JP2002308190A - Optimizing system for four-dimensional motion route and its optimizing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To establish an art instantaneously deducing a four-dimensional solution of an optimal flying route. SOLUTION: This optimizing system is constituted of a four-dimensional navigation unit 1 and an optimal solution search unit 11. The four-dimensional navigation unit 1 deduces physical evaluation functions Ff and Ft with four-dimensional initial setting coordinates X0j and three-dimensional initial setting speed V0j set to variables according to inverse dynamics. The optimal solution search unit 11 is found by searching optimal solutions of the evaluation functions Ff and Ft. A single solution can be obtained from numerous solutions by the combination between the calculation of the inverse dynamics and an optimizing calculation. Through various optimizing methods for the optimizing calculation are known, an appropriate optimization solution can be adopted based on a property of emergency at that time in points of convergence speed and a single solution. In a control such as an aircraft control with fewer variables, a solution to be described later is the most effective. This method can instantaneously deduce the four-dimensional solution of the optimal flying rout of the minimum fuel and the shortest flying time and automate the flying control in emergency in particular.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for optimizing four-dimensional navigation and a method for optimizing the system.

[0002]

2. Description of the Related Art The motion path between two points is innumerable in space. Furthermore, there are innumerable spatially defined movement paths in time. One four-dimensional motion path is selected from the innumerable motion paths based on the remaining fuel amount and the motion / movement time. The choice of the motion path by the pilot is not the optimal solution. In an emergency situation such as a sudden change in the weather or a fuel shortage due to fuel disposal or the like, it is required that the optimal flight route solution be instantaneously derived, especially in an emergency, without depending on the pilot's empirical judgment. Optimality is a physical, economic property such as safety, minimum time, and minimum fuel consumption.

[0003]

SUMMARY OF THE INVENTION An object of the present invention is to provide a four-dimensional navigation optimizing system and a method for optimizing a technique for instantaneously deriving a four-dimensional solution of an optimal flight path. Is to provide.

[0004]

Means for solving the problem are described as follows. The technical items appearing in the expression are appended with numbers, symbols, and the like in parentheses (). The numbers, symbols, and the like are technical items that constitute at least one embodiment or a plurality of the embodiments of the present invention, in particular, the embodiments or the examples. Corresponds to the reference numerals, reference symbols, and the like assigned to the technical matters expressed in the drawings corresponding to the above. Such reference numbers and reference symbols clarify the correspondence and bridging between the technical matters described in the claims and the technical matters of the embodiments or examples. Such correspondence / bridge does not mean that the technical matters described in the claims are interpreted as being limited to the technical matters of the embodiments or the examples.

[0005] The optimization system for four-dimensional navigation according to the present invention comprises a four-dimensional navigation unit (1) and an optimum solution search unit (11). The four-dimensional navigation unit (1) performs a physical evaluation function (Ff, Ff) using the four-dimensional initialization coordinates X0j and the three-dimensional initialization speed V0j as variables.
t) is derived according to the inverse dynamics. The optimum solution search unit (11) searches for and obtains an optimum solution of the evaluation function (Ff, Ft). By combining the inverse dynamics calculation and the optimization calculation, a single solution can be obtained from an infinite number of solutions. Although various optimization methods are known for the optimization calculation, an appropriate optimal solution can be adopted based on the nature of the emergency at that time in terms of convergence speed, single solution, and the like.
For control with a small number of variables, such as aircraft control, the solution described below is most effective.

The countless flight paths satisfying the three-dimensional position coordinates and time of two four-dimensional points (or multiple points) and the speeds of the two points at the time are represented by three-dimensional position coordinates, time and Includes the optimal solution (single) of the evaluation function with speed as a variable. The momentary variable values of the flight path correspond to the momentary thrust and attitude angle according to the equation of motion. The optimal solution is
Gives four-dimensional two-point thrust and attitude angle. By such a solution, the optimal flight is calculated in real time, and in the event of a fuel shortage such as fuel disposal, to guide the aircraft safely and land safely at the nearest airport regardless of the pilot's judgment. Can be.

