle center of the envelope circle as O', and a position vector r O′＝[rO′x,rO′y, wherein two components r O′x,rO′y of r O′ respectively represent the position components of the missile position on the x axis and the y axis; the radius is R O′.
2-2-1) Calculate the radius of a circle of the missile centroid and boundary point i, and tangent to the missile velocity direction, i=1, 2. The radius of each circle R i is determined by the following analytical formula:
Ri＝|ρi|，i＝1，2，...，6 (9)
Where ρ i is a parameter for determining the direction of the missile steering, ρ i is positive for the missile steering to the left.
2-2-2) Compares the sizes of 6 circle radii, and sets the largest circle radius for the sequence i=k, k e {1, 2..6 }. The envelope circle center position and radius are determined by:
rO′x＝rBx-ρk sinθB
rO′y＝rBy+ρk cosθB
RO′＝Rk (10)
2-3) calculating a central angle corresponding to the missile flight circle track;
Assuming that the central angle corresponding to the missile flight circle track is alpha B, alpha B is calculated by the following formula:
Wherein, two components r O′x,rO′y of r O′ respectively represent position components of the missile position on the x and y axes;
2-4) calculating the target hitting time of the missile along the circular track;
the distance S required by the missile to hit the target along the enveloping circle is as follows:
S＝αBRO′ (12)
the time it takes for the missile to hit the target:
2-5) iteratively calculating a circle guiding track;
2-5-1) recalculating the target reachable domain with t f as an iteration initial value, and recalculating 2-2), 2-3), 2-4);
2-5-2) repeating 2-5-1) if the iteration does not meet the accuracy requirement. If the iteration reaches the precision requirement, t f is used as an iteration initial value in the next round track calculation. The envelope circle obtained by calculation is the current moment circle guiding track. As shown in fig. 3, the guided circle track is an envelope circle of a target reachable domain, and the target is always on one side of the guided circle track, so that the requirement of overload non-zero crossing can be met;
2-6) calculating missile overload;
missile overload is calculated by the following formula:
Where n is positive indicating that the missile is turning left. ρ k is given by equation (9).
3) Judging guidance stability;
Let the target acceleration a t degrees satisfy the constraint:
||at||≤atmax (15)
Where a tmax is the maximum value of the target acceleration magnitude. The target motion is decomposed into uniform linear motion and acceleration motion with zero initial speed, and the absolute value of the acceleration motion is not more than a max. The target reachable field can be enveloped by an envelope circle with radius R:
the reduction of the envelope circle diameter over a short period of time Δt f is:
Δ2R＝-2atmaxtfΔtf (17)
The shot point offset caused by the missile acceleration increment is approximately:
the differential equation can be obtained:
When the missile reaches the vicinity of the target, the round track guidance is finished, and the missile realizes control by using a track control engine. Let t f＝tf0 be the beginning of the circular trajectory guidance and t f＝tf1 be the end. Wherein t f0 can be derived from the planned circular trajectory when the missile is launched. Calculating integral (19) can obtain the normal acceleration magnitude of the end of the circular track guidance:
Calculating whether the stability criterion is satisfied by the A Bn2:
0＜||aBn2||≤aBnmax (21)
if so, the missile performance meets the guidance requirement, and the guidance can be stabilized. If not, the missile launching position and direction are adjusted until the criterion is met.
Example verification
In an embodiment, it is assumed that the known target parameters are shown in the following table:
table 2 hit target parameter settings
TABLE 3 BTT missile parameter settings
| Parameters (parameters) | aBmax＝25g,g＝9.8m/s2 | vB＝1000m/s |
| Initial state | rB0＝[0，0] | θB0＝90° |
In step 1), an initial time t 0 =80 s is given. Calculating to obtain the target reachable domain boundary points respectively as ：r1＝[-44.06km,61.01km],r2＝[-50.00km,62.80km],r3＝[-55.94km,61.01km],r4＝[-53.44km,54.69km],r5＝[-50.00km,56.40km],r6＝[-46.56km,54.69km].
