CN108050888B - A kind of explicit guidance method with no-fly zone constraint - Google Patents
A kind of explicit guidance method with no-fly zone constraint Download PDFInfo
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Abstract
A kind of explicit guidance method with no-fly zone constraint does not need that reference trajectory is stored in advance, acceleration instruction is the explicit expression of guided missile and target current state, no-fly zone characterising parameter different from the method for track reference trajectory.This method of guidance is made of virtual target guidance law and boundary constraint scheme.Target is first mapped to virtual target, then obtain virtual target and guided missile relative motion relation, last proportion of utilization guidance law by missile-operation control to virtual target, to get around no-fly zone.When guided missile hits virtual target, virtual target is overlapped with realistic objective, i.e., guided missile hits realistic objective.In some special circumstances, guided missile still is possible to then need to guarantee using boundary constraint scheme that no-fly zone constrains at this time because turning enters no-fly zone not in time.The acceleration instruction of boundary constraint scheme can smart missiles close to and along no-fly zone boundary flight.Using analytic solutions relevant to proportional guidance law to determine whether needing boundary constraint scheme.
Description
Technical Field
The invention relates to an explicit guidance method with a no-fly zone constraint, belonging to the fields of aerospace technology, weapon technology and guidance control.
Background
In modern wars, both parties to the battle generally deploy air defense systems in the core area and the frontier position to protect high-value targets of the own party and compress the range of activities of enemies in the air. The effective range of an air defense missile is generally influenced by the flight speed, the height and the RCS size of a target. From the perspective of an attacker, common defense means include increasing the speed and maneuverability of own aircraft, reducing the flying height, reducing the RCS, using baits, adopting saturation attack and the like, but when the target moves outside the no-fly zone, the best way is to bypass the no-fly zone formed by the air defense missile system.
Proportional guidance is a typical representation of guidance methods, with acceleration commands proportional to the rate of change of line-of-sight angle and the velocity of the missile relative to the target. Because the proportional guidance method is simple, effective and easy to implement, proportional guidance is widely used. Although some explicit guidance methods developed on the basis of proportional guidance can constrain terminal velocity and ballistic dip constraints, it is not possible to handle cases with no-fly zone constraints. Currently, a common method for considering the no-fly zone constraint is as follows: planning a trajectory which bypasses the no-fly zone, and controlling the missile to track the reference trajectory. Although this method is easy to deal with various complex track constraint problems, it requires the pre-storage of reference trajectories, which are only suitable for hitting fixed or low-speed moving targets.
Disclosure of Invention
The invention aims to solve the problems and provides an explicit guidance method with a no-fly zone constraint. Unlike the method of tracking the reference trajectory, the guidance method does not need to store the reference trajectory in advance, and the acceleration command is an explicit expression of the description parameters of the missile and the current state and the no-fly zone of the target. The guidance method consists of a virtual target guidance law and a boundary constraint scheme. The idea of the virtual target guidance law is as follows: firstly, mapping a target to a virtual target, then obtaining the relative motion relation between the virtual target and the missile, and finally guiding the missile to the virtual target by utilizing a proportional guidance law so as to bypass a no-fly zone. When the missile hits the virtual target, the virtual target is superposed with the actual target, namely the missile hits the actual target. However, in some special cases, the missile still may enter the no-fly zone due to untimely turning, and at this time, a boundary constraint scheme is required to ensure the no-fly zone constraint. The acceleration instructions of the boundary constraint scheme can guide the missile to approach and fly along the boundary of the no-fly zone. Using and proportional-pilot law phase in text
Step 1: establishing kinematic and kinetic equations
The method comprises the steps of establishing a reference system o-xy for the engagement problem of the missile and a target in a horizontal plane, wherein M is the missile mass center, T is the target mass center, the missile needs to avoid the condition that the E point is taken as the central point and the radius is rEThe position vector of the central point E is XE＝[xE,yE]TWherein x isE,yEThe components of the center point position vector on the coordinate axes x-, y-, respectively. There are the following motion equation sets
Wherein, XM＝[xM,yM]TAs a missile position vector, xM,yMAre the components of the missile position vector on the coordinate axis x-and y-respectively,is the vector of the speed of the missile,are respectively the components of the missile velocity vector on the coordinate axis x-and y-respectively,is the vector of the acceleration of the missile,respectively the components of the missile acceleration vector on the coordinate axis x-and y-respectively; xT＝[xT,yT]TIs a target position vector, xT,yTThe components of the target position vector on the coordinate axes x-, y-, respectively,in order to be the target velocity vector,the components of the target velocity vector on the coordinate axes x-, y-, respectively,is a vector of the target acceleration and is,the components of the target acceleration vector on the coordinate axes x-, y-, respectively. The superscript "T" represents the transpose of the vector. From the missile perspective, the target acceleration vector aTCan be estimated by using a filter to obtain a missile acceleration vector aMIs the control variable that needs to be determined. The unit vector shown in FIG. 1 is defined belowAnd andare respectively a vectorAndunit vector of (1), as follows
Wherein,andis a 2-norm. Respectively to be provided withAndclockwise rotating by 90 degrees to obtain a unit vector
Step 2: virtual target guidance law design
Establishing a non-inertial reference system M-x by taking the missile mass center M as an originMMyMM，xMMAxial direction and unit vectorSame, yMMAxial direction and unit vectorThe same is true. The coordinate system has translation and rotation, and because the origin of coordinates is located on the center of mass of the missile, the translation speed is the velocity vector V of the missileMThe translational acceleration is missile acceleration vector aM，ωMAnd betaMThe rotation angular velocity and the angular acceleration are respectively, the anticlockwise direction is taken as the positive direction, and the calculation is carried out by the following formula