The four-dimensional initial setting coordinates X0j are four-dimensional coordinates (t01, x01, y01, z01) of the guidance start time.
And the four-dimensional coordinates (t02, x02, y0) of the guidance end time.
2, z02). The three-dimensional initial setting speed V0j is a three-dimensional speed (vx01, v
y01, vz01) and the three-dimensional speed (v
x02, vy02, vz02).
In this case, the guidance end time is a time when the vehicle reaches the air near the start end of the runway. The speed at that time is determined by the runway of the airport and the type of aircraft.

[0008] The optimal solution of the evaluation function is an optimal solution that minimizes the minimum fuel consumption solution and the weighted sum of the fuel consumption and the flight time, or the minimum solution of the flight time and the weighted sum of the fuel consumption and the flight time. This is the optimal solution to be minimized. It is preferable that these optimal solutions are derived simultaneously, and it is often preferable to select which of the solutions is artificial.

The optimum solution search unit (11) gradually narrows the range of variables including the optimum solution by changing the search area of the solution stepwise. Such a solution is called Ta
This is a known solution called the bu-Search method. It is practically very significant that such a purely mathematical method is applied to the physical control of aircraft control (the number of variables is small).

[0010] The four-dimensional navigation unit (1) includes a command generation unit (5) together with an inverse dynamics calculation unit (2). Command generation unit (5)
Is the four-dimensional initial coordinate X0j and the three-dimensional initial speed V
The above-mentioned variables are converted into a three-dimensional attitude angle and a thrust on a motion path connecting each of 0j and 0j to generate a drive signal of a mechanical element corresponding to the three-dimensional attitude angle and the three-dimensional thrust. The mechanical elements are a steering device for controlling the attitude of the fuselage, a fuel supply device for controlling the engine speed, and the like. At the time of landing, it is particularly important that the attitude of the aircraft is determined. The attitude of the aircraft at the time of landing and at the start of guidance matches the three-dimensional velocity (velocity vector) of the aircraft on a coordinate system fixed to the aircraft. The coordinate transformation between the runway fixed coordinate system and the aircraft fixed coordinate system is calculated according to a coordinate transformation matrix.

The method for optimizing four-dimensional navigation according to the present invention is as follows.
Setting four-dimensional two points and the three-dimensional velocity of the four-dimensional two points as initial conditions; and performing inverse dynamics on the basis of the initial conditions, and using the four-dimensional two points and the three-dimensional velocity as variables, from moment to moment. It consists of calculating a three-dimensional attitude angle and a three-dimensional thrust, determining an evaluation function using the three-dimensional attitude angle and the three-dimensional thrust as variables, and obtaining an optimal solution of the evaluation function. When finding the optimal solution, the above-described convergence solution is applied.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Corresponding to the drawings, an embodiment of a four-dimensional navigation optimization system according to the present invention comprises a four-dimensional navigation unit and an optimization unit. Part 4
The three-dimensional navigation unit 1 includes an inverse dynamics calculation unit 2 as shown in FIG. When the four-dimensional motion path 3 is initially given, the inverse dynamics calculation unit 2 calculates the four-dimensional motion data (acceleration with time, etc.) 4 based on the motion equation. The four-dimensional navigation unit 1 further includes a command generation unit 5. The four-dimensional motion data 4 output by the inverse dynamics calculation unit 2 is input to a command generation unit 5. The command generation unit 5 positions a moving object (for example, a flying object such as an aircraft that is a flying object in the atmosphere and a spacecraft that is a flying object outside the atmosphere) on the four-dimensional movement path 3 based on the four-dimensional movement data 4. A motion control (steering, steering) command 6 is generated. The four-dimensional navigation unit 1 further includes an evaluation simulator 7. The exercise control command 6 is input to the evaluation simulator 7. The evaluation simulator 7 calculates and outputs an evaluation value 8 based on the exercise control command 6.