In the step 2), the missile guidance circle track is obtained through iterative calculation: the center of a circle is on a straight line passing through the mass center of the missile and perpendicular to the speed direction, and the radius is 66.71km. Fig. 3 shows the relationship between the guided circle track and the target reachable domain, and as can be seen from fig. 3, the target reachable domain is all located at one side of the guided track, and the missile guidance route can ensure that the missile overload does not cross no matter where the target is finally located in the reachable domain.
In the step 3), when the round track guidance is finished, t f1 =0.1 s is taken, the a Bn2 =5.49 g is calculated (20), the maximum overload condition is met, and the stability of missile control in the guidance process can be ensured. The magnitude of the overload and the change of the distance from the target during the missile flight are shown in fig. 4 and 5 respectively. From fig. 4, the missile is more stable in overload change in the early stage of guidance, and the maximum overload requirement is met in the final stage of guidance. From fig. 5, the missile distance from the target is uniformly reduced along with time, and the flying process is stable.
The circular track guidance law provided by the invention has instantaneity, the guidance track is planned in real time according to the position speed of the target and the missile, and the algorithm solving speed meets the instantaneity requirement. After the missile is launched, the accuracy requirement can be met by only one iteration for each calculation of the trajectory, the average calculation time is not more than 10ms, and the real-time requirement is met.
In conclusion, compared with the traditional method, the method is applied to the guidance task of the BTT missile, and has the characteristics of ensuring that overload is not zero crossing and having good real-time performance. Aiming at a general BTT missile hitting task scene, the circular track guidance method with zero crossing of overload is provided, and guidance and control tasks of the BTT missile can be effectively realized.
Claims (1)
1. The circular track guidance method without zero crossing of overload is characterized by comprising the following steps:
step 1: establishing a target dynamics equation based on a dynamics theory, and calculating a target reachable domain according to the target dynamics equation;
Step 2: according to the target reachable domain range obtained in the step 1, updating and calculating a guidance track at each moment of missile flight; firstly, establishing a BTT missile dynamics equation, calculating an envelope circle of a reachable domain, calculating a central angle corresponding to a track of a missile flying along the envelope circle, calculating the missile flight time, and iteratively calculating a target reachable domain and the envelope circle by the missile flight time to obtain a guided circle track and a guided missile maneuvering overload;
Step 3: if the guidance track is updated and calculated for the first time, calculating a guidance stability criterion according to the missile flight time obtained in the step 2, and adjusting the missile launching direction;
in the step1, the establishment of the target kinetic equation is realized as follows:
taking two-dimensional condition into consideration, taking the missile launching place as an origin to establish a ground surface fixed coordinate system, Shaft and method for producing the sameThe axes being horizontalDirection and directionA direction;
definition of vectors Representing the position of an objectWherein,Is a component of (2)Respectively represent the targets at、A position component on the shaft; Representing the position Is used to determine the initial time value of (1),Let the speed scalar value be；Indicating speedIs set to the initial time value of (1); setting the speed directionThe included angle of the axial positive direction is，Indicating the included angleDefining the initial time value of (1)For the tangential acceleration of the object to be achieved,For a target normal acceleration, scalar values defining the target tangential and normal acceleration are respectively:
，
（1）
Wherein, Representing the two norms of a vector, the equation taking "to the right" when the object is accelerating or steering to the left "Number and conversely take "The number of the product is the number,And (3) withThe constraint is satisfied:
，
（2）
Wherein, And (3) withThe target minimum tangential acceleration and the target maximum tangential acceleration are respectively regulated to be taken by acceleration "The number of the product is the number,And (3) withThe maximum normal acceleration and the minimum normal acceleration are respectively defined to be taken when steering leftwards "Number "a;
establishing a target kinetic equation:
，
（3）；
In the step 1: the calculation target reachable domain is realized as follows:
