RU2318188C1 - Method for autonomous navigation and orientation of spacecrafts - Google Patents

Abstract

FIELD: onboard system for controlling spacecrafts for autonomous estimation of orbit and orientation of spacecraft body.

SUBSTANCE: method for autonomous navigation and orientation of spacecrafts includes computer calculation of position in three-dimensional space of ort of radius-vector of support (calculated, a priori assumed) orbit, rigid attachment of optical-electronic device on the body of spacecraft and measurement of coordinates and brightness of stars, which are in the field of view during navigational sessions, in it.

EFFECT: increased number of performed tasks, expanded capabilities of method application environment for any orbits, reduced number of measuring devices and mass and size characteristics of onboard system for controlling a spacecraft.

2 dwg

Description

The invention relates to an onboard spacecraft control system for an autonomous (independent of the ground control complex - GCC) orbit assessment and orientation of the spacecraft hull.

Known methods of autonomous navigation, used both on manned and unmanned spacecraft. The first method was implemented at the Salyut manned stations. It included measuring the moments of sunrise (sunset) of stars beyond the horizon of the planet during the orbital motion of the station. In order to increase navigation accuracy, we additionally measured the speed of movement relative to terrestrial radio beacons and the flight altitude. The theoretical foundations of this system are described in the article by Yu.N. Zybin "On a Method of Autonomous Navigation of Artificial Satellites" (Cosmic Research Journal, vol. VII, issue 2, 1969). The second method was used on 11 F624 devices and consisted in measuring the zenith distances of two stars with the help of two astroizing devices (AVU) and a radio engineering local vertical builder. Additionally, to measure the flight altitude, the local vertical builder was equipped with one more transmitter-receiver. This method is described in the book "Mathematical and Software of the Autonomous Navigation System KA 11 F624", edited by Yu.G. Antonov and S. I. Markov, Ministry of Defense of the USSR, 1986.

The closest in technical essence to the claimed invention should be considered the second method, which is adopted as a prototype. A common feature of the prototype and the proposed method is the presence on board two optoelectronic devices. In addition to these devices in a known method uses a radio vertical builder, whose work is limited to a flight altitude of about 500 km. This builder is necessary because in order to solve the navigation problem, in addition to the direction to the infinitely distant star, it is necessary to have a second direction, which is associated precisely with the orbital motion of the spacecraft.

The algorithm of the AVU operation is based on combining the optical axis of the sight with the image of the specified star of the NKU. To do this, the AVU is placed in a gimbal.

The disadvantage of this method is the forced spacing on the spacecraft body of the cardan suspension and mounting of the vertical builder, which reduces the accuracy of measuring the zenith distance of the star due to temperature deformations of the spacecraft body. To maintain navigation accuracy, flight altitude over the oceans is additionally measured. However, the number of measurements due to the shift of the orbit trace on the Earth's surface varies with time. In addition, the number of measurements depends on the inclination of the orbit. The operability of the radio altimeter, as noted, is limited by the altitude of the spacecraft. As a result, to maintain the required accuracy in determining the orbit, periodic correction by the NKU of the information of the autonomous system is necessary, that is, such a system is actually only partially autonomous, which its developers also acknowledge. In addition, with the help of the local vertical builder, only two angles of body orientation (pitch and roll) are roughly determined (up to several tens of arc minutes) and the yaw angle is not determined. As a result, the orientation of the spacecraft cannot be determined completely and with sufficiently high accuracy.

The aim of this invention is to increase the accuracy of navigation estimates and obtain complete orientation estimates while reducing the weight and size characteristics of the onboard spacecraft control system, as well as expanding the application environment of this method of autonomous navigation and orientation for spacecraft in any orbits (up to heights of the geostationary station and more and any inclinations).

The proposed method consists in using an optical-electronic device (OED) instead of the AVU, which allows not only to sight the star, but also to measure the instrumental coordinates of stars that have fallen into the field of view of the device, and the vertical radio plotter is replaced by computer calculation of the unit vector of the reference radius vector ( a priori assumed) orbits. This unit acts as a line associated with the orbital motion of the spacecraft, and allows you to calculate the zenith distance of the star.

