CN110032214B - Vector field-based fast Standoff target tracking method - Google Patents
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Abstract
The invention belongs to a target tracking technology, and provides a vector field-based fast Standoff tracking method aiming at the problem that a single carrier needs to be separated from a target by a certain distance and continuously track the target. In consideration of the condition that the traditional vector field-based guidance method converges to a tracking circle slowly, a new guidance function is constructed to replace the original guidance parameter, and the convergence speed is effectively improved. Considering the performance constraint of the unmanned aerial vehicle, the parameters in the guidance function are determined by using an off-line searching method, so that the fastest convergence speed is achieved, stable tracking can be directly formed on a standoff circle, and the problem that stable convergence is achieved after repeated fluctuation is avoided. In addition, two solutions are provided for a standoff tracking scene of a moving target, and different solutions and guidance functions can be selected according to task requirements in practical application.
Description
Technical Field
The invention belongs to a target tracking technology, and provides a vector field-based fast Standoff tracking method for the problem that a single unmanned aerial vehicle needs to be separated from a target by a certain distance and continuously track the target.
Background
With the development of automatic Control and navigation technologies, cheap unmanned aerial vehicles equipped with Flight Control Systems (FCS) are widely used in the fields of military reconnaissance, target tracking, power patrol, disaster assessment, etc., and an important application scenario is that fixed-wing unmanned aerial vehicles are used to continuously track and observe a single target or a certain area, which requires that the unmanned aerial vehicles fly at a certain cruising speed and keep a certain distance from the target or an area of interest to keep the target or the area of interest within an observation range, so that it is necessary to research a Standoff tracking method.
The traditional Standoff target tracking method based on the vector field has the advantages of simple control method, stable convergence and the like, but the problem of low convergence speed is also obvious. And determining parameters in the guidance function by considering the performance constraint of the unmanned aerial vehicle by using an off-line searching method so as to achieve the optimal convergence effect. Meanwhile, the method is popularized to a Standoff tracking scene of the moving target.
Disclosure of Invention
The invention aims to provide a vector field-based fast Standoff tracking method aiming at the problem of tracking a Standoff target, a new guidance function is constructed to replace the original guidance parameters, and the parameters in the guidance function are determined by using an off-line searching method under the constraint condition of the performance of an unmanned aerial vehicle, so that the fastest convergence speed is achieved, the stable tracking can be directly formed on a Standoff circle, and the problem of stable convergence after repeated fluctuation is avoided. Meanwhile, the invention is improved to be popularized to the situation of moving targets.
The method is suitable for the problem of tracking the Standoff target of a single machine with a single target, and is easy to be popularized to the situation of multiple machines and multiple targets by combining the prior art. The invention comprises the following steps:
1 description of the problems
Setting a fixed target position vector as x under a two-dimensional scenet＝[xt yt]TThere is a shelf at x ═ x y]TThe fixed-wing drone of which the velocity vector is
The heading angle is χ in terms of rdStando target for circle of radiusff tracking. Without loss of generality, the target position vector may be represented as x in the local coordinate system of the targetr＝[xr yr]TIt can also be expressed in polar form by the radial distance r and the azimuth angle θ.
The unmanned aerial vehicle is equipped with a low-order Flight Control System (FCS) to realize stable tracking Control of speed and heading. For guidance of the aircraft, the FCS may track speed commands, turn angle speed commands, and the like.
Wherein, s is unmanned aerial vehicle speed, chi is unmanned aerial vehicle course, chidIn order to be in the required course,
and k is a first-order dynamic time constant of the heading.
2 guidance framework based on vector field
Under a local polar coordinate frame, the vector field-based guidance frame is
Wherein the content of the first and second substances,
s is the speed of the unmanned aerial vehicle, c is the guidance parameter,
is a velocity normalization term.
In the traditional vector field-based Standoff target tracking method, a guidance parameter c is a constant 2, and a corresponding guidance law is
Order to
Represents a compression term whose magnitude characterizes the radial rate of motion of the drone towards the Standoff circle, order
A circular item is represented, the size of which characterizes the tangential velocity of the drone to the Standoff circle. Due to the existence of the speed normalization term, when the flight speed of the unmanned aerial vehicle is unchanged, the larger the guidance parameter c is, the smaller the compression term is, the larger the circular ring term is, and the change is not linear. To improve the convergence speed of the unmanned plane to the Standoff circle and ensure that the unmanned plane keeps r with the targetdIs stable for Standoff tracking, the guidance parameter c should be a function of the radial distance of the drone to the target, and the following condition is satisfied:
1)r＝rdwhen c reaches a maximum value;
2) r → ∞ or r → ∞, c → 0.
Under the local rectangular coordinate frame, the guidance frame based on the vector field is rewritten into
Wherein
Representing the required speed of the drone under the frame.
Under the guidance framework, the course angle of the unmanned aerial vehicle can be further obtained as
The time differential of equation (5) is obtained to obtain a curvature of
By bringing formula (4) and its time derivative into formula (6), the curvature function can be obtained as
3 fast Standoff target tracking method based on vector field
(1) Rapid Standoff target tracking method
Based on the analysis, two types of guidance functions are constructed
Wherein the parameter n is a pending parameter.
The guidance functions all meet the characteristics of the fast Standoff tracking method. Bringing the extracted derivative function and its derivative into formula (7) to obtain a corresponding curvature function of
And
fig. 1 shows the curvature of different guidance methods as a function of the radial distance for different n.
In FIG. 1, the dotted line is
The dotted line is
The chain line is
Solid line is κ2The horizontal dotted line is κ ═ 1/rdThe vertical dotted line is r ═ rd. When the unmanned aerial vehicle is in the Standoff circle or is far away from the Standoff circle, curvatures corresponding to the two types of designed guidance functions are both near a value of 0, so that the unmanned aerial vehicle is ensured to move directly to a target, and the method is obviously superior to the traditional method; the larger the parameter n is, the larger,
and
the longer the distance clinging to the x-axis, the longer the unmanned aerial vehicle has time to radially tend to wander to circle according to the maximum speed, thereby improving the convergence speed.
The unmanned aerial vehicle movement routes corresponding to different parameters n are shown in fig. 2. The vector field constructed by smaller n value makes the target slowly approach the Standoff circle and forms stable tracking (dot-dash line); while a larger value of n causes more area of the vector field to be radially directed, while converging very quickly to the Standoff circle, it requires repeated passes through the Standoff circle to converge steadily (dashed line). The ideal track should both approach the target quickly and track the target stably, i.e. the situation of crossing the Standoff circle (solid line) does not occur, so that for the selection of the n value, an instructive principle needs to be provided to balance the contradiction, and the rapid and stable tracking of the unmanned aerial vehicle is realized.
(2) Selection of optimal parameters
When the curvature function is always within the performance constraint of the unmanned aerial vehicle, the unmanned aerial vehicle can realize the course required by the vector field according to the course control command, and n value as large as possible is selected, namely the optimal parameter is
Wherein κmaxIs the curvature threshold under the performance constraint.
During practical application, the maximum angle of inclination constraint usually exists in the unmanned aerial vehicle, and the maximum value of the angular velocity when the unmanned aerial vehicle turns is limited. When the curvature function is overWhen the vehicle passes the threshold, the vehicle is influenced by the inclination angle constraint, and the unmanned vehicle can turn according to the maximum inclination angle in a certain voyage. A schematic representation of a moving flight path under the influence of aircraft performance saturation constraints is shown in FIG. 3, where rminRepresents the minimum turning radius of the unmanned aerial vehicle, the solid line circle represents the corresponding minimum turning radius circle when the unmanned aerial vehicle turns according to the maximum inclination angle, and the point pinAnd point poutRespectively representing the tangent points when the drone enters and flies out of this circle.
As can be seen from the figure, when the minimum turning radius circle is away from the Standoff circle, the drone needs additional time to converge to the loiter circle; when the n value is increased to a certain degree, a section of arc formed when the unmanned aerial vehicle turns according to the maximum inclination angle is intersected with the Standoff circle, so that stable tracking can be formed after the unmanned aerial vehicle passes through the Standoff circle for a plurality of times, the time for forming stable tracking is prolonged, and even the safety of the unmanned aerial vehicle is threatened. Therefore, the optimal route is that the unmanned aerial vehicle directly forms stable Standoff tracking after turning according to the maximum inclination angle, namely the optimal parameter noptThe minimum turning circle of the unmanned plane is tangent to the Standoff circle.
Maximum turning curvature kappa from aircraft performance conditionsmaxCombining curvature functions for a given guidance function, given a value of n
Point of attainment pinDistance to target rin. The included angle beta between the speed and the radial speed of the unmanned aerial vehicle can be obtained by guidance law
The distance between the center of the minimum circle and the target is
Wherein < rmin,rin< represents rminAnd rinThe included angle therebetween. Using trigonometric function formula and geometric relationship, and substituting formula (2) and formula (12) into the above formula to rewrite
To obtain rouThen, the positional relationship between the minimum turning radius circle and the Standoff circle is easily obtained, when r isou＜δout(rou＞δin) When two circles intersect, the flight path is stable after fluctuation, wherein deltain＝rd-rminAnd deltaout＝rd+rminThe discrimination thresholds are respectively when the initial position of the unmanned aerial vehicle is positioned in the circle and outside the circle. When r isou＞δout(rou＜δin) In time, the two circles are separated (inclusive), the farther apart, the slower the unmanned aerial vehicle converges. r isou＝δout(rou＝δin) And when the two circles are externally tangent (internally tangent), the unmanned aerial vehicle can quickly converge to the Standoff circle and directly form stable tracking, and the corresponding parameters are the optimal parameters.
Will r isouD is taken in (13) because of rinAnd ciAre functions related to the parameter n, and it is difficult to directly obtain a closed-form solution on n. From the foregoing analysis, it can be seen that the larger n, the closer the saturation value of the curvature function is to the Standoff circle, i.e., the closer the minimum turning circle is to the loiter circle, and therefore rouIs a monotone decreasing function of n, and can be selected by off-line searchingou≤δin(rou≥δout) The maximum value of the time parameter n is the optimal parameter nopt。
When the maneuvering capability of the unmanned aerial vehicle is weak, the initial position and the initial course of the unmanned aerial vehicle still cause that the unmanned aerial vehicle cannot design a vector field-based guidance method which not only can quickly converge but also can avoid fluctuation by only adjusting the parameter n. At this moment, can reduce turning radius through reducing unmanned aerial vehicle speed, improve mobility and solve.
In practical application scenes, when the unmanned aerial vehicle starts from the interior of the Standoff circle, the unmanned aerial vehicle is generally used for non-hostile scenes such as regional survey, peripheral monitoring and the like, so that the requirements on convergence speed and stability of a guidance method are not high. When the unmanned aerial vehicle starts from a position far outside the Standoff circle, especially for the situation of enemy targets, the Standoff distance is usually the safe distance, the requirement for the unmanned aerial vehicle to directly form stable Standoff tracking is more urgent, and the unmanned aerial vehicle has important significance for ensuring the unmanned aerial vehicle to safely complete tasks.
In general, the search method to determine the optimal parameter n is time consuming, and the time consumed and the accuracy of the results are closely related to the search interval. When the unmanned aerial vehicle carries out a real-time online task, the Standoff distance is determined, and the maneuvering capacity (speed and maximum steering) of a specific unmanned aerial vehicle is also determined, so that parameters meeting requirements can be calculated and selected off-line according to task requirements before the unmanned aerial vehicle carries out the task.
(3) Modifying parameters when moving an object
When a guidance method of a vector field is used for tracking a moving target, correction factors are usually introduced to correct the moving direction of the unmanned aerial vehicle. Let the correction factor be lambda and the speed of motion of the target be vtAnd the motion vector of the unmanned aerial vehicle under the global coordinate system after correction is vgIf the unmanned aerial vehicle is to move in the local coordinate system of the target according to the movement direction designed in the guidance vector field, the relationship between the movement speed of the target and the corrected speed of the unmanned aerial vehicle is
vg-vt＝λvd (14)
Wherein v isdFor the required velocity in the guided vector field, | vg|＝s，st＝|vtI is the target rate, sr＝|λvdAnd | is the relative rate.
Taking a model of the above formula to obtain a quadratic equation of a unit related to lambda, discarding the impossible negative root, the larger positive root being the correction factor to be obtained, and s being the larger root positivetS, i.e. the drone should maneuver at a greater speed than the target to achieve effective stable tracking.
Fig. 4 shows a schematic diagram of correction factor versus drone velocity correction.The unmanned aerial vehicle moves in the local coordinate system of the target according to the designed movement direction in the guidance vector field by the correction method, and the tracking of the Standoff target is realized. Correction factor is known at vgAnd vtObtaining an extreme value when the two lines are collinear, wherein the value range is
Delta χ is the angle of the unmanned aerial vehicle course change before and after correction, has no directivity, and can be known from figure 4 to have the value range of
In order to ensure that the unmanned aerial vehicle has enough time and space steering when approaching the Standoff circle, the maximum steering change rate is calculated
Minimum turning radius rminRelative speed v between unmanned aerial vehicle and targetr＝vg-vt＝λvd(ii) a Meanwhile, the course of the unmanned aerial vehicle is corrected by the correction factor, so that the corrected < rmin,rinIs greater than rmin,rin＞c＝＜rmin,rin＞d±Δχ (15)
Wherein < rmin,rin＞cAnd < rmin,rin＞dRespectively represent corrected rminAnd rinThe included angle between the two and r given by the original guidance lawminAnd rinThe included angle therebetween.
Scheme 1:
the steering time can be greatly shortened due to the large relative speed of the unmanned aerial vehicle and the target, and the steering space of the unmanned aerial vehicle can be limited due to the large angle correction factor, so that the simplest and direct correction scheme is to select the maximum relative speed srAnd a maximum Δ χ, wherein
max(sr)＝s+st (16)
Scheme 2:
as can be seen from the observation of FIG. 4, when the relative velocity is maximized, vgAnd vtCollinear reversal, at which time Δ χ reaches a minimum value of 0; when Δ χ takes a maximum value, vrAnd vtPerpendicular to each other, sr<s, i.e. substantially srAnd the maximum of Δ χ cannot be taken at the same time. Further, s can be obtained from the formula (14)rThe relationship with Δ χ is as follows
The parameter n may be searched off-line according to the grid points of the relative velocity, while the heading angle is corrected using the corresponding Δ χ calculated by equation (18).
Drawings
FIG. 1: the curve of curvature of different guidance methods as a function of radial distance;
FIG. 2: the unmanned aerial vehicle movement routes corresponding to different parameters n;
FIG. 3: the schematic diagram of the unmanned aerial vehicle movement route under the saturation constraint condition;
FIG. 4: schematic diagram of correction factor to unmanned aerial vehicle speed correction;
FIG. 5: the method implements a flow diagram.
Detailed Description
The present invention is further described in detail with reference to the flow chart of the implementation of the present invention illustrated in fig. 5.
The invention provides a design method of a fast vector field aiming at a specific Standoff target tracking scene, so that an unmanned aerial vehicle can be ensured to be fast converged to a Standoff circle, stable and stable tracking is directly formed, and the situation of repeated fluctuation is avoided.
When multiple unmanned aerial vehicles carry out multitasking, the multitasking can be simplified into a plurality of single-machine single-target subtasks through task planning and target allocation. For a single machine to carry out a Standoff tracking task on a single target, a Standoff distance r needs to be determined according to the task requirementdAnd determining the target position and the initial position of the unmanned aerial vehicle. Meanwhile, according to the type of the unmanned aerial vehicle executing the task, the maximum steering angular speed of the unmanned aerial vehicle is determined
And a cruising speed s.
(1) If the target is a stationary target, let the relative velocity srS, the course angle correction term delta x is 0, and the optimal undetermined parameter n is obtained by the optimal parameter searching methodopt。
(2) If the target is a moving target, determining a target speed stIf option 1 is chosen, let sr＝s+st，
And obtaining n by the optimal parameter searching methodopt(ii) a If scheme 2 is chosen, it is necessary to rely on the range of relative rates s-st,s+st]Setting grid points
According to different grid points
Respectively calculating corresponding delta xj(ii) a And obtaining corresponding optimal parameters by utilizing an optimal parameter searching method
After traversing all the grid points, the optimal undetermined parameter is taken as
In the method, the optimal parameter searching method is used for multiple times, and the algorithm flow is as follows:
step 1: given a guidance function, calculating a minimum turn radius
Determining a search interval Δ n, initializing nopt＝0；
Step 2: let n equal nopt+ Δ n, calculating the curvature function from the guidance function and its time differential according to equation (7) if the maximum curvature is less than
Then n isoptRepeating the step when the value is n; otherwise, carrying out the next step;
and step 3: calculating rinThe angle < r is corrected according to the formula (15)min,rin＞；
And 4, step 4: calculating r according to equation (12)ouWhen r isou≥δoutOr rou≤δinWhen, let noptN and jump to step 2, otherwise noptI.e. the found optimal parameters.