The following describes calculating unit vectorsDerivative of (2)Assuming a minute period of time dt, a unit vectorThrough an angle d theta to vectorThen there is
dθ＝ωMdt (11)
Unit vectorIs a derivative of
By means of Taylor's expression has
Wherein, o [ (d θ)2]And o [ (d θ)3]The Peanenoy terms developed for Taylor are high-order infinitesimal terms, and the substitution into the formula (13) has
Can be derived by the same principle
Equation (10) can be further solved as
Note the unit vectorThe above equation can be simplified to
The same can be obtained, unit vectorAndangular velocity of rotation of omegaTAnd angular acceleration betaTAs follows
In order to bypass the no-fly zone, the virtual target guidance law firstly maps the target centroid T to the virtual target point TmThen, the missile is guided to the virtual target point TmAnd (5) flying. Virtual target point TmIs determined by the following method
1) Establish with E pointA great circle C with the center as ME as radius2；
2) Big circle C2Intersecting the extension line of the line segment ET at a point N, and mapping the point N to a non-inertial reference system M-xMMyMMX ofMMOn-axis NmSatisfies the line segment MNmAndare equal in arc length. N is a radical ofmIn a non-inertial frame of reference M-xMMyMMHas the coordinates ofWhere η is a vectorAndis determined by the following method;
3)Tmpoint in non-inertial frame of reference M-xMMyMMHas the coordinates of
Note the bookIs TmRelative to M-xMMyMMVelocity vector of (1), thenAlong xMMComponent of axisIs composed of
Along yMMComponent of axisIs composed of
Is a virtual target point TmRelative to a non-inertial frame of reference M-xMMyMMAcceleration vector of (2).Along xMMComponent of shaftAs follows
Substituting the formula (9) and the formula (21-23) into the above formula, and finishing to obtain
Along yMMComponent of axisAs follows
Substituting the formulas (9) and (22) into the above formulas
The virtual target guidance law a can be obtained from the equations (28) and (30)M0As follows
Wherein
To determine aM0Must be determined firstIn a non-inertial frame of reference M-xMMyMMObserving a virtual target point TmHere guiding the virtual target point T using the proportional guidance lawmMove to point M. Obviously, when M and T aremWhen they coincide, the missile now hits the target. Obtained by the proportional-pilot law
Wherein k isPNAnd more than or equal to 3 is a proportional steering coefficient. The above formula is arranged in a non-inertial reference frame M-xMMyMMMedium expansion, can
Wherein,andcan be calculated by equations (25) and (26), respectively.Is a line segment MTmIn a non-inertial reference system M-xMMyMMThe rotation angular rate of (1) is positive in the counterclockwise direction and is calculated by the following formula
The virtual target guidance law acceleration command a can be obtained by substituting the formula (35) into the formula (31-33)M0。
And step 3: boundary constraint scheme design
To bypass the no-fly zone, hit targets outside the no-fly zone, virtual target-guided law aM0Guiding the missile to move to the virtual target point TmAnd (5) flying. When missile mass center M and TmWhen they coincide, the missile hits the target. However, in a few special cases, the missile still has the possibility of touching the no-fly zone, namely the following two cases
Case 1: the initial speed of the missile points to a virtual target point, the missile gradually approaches a no-fly zone under the action of a virtual target guidance law, and the missile hits a target before entering the no-fly zone;
case 2: the initial speed of the missile points to the center E of the no-fly zone, at the moment, under the action of the virtual target guidance law, the missile firstly turns towards the direction of the virtual target point, but the missile enters the no-fly zone to fly due to insufficient maneuvering acceleration of the turning.
Obviously, for a trajectory similar to Case 1, a missile enters a no-fly zone after hitting a target, no extra measures are needed, otherwise, the missile hits the target, but for a trajectory similar to Case 2, a boundary constraint scheme is needed to meet the no-fly zone constraint. The boundary constraint scheme of the invention generates an acceleration instruction vector vertical to the speed directionThe aircraft can be guided to slowly approach the no-fly zone and fly along the boundary of the no-fly zone without entering the no-fly zone.
Missile velocity vector V guided by center point E of no-fly zoneMThe vertical line is made, and the foot is F. Definition ofIs a unit vector perpendicular to the velocity, as shown below
Unit vector of vectorAs shown below
The inventive boundary constraint scheme acceleration vectorCan be described as
Wherein,is the acceleration vectorThe modulus value of (a).
Defining the distance from the missile to the boundary of the no-fly zone as H, and the radius of the circular no-fly zone as rEDirection of missile velocityThe included angle between the quantity and the tangential direction of the no-fly zone is sigma, and the specific calculation rule is as follows
Wherein VMI is missile velocity vector VM2-norm of (d). The derivative of H with respect to time is
The derivative of σ with respect to time is
Substituting the formula (9) and the formula (39) into the above formula
Due to the fact thatPerpendicular to the velocity direction, | | VMAnd | is a constant value. Then the nonlinear system S1 is formed by the equations (40), (42), (44):
for the nonlinear control system S1, H and σ are state variables,is a control variable. The invention imitates the resistanceA damping spring system constructedThe control law of (1), i.e. the boundary constraint scheme, is as follows
Wherein, ω isnSimilar to natural vibration frequency, the value of the natural vibration frequency influences the approaching speed of the missile to the boundary of the no-fly zone, and can be calculated by the following formula
Wherein k isωIs a constant. Xi is similar to the damping coefficient and satisfies
Wherein H0And σ0Is the state at the initial time.
And 4, step 4: design of coordination scheme between virtual target guidance and boundary constraint scheme
The coordination scheme between the virtual target guidance and boundary constraint schemes requires that: under the premise that the virtual target guidance law plays a main role, the boundary constraint scheme plays a timely role, namely boundary constraint is guaranteed when necessary, and the target hit by the missile is not interfered. The strategy of the invention here is: forecasting the engagement process by simulation, if everThe boundary constraint scheme does not work if at a certain momentIs provided withThe boundary constraint scheme works.