With the OEP fixed on the spacecraft’s hull and tracking by the spacecraft’s stabilization system, at least roughly (within ± 5 °), directions to the center of the planet, it is possible to solve navigation and orientation problems together.

In this case, the coordinates of the working star (that is, the brightest of the stars that fell into the field of view of the instrument) contain information about the location of the spacecraft in inertial space (because the coordinates change as you move in orbit), and information about the actual orientation of the spacecraft’s body (axis of the associated coordinate system) relative to the axes of the current orbital coordinate system (TOSK), taken as the base. The problem is how to use this information together with the data about the reference orbit, and solve both problems: navigation and orientation.

For the correct solution of both problems, the coordinates and brightness of the stars that fall into the field of view of the device are measured, and using the data about the reference orbit and the base of stars, the working star is recognized, that is, its position is determined in the geocentric equatorial inertial coordinate system (GEISC). After that, calculate the angle "axis TOSK-star" in the current coordinate system, take this angle as the angle in the GEISK system and, if there are at least two such angles in the navigation session, solve the navigation problem for the totality of navigation sessions.

Figure 1 shows the measurement scheme in the EIA. In the instrument coordinate system ξ, η, ζ from the similarity of parallelepipeds built on the coordinates of the unit vector of the star (-ξ ⁰ , -η ⁰ , ζ ⁰ ) and the image coordinates of this star (ξ, η, ζ), determine, on the one hand, the value measured coordinates:

and, accordingly, on the other hand, the coordinates of the unit vector

where ξ ⁰ , η ⁰ , ζ ⁰ are the coordinates of the unit vector,

ξ, η, f are the coordinates of the star image,

, f - фокусное расстояние.

, f is the focal length.

When the EIA is rigidly fixed at angles α and β relative to the spacecraft axes (X _{s in} Y _{s in} Z _{s in} ; X _{s in} - along the longitudinal axis of the spacecraft; Y _st - along the lateral axis) the unit vector in the associated system determines:

where MP1 is the transition matrix from the instrument to the associated coordinate system:

непосредственно переводят в орт звезды в ТОСК

с учетом различного направления осей связанной и текущей систем координат (ТОСК: ось S - по радиус-вектору, ось Т - по трансверсали, ось W - по бинормали орбиты):At the beginning of the calculations, when the orientation errors are unknown, they are assumed to be zero, therefore the unit vector

directly translate into orth stars in TOSK

taking into account the different directions of the axes of the connected and current coordinate systems (TOSK: the S axis is along the radius vector, the T axis is along the transversal, the W axis is along the binormal of the orbit):

After working out the orientation angles, an MP2 matrix is formed. Then:

where MP2 is the transition matrix from the reference orbit connected to TOSK. One of the possible approximate forms of this matrix, convenient for differentiation:

where ϑ is the pitch angle,

ψ is the yaw angle,

γ is the angle of heel.

From figure 2 it is clear that if the desired angle φ is determined in GEISK, then the different spatial position of the axes S 'and S will lead to an error in the calculation of the measured value. If the calculation of φ is carried out in TOSK, then it is obvious: both in the S'W'T 'system and in the STW system, the unit vectors of the corresponding axes S ⁰ , T ⁰ , W ⁰ will consist of ones and zeros.

запишется

. Поэтому косинус угла между соответствующей осью ТОСК и направлением на звезду будет в точности равен соответствующей координате орта

например:For example, ort

will be recorded

. Therefore, the cosine of the angle between the corresponding TOSC axis and the direction to the star will be exactly equal to the corresponding unit vector coordinate

eg:

, и поскольку последний сформирован на основе фактических измерений в ОЭП (формулы (2÷6)), ясно, что это и есть значение виртуального измерения зенитного расстояния звезды на фактической (истинной) орбите.At the same time, to which orbit - reference or true - the angle φ _{i belongs} , depends on the vector

, and since the latter is formed on the basis of actual measurements in the EIA (formulas (2 ÷ 6)), it is clear that this is the value of the virtual measurement of the zenith distance of a star in the actual (true) orbit.

