RU2419072C2 - Simulation method of motion trajectories of air objects - Google Patents

Abstract

FIELD: instrument making.

SUBSTANCE: motion trajectory of air object consists of differently directed sections of straight-line movement and transition curves. Each of the curves consists of two branches of cubic parabola, which are adjacent to each other with circular arc or directly combined. The trajectory is pre-set by introducing coordinates of node points of reference broken line outlining the movement trajectory of air object. In initial section of transition curve the trajectory of conjugation of straight-line segments is reproduced with segment of cubic parabola with curvature radius providing smooth (without velocity jumps and acceleration) transition from straight-line section to the beginning of the second section with minimum curvature radius.

EFFECT: enlarging functional capabilities.

6 cl, 8 dwg

Description

The invention relates to location technology and can be used in training simulators for operators of location stations, as well as for functional diagnostic monitoring of location systems.

A known method of simulating the trajectories of motion of air objects [1], which is carried out by manually entering the initial polar coordinates of the object in the form of bearing P ₀ , range d ₀ , course k _about and the initial speed ν _about and the subsequent automatic formation of the trajectory of motion in the form of a straight line, outgoing from the point (P ₀ ; d ₀ ) in the direction of k _about . The signal to the beginning of the maneuver (turn) arrives synchronously with the introduction of a new course of movement k _about and the speed of the object ν _about at the time of entering a new course. As a result, rotation is simulated by pairing two rectilinear multidirectional sections of motion with an arc of a circle whose radius is determined by the rate of change of the course ω _k , which is also set at the moment the maneuver begins.

This method is carried out in a known simulator device (Fig. 1) of radar operators [1], containing a teacher’s console 1, intended for a set of object motion parameters in the form of digital codes, the first output of which is connected to the first input of coordinate transformer 2, designed to calculate current coordinates when simulating the movement of an air object, and the second exit - with the first input of the smoothing unit 3, which turns the jumps in the course and speed of the moving object into smooth movement along an arc of a circle, the second input of which oedinen the first output coordinate converter 2, the output of the smoothing unit 3 is connected to the second input coordinate converter 2; the second output of the coordinate converter 2 is connected to the input of the operator panel 4 with a built-in remote panoramic indicator for tracking and calculating the coordinates of the object.

The known method has the following two main disadvantages. On the one hand, this is an unrealistic simulation of the trajectory, taking into account the kinematics of the maneuver of an air object, when the object (its pilot) experiences instantaneous overload due to a jump in the centrifugal force F _c = mυ ² / R (m and υ are the mass and speed of the air object, respectively), which inevitably arises during the transition from a motion path in a straight line with a radius of curvature R → ∞ to a motion path with a finite radius R _okr . On the other hand, the simulated trajectory is a plane curve, all points of which are located at some conditionally specified height above the earth's surface, which is not typical for real flights of air objects in three-dimensional space.

The disadvantage of the simulator device is also the approximate setting of the values of the motion parameters along the transition curve and the limited accuracy of the possibility of imposing secondary simulated information on the primary radar situation.

The aim of the invention is to expand the functionality of the device simulating the trajectories of airborne objects with the expectation of the formation of the most realistic flight paths in three-dimensional airspace without jumps in speed and acceleration, as well as providing more efficient functional diagnostic monitoring of radar equipment, improving the quality of training of operators.

