Guidence system(craft)

Mar 6, 2013 Now, after communication system design done, it is the time to place everything together

When you meet your physics teacher 30 years after the school, and old man told that he do not remember how did you study physics in his class, it mean only one – needs to be careful with anything related to a physics. Specifically needs to RFM old lectures – gravitational potential is a scalar value, to get force from gravitational potential needs to get partial derivative. Particularly:

U (gravitational potential) = sum of Unk = fm/r (r0/r)**n Pnk(sinTetta) [Cnk*cos(k*lambda) + Snk*sin(k*lambda). Where Tetta is a latitude and lambda is longitude. Cnk/Snk is a constants from a model. fm= G*M, and r0 is equatorial radius. Partial derivative is (page 90 from Akesenov’s lectures http://vadimchazov.narod.ru/lepa_zov/lesat.pdf):

Then: Unk separates into 3 parts:

(part 1) Rn(1/r) = fm/r *(r0/r)**n

derivative => Rn(1/r)' = (n+1) * fm * r0**n * (1/r)**n = (n+1) * fm * (r0/r)**n)

on a page 12 is (it is kind of hard to write formulas in C code)

Pnk(sinTetta) = (1-sinTetta**2) ** (k/2) * dk (Pn(sinTetta))/ d(sinTetta)**k

= cosTetta **k * dK(Pn(sinTetta))/ d(sinTtta)**k

now cosTetta**k separated from Pnk(sinTetta) to get clear part 2 and CosTetta**k will end up at part 3.

(part 2) Znk(z/r) = dK(Pn(sinTetta)/ d(sinTetta)**k =

= Pnk’[n][k]

Derivative => Znk(z/r)' = Pnk’[n][k+1]

also in (part 2) for K == 0 is:

Zn0 = Pn(sinTetta)

Finally cosTetta goes to a last part:

(part 3) Qnk(x/r,y/r) = cosTetta**k * [Cnk*cos(k*lambda) + Snk * sin(k*lambda)]

= [Cnk*cosTetta**k * cos(k*lambda) + Snk * cosTetta**k * sin(k*lambda)]

= [Cnk* Xk + Snk*Yk] and

Xk = (cosTetta)**k * cos(k*Lambda) Yk = (costetta)**k * sin(k*Lambda)

or recurcevly:

X0 =1, Y0 = 0

X1 = cosTeatta * Cos(Lambda) = x/r; Y1 = cosTetta * sin(Lambda) = y/r

X[k+1] = Xk * x/r - Yk* y/r Y[k+1] = Yk* x/r + Xk * y/r

D(Unk)/D(x) = d(Rn) / d(1/r) * D(1/r)/D(x) * Znk * Qnk + Rn * d(Znk)/d(z/r) * D(z/r)/D(x) * Qnk + Rn * Znk * [D(Qnk)/D(x/r) * D(x/r)/D(x) + D(Qnk)/D(y/r)*D(y/r)/D(x)]

D(Unk)/D(y) = d(Rn) / d(1/r) * D(1/r)/D(y) * Znk * Qnk + Rn * d(Znk)/d(z/r) * D(z/r)/D(y) * Qnk + Rn * Znk * [D(Qnk)/D(x/r) * D(x/r)/D(y) + D(Qnk)/D(y/r)*D(y/r)/D(y)]

D(Unk)/D(z) = d(Rn) / d(1/r) * D(1/r)/D(z) * Znk * Qnk + Rn * d(Znk)/d(z/r) * D(z/r)/D(z) * Qnk + Rn * Znk * [D(Qnk)/D(x/r) * D(x/r)/D(z) + D(Qnk)/D(y/r)*D(y/r)/D(z)]

All Rnk, Qnk and it’s derivatives calculates recursively, on page 91-92 presents formulas to get partial derivatives for D(1/r)/D(x) and etc. At the end needs to move out of brackets for each partial derivative values fm * x/r**3, fm * y/r**3, fm*z/r**3. And explanation of a stupidity of Alex Dobrianski shines up – in a C code J2 constant really bigger 10 times for 75 degree(just coincident normally it bigger 3 times), in Fx,Fy presents sin(co-latitude), in Fz presents cos(latitude)**2 / sin(latitude), and error drops from 30km to 685m. Needs to read (couple of times) manual (lectures) does not matter how many pages in it.