Since both TOSK and GEISK are orthogonal systems, the angle value is preserved during the transition between them. This means that by calculating the angle in this way, we circumvent the issue of the actual mismatch of the TSC axes of the reference orbit in comparison with the TSC of the true orbit.

The latter circumstance is the basis of the statement on the practical feasibility of the algorithm for solving the navigation problem in virtual measurements. In other words, despite the fact that the entire solution to the navigation problem goes to the SEISC (as the classical approach provides), the angle is calculated in TOSK.

In turn, the exclusion from the calculation of the angle φ _{i of the} transition between TOSK and GEISK leads to a significant increase in the accuracy of this calculation and, ultimately, to an increase in navigation accuracy.

, где

- радиус-вектор орбиты,

, то градиенты рассчитываются таким образом:The calculation of the local gradients of the angle φ _{i is} carried out in GEISK using the reference orbit. Since in GEISK

where

is the radius vector of the orbit,

, then the gradients are calculated as follows:

,

,

- орт опорной орбиты в ГЭИСК,Where

- orth of the reference orbit in GEISK,

- орт направления на звезду в ГЭИСК,

- direction direction star in GEISK,

q is an element of the array of parameters of the spacecraft reference position in GEISC, q = {x, y, z}.

After calculating the angle and its gradients, the navigation task itself is traditionally solved using the selected smoothing filter. For example, when applying the least squares method, the corrections to the starting point of the reference orbit are determined by the formula:

,

,

where j is the number of the navigation session,

n is the number of navigation sessions on the measured interval,

G _0j = G _j · Ф _0j are the initial gradients, that is, the derivatives of the current measured function φ _{ij with} respect to the initial parameters of the reference orbit q ₀ ,

- текущие (местные) градиенты,

- current (local) gradients,

i = 1, 2 - the number of measurements in the navigation session,

- весовая матрица измерений на j-м навигационном сеансе,

- weighted matrix of measurements on the j-th navigation session,

To _φj is the matrix of the second moments of measurement errors,

- баллистические (изохронные) производные,

- ballistic (isochronous) derivatives,

q ₀ , q _j - respectively, the initial and current parameters of the reference orbit,

Δq _0s - an amendment to the initial parameters in the reference orbit with the first iteration,

Δφ _ij = φ _{ij ism} -φ _{ij calculation} is the measurement discrepancy, Δφ _j = {Δφ _1j , Δφ _2j }.

The matrix K _φj and the residuals of measurements are calculated taking into account the influence of the angles of deflection of the spacecraft relative to the axes TOSK:

where σ _S , ΔS is the mean square and systematic errors of calculation of the unit vector of the radius vector of the orbit,

σ _OEP , Δ _OEP - similar measurement errors in the OEP.

For independent axes:

,

,

,

,

where σ _ϑ , σ _ψ , σ _γ , Δϑ, Δψ, Δγ are the corresponding errors of the spacecraft stabilization system, for the on-board algorithm they must be specified a priori.

The final expressions for calculating close to true derivatives are obtained using the expressions for the unit vector of the OED axis in the associated coordinate system and the expressions for the coordinates of the S axis from the transition matrix (MP2) ^T.

According to the same initial information: the measured coordinates of the recognized working stars in two EIAs and the reference orbit solve the orientation problem.

To do this, determine the value of the matrix (MP2) ^T by calculating the coordinate matrices of the unit vectors of the same stars in the true and reference orbits.

According to (6):

where B is the coordinate matrix of the measured unit vectors of three stars in the system X _{c in} , Y _{c in} , Z _{c in the} true orbit,

C is the coordinate matrix of the calculated unit vectors of the same stars in the TOSK system of the reference orbit. In the matrices, the coordinates of the unit vectors are arranged in columns.

Based on the coordinates of the image of the star, ξ, η according to (2) and (3) calculate B. The calculated values of the columns of the matrix C are formed as follows:

,

,

- орты проекций осей ТОСК опорной орбиты в ГЭИСК, которые определяют на основе соотношений:Where

- the unit vectors of the projections of the TOSK axes of the reference orbit in the GEISK, which are determined on the basis of the relations:

,

,

- вектор скорости.Where

is the velocity vector.