This goal is achieved by the fact that in the method and device for simulating the trajectories of motion of air objects, it is proposed by manually entering the coordinates of the reference points of the motion path with an indication of the flight speeds at these points and automatically calculate the equations of motion in three coordinates x (t), y (t) , z (t) and speed ϑ (t) immediately after entering the initial data at the operator’s workplace 5 (which replaces the teacher’s console) made on the basis of a PC-like personal computer, then transmit the coefficient nts of the indicated equations of motion to coordinate calculation block 6 (which replaces the smoothing block), implemented as an ADP24PCI module based on the 1892ВМ2Т signal processor manufactured by GUP SPC “ELVIS”, the input of which is connected to the output of the operator’s workstation 5 (Fig. 2), and later in it, in response to a request for information about the current position of the object coming through the external query interface, calculate its Cartesian coordinates and convert them into a polar system in coordinate converter 7, the input of which is connected to the output of the calculation unit and coordinates 6, and the output serves as the output of the device, by substituting the time parameter t in the equations of motion corresponding to the trajectory section to be overcome at time t, and for this it is proposed to represent the trajectory of the movement of an air object consisting of elementary segments in the form of straight segments whose conjugation at an angle between them φ <90 ° is performed with the exception of jumps in speed and acceleration by matching sections in the form of an arc of a circle and two segments of cubic parabolas, on which the radius of curvature R _to smoothly varies from infinite at the junction points with straight sections to the matching radius R _c at the junction points with a section in the form of a circular arc or with the exception of the section in the form of a circular arc for the angle between the aligned straight line segments φ≥90 °.

In the initial section of the transition curve, the conjugation trajectory of line segments is reproduced by the segment of the cubic parabola y = x ³ / 6q with the radius of curvature

обеспечивающим плавный (без скачков скорости и ускорения) переход с прямолинейного участка при х=0 и R_к=∞ на начало второго участка с минимальным радиусом кривизны R_к=R_min.

providing a smooth (without jumps in speed and acceleration) transition from a straight section at x = 0 and R _k = ∞ to the beginning of the second segment with a minimum radius of curvature R _k = R _min .

If the angle between the two line segments defining the direction of rectilinear movements is φ <90 °, the conjugation path of the two line segments is successively divided into three sections: a segment of a cubic parabola, a section of a circular arc with a radius of R _min and a third section in the form of a segment of a cubic parabola with a smooth change the radius of curvature R _k from the value of R _k = R _min to R _k = ∞. At φ≥90 °, the conjugation path of two line segments consists of two segments of cubic parabolas with a smooth decrease for the first segment of the radius of curvature R _к from the value of R _к = ∞ to R _c = R _к at the junction and subsequent increase for the second segment R _к from the values of R _c to R _k = ∞.

Figure 1 presents a structural diagram of a device for simulating motion trajectories (prototype), consisting of a remote control teacher 1, a coordinate transformer 2, a smoothing unit 3 and a remote control 4.

Figure 2 presents the structural diagram of the inventive device, consisting of a workplace of the operator 5, the coordinate calculation unit 6 and the coordinate transformer 7.

The principle of operation of the proposed method and device can be shown as follows.

The operator selects the mode of creating a simulated air situation file from the functional menu at the teacher’s workplace and sets the trajectory of the movement of air objects using the mouse and keyboard. One of the options for implementing the functional menu is given in [2; 3].

The trajectory of the movement of an air object is considered as a section of a smooth (without kinks) spatial curve, extended in time from the moment T ₀ begins to move until its completion T _L , which is formed when the coordinates of the object are fixed at each time point in the absence of speed and acceleration jumps in its movement. Such a curve is defined by the set of support vertices {M _n (x _n , y _n , z _n )} of the broken line outlining the trajectory of the object (Fig. 3) [4].

The input of points M _{n is} carried out in a natural form for the operator {M _n (x _n , y _n , h _n )}, when the height h _{n of an} air object above the Earth's surface acts as the third coordinate (Fig. 4).

The subsequent calculation of the kinematics of motion is performed using a rectangular coordinate system in which the axes OX, OY and OZ are pairwise perpendicular and the value z _n is expressed in terms of height h _n as follows:

- радиус Земли.Where

is the radius of the earth.

The values x _n and y _{n are} also set by the operator relative to the surface of the Earth, however, they are not subjected to transformations due to their insignificant discrepancy with the coordinates in the selected rectangular system XYZ.

For each point M _n, not only its spatial position relative to some selected rectangular coordinate system (the center of which the radar antenna can happen) is set, but also the value of the linear velocity of the object ν _n . The trajectory of the object repeats the reference broken line, coinciding with it only in the central sections of the segments M _n M _{n + 1} . The kink of the reference line should be smoothed out by the correct selection of the maneuver route, taking into account the maximum overload tolerated by the pilot. As a result, an airborne object will never be at any of the points M _n , except for the first and last. Therefore, the value of ν _{n is} interpreted as the speed that the object has at the moment of exit from the transition curve to the straight section M _n M _{n + 1} .