Andthe size of the ratio pilot is judged by the analytic solution of the ratio pilot law, and the ratio pilot analytic solution is deduced without any linearization or assumption.
In a non-inertial frame of reference M-xMMyMMIn the middle, due to the action of the proportional guidance lawPerpendicular toThus, it is possible to provideIs not changed. λ is the virtual line of sightRelative to xMMThe included angle of the axes is positive in the counterclockwise direction. Psi isRelative to xMMThe angle of the axes is also positive in the counterclockwise direction. They are respectively calculated by the following formula
In addition noteRelative virtual line of sightIs at an included angle ofIn FIG. 6, when λ - ψ < 0, letWhen λ - ψ > 0, letThenNote that nothing is considered hereSince this is a singular point for the scale-guided law. Brief bulletin distanceAnd magnitude of relative velocityThen there is
Derived from the proportional guidance law
Substituting the formula (52) into the above formula to obtain
ByTo obtain
In addition, there are kinematic relationships
Dividing formula (55) by the above formula and finishing to obtain
Integrating the above equation to obtain
Wherein, C1Is an integral constant, derived from an initial state
Wherein R is0Is the initial distance of the bullet eyes,is at the beginningRelative virtual line of sightThe included angle of (1) is
Integration of equation (53) can be obtained
Δψ＝kPNΔλ (61)
Wherein, the delta psi is psi-psi0，Δλ＝λ-λ0，ψ0And λ0Is the initial time state. In addition from the frontRelate toIs defined as
WhereinObtained by the formulae (61) and (62)
Due to the bullet distance R of the terminal at the momentfIs 0, then the terminal time can be obtained from equation (60)Relative virtual line of sightAngle of (2)Is also 0, then
Wherein λf，ψfIn the terminal state, when λ0-ψ0When the ratio is less than 0, the reaction mixture is,when lambda is0-ψ0When is greater than 0，
And is provided withDue to kPNAnd the available range is more than or equal to 3: lambda [ alpha ]f∈(-1.5π,1.5π)，
ψfEpsilon (-2.5 pi, 2.5 pi). In addition, the virtual target point T can be obtained from the formula (60) and the formula (63)mPolar coordinate equation relative to missile mass center M motion trail
Wherein λ is between λ0And λfAnd is an independent variable. Incidentally, when k isPNWhen the polar coordinate is converted to the rectangular coordinate, it is easy to prove that the relative trajectory is a circular arc.
The polar coordinate analytic solution of the proportional guidance law is converted into a rectangular coordinate analytic solutionAnd judging the size of the boundary constraint scheme, thereby determining whether the boundary constraint scheme works.
Virtual target guidance law aM0Edge ofHas a component size of
Wherein, aM0As calculated by the formula (31),calculated by equation (38). Virtual target guidance law aM0And boundary constraint scheme guidance lawThe coordination scheme between (1) is as follows:
if the boundary constraint scheme is functional, then
Otherwise
aM＝aM0 (70)
Wherein,calculated by equation (47). Under the action of the coordination scheme, if the target flies outside the no-fly zone, the guidance law can ensure that the missile does not enter the no-fly zone; if the target enters the no-fly zone, becauseThe virtual target guidance law acts, so the guidance law also considers the capability of hitting the target entering the no-fly zone.
For some missiles, only the control force is perpendicular to the velocity direction, and the axial acceleration is not adjustable. At this time, only take aMComponent perpendicular to velocityAs the command acceleration, the following
And 5: three-dimensional form of the guidance law of the invention
Respectively in original two-dimensional coordinate systems o-xy and M-xMMyMMOn the basis of (1), increasing the vertical upward z-and z-MMAxes, establishing three-dimensional spatial coordinate systems o-xyz and M-xMMyMMzMMThen the virtual target point T corresponding to the targetmA position vector ofWhereinAre respectively virtual target points TmThe component of the position vector of (a) on the corresponding coordinate axis.
WhereinIs along zMM-a unit vector of the axis,is the unit vector in the vertical direction passing through the centroid T of the target point, and η can be calculated by the formula (24). The three-dimensional spatial guidance law can be written as
Wherein
Wherein,calculated by formula (34), and the virtual target T in formula (34)mIn a coordinate system M-xMMyMMzMMVelocity inIs composed of
Wherein
Thus, an analytic solution form of the guidance law applied to the three-dimensional space is obtained.
The invention has the advantages that:
(1) the method is simple, effective and easy to realize, and the guidance problem with the restricted flight forbidden zone is converted into guidance for a virtual target in a non-inertial reference system through space transformation;
(2) the boundary constraint scheme in the guidance method can strictly ensure the boundary constraint of the no-fly zone, thereby improving the penetration resistance of the missile;
(3) unlike the traditional reference trajectory tracking method, the guidance method does not need to store the reference trajectory in advance, and the acceleration instruction is an explicit expression of the description parameters of the missile and the current state and the no-fly zone of the target, so that the onboard computer can calculate and update the instruction in real time.
Drawings
Fig. 1 is a schematic illustration of a battle including a no-fly zone in a horizontal plane.
FIG. 2 is a non-inertial frame of reference M-xMMyMMAnd a virtual target point Tm。
FIG. 3 is a unit vectorDerivative solving the auxiliary schematic.
Fig. 4 shows a case where the no-fly zone is touched.
Fig. 5 is a command for acceleration of flight around a no-fly zone.
FIG. 6 shows a virtual target at M-xMMyMMSchematic diagram of relative motion in (1).
Fig. 7 is a ballistic trajectory curve of the first embodiment.
Fig. 8 is an acceleration command curve according to the first embodiment.
Fig. 9 is a ballistic trajectory curve of the second embodiment.