Feb 1, 2011. For a simulation of a correct position calculations needs to develop a software with 3 simulation satellites on different orbits with a simulation probe calculating distances btw a probe and satellites with a random (set by some parameters) error. Output must be in ID 28 ID 30 format (a floating point). The output fill be stored in onboard storage. Then main onboard computer (backup too) can have access to the data – to process and to calculate current position. For a calculation of a such position enough to calculate Kepler’s elements of a probe’s orbit in a moment of time in a past.

The Simulation software will be based on an existing Sun-Earth-Moon-satellite simulation package developed for a probe’s orbit/flight-path calculation by adding 3 more bodies (satellites) to simulate. A random error will be introduced to estimate correct orbit’s calculation time, and a possible error in a positioning.

It is impossible to do a mission without the ability to orient probe in flight, to calculate position, orientation, center of gravity and speed of a probe. All this is a task for orientation system. Modern technologies allow the use of compact gyroscopes to detect probe's X-Y-Z axes orientation, cameras to make pictures of starts, infrared sensible sensors (cameras) to calculate celestial’s bodies horizons, computers to make calculation and predict location of a probe.

For a prime orbit’s Keplers elements calculation considered to use GPS receiver. It is unknown for now how GPS receiver will perform on flight with speed around 10km/s. Investigation should be done but data from experiment on satellite position calculation was already done and published.

GPS raw data from a SiRF capable receiver with records ID 28,30 will be enough to produce current positions of observing satellites (ID 30), and distances to it (ID 28). Moment of each observation will be recorder in real time. Analyzing data with assumption that orbit is ellipsoid lay in one plane can give data to calculate major axes and parameters for a plane. Algorithms first will approximate plane direction (inclination, longitude of ascending node), then major axes (eccentricity, argument of perihelion) , then point on an ellipse can be calculated to get mean anomaly.

Kepler’s elements needs to be assumed stable (atmospheric influence will be small and can be accounted) that limitation will give constrain on errors sampling GPS raw data. For testing formulas and algorithms on a ground prior launch can be assumed that initial plane is defined by north/south/some-equatorial points, major axes not equal each other and equal earth radius. Then algorithms should produce plane parallel equator and point with location of a receiver, and major exes will be equal radius of calculated plane.

Different type gyroscopes was investigated by parameters and tested. Results give requirements for gyro-platform design, which include temperature restriction, functionality, location, precision, data bandwidth requirements. Precision of a collected data should give requirements for high-thrust engine and low-thrust engine. For example: delays in gyroscopes sensor’s calculation and delays in orientation’s controls motors can create unstable thrust’s vectors, and compensation by reducing thrust must be apply.

Performance in vacuum, in different temperature conditions, under stress of vibration, at landing impact have to be tested. Performance of different lenses (plastic, glass, diaphragms) for different wavelength has to be performed. Power consumptions, assembling capabilities, supporting electronics have to investigate and consider in requirements for probe’s imaging system. Data capabilities / compression capabilities of supporting electronics has to give requirements for Communication system and Data Transfer system.

Position, orientation, speed, centre of gravity of a probe will be stored in 3 separated location. This will include computer's memory and non voltage memory. Verification, calculation and correction of position + orientation can be update by astro-orientation, gyro-orientation system and from mission control. History data of position and orientation enough for on board calculation should be stored in on board computers and can be update/corrected by mission control.

Probe’s orientation on all stages must be able to execute 4 different tasks:e 4 different tasks:

- centre of gravity positioning, for orientation at main impulses engine’s firing;

- centre of gravity positioning, for changing vector of thrust for low-thrust engine;

- probe’s rotation in axes X-Y-Z of a probe's manipulator(s), antenna(s), tools, engines components positioning.

All orientation commands have to be done by (a) main on board computer; (b) backup on board computer; (c) mission control. In an absence of communication with mission control all pre-programmed orientations targets will be executed. Mission control can specify source for control devices either with on-board computers, or mission control itself, all settings for all control devices must time out to execute, first-in-last-out fixed size command stack with default (top-of-stack) command's values.