The optimizing unit 9 has an optimum solution searching unit 11. The evaluation value 8 is the optimization unit 9
Is input to The optimum solution search unit 11 calculates the feedback gain used for calculating the three-dimensional target speed vector and
An optimal solution for minimizing the evaluation value 8, which is the value of the evaluation function using the dimensional coordinate vector as a variable of the optimization problem, is derived. The optimal solution search unit 11 is an initial position setting input line that initially gives the four-dimensional initial setting coordinates (t0j, x0j, y0j, z0j) 12 and the three-dimensional velocity of the four-dimensional motion path 3 to the four-dimensional motion path 3. have. The optimal solution search unit 11 further calculates the initial evaluation value 13
1 is provided with an initial evaluation value setting input line which is initially given to 1. j is 0 to n.

In the four-dimensional movement path 3, four-dimensional set coordinates (t, x, y, z) 12, which are essential passing points, are initially inputted. As the four-dimensional set coordinates (t, x, y, z) 12, control start set coordinates (t00, x00, y00, z00) for starting motion control of a moving object during navigation and motion control of the moving object are described. Control end set coordinates (t0 to end)
n, x0n, y00n, z0n) (e.g., runway start coordinates corresponding to a moving object on the verge of landing) at least initially, and further in the middle of a finite point on a motion path connecting both coordinates. Set coordinates (t0j, x0j, y0j, z0
j) is initially included. These coordinates are hereinafter referred to as four-dimensional initial coordinates (way points) (t0j, x0j, y0).
j, z0j).

Each unit has the following mathematical functions. Inverse dynamics calculation unit 2: Inverse dynamics calculation unit 2 has four-dimensional initialization coordinates (t0j, x0
(j, y0j, z0j) 12 (or the four-dimensional motion path 3), and includes a motion path generation unit 14 that performs spline interpolation to generate an initial motion path. The dynamics uniquely determines a four-dimensional motion path when physical and geometric initial conditions (four-dimensional position and external force) are given to the dynamic system. In the case where the motion path is initially given, the four-dimensional inverse dynamics cannot uniquely give the physical (mechanical) initial condition (including the momentary initial condition) of the dynamic system. The four-dimensional inverse dynamics in which the time is specified according to the three-dimensional motion position is the physical initial condition of the dynamical system if the four-dimensional motion path is initially given and the necessary degree of interpolation is performed. (Including the initial conditions every moment) can be uniquely given within the required accuracy range, but the physical initial conditions every moment cannot be uniquely determined based on the four-dimensional positions of the two points. Exist innumerably. Innumerable solutions are expressed mathematically using four-dimensional coordinates as variables. Of the myriad solutions, the optimal solution may be limited to one or more finite poles. The optimal solution includes a physical optimal solution and a geometric optimal solution. The minimum fuel consumption solution, exemplified as a physical optimal solution, is important for aircraft control. The minimum time solution, exemplified as a geometric optimal solution, is important for aircraft control. Derivation of the optimal solution is
The search is performed by the optimum solution search unit 11 described later.

The inverse dynamics calculation unit 2 includes a four-dimensional initial coordinate (t0j, x0j, y0j, z0j) 12, which is a given four-dimensional target motion path, and a given three-dimensional initial velocity vector (vx0j, vy0j,
vz0j) 13 ′ and the physical condition for each moment corresponding to the four-dimensional motion path, which is the solution of the three-dimensional velocity at the target position, is calculated. Inverse dynamics calculation unit 2
Are the four-dimensional initial coordinates (t0j, x0j, y0j, z
0j) 12 and the three-dimensional initial velocity vector (vx0j,
vy0j, vz0j) 13 'as a known number, and according to the coordinate transformation matrix relational expression (transformation matrix between the machine fixed coordinate system and the earth fixed coordinate system) and the equation of motion, the three-dimensional position of the moving object at every moment is calculated. Targets three-dimensional target attitude angles (three-dimensional geometric vectors with four-dimensional coordinates as variables) and instantaneous three-dimensional target thrusts (corresponding to three-dimensional acceleration with four-dimensional coordinates as variables) of moving objects. Calculate as a value. In the target motion path, the tracking error can be compensated by the PD control.