The inventive device calculates the coordinates (x, y, z) of the position of the object at a given point in time t∈ [T ₀ ; T _L ] and generates at the output signals corresponding to the coordinate values.

и

острый) или совмещенных непосредственно (если угол φ_n прямой или тупой).To this end, the trajectory of motion is represented by segments of straight lines and maneuvering sections (Fig. 3), such that each maneuvering section can be adequately represented by a combination of two branches of a cubic parabola, interconnected by an arc of a circle (if the angle φ _n between the directions

and

acute) or combined directly (if the angle φ _{n is} straight or obtuse).

Thus, the entire trajectory is divided into adjacent segments of three types: rectilinear (DS), parabolic (PS) and circular (RS). The alternation of segments occurs, as a rule, cyclically in the order: K → DS → PS → RS → PS → K, however, in some specific cases, the DS and RS segments can be excluded. In this case, the selection of the boundary points of the segments is made so as to ensure a smooth line of movement of the object without jumps in speed and acceleration.

For each of the three types of segments of the trajectory, a law of motion is formulated, which allows one to determine the spatial position of the object, as well as its radial velocity at a given point in time t. Each of the three laws is applicable only for its type of segment and has in its mathematical notation both time-constant coefficients and parameters depending on t. Therefore, before calculating the position of the object on the trajectory within the given segment, constant coefficients are calculated at the operator’s workplace 5 and stored in the computer memory. Such an operation is carried out for each segment, as a result of which the main calculation table is formed.

Table 1 The coefficients of the equations of motion of the object along the segments of the trajectory Segment number Segment type T _n, s T _to , s A _x And _at A _z B _x B _y B _z C _x C _y C _z ω ¹ , rad / s ε ¹ , rad / s ² ψ ₀ ² , glad h ₀ ² 0 ... N-1 ¹ Defined only for circular and parabolic segments ² Defined only for parabolic segments

where T _n and T _to are the moments of the beginning and end of the movement of the object along the segment, which allow us to identify exactly the segment along which the object moves at time t;

ω is the angular velocity;

ε is the angular acceleration.

The values of ω and ε are determined only for curved segments of the trajectory.

To calculate the radial velocity and coordinates of the object at a given point in time, knowledge of the values taken from the column of the table for which the condition T _n ≤t <T _k is satisfied is sufficient.

2. The calculation formulas for determining the coordinates of the object at a given point in time t

2.1 Rectilinear path segments

For straight segments, the calculation of the current values of coordinates and radial velocity is performed according to the formulas:

The values of the coefficients of table 1 for formulas (1a) - (1g) are taken as follows:

Here:

Δx ₀₁ = x _n -x _n-1 , Δy ₀₁ = y _n -y _n-1 , Δz ₀₁ = z _n -z _n-1 is the distance from the point M _n-1 to the point M _n in the projection on the x axis, y and z, respectively.

- расстояние от точки M_n-1 до точки M_n.

- the distance from the point M _n-1 to the point M _n .

Similarly:

Δx ₀₂ = x _{n + 1} -x _n , Δy ₀₂ = y _{n + 1} -y _n , Δz ₀₂ = z _{n + 1} -z _n is the distance from the point M _n to the point M _{n + 1} in the projection on the x axis, y and z, respectively.

- расстояние от точки M_n до точки M_n+1.

- the distance from the point M _n to the point M _{n + 1} .

- угол между направлениями движения.

- the angle between the directions of motion.