Fig. 10 is an acceleration command curve of the second embodiment.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The invention relates to a display guidance method with no-fly zone restriction, which is mainly used for striking a target moving at high speed near the no-fly zone. Unlike the method of tracking the reference trajectory, the guidance law method does not need to store the reference trajectory in advance, and the acceleration instruction is an explicit expression of the description parameters of the missile and the current state of the target and the no-fly zone, so that the onboard computer can calculate and update the instruction in real time. The guidance method consists of two parts: virtual target guidance law and boundary constraint scheme. In order to bypass the no-fly zone, the virtual target guidance law is to map the target to the virtual target first and then guide the missile to the virtual target by using a proportional guidance method. When the missile reaches the virtual target, the virtual target is superposed with the actual target, and the missile hits the target at the moment. However, in some special cases, the missile still has the possibility of entering the no-fly zone before hitting the target, and a boundary constraint scheme is needed to guarantee the no-fly zone constraint. Here, the analytic solution of the proportional-pilot law is used to determine whether the boundary constraint scheme works. The whole process comprises the following steps:
step 1: establishing kinematic and kinetic equations
FIG. 1 shows the problem of engagement of a missile with a target in a horizontal plane, wherein M is the missile mass center, T is the target mass center, the missile needs to avoid the missile, the E point is taken as a central point, and the radius is rEThe position vector of the central point E is XE＝[xE,yE]TWherein x isE,yEThe components of the center point position vector on the coordinate axes x-, y-, respectively. In the reference system o-xy, there are the following motion equations
Wherein, XM＝[xM,yM]TAs a missile position vector, xM,yMAre the components of the missile position vector on the coordinate axis x-and y-respectively,is the vector of the speed of the missile,are respectively the components of the missile velocity vector on the coordinate axis x-and y-respectively,is the vector of the acceleration of the missile,respectively the components of the missile acceleration vector on the coordinate axis x-and y-respectively; xT＝[xT,yT]TIs a target position vector, xT,yTThe components of the target position vector on the coordinate axes x-, y-, respectively,in order to be the target velocity vector,the components of the target velocity vector on the coordinate axes x-, y-, respectively,is a vector of the target acceleration and is,the components of the target acceleration vector on the coordinate axes x-, y-, respectively. The superscript "T" represents the transpose of the vector. From the missile perspective, the target acceleration vector aTCan be estimated by using a filter to obtain a missile acceleration vector aMIs the control variable that needs to be determined. The unit vector shown in FIG. 1 is defined belowAnd andare respectively a vectorAndunit vector of (1), as follows
Wherein,andis a 2-norm. Respectively to be provided withAndclockwise rotating by 90 degrees to obtain a unit vector
Step 2: virtual target guidance law design
FIG. 2 is a non-inertial frame of reference M-xMMyMMThe origin of coordinates is located at the missile center of mass M, xMMThe direction of the axis being the unit vector in FIG. 1Same, yMMThe direction of the axis corresponding to the unit vector in FIG. 1The same is true. The coordinate system has translation and rotation, and because the origin of coordinates is located on the center of mass of the missile, the translation speed is the velocity vector V of the missileMThe translational acceleration is missile acceleration vector aM，ωMAnd betaMThe rotation angular velocity and the angular acceleration are respectively, the anticlockwise direction is taken as the positive direction, and the calculation is carried out by the following formula
The following describes calculating unit vectorsDerivative of (2)In FIG. 3, unit vectors are shown over a small period of time dtAngle of rotation d θ to vectorThen there is
dθ＝ωMdt (93)
Unit vectorIs a derivative of
By means of Taylor's expression has
Wherein, o [ (d θ)2]And o [ (d θ)3]The Peanenoy terms developed for Taylor are high-order infinitesimal terms, and the substitution into the formula (95) has
Can be derived by the same principle
Equation (92) can be further solved as
Note the unit vectorThe above equation can be simplified to
The same can be obtained, unit vectorAndangular velocity of rotation of omegaTAnd angular acceleration betaTAs follows
In fig. 2, to bypass the no-fly zone, the virtual target guidance law maps the target centroid T to the virtual target point TmThen guide the missile to the virtual target point TmAnd (5) flying. Virtual target point TmIs determined by the following method
1) Establishing a large circle C with the point E as the center and the ME as the radius2；
2) Big circle C2Intersecting the extension line of the line segment ET at a point N, and mapping the point N to a non-inertial reference system M-xMMyMMX ofMMOn-axis NmSatisfies the line segment MNmAndare equal in arc length. N is a radical ofmIn a non-inertial frame of reference M-xMMyMMHas the coordinates ofWhere η is a vectorAndis determined by the following method;
3)Tmpoint in non-inertial frame of reference M-xMMyMMHas the coordinates of
Note the bookIs TmRelative to M-xMMyMMVelocity vector of (1), thenAlong xMMComponent of axisIs composed of
Along yMMComponent of axisIs composed of
Is a virtual target point TmRelative to a non-inertial frame of reference M-xMMyMMAcceleration vector of (2).Along xMMComponent of shaftAs follows
Substituting the formulas (91) and (103-105) into the above formulas and arranging to obtain
Along yMMComponent of axisAs follows
Substituting the above formulas (91) and (104) to obtain
The virtual target guidance law a can be obtained from the formulas (110) and (112)M0As follows
Wherein
To determine aM0Must be determined firstIn a non-inertial frame of reference M-xMMyMMObserving a virtual target point TmHere using the proportional guidance law to guide the virtualTarget point TmMove to point M. Obviously, when M and T aremWhen they coincide, the missile now hits the target. Obtained by the proportional-pilot law
Wherein k isPNAnd more than or equal to 3 is a proportional steering coefficient. The above formula is arranged in a non-inertial reference frame M-xMMyMMMedium expansion, can
Wherein,andcan be calculated by equations (107) and (108), respectively.Is a line segment MTmIn a non-inertial frame of reference M-xMMyMMThe rotation angular rate of (1) is positive in the counterclockwise direction and is calculated by the following formula
The virtual target guidance law acceleration command a can be obtained by substituting the formula (117) into the formula (113-115)M0。
And step 3: boundary constraint scheme design
To bypass the no-fly zone, hit targets outside the no-fly zone, virtual target-guided law aM0Guiding the missile to move to the virtual target point TmAnd (5) flying. When missile mass center M and TmWhen they coincide, the missile hits the target. In a few special cases, however, it is still possible for the missile to touch the no-fly zone. FIG. 4 shows two special cases of touching no-fly zone, where M is missile centroid position and T is missile centroid positionThe target centroid position is fixed, point E is the no-fly zone center point, and the no-fly zone boundary is represented by the dashed line.