Command generation unit 5: The three-dimensional target attitude angle and the three-dimensional target thrust correspond to mechanical elements of a moving object. The mechanical element is a device that generates an operating force such as an engine output and a steering control force (a hydraulic pressure and a hydraulic pressure amount for driving the wing). An electric signal (including an electric signal corresponding to the steering force of the pilot) for controlling the driving of the device that realizes such an operation force is referred to as a motion control (steering) command 6 as described above.

Evaluation simulator 7: A time delay always occurs between the time of generation and output of a control command and the actual effective movement control time of a moving object. Evaluation simulator 7
In a time coordinate system incorporating such a time delay, a three-dimensional target speed vector corresponding to the motion control command 6 is numerically integrated, and the position, speed, angle of attack, and sideslip angle of the moving object are obtained by calculation. . The three-dimensional target velocity vector is 3
It is obtained by minute minute integration of the dimensional target acceleration vector every moment. The trajectory of a moving object such as an aircraft is uniquely determined if its instantaneous position, speed, angle of attack, and sideslip angle are determined. As a preferred method of the integration, Ru
The nge-Kutta-Gill method is known. The position, speed, angle of attack, and sideslip angle (hereinafter referred to as evaluation target value variables) of the moving object are evaluated according to the following criteria.

The angles of attack and sideslip do not exceed the limits.・ The load multiple does not exceed the limit.・ The position is not below the ground.・ Possible to land when landing.・ Tracking error is within the allowable range.

Optimal solution search unit 11: Tabu-Search is known as a suitable optimization search method. This known method, especially the optimization problem search method known as the R-Tabu method, uses the initial point (starting point) as the center point,
A search area group whose width is reduced in geometric progression is set, a random search is performed in each area, and the best solution among the solutions corresponding to the search points in all areas is determined as the next initial solution (starting solution). Is a purely mathematical solution that seeks a global optimal solution.

In this problem of minimizing the value to be evaluated, the evaluation simulator 7 uses a three-dimensional initial setting velocity vector (vx
0j, vy0j, vz0j) The value of the feedback gain used for calculating 13 'and the previously described four-dimensional initial coordinates (way points) (t0j, x0j, y0j, z0j)
12 is a function having 12 as a variable. The evaluation function is expressed as follows: F = F (X0j, V0j) X0j = t0j, x0j, y0j, z0j V0j = vx0j, vy0j, vz0j As the evaluation functions, the fuel consumption function Ff and the flight time function F
t is important. Ff = Ff (X0j, V0j) Ft = Ft (X0j, V0j)

Tabu, a solution for finding the optimal solution of the evaluation function
The -Search method has mathematical properties with stable convergence, and is superior in terms of solution convergence to other known trajectory optimization methods, especially when the number of variables to be handled is small. It is known.

Variables of the function to be evaluated (X0j, V0j)
Is equivalently converted into variables of the attitude angle and the thrust based on the equation of motion. From the attitude angle and the thrust, the fuel consumption and the exercise elapsed time are represented by variables. The evaluation target values are fuel consumption and exercise elapsed time. An evaluation function that describes an evaluation target value is represented by two variables: attitude angle and thrust. As described above, the attitude angle and the thrust are represented by the velocity vector and the four-dimensional coordinates.

The parameters set by the R-Tabu method include a reduced value (parameter for converging to an optimum solution) L of a divided region divided in geometric series, a number r of regions, and a search in each region. This is the number of searches C to be performed. The R-Tabu method is basically a random search method, and is excellent in that a blind search is improved by dividing a search region into multiple regions having different sizes. The algorithm for this is as follows.