и R_min определяются в зависимости от характера переходной кривой на предшествующем участке поворота (соответствующем т. M_n-1) и влияют на вид траектории, огибающей точку M_n. Поскольку отрезок ломаной линии M_n-1M_n является для двух рассматриваемых участков общим и длина его ограничена, радиус кривизны поворота (с учетом максимальной переносимой перегрузки) вблизи т. M_n подбирается таким, что точка начала переходной кривой

не заходит за точку

и не оказывается ближе нее к вершине M_n-1 (см. фиг.5).Quantities

and R _{min are} determined depending on the nature of the transition curve in the previous section of the rotation (corresponding to the so-called M _n-1 ) and affect the shape of the path enveloping the point M _n . Since the segment of the broken line M _n-1 M _n is common for the two sections under consideration and its length is limited, the radius of curvature of rotation (taking into account the maximum tolerated overload) near t. M _{n is} selected such that the starting point of the transition curve

does not go beyond the point

and does not appear closer to the vertex M _n-1 (see Fig. 5).

To avoid discontinuity of the trajectory, the calculation is as follows. First, the maximum speed is determined from two given nominal speeds at points M _n-1 and M _n : ϑ _max = max (ϑ _n-1 , ϑ _n ). Then the nominal (comfortable) level of overload is selected, expressed as the number of accelerations of gravity, for example, n _{c_nom} = 0.1, and the minimum radius of curvature of rotation is calculated by the formula:

:The nominal value of the minimum radius of curvature corresponds to

:

, возможна ситуация, проиллюстрированная фиг.5б. Для ее исключения осуществляется проверка условий:When the value of S _b equal to

, a situation illustrated in figb. To exclude it, the following conditions are checked:

.

.

соответственно, иначе расчет производится следующим образом:If both conditions are satisfied, then R _min and S _b are taken equal to R _{min_nom} and

accordingly, otherwise the calculation is as follows:

,

,

.

.

длиной S₂₁/2 позволяет получить заявленный результат. Если в ходе дальнейших вычислений окажется, что поворот на опорной точке M_n+1 задан более крутым и для его осуществления требуется участок

, больший чем S₂₁/2, то в этом случае недостаток пространства для маневра компенсируется более резким поворотом с увеличением перегрузки.Section reservation

length S _21/2 allows you to get the declared result. If in the course of further calculations it turns out that the rotation at the reference point M _{n + 1 is} set steeper and its implementation requires a section

greater than S _21/2 , then in this case the lack of space for maneuver is compensated by a sharper turn with an increase in overload.

, показывает расстояние от точки M_n до ближайшего края прямолинейного отрезка движения, выраженное в числе R_min. The value of K (φ _n ) used in the calculation

, shows the distance from the point M _n to the nearest edge of the rectilinear motion segment, expressed as R _min.

2.2 Transition curve

до точки

при каждой вершине M_n опорной ломаной линии объект движется по переходной кривой. Она, как было условлено, может быть представлена совокупностью двух ветвей параболы, которые стыкуются между собой при φ_n≥90°, а при φ_n<90° - совмещаются посредством дуги окружности. При движении объекта по сегменту кубической параболы воспроизведение текущих значений координат в функции времени производится замещением дуги кубической параболы дугой окружности, совмещенной с ней в трех точках, с представлением значений координаты x через параметрическое представление координаты x(t) окружности и выражением значений координаты y(t) через координату x(t) в соответствии с уравнением кубической параболы. На фиг.6 представлены оба вида сопряжения: двухсегментное (а) и трехсегментное (б).On the trajectory from the point

to the point

at each vertex M _{n of the} reference polyline, the object moves along a transition curve. As agreed, it can be represented by a combination of two parabola branches that are joined together at φ _n ≥90 °, and at φ _n <90 ° - they are combined using an arc of a circle. When an object moves along a segment of a cubic parabola, the current coordinate values are reproduced as a function of time by replacing the arc of the cubic parabola with an arc of a circle combined with it at three points, with the representation of the x coordinate values through the parametric representation of the x coordinate (t) of the circle and the expression of the y coordinate coordinates (t ) through the coordinate x (t) in accordance with the equation of the cubic parabola. Figure 6 shows both types of pairing: two-segment (a) and three-segment (b).

In both cases, the transition curve is symmetric with respect to the bisector of the angle φ _n and does not form kinks at the points where the segments coincide.