Case 1: the initial speed of the missile points to a virtual target point, the missile gradually approaches a no-fly zone under the action of a virtual target guidance law, and the missile hits a target before entering the no-fly zone;
case 2: the initial speed of the missile points to the center E of the no-fly zone, at the moment, under the action of the virtual target guidance law, the missile firstly turns towards the direction of the virtual target point, but the missile enters the no-fly zone to fly due to insufficient maneuvering acceleration of the turning.
Obviously, for a trajectory similar to Case 1, a missile enters a no-fly zone after hitting a target, no extra measures are needed, otherwise, the missile hits the target, but for a trajectory similar to Case 2, a boundary constraint scheme is needed to meet the no-fly zone constraint. The boundary constraint scheme of the invention generates an acceleration instruction vector vertical to the speed directionThe aircraft can be guided to slowly approach the no-fly zone and fly along the boundary of the no-fly zone without entering the no-fly zone.
In FIG. 5, F is the vector V from the center point E of the no-fly zone to the velocity of the missileMIs used for the foot drop. Definition ofIs a unit vector perpendicular to the velocity, as shown below
Unit vector of vectorAs shown below
The inventive boundary constraint scheme acceleration vectorCan be described as
Wherein,is the acceleration vectorThe modulus value of (a).
Defining the distance from the missile to the boundary of the no-fly zone as H, and the radius of the circular no-fly zone as rEThe included angle between the missile velocity vector and the tangent direction of the no-fly zone is sigma, and the specific calculation rule is as follows
Wherein VMI is missile velocity vector VM2-norm of (d). The derivative of H with respect to time is
The derivative of σ with respect to time is
Substituting the formula (91) and the formula (121) into the above formula
Due to the fact thatPerpendicular to the velocity direction, | | VMAnd | is a constant value. Then the nonlinear system S1 is formed by the equations (122), (124), (126):
for the nonlinear control system S1, H and σ are state variables,is a control variable. The invention imitates a damping spring system to constructThe control law of (1), i.e. the boundary constraint scheme, is as follows
Wherein, ω isnSimilar to natural vibration frequency, the value of the natural vibration frequency influences the approaching speed of the missile to the boundary of the no-fly zone, and can be calculated by the following formula
Wherein k isωIs a constant. Xi is similar to the damping coefficient and satisfies
Wherein H0And σ0Is the state at the initial time.
And 4, step 4: design of coordination scheme between virtual target guidance and boundary constraint scheme
The coordination scheme between the virtual target guidance and boundary constraint schemes requires that: under the premise that the virtual target guidance law plays a main role, the boundary constraint scheme plays a timely role, namely boundary constraint is guaranteed when necessary, and the target hit by the missile is not interfered. The strategy of the invention here is: forecasting the engagement process by simulation, if everThe boundary constraint scheme does not work if at a certain momentIs provided withThe boundary constraint scheme works.
Andthe size of the ratio pilot is judged by the analytic solution of the ratio pilot law, and the ratio pilot analytic solution is deduced without any linearization or assumption.
In FIG. 6, in a non-inertial frame of reference M-xMMyMMIn the middle, due to the action of the proportional guidance lawPerpendicular toThus, it is possible to provideIs not changed in size. λ is the virtual line of sightRelative to xMMThe included angle of the axes is positive in the counterclockwise direction. Psi isRelative to xMMThe angle of the axes is also positive in the counterclockwise direction. They are respectively calculated by the following formula
In addition noteRelative virtual line of sightIs at an included angle ofIn FIG. 6, when λ - ψ < 0, letWhen λ - ψ > 0, letThenNote that nothing is considered hereSince this is a singular point for the scale-guided law. Brief bulletin distanceAnd relative speedSize of degreeThen there is
Derived from the proportional guidance law
Substituting the formula (134) into the above formula to obtain
ByTo obtain
In addition, there are kinematic relationships
Dividing formula (137) by the above formula and finishing to obtain
Integrating the above equation to obtain
Wherein, C1Is an integral constant, derived from an initial state
Wherein R is0Is the initial distance of the bullet eyes,is at the beginningRelative virtual line of sightThe included angle of (1) is
Integration of equation (135) can be obtained
Δψ＝kPNΔλ (143)
Wherein, the delta psi is psi-psi0，Δλ＝λ-λ0，ψ0And λ0Is the initial time state. In addition to the foregoingIs defined as
WhereinFrom the equations (143) and (144)
Due to the bullet distance R of the terminal at the momentfIs 0, then the terminal time can be obtained from equation (142)Relative virtual line of sightAngle of (2)Is also 0, then
Wherein λf，ψfIn the terminal state, when λ0-ψ0When the ratio is less than 0, the reaction mixture is,when lambda is0-ψ0When the pressure is higher than 0, the pressure is higher,and is provided withDue to kPNAnd the available range is more than or equal to 3: lambda [ alpha ]f∈(-1.5π,1.5π)， ψfEpsilon (-2.5 pi, 2.5 pi). In addition, the virtual target point T can be obtained by the formula (142) and the formula (145)mPolar coordinate equation of relative missile centroid M motion track
Wherein λ is between λ0And λfAnd is an independent variable. Incidentally, when k isPNWhen the polar coordinate is converted to the rectangular coordinate, it is easy to prove that the relative trajectory is a circular arc.