Step S1: k = 1 Step S2: initial point xk, initial temperature T0, number of regions r,
From the count number C and the step reduction value (ratio) L, an area set H is obtained. Where a range of x is represented by [a, b], the set H is a center point _{xk, H = {h 1,} h 2, ···, h r} h 1 = b-a h i = h _i−1 / L (i = 2, 3,..., r).

Step S3: Region hi (i = 1, 2,...)
.., R), a random walk search is performed up to the count number C. Specifically, the base point is x0, the search direction and the step width are randomly selected in the region of hi, and the variable yi for improving the evaluation function within the count C is stored. Step S4: A variable yi that maximizes (or minimizes) the evaluation function is selected from all the regions H and is set as yk.

Step S5: k = k + 1 Return to step S2.

Example of Simulation: The case where an aircraft flying around an airport makes an emergency landing at the airport is considered as follows. If the aircraft has sufficient remaining fuel and the aircraft will land at the airport in the shortest time (case 1), if the remaining fuel is small and the aircraft will land in the shortest time (case 2a), the remaining fuel is low and the minimum fuel In the case where the landing is performed (case 2a), three cases are considered. For each case, the flight path (the previously described movement path) and the command are determined.

The attitude angle command is an Euler angle of the body coordinate system with respect to the inertial coordinate system. Jet engines have a time lag with respect to the actual thrust command. The flight conditions are shown in the following table.

North East Down Initial position (m) 2000 18000 1000 Runway position (m) 0 0 0 Initial speed (m / s) 20 180 0 Landing speed (m / s) 167 0 1

The remaining fuel and optimization targets are shown in the following table.

Interpretation of Case 1: FIG. 2 shows the variation of the three elements of the Euler angle of Case 1 by a solid line, a short broken line, and a long broken line, respectively. FIG. 3 shows changes in thrust of the two engines of Case 1 by solid lines and broken lines, respectively.
FIG. 8 shows the speed, fuel consumption, and three-dimensional flight path for each of the three cases. In case 1,
Immediately after the guidance starts, the bank angle is set to the full limit (30 degrees), and the nose is immediately turned to the runway direction. As shown in FIG. 3, the maximum thrust is obtained up to 80 seconds, and as shown in FIG. 8, the speed is increased as much as possible at a constant (smooth) acceleration. It is interpreted that it is decelerating in reverse symmetry. As shown in FIG. 10, the vehicle smoothly moves on a route close to the shortest line, and no large maneuver is seen. As shown in FIG. 9, the fuel consumption is high. The required time is 138 seconds.

Interpretation of case 2a: As shown in FIG. 5 and FIG. 9, the fuel is well distributed in time, but the maneuver is running out of fuel, and as shown in FIG. It cannot be denied that there is a risk of danger because the speed is below the target speed (168 m / s). Such a calculation result is interpreted that the optimal solution search unit 11 has made an unavoidable determination to satisfy the strict requirement of landing in a shortest time with a small amount of remaining fuel.
The required time is 148 seconds.

Interpretation of case 2b: As shown in FIG. 6, after starting the guidance, the nose is gradually turned toward the runway without a large bank. As shown in FIGS. 7 and 9,
The engine was not used until 220 seconds, and thrust was generated during the last 50 seconds or so. Because we do n’t run out of fuel,
Although landing is safer than in case 2a, the required time is twice as long as in case 1 and case 2a.

[0035]

The optimization system and the optimization method of the four-dimensional navigation according to the present invention optimize the evaluation obtained by the inverse dynamics, thereby realizing the real-time operation of the aircraft regardless of the pilot's judgment. The exercise control can be made more secure. As an optimal solution derivation method, Tabu
If the -Search method is adopted, the optimum solution can be obtained in real time with higher accuracy without omission.

[Brief description of the drawings]

FIG. 1 is a system block diagram showing an embodiment of a four-dimensional navigation optimization system according to the present invention.

FIG. 2 is a graph showing a real-time attitude angle.

FIG. 3 is a graph showing real-time thrust.

FIG. 4 is a graph showing a posture angle of another case in real time.

FIG. 5 is a graph showing thrust in another case in real time.