The calculation of the kinematics of the object’s movement on a parabolic section of the trajectory is carried out by replacing the parabola branch with an arc of a circle, which is combined with the parabola at the extreme points and in the middle. However, the coordinates are recalculated in such a way that the object does not deviate from the path defined by the parabola. This result is achieved by calculating the x coordinate of the position of the object on a circular path and then substituting it into the expression for calculating the coordinate of the point belonging to the parabola.

The calculation of the movement of an object on each such segment is carried out in a local coordinate system associated with it. This system is selected for a whole section of maneuver (turn) with sections of rectilinear motion adjacent to the bend trajectory.

и перпендикулярная ей ось O'Y', направленная в сторону движения объекта (фиг.7). Началом координат служит точка M_a, в которой начинается переход на криволинейный участок.The transition curve lies in the plane M _n-1 M _n M _{n + 1} , and the natural coordinate system in which the transition curve has the simplest form is the O'X 'axis, which coincides with the vector

and the axis O'Y 'perpendicular to it, directed towards the movement of the object (Fig.7). The origin is the point M _a at which the transition to the curved section begins.

The trajectory of motion calculated in the local coordinate system is then translated into coordinates uniform for the entire trajectory (XYZ system, in which reference points are specified). For this, the coordinate transformation coefficients (directing cosines of the axes) are calculated. For the initial section of the transition curve (to the bisector of the angle φ _n ):

To calculate the motion along the final section of the transition curve (behind the bisector of the angle φ _n ), this fragment of the trajectory undergoes additional affine transformations, therefore, the coordinate transformation coefficients are different for it:

2.2.1 Circular segments

The circular segment is added to the transition curve at small rotation angles (φ _n <90 °) in order to prevent a significant distance from the vertex M _{n of} the junction point M _{c of} two parabolic segments (Fig. 8).

The movement in a circular segment is calculated by the formulas:

Where

The values of the coefficients used are the same as for the straight section.

2.2.2 Parabolic segments

For parabolic segments, the following calculation formulas apply:

Where

The values of the coefficients for parabolic sections differ for the initial and final sections of the transition curve, and also depend on the method of its construction (two- or three-segment).

For φ _n ≥90 ° the following auxiliary quantities are determined:

- the ratio of the radius of the circle replacing the cubic parabola to the minimum radius of curvature R _min :

;

;

- maximum movement along the parabola:

- the angle between the axis O'Y 'and the radius vector from the center of the replacement circle to the transition point (M _a ):

.

.

Calculation of the kinematics of movement is accompanied by verification of overloads that inevitably arise when an object moves along a curved section of the trajectory (whether it is a circular or parabolic segment). For this, the maximum centripetal acceleration is calculated:

.

.

To calculate the linear acceleration, the total distance traveled along the path enveloping the peak M _n (transition curve and the preceding portion of the rectilinear motion) is calculated:

Where

.

.

The total load tested by the facility is calculated by the formula:

.

.

If a _total <8g, then the calculation continues, otherwise the path (vertex M _n ) is rejected.

At the moment the device enters the coordinate calculation mode, the coefficients of table 1 calculated at the operator’s workplace 5 are transferred to the coordinate calculation unit 6, which implements the calculations according to formulas (1a) - (1d), (2a) - (2d), (3a) - (3d) with the substitution of the time parameter t in them. Requests for the calculation of coordinates are received in the coordinate calculation unit 6 through the interface of the information transmission channel with an interval of 5-10 ms.

The output of the device receives the coordinates translated by the coordinate transformer 7 into the polar system, the pole of which is the installation of the radar, and the angle is counted, for example, from the north direction. The calculation is carried out in accordance with the expressions:

;range:

;

azimuth (counting from the northward direction clockwise):

,

,

Where:

,

,

φ (t) = φ (t) + 2π for φ (t) <0;

elevation angle (counting from horizontal):

,

.

,

.

Literature

1. AS No. 991479 of the USSR. Simulator operator location stations. A.V. Gusev. Publ. 1983 Bull. Number 3.

2. Chekushkin VV, Yurin OV, Bulkin VV Implementation of computational processes in information-measuring systems: Monograph. Murom: Publishing house-printing center MI VlSU. 2005 - 158 p.