Converting into right angle by polar coordinate analytic solution of the above proportional guidance lawThe coordinate analytic solution can be usedAnd judging the size of the boundary constraint scheme, thereby determining whether the boundary constraint scheme works.
Virtual target guidance law aM0Edge ofHas a component size of
Wherein, aM0As calculated by the formula (113),calculated by equation (120). Virtual target guidance law aM0And boundary constraint scheme guidance lawThe coordination scheme between (1) is as follows:
if the boundary constraint scheme is functional, then
Otherwise
aM＝aM0 (152)
Wherein,calculated by equation (129). Under the action of the coordination scheme, if the target flies outside the no-fly zone, the guidance law can ensure that the missile does not enter the no-fly zone; if the target enters the no-fly zone, becauseThe virtual target guidance law acts, so the guidance law also considers the capability of hitting the target entering the no-fly zone.
For some missiles, only the control force is perpendicular to the velocity direction, and the axial acceleration is not adjustable. At this time, only take aMComponent perpendicular to velocityAs the command acceleration, the following
And 5: three-dimensional form of the guidance law of the invention
Respectively in original two-dimensional coordinate systems o-xy and M-xMMyMMOn the basis of (1), increasing the vertical upward z-and z-MMAxes, establishing three-dimensional spatial coordinate systems o-xyz and M-xMMyMMzMMThen the virtual target point T corresponding to the targetmA position vector ofWhereinAre respectively virtual target points TmThe component of the position vector of (a) on the corresponding coordinate axis.
WhereinIs along zMM-a unit vector of the axis,is the unit vector in the vertical direction passing through the centroid T of the target point, η can be calculated by the formula (106). The three-dimensional spatial guidance law can be written as
Wherein
Wherein,calculated by formula (116), and the virtual target T in formula (116)mIn a coordinate system M-xMMyMMzMMVelocity inIs composed of
Wherein
Thus, an analytic solution form of the guidance law applied to the three-dimensional space is obtained.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
Example one
The embodiment requires that the missile strictly guarantees the boundary constraint of the no-fly zone while hitting the target. In this embodiment, the center of the no-fly zone is E (0,0), and the radius rEA circular area of 20 km. Table 1 lists the initial positions, velocity parameters, and parameter settings in the boundary constraint scheme of the simulated missiles and targets of the present embodiment.
TABLE 1
The target is snaked maneuvered in the subsequent movement with maneuvering acceleration perpendicular to the velocity direction, as follows
Wherein d is0＝23km，May be calculated by the formula (88),is perpendicular to the target speed VTThe unit vector of (2).
FIG. 7 is a ballistic trajectory curve, and FIG. 8 is an acceleration command curve, whereinIs the axial acceleration of the missile,is normal acceleration. As can be seen from the figure, the missile flies to the target along a smooth trajectory without breaking the boundary constraint of the no-fly zone in the whole intercepting process. In which the flight-forbidden zone is only adhered to for a period of timeFlying, and at this time due to the BCHS solution,the curve is convex upward.
Example two
The embodiment verifies the avoidance effect of the guidance law on the no-fly zone in the three-dimensional space. In this embodiment, the no-fly zone is centered at E (0,0) and has a radius rEAn infinite height cylinder of 20 km. Table 2 lists the initial positions, velocity parameters, and parameter settings in the boundary constraint scheme of the simulated missiles and targets of the present embodiment.
TABLE 2
The subsequent motion of the target is a horizontal circular motion at a height of 5 km. FIG. 9 shows the trajectory of the missile and the target and their projection onto a cylindrical surface. FIG. 10 is an acceleration curve for a missile, where aM|x,aM|y,aM|zThe components of acceleration in the x-, y-, z-axes, respectively. The guidance law can control the missile to fly to the target along a smooth and stable trajectory, and the boundary constraint of the no-fly zone is strictly ensured.
Claims (1)
1. An explicit guidance method with no-fly zone constraints, comprising the steps of:
step 1: establishing kinematic and kinetic equations
The method comprises the steps of establishing a reference system o-xy for the engagement problem of the missile and a target in a horizontal plane, wherein M is the missile mass center, T is the target mass center, the missile needs to avoid the condition that the E point is taken as the central point and the radius is rEThe position vector of the central point E is XE＝[xE,yE]TWherein x isE,yEThe components of the central point position vector on the coordinate axes x-and y-are respectively; then there is the following system of equations of motion
Wherein, XM＝[xM,yM]TAs a missile position vector, xM,yMAre the components of the missile position vector on the coordinate axis x-and y-respectively,is the vector of the speed of the missile,are components of the missile velocity vector on the coordinate axis x-and y-respectively,is the vector of the acceleration of the missile,components of the missile acceleration vector on coordinate axes x-and y-are respectively; xT＝[xT,yT]TIs a target position vector, xT,yTThe components of the target position vector on the coordinate axes x-, y-, respectively,in order to be the target velocity vector,the components of the target velocity vector on the coordinate axes x-, y-, respectively,is a vector of the target acceleration and is,the components of the target acceleration vector on the coordinate axes x-and y-are respectively; the superscript "T" represents the transpose of the vector; from the missile perspective, the target acceleration vector aTEstimated by a filter to obtain the missile acceleration vector aMIs a control variable to be determined; defining unit vectorsAndandare respectively a vectorAndunit vector of (1), as follows
Wherein,andis a 2-norm; respectively to be provided withAndclockwise rotating by 90 degrees to obtain a unit vector
Step 2: virtual target guidance law design