FIG. 6 is a graph showing a posture angle of still another case in real time.

FIG. 7 is a graph showing the thrust of still another case in real time.

FIG. 8 is a graph showing speed in three cases in real time.

FIG. 9 is a graph showing fuel consumption in three cases in real time.

FIG. 10 is an oblique projection showing three-dimensional flight paths in three cases.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 ... Four-dimensional navigation unit 5 ... Command generation unit 11 ... Optimal solution search unit Ff, Ft ... Physical evaluation function

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Masanobu Mizoguchi 1 Ishizumi, Iwatsuka-cho, Nakamura-ku, Nagoya-shi, Aichi Prefecture Inside the Industrial Equipment Division of Mitsubishi Heavy Industries, Ltd. Nagoya Guidance & Propulsion System Works, Mitsubishi Heavy Industries, Ltd. (72) Inventor Shinji Suzuki 2-17-7-101 Koishikawa, Bunkyo-ku, Tokyo (72) Inventor Satoshi Ueda 1-15-12-202, Gotenyama, Musashino-shi, Tokyo F-term (reference) 5H004 GA29 GB13 KC12

Claims (10)

[Claims] 1. A four-dimensional navigation unit, and an optimal solution search unit, wherein the four-dimensional navigation unit has four-dimensional initial coordinates X0j.
And a three-dimensional initialization speed V0j as a variable to derive a physical evaluation function according to inverse dynamics, wherein the optimal solution search unit searches for an optimal solution of the evaluation function and obtains the optimal solution. 2. The four-dimensional initial setting coordinates X0j are four-dimensional coordinates (t01, x01, y01, y01,
z01) and the four-dimensional coordinates (t02, x02, y02,
z02), and the three-dimensional initial setting speed V0j is a three-dimensional speed (vx01, vy01, vy01,
vz01), and the three-dimensional velocity (vx02, vy02,
vz02). The system for optimizing four-dimensional navigation according to claim 1, comprising: 3. The four-dimensional navigation optimization system according to claim 2, wherein the guidance end time is a time at which the vehicle arrives in the air near the start end of the runway. 4. The four-dimensional navigation optimization system according to claim 2, wherein the optimal solution of the evaluation function is a minimum fuel consumption solution. 5. The optimization system for four-dimensional navigation according to claim 2, wherein the optimal solution of the evaluation function is a minimum solution in time of flight. 6. An optimum solution of the evaluation function is derived from a minimum fuel consumption solution, a minimum flight time solution, and a weighted sum of fuel consumption and flight time, and an actual motion path is determined from these solutions. 4. The four-dimensional navigation optimization system according to claim 2, which is selected artificially. 7. The four-dimensional navigation system according to claim 1, wherein the optimal solution search unit derives a range of the variable including the optimal solution by gradually reducing a search area. Optimization system. 8. The four-dimensional navigation unit includes a command generation unit, and the command generation unit connects the four-dimensional initial setting coordinate X0j and the three-dimensional initial setting velocity V0j to a three-dimensional movement path. 8. The four-dimensional navigation system according to claim 1, wherein the variables are converted into attitude angles and thrusts, and drive signals for mechanical elements corresponding to the three-dimensional attitude angles and the three-dimensional thrust are generated. System. 9. A method for setting two-dimensional four-points and a three-dimensional velocity of the four-dimensional two points as an initial condition, based on the initial conditions, by inverse dynamics, the four-dimensional two points and the three-dimensional Calculating the momentary three-dimensional attitude angle and three-dimensional thrust with speed as a variable; determining an evaluation function with the three-dimensional attitude angle and the three-dimensional thrust as variables; obtaining an optimal solution of the evaluation function And a method for optimizing four-dimensional navigation. 10. The method for determining the optimal solution is performed by: ^J of the exponential function e ^J is a function having the temperature T as a denominator, and dynamically changing the temperature T in a stepwise manner. The method for optimizing four-dimensional navigation according to claim 9, comprising narrowing a range stepwise.