Software Integration and Trajectory Prediction

Arduino Mega 2560

Arduino IDE

Main artile: <a href="https://paulplusx.wordpress.com/2016/03/05/rtpts_sitrajec/">https://paulplusx.wordpress.com/2016/03/05/rtpts_sitrajec/</a>Now after connecting all the hardware to the respective pins we start integrating the software for1. Getting MPU readings (discussed before)2. Getting gps readings – using the codelines discussed before and using smartDelay() for updation,I have also attached a switch at pin 46 to change from normal to trajectory mode:<pre ><code >if (gps.location.isValid()) { Lat = gps.location.lat(); Long = gps.location.lng(); } else { Lat = 12.82; /*my location in case there is no gps readings*/ Long = 80.04; } yy = gps.date.year(); //yy=2016; // Serial.println(yy); mu = gps.date.month(); //mu=5; // Serial.println(mu); dd = gps.date.day(); // dd=4; // Serial.println(dd); if (digitalRead(46) == 1) { if(gps.time.isValid()) { hh = gps.time.hour(); //Serial.println(hh); mm = gps.time.minute(); } else { hh=3; mm=0; } } else if((digitalRead(46) == 0)) { int ss=trajec(); hh = gps.time.hour(); mm = gps.time.minute(); } //smartDelay function static void smartDelay(unsigned long ms) { //Serial.println(“C”); unsigned long start = millis(); do { while (Serial2.available()) gps.encode(Serial2.read()); } while (millis() – start &lt; ms); //Serial.println(“D”); } </code></pre>3. Calculation of azimuth -altitude : This has already been discussed , here is the consolidated code snippet (The osculating elements are mentioned separately below )<pre ><code >double ipart(double xx) { //Serial.println(“IPART”); double sgn; if (xx &lt; 0) { sgn = -1.0; } else if (xx == 0) { sgn = 0.0; } else if (xx &gt; 0) { sgn = 1.0; } double ret = sgn * ((int)fabs(xx)); return ret; } double FNdegmin(double xx) { //Serial.println(“DEGMIN”); double a = ipart(xx) ; double b = xx – a ; double e = ipart(60 * b) ; // deal with carry on minutes if ( e &gt;= 60 ) { e = 0 ; a = a + 1 ; } return (a + (e / 100) ); } double dayno(int dx, int mx, int yx, double fx) { //Serial.println(“DAY NO”); //dno=(367 * yx) – (int)(7*(yx + (int)((mx + 9) / 12)) / 4) + (int)(275 * mx / 9) + dx – 730531.5 + fx; dno = 987 + dx + (fx / 24); //Serial.print(“\ days:”); //Serial.println(dno); return dno; } double frange(double x) { //Serial.println(“FRANGE”); x = x / (2 * pi); x = (2 * pi) * (x – ipart(x)); if (x &lt; 0) x = x + (2 * pi); return x; } double fkep( double m, double ecc) { // Serial.println(m); Serial.println(ecc); //Serial.println(“FKEPA”); // Serial.println(m); Serial.println(ecc); double e = ecc; // do // { dyo = e – (ecc * sin(e)) – m; // e = e – (dyo / (1 – (ecc * cos(e)))); // delay(1); ////Serial.print(“fabs”);Serial.print((fabs(dyo)*pow(10, 6)+1),8);Serial.print(” “);Serial.print(“pow”);Serial.println((pow(10, -6)+1),8); // } while (fabs(dyo)&gt;= pow(10, -12)); // //Serial.println(“fkepB”); // double v = 2 * atan(sqrt((1 + ecc) / (1 – ecc)) * tan(e / 2)); double v = m + (2 * e – 0.25 *pow(e,3) + 5/96 * pow(e,5)) * sin(m) + (1.25 * pow(e,2) – 11/24 * pow(e,4)) * sin(2*m) + (13/12 * pow(e,3) – 43/64 * pow(e,5)) * sin(3*m) + 103/96 * pow(e,4) * sin(4*m) + 1097/960 * pow(e,5) * sin(5*m); if (v &lt; 0) v = v + (2 * pi); return v; } double fnatan(double x, double y) { //Serial.println(“ATAN”); double a = atan(y / x); if (x &lt; 0) a = a + pi; if ((y &lt; 0) &amp;&amp; (x &gt; 0)) a = a + (2 * pi); return a; } void AltAzCalculate(double RA, double Dec, double Lat, double Long, double hrs, double minut, double dy) { //Serial.println(“G”); // Day offset and Local Siderial Time dy = dy + 4975.5; double LST = (100.46 + 0.985647 * dy + Long + 15 * (hrs + minut / 60) + 360) – (((int)((100.46 + 0.985647 * dy + Long + 15 * (hrs + minut / 60) + 360) / 360)) * 360); // Hour Angle double HA = (LST – RA + 360) – ((int)((LST – RA + 360) / 360)) * 360 ; // HA, DEC, Lat to Alt, AZ double x = cos(HA * (pi / 180)) * cos(Dec * (pi / 180)); double y = sin(HA * (pi / 180)) * cos(Dec * (pi / 180)); double z = sin(Dec * (pi / 180)); double xhor = x * cos((90 – Lat) * (pi / 180)) – z * sin((90 – Lat) * (pi / 180)); double yhor = y; double zhor = x * sin((90 – Lat) * (pi / 180)) + z * cos((90 – Lat) * (pi / 180)); Azimuth = atan2(yhor, xhor) * (180 / pi) + 180; Elevation = asin(zhor) * (180 / pi); } void earth() { //Serial.println(“B”); M[3] = ((n[3] * rads) * d) + (L[3] – p[3]) * rads; M[3] = frange(M[3]); v[3] = fkep(M[3], e[3]); r[3] = a[3] * ((1 – (pow(e[3], 2))) / (1 + (e[3] * cos(v[3])))); x[3] = r[3] * cos(v[3] + p[3] * rads); y[3] = r[3] * sin(v[3] + p[3] * rads); z[3] = 0; } void mainCalculations() { dfrac = hh + (mm / 60); d = dayno(dd, mu, yy, dfrac); //Serial.println(“E”); earth(); //Serial.println(“F”); //Serial.println(“E”); int j; for (j = 0; j &lt;=9; j++) { if (j == 3) continue; if(j==9); // Serial.println(“A”); M[j] = ((n[j] * rads) * d) + (L[j] – p[j]) * rads; if(j==9); // Serial.println(“B”); M[j] = frange(M[j]); if(j==9); // Serial.println(“C”); v[j] = fkep(M[j], e[j]); if(j==9); // Serial.println(“D”); r[j] = a[j] * ((1 – pow(e[j], 2)) / (1 + (e[j] * cos(v[j])))); x[j] = r[j] * (cos(o[j] * rads) * cos(v[j] + p[j] * rads – o[j] * rads) – sin(o[j] * rads) * sin(v[j] + p[j] * rads – o[j] * rads) * cos(i[j] * rads)); y[j] = r[j] * (sin(o[j] * rads) * cos(v[j] + p[j] * rads – o[j] * rads) + cos(o[j] * rads) * sin(v[j] + p[j] * rads – o[j] * rads) * cos(i[j] * rads)); z[j] = r[j] * (sin(v[j] + p[j] * rads – o[j] * rads)) * sin(i[j] * rads); Xi[j] = x[j] – x[3]; Yi[j] = y[j] – y[3]; Zi[j] = z[j]; Xq[j] = Xi[j]; Yq[j] = (Yi[j] * cos(ec)) – (Zi[j] * sin(ec)); Zq[j] = (Yi[j] * sin(ec)) + (Zi[j] * cos(ec)); ra[j] = fnatan(Xq[j], Yq[j]); dec[j] = atan(Zq[j] / sqrt(pow(Xq[j], 2.0) + pow(Yq[j], 2.0))); // Serial.println(j); } //Serial.println(“H”); double alpha = FNdegmin((ra[pno] * degs) / 15); double