Establishing a non-inertial reference system M-x by taking the missile mass center M as an originMMyMM，xMMAxial direction and unit vectorSame, yMMAxial direction and unit vectorThe same; the coordinate system has translation and rotation, and because the origin of coordinates is located on the center of mass of the missile, the translation speed is the velocity vector V of the missileMThe translational acceleration is missile acceleration vector aM，ωMAnd betaMThe rotation angular velocity and the angular acceleration are respectively, the anticlockwise direction is taken as the positive direction, and the calculation is carried out by the following formula
The following describes calculating unit vectorsDerivative of (2)Assuming a minute period of time dt, a unit vectorThrough an angle d theta to vectorThen there is
dθ＝ωMdt (11)
Unit vectorIs a derivative of
By means of Taylor's expression has
Wherein, o [ (d θ)2]And o [ (d θ)3]The Peyanuoyun items developed for Taylor are allA high order infinitesimal quantity, substituted into the formula (13) having
By the same principle
Equation (10) is further solved as
Note the unit vectorThe above equation is simplified to
By the same token, the unit vectorAndangular velocity of rotation of omegaTAnd angular acceleration betaTAs follows
In order to bypass the no-fly zone, the virtual target guidance law firstly maps the target centroid T to the virtual target point TmThen guide the missile to the virtual target point TmFlying; virtual target point TmIs determined by the following method
2.1) establishing a great circle C with the E point as the center and the ME as the radius2；
2.2) great circle C2Intersecting the extension line of the line segment ET at a point N, and mapping the point N to a non-inertial reference system M-xMMyMMX ofMMOn-axis NmSatisfies the line segment MNmAndare equal in arc length; n is a radical ofmIn a non-inertial frame of reference M-xMMyMMHas the coordinates ofWhere η is a vectorAndis determined by the following method;
2.3)Tmpoint in non-inertial frame of reference M-xMMyMMHas the coordinates of
Note the bookIs TmRelative to M-xMMyMMVelocity vector of (1), thenAlong xMMComponent of axisIs composed of
Along yMMComponent of axisIs composed of
Is a virtual target point TmRelative to a non-inertial frame of reference M-xMMyMMAn acceleration vector of (1);along xMMComponent of axisAs follows
Substituting the formula (9) and the formula (21-23) into the above formula, and finishing to obtain
Along yMMComponent of axisAs follows
Substituting the formula (9) and the formula (22) into the above formula
The virtual target guidance law a is obtained from the formula (28) and the formula (30)M0As follows
Wherein
To determine aM0Must be determined firstIn a non-inertial frame of reference M-xMMyMMObserving a virtual target point TmHere guiding the virtual target point T using the proportional guidance lawmMoving to the M point;obviously, when M and T aremWhen the missile is coincident, the missile also hits the target; obtained by the proportional-pilot law
Wherein k isPNNot less than 3 is a proportional guidance coefficient; the above formula is arranged in a non-inertial reference frame M-xMMyMMMiddle development to obtain
Wherein,andcalculated by equations (25) and (26), respectively;is a line segment MTmIn a non-inertial frame of reference M-xMMyMMThe rotation angular rate of (1) is positive in the counterclockwise direction and is calculated by the following formula
Substituting the formula (35) into the formula (31-33) to obtain the virtual target guidance law acceleration command aM0；
And step 3: boundary constraint scheme design
To bypass the no-fly zone, hit targets outside the no-fly zone, virtual target-guided law aM0Guiding the missile to move to the virtual target point TmFlying; when missile mass center M and TmWhen the missile is coincident, the missile hits the target; in a few cases, however, the missile can still touch the flight-forbidden zone, as follows:
3.1: the initial speed of the missile points to a virtual target point, the missile gradually approaches a no-fly zone under the action of a virtual target guidance law, and the missile hits a target before entering the no-fly zone;
3.2: the initial speed of the missile points to the center E of the no-fly zone, at the moment, under the action of a virtual target guidance law, the missile firstly turns towards the direction of a virtual target point, but the missile enters the no-fly zone to fly due to insufficient maneuvering acceleration of the turning;
obviously, for a trajectory similar to the case 3.1, a missile enters a no-fly zone after hitting a target, no extra measures need to be taken, otherwise, the missile hits the target, but for a trajectory similar to the case 3.2, a boundary constraint scheme needs to be utilized to meet the constraint of the no-fly zone when the missile enters the no-fly zone before hitting the target; the boundary constraint scheme generates an acceleration command vector perpendicular to the velocity directionThe aircraft can be guided to slowly approach the no-fly zone and fly along the boundary of the no-fly zone without entering the no-fly zone;
missile velocity vector V guided by center point E of no-fly zoneMMaking a vertical line, wherein the vertical foot is F; definition ofIs a unit vector perpendicular to the velocity, as shown below
Unit vector of vectorAs shown below
Then the boundary constraint scheme acceleration vectorIs marked as
Wherein,is the acceleration vectorA modulus value of (d);
defining the distance from the missile to the boundary of the no-fly zone as H, and the radius of the circular no-fly zone as rEThe included angle between the missile velocity vector and the tangent direction of the no-fly zone is sigma, and the specific calculation rule is as follows
Wherein VMI is missile velocity vector VM2-norm of (d); the derivative of H with respect to time is
The derivative of σ with respect to time is
Substituting the formula (9) and the formula (39) into the above formula
Due to the fact thatPerpendicular to the velocity direction, | | VM| is a constant value; the nonlinear system S1 is composed of the formula (40), the formula (42), and the formula (44):
for the nonlinear control system S1, H and σ are state variables,is a control variable; imitating a damping spring system, constructedThe control law of (1), i.e. the boundary constraint scheme, is as follows
Wherein, ω isnSimilar to natural vibration frequency, the value of the natural vibration frequency influences the approaching speed of the missile to the boundary of the no-fly zone, and the value is calculated by the following formula
Wherein k isωIs a constant; xi is similar to the damping coefficient and satisfies
Wherein H0And σ0Is in the state of the initial time;