Although solutions of (10) require the unit vectors of three stars, in fact, it suffices to measure the coordinates of two working stars in two OEDs, respectively. Orth of the third star is obtained by calculation, assuming that the virtual star is perpendicular to the plane containing two measured stars and the reference position of the spacecraft.

The product of the matrices B · ^-1 gives the numerical values of the elements of the matrix (MP2) ^T , but the element 1.3 of this matrix is equal to sinψ. For small values of orientation angles

.

.

Similarly, using the expressions of elements 2,3 and 1,2, the values of γ and ϑ are found. The matrix calculated according to (10) is checked for its orthogonality. If the orthogonality is violated by more than 10%, the measurement is rejected.

The described algorithm gives an instantaneous value of the orientation angles; they are used in the algorithm for solving the navigation problem, forming (7).

Since the navigation and orientation problems are solved in one general algorithm almost simultaneously, the refinement of the orientation of the spacecraft hull depends on the refinement of the reference orbit and vice versa. Therefore, a cyclic mode of solving these problems is used.

On the first cycle (and subsequent odd cycles), both problems are solved simultaneously: corrections to the reference orbit and orientation angles are determined. After the end of the iterations of the first cycle (and subsequent odd cycles), the orientation angles are smoothed by the least squares method and stored. In this case, the weight matrix of measurement errors is defined as the sum of the errors of the axis orientation and the errors of measuring the coordinates of the stars in the EIA (9). In the second cycle, the starting point of the reference orbit is corrected by the amount of corrections and only the navigation problem is solved taking into account the orientation angles developed in the first cycle. The weight matrix of measurement errors is determined only by the EIA errors. As a rule, this leads to an improvement in the estimates of the reference orbit in the sense of approximating its parameters to the true (actual) parameters. The third cycle begins with the specified starting point of the reference orbit, orientation estimates nullify and solve both problems again. Given the newly developed orientation estimates, the fourth cycle is carried out, on which only the navigation problem is solved. On even cycles, the residuals of measurements Δφ _k are summed over all iterations of these cycles. According to this algorithm, even and odd cycles are alternated further. The end of the calculations is made upon reaching the conditions:

Δφ _{k + 2} > Δφ _k ,

where k is the number of the even cycle.

The number of cycles cannot exceed ten. For the final results of solving problems, take the results of the kth (or 8th) cycle. In this case, the actual measurements are simulated only at zero iteration of the first cycle. All calculations are carried out on a reference orbit that varies in each iteration of each cycle.

Simulation of solving navigation and orientation problems using two OEPs in a cyclic mode showed high accuracy and stability of obtaining estimates for large (up to 3-5 °) errors of the spacecraft stabilization system, significant initial uncertainty in orbital knowledge (up to several hundred kilometers), as for near-circular orbits, and with their significant ellipticity (eccentricity of the order of 0.7).

The simulation results are given in the attached test report of the autonomous navigation model and spacecraft orientation.

Claims (1)

A method for autonomous navigation and orientation of spacecraft (SC), including the calculation of the zenith distances of two stars, characterized in that they measure the instrumental coordinates and brightness of stars that have fallen into the field of view of optoelectronic devices (OEDs) rigidly fixed to the SC’s body, the stars recognize, and to determine the zenith distance of the workers, that is, the brightest stars, to solve the navigation problem, to determine the orientation of the spacecraft’s hull relative to the current orbital coordinate system, in addition to the EIA information, spatial the position of the radius vector of the reference (a priori assumed) orbit and other elements of this orbit, which are determined by computer calculation, as well as a priori assumed (passport) data on the functioning parameters of the spacecraft stabilization system; navigation and orientation problems are solved in parallel, and since the refinement of the orientation of the spacecraft’s hull relative to the current orbital coordinate system leads to an increase in the accuracy of solving the navigation problem and vice versa, the solution of both problems is carried out in a cyclic mode.

Images