Given a certain time Will respectivelyAnd (3) withThe values of (2) are substituted into the set-up target kinetic equation according to the combinations shown in the following table:
，
（3）
calculating six boundary points of the reachable domain, wherein the position vector is ，Connecting 6 points end to obtain an reachable domain;
In the step 2: the establishment of the missile dynamics equation is realized as follows:
definition of vectors Indicating the position of the missile, wherein,Is a component of (2)Respectively indicate the position of the missile、A position component on the shaft; Representing the position Is used to determine the initial time value of (1),Is a component of (2)Respectively indicate the initial time position of the missile at、A position component on the shaft; let the missile speed scalar value be; Set the missile velocity directionThe included angle of the axial positive direction is；Indicating the included angleIs set to the initial time value of (1); is provided withFor a missile normal acceleration vector, define:
（4）
Wherein, when the missile turns leftwards, the right side of the equation is taken as' Number and conversely take "The number of the product is the number,The constraint is satisfied:
（5）
Wherein, The maximum normal acceleration of the missile;
The missile dynamics equation is:
，
，
，
（6）；
In the step 2: the envelope circle is calculated as follows:
set the circle center of enveloping circle ; Position vectorWherein, the method comprises the steps of, wherein,Is a component of (2)Respectively indicate the position of the missile、A position component on the shaft; radius is of；
Setting mass center and boundary point of missileRadius of circle tangential to missile velocity direction，The following formula is calculated to obtain：
，
，（7）
Wherein the method comprises the steps ofThe absolute value is represented by a value of,For the parameters used to determine the direction of the missile steering,Is representing steering of the missile to the left;
Serial number setting Is used for the purpose of the present invention,Calculating the following formula to determineAnd (3) with：
，
，
（8）；
In the step 2: the calculation of the corresponding central angle of the circular track is realized as follows:
setting the central angle corresponding to the missile flight circle locus as Calculated by the following formula：
，
（9）
Wherein,Connecting line for target and origin of coordinate system and method thereofThe included angle of the axes is that,Given by formula (7);
In the step 2: iterative calculation of the circle guide track and corresponding overload is as follows:
calculating the distance required by the missile to hit the target along the enveloping circle ：
（10）
Calculating the time required for the missile to hit the target:
（11）
To be used for As an iteration initial value, the target reachable domain is recalculated, and the envelope circle are recalculatedIterative calculation is carried out until the precision requirement is met, the final envelope circle is taken as a guided circle track, andAs the iteration initial value in the next round track calculation;
Calculating missile overload by the following calculation ：
，
（12）
Wherein,To be a positive indication that the missile is turning to the left,Given by formula (9);
in the step 3: the guidance stability is determined as follows:
when the missile launches to calculate the first guidance track, the guidance stability is judged, and the target acceleration is set The constraint is satisfied:
（13）
Wherein the method comprises the steps of Is the maximum value of the target acceleration; at the beginning of circle track guidanceAt the end of guidanceWherein, the method comprises the steps of, wherein,The method is obtained by a missile launching calculation step2, and the normal acceleration of the missile at the end of guidance is obtained by calculating the following steps：
（14）
Calculation ofWhether a stability criterion is satisfied:
（15）
if the requirements are met, the missile performance meets the guidance requirements, the guidance can be stabilized, and if the requirements are not met, the missile launching position and direction are required to be adjusted until the criteria are met.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106843272A (en) * | 2017-02-28 | 2017-06-13 | 北京航空航天大学 | A kind of explicit Guidance rule with terminal velocity, trajectory tilt angle and overload constraint |
| CN112269394A (en) * | 2020-09-28 | 2021-01-26 | 北京航空航天大学 | Aircraft path point tracking guidance method |
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106843272A (en) * | 2017-02-28 | 2017-06-13 | 北京航空航天大学 | A kind of explicit Guidance rule with terminal velocity, trajectory tilt angle and overload constraint |
| CN112269394A (en) * | 2020-09-28 | 2021-01-26 | 北京航空航天大学 | Aircraft path point tracking guidance method |
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