and 4, step 4: design of coordination scheme between virtual target guidance and boundary constraint scheme
The coordination scheme between the virtual target guidance and boundary constraint schemes requires that: under the premise that the virtual target guidance law acts, the boundary constraint scheme acts timely, namely boundary constraint is guaranteed when necessary, and the target hit by the missile is not interfered; the strategy is as follows: forecasting the engagement process by simulation, if everThe boundary constraint scheme does not work if at a certain momentIs provided withThe boundary constraint scheme comes into play;
andthe size of the ratio is judged by the analytic solution of the ratio guidance law, and the derivation of the ratio guidance analytic solution is carried out on the premise of no linearization or assumption;
in a non-inertial frame of reference M-xMMyMMIn the middle, due to the action of the proportional guidance lawPerpendicular toThus, it is possible to provideIs not changed; λ is the virtual line of sightRelative to xMMThe included angle of the shaft is positive in the anticlockwise direction; psi isRelative to xMMThe included angle of the shaft is positive in the counterclockwise direction; they are respectively calculated by the following formula
In addition noteRelative virtual line of sightIs at an included angle ofWhen λ - ψ is less than 0, letWhen λ - ψ > 0, letThenNote that nothing is considered hereIn the case of (a) in (b),since this is a singular point for the scale-guided law; brief bulletin distanceAnd magnitude of relative velocityThen there is
Derived from the proportional guidance law
Substituting the formula (52) into the above formula
ByTo obtain
In addition, there are kinematic relationships
Dividing the formula (55) by the above formula, and finishing to obtain
Integrating the above equation to obtain
Wherein, C1Is an integral constant, derived from the initial state
Wherein R is0Is the initial distance of the bullet eyes,is at the beginningRelative virtual line of sightThe included angle of (1) is
Integration of equation (53) yields
Δψ＝kPNΔλ (61)
Wherein, the delta psi is psi-psi0，Δλ＝λ-λ0，ψ0And λ0Is the initial time state; in addition to the foregoingIs defined as
WhereinObtained by the formulae (61) and (62)
Due to the bullet distance R of the terminal at the momentfIs 0, then the terminal time is obtained from equation (60)Relative virtual line of sightAngle of (2)Is also 0, then
Wherein λf，ψfIn the terminal state, when λ0-ψ0When the ratio is less than 0, the reaction mixture is,when lambda is0-ψ0When the pressure is higher than 0, the pressure is higher,and is provided withDue to kPNAnd more than or equal to 3, the range is: lambda [ alpha ]f∈(-1.5π,1.5π)，ψfEpsilon (-2.5 pi, 2.5 pi); in addition, the virtual target point T is obtained from the formula (60) and the formula (63)mPolar coordinate equation relative to missile mass center M motion trail
Wherein λ is between λ0And λfIn between, is an independent variable; when k isPNWhen the coordinate is 2, the relative track is easily proved to be a section of circular arc as long as the polar coordinate is converted into a rectangular coordinate;
converting the polar analytic solution of the proportional guidance law into rectangular analytic solutionJudging the size of the boundary constraint scheme so as to determine whether the boundary constraint scheme plays a role or not;
virtual target guidance law aM0Edge ofHas a component size of
Wherein, aM0As calculated by the formula (31),calculated by equation (38); virtual target guidance law aM0And boundary constraint scheme guidance lawThe coordination scheme between (1) is as follows:
if the boundary constraint scheme is functional, then
Otherwise
aM＝aM0 (70)
Wherein,calculated by equation (47); under the action of the coordination scheme, if the target flies outside the no-fly zone, the guidance law can ensure that the missile does not enter the no-fly zone; if the target enters the no-fly zone, becauseThe virtual target guidance law acts, so that the guidance law also considers the capability of hitting the target entering the no-fly zone;
for some missiles, only the control force perpendicular to the speed direction is required, and the axial acceleration is not adjustable; at this time, only take aMComponent perpendicular to velocityAs the command acceleration, the following
And 5: three-dimensional form of guidance law
Respectively in original two-dimensional coordinate systems o-xy and M-xMMyMMOn the basis of (1), increasing the vertical upward z-and z-MMAxes establishing the three-dimensional spatial coordinate systems o-xyz and M-xMMyMMzMMThen the virtual target point T corresponding to the targetmA position vector ofWhereinAre respectively virtual target points TmThe component of the position vector of (a) on the corresponding coordinate axis;
whereinIs along zMM-a unit vector of the axis,is a unit vector passing through the vertical direction of the centroid T of the target point, and eta is calculated by a formula (24); the three-dimensional space guidance law is written as
Wherein
Wherein,calculated by formula (34), and the virtual target T in formula (34)mIn a coordinate system M-xMMyMMzMMVelocity inIs composed of
Wherein
Thus, an analytic solution form of the guidance law applied in the three-dimensional space is obtained.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| EP0807876A1 (en) * | 1996-05-13 | 1997-11-19 | Aerospatiale Societe Nationale Industrielle | Missile steering device |
| CN103090728A (en) * | 2013-01-07 | 2013-05-08 | 北京理工大学 | Tail angle restraining guidance method based on sliding mode control |
| CN106020231A (en) * | 2016-05-30 | 2016-10-12 | 中国人民解放军国防科学技术大学 | Hypersonic air vehicle reentry trajectory optimization method based on reentry point parameter |
| CN107065928A (en) * | 2017-05-04 | 2017-08-18 | 广西大学 | A kind of control method in unmanned plane during flying region |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| EP0807876A1 (en) * | 1996-05-13 | 1997-11-19 | Aerospatiale Societe Nationale Industrielle | Missile steering device |
| CN103090728A (en) * | 2013-01-07 | 2013-05-08 | 北京理工大学 | Tail angle restraining guidance method based on sliding mode control |
| CN106020231A (en) * | 2016-05-30 | 2016-10-12 | 中国人民解放军国防科学技术大学 | Hypersonic air vehicle reentry trajectory optimization method based on reentry point parameter |
| CN107065928A (en) * | 2017-05-04 | 2017-08-18 | 广西大学 | A kind of control method in unmanned plane during flying region |
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