delta = FNdegmin(dec[pno] * degs); //Serial.println(“G”); AltAzCalculate((alpha * 15), delta, Lat, Long, hh, mm, d); } </code></pre>Here are the Osculating elements of 16th August 2013<pre ><code >double i[10] = {0.0, 7.0052, 3.3949, 0.0, 1.8496, 1.3033, 2.4869, 0.7728, 1.7692, 17.1695}; double o[10] = {0.0, 48.493, 76.804, 0.0, 49.668, 100.629, 113.732, 73.989, 131.946, 110.469}; double p[10] = {0.0, 77.669, 131.99, 103.147, 336.322, 14.556, 91.500, 169.602, 6.152, 223.486}; double a[10] = {0.0, 0.387098, 0.723327, 1.0000, 1.523762, 5.20245, 9.52450, 19.1882, 29.9987, 39.2766}; double n[10] = {0.0, 4.09235, 1.60215, 0.985611, 0.523998, 0.083099, 0.033551, 0.011733, 0.006002, 0.004006}; double e[10] = {0.0, 0.205645 , 0.006769, 0.016679, 0.093346, 0.048892, 0.055724, 0.047874, 0.009816, 0.246211}; double L[10] = {0.0, 93.8725, 233.5729, 324.5489, 82.9625, 87.9728, 216.6279, 11.9756, 335.0233, 258.8717}; </code></pre>4. Servo mapping and servo feed (discussed before)5. Planet Selection – I have used a small potentiometer to select different planets as:<pre ><code >int planetInput(int potval) { if ((potval &gt;= 0) &amp;&amp; (potval &lt;= 90)) { Serial.print(“Mercury”); return 1; } if ((potval &gt;= 91) &amp;&amp; (potval &lt;= 191)) { Serial.print(“Venus”); return 2; } if ((potval &gt;= 192) &amp;&amp; (potval &lt;= 292)) { Serial.print(“Mars”); return 4; } if ((potval &gt;= 293) &amp;&amp; (potval &lt;= 393)) { Serial.print(“Jupiter”); return 5; } if ((potval &gt;= 394) &amp;&amp; (potval &lt;= 494)) { Serial.print(“Saturn”); return 6; } if ((potval &gt;= 495) &amp;&amp; (potval &lt;= 595)) { Serial.print(“Uranus”); return 7; } if ((potval &gt;= 596) &amp;&amp; (potval &lt;= 696)) { Serial.print(“Neptune”); return 8; } if ((potval &gt;= 697) &amp;&amp; (potval &lt;= 1023)) { Serial.print(“Pluto”); return 9; } } </code></pre>6. Trajectory prediction – I have used a switch to change from normal mode to trajectory mode In this mode the servos move a little fast giving the future locations of a planet for the complete day. Here is the snippet:<pre ><code >int trajec() { hh=0; mm=0; while(hh&lt;24&amp;&amp; (digitalRead(46) == 0)) { while(mm&lt;60&amp;&amp; (digitalRead(46) == 0)) { mainCalculations(); nyaw = 360 – yaw; Azim = Azimuth – nyaw; Azim -= 90; while (Azim &lt; 0) Azim = 360.0 – abs(Azim); Azi = map(Azim, 0, 360, 5, 29); Az = (int)Azi; Elev = map(Elevation, -90, 90, 2, 178); El = (int)Elev; myservoAz.write(Az); myservoEl.write(El); mm++; Serial.print(hh); Serial.print(“:”); Serial.println(mm); } mm=0; hh++; while(hh==19) hh=20; Serial.println(“good”); } return 5; } </code></pre>As you can see I have just fast forwarded time manually using a loop and calculated the trajectory for a day is relayed through the servo in a  minute which makes it move faster showing a trajectory of planets.Here is final Rough (non – formated ) working code which includes everything :