A large number of simulation results show that compared with the second type of guidance function, the first type of guidance function has a better effect, and probably the main reason is that the influence of the first type of guidance function on the guidance law is milder for different parameters n, and when the optimal parameters are searched by using the same search interval, the obtained result is closer to the actual optimal parameters. The first type of guidance function can further improve tracking performance. However, the influence of the difference on the tracking performance is limited, and the second type of guidance function is selected, so that the search range can be reduced, and the search speed can be increased. Therefore, the characteristics of different guidance functions can be combined for flexible selection in practical application.
Further simulation shows that for the same guidance function, the parameters searched by the scheme 2 have faster convergence time and guidance performance, but the calculation complexity of the search process is higher, the calculation complexity is o (mp), and m and p are the grid point numbers of the parameter n and the relative speed respectively. When the maximum relative rate is directly selected by using the scheme 1, the search process for the relative rate can be avoided, so the computational complexity is only O (m). By combining the characteristics of the guidance functions, for a moving target, the tracking performance can be improved by using the scheme 2 and the first type of guidance functions, or the search efficiency can be improved by using the scheme 1 and the second type of guidance functions at the cost of increasing the partial convergence time, and different combinations can be selected according to task requirements in practical application.
Claims (5)
1. The vector field-based fast Standoff target tracking method is characterized in that a guidance function is used for replacing guidance parameters in a ring term, and the guidance function is as follows:
wherein r isdAnd the distance is the Standoff distance, r is the radial distance from the unmanned aerial vehicle to the target, and n is a parameter to be determined.
2. The vector field-based fast Standoff target tracking method according to claim 1, wherein the optimal undetermined parameter is obtained by using an optimal parameter search method, specifically comprising the steps of:
step 1: the Standoff distance r needs to be determined according to the task requirementdDetermining a target position and an initial position of the unmanned aerial vehicle; meanwhile, according to the type of the unmanned aerial vehicle executing the task, the maximum steering angular speed of the unmanned aerial vehicle is determined
And a cruising rate s; determining the relative speed s of the unmanned aerial vehicle relative to the target according to the motion state of the targetrA course angle correction term delta x; given a guidance function, a minimum turning radius r is calculatedminDetermining a search interval Δ n, initializing nopt＝0；
Step 2: let n equal nopt+ Δ n, calculating the curvature function from the guidance function and its time differential if the maximum curvature is less than
Then n isoptIf n, the step is carried out again, otherwise, the next step is carried out;
and step 3: calculating rinCorrection of included angle < rmin,rin＞
＜rmin,rin＞c＝＜rmin,rin＞d±Δχ
Wherein < rmin,rin＞cAnd < rmin,rin＞dRespectively represent corrected rminAnd rinThe included angle between the two and r given by the original guidance lawminAnd rinThe included angle between them; r isinRepresenting point PinDistance to the target;
and 4, step 4: calculating rou
When r isou≥δoutOr rou≤δinWhen, let noptN and jump to step 2, otherwise noptI.e. the optimum undetermined parameter, where deltain＝rd-rminAnd deltaout＝rd+rminThe judgment thresholds are respectively the initial position of the carrier in the circle and the initial position of the carrier out of the circle; r isouIs a monotone decreasing function with respect to n.
3. The vector field-based fast Standoff target tracking method of claim 2, wherein s is set when the target is a stationary targetrThe heading angle correction term Δ x is 0.
4. The vector field-based fast Standoff target tracking method of claim 2, wherein when the target is a moving target, the relative velocity is set to sr＝s+stThe course angle correction term is
Wherein s istIs the target speed.
5. The vector field-based fast Standoff target tracking method of claim 2, wherein when the target is movingAt target, according to the range s of relative velocityr∈[s-st,s+st]Setting grid points
Wherein s istIs the target speed;
according to different grid points
Respectively calculate corresponding deltaxjAnd then obtaining corresponding optimal parameters by using the steps 2-4
After traversing all the grid points, the optimal undetermined parameter is taken as
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