3. Yurin OV, Chekushkin VV, Dudarev V.A. Automated radar control system. Devices and systems. Control. The control. Diagnostics 2004, No. 1, pp. 18-21.

4. Certificate of state. registration of a computer program No. 20099611848 dated 04/09/2009 "Program for smoothing the trajectories of airborne objects for radar control systems (Trajectory)." Application No. 20099610537 dated February 16, 2009.

Claims (6)

1. A method of simulating the trajectories of motion of airborne objects by manually entering the initial polar coordinates of the object in the form of bearing P ₀ , range d ₀ , course k _rev , initial speed v _rev and the subsequent automatic formation of the trajectory of motion in the form of a straight line starting from a point (P ₀ ; d ₀₎ in the direction of k _on, until the signal proceeds to the top of maneuver (turn), synchronous with the input of a new rate of motion k _on and the object velocity v _on the time of entering the new program, with simulated maneuver (turn) by coupling two rectilinear s divergent portions motion arc of a circle whose radius is determined by the speed changing rate ω _k, which is also given at the beginning of the maneuver, characterized in that the simulation trajectories of objects is carried out by manually entering coordinates of control points of the path of movement indicating the flight velocities at these points and automatic calculation of the equations of motion along the three coordinates x (t), y (t), z (t) and speed v (t) immediately after entering the initial data at the operator’s workplace with subsequent transfer of the coefficient Ienti of the indicated equations to the coordinate calculation unit, in which, in response to a request for information on the current position of the object, its Cartesian coordinates are calculated by substituting the time parameter t into the equations of motion corresponding to the trajectory section to be overcome at time t, for which the trajectory of the movement of the air object appears to consist of elementary segments in the form of straight lines, the conjugation of which at a value of the angle between them φ <90 ° is performed with the exception of speed jumps and acceleration by matching sections in ide of an arc of a circle and two segments of cubic parabolas, on which the radius of curvature R _k smoothly changes from infinite at the junction with straight sections to the radius of matching R _c at the junction with a segment in the form of a circular arc or with the exception of the section in the form of a circular arc at an angle between the coordinated line segments φ≥90 °, the Cartesian coordinates of the air object calculated in the coordinate calculation block at time t are then converted into polar coordinates in the coordinate converter. 2. The method according to claim 1, characterized in that in the initial section of the transition curve, the conjugation path of line segments is reproduced by a segment of a cubic parabola y = x ³ / 6q with a radius of curvature

providing a smooth (without jumps in speed and acceleration) transition from a rectilinear section at x = 0 and R _k = ∞ to the beginning of the second section with a minimum radius of curvature R _k = R _min . 3. The method according to claim 1, characterized in that when the angle between two straight segments defining the direction of rectilinear movements, φ <90 °, the conjugation path of two straight segments is sequentially divided into three sections: a segment of a cubic parabola, a section of a circular arc with a radius R _min , and the third section in the form of a segment of a cubic parabola with a smooth change in the radius of curvature R _k from the value of R _k = R _min to R _k = ∞. 4. The method according to claim 1, characterized in that when the angle between two segments of lines defining the direction of rectilinear movements, φ≥90 °, the conjugation path of two segments of lines consists of two segments of cubic parabolas with a smooth decrease for the first segment of the radius of curvature R _to from the value of R _to = ∞ to R _c = R _to at the junction and a subsequent increase for the second segment R _to from the value of R _c to R _to = ∞. 5. The method according to claim 1, characterized in that to reproduce the trajectory of movement along an arc of a circle as a function of time t in a rectangular coordinate system, the current values of the coordinates of the object are represented by the parametric equations of the arc of a circle as a function of time. 6. The method according to claim 1, characterized in that when the object moves along a segment of a cubic parabola, the current coordinate values are reproduced as a function of time by replacing the arc of the cubic parabola with an arc of a circle combined with it at three points, with the representation of the x coordinate values through a parametric representation of the coordinate x (t) of the circle and the expression of the values of the coordinate y (t) in terms of the coordinate x (t) in accordance with the equation of the cubic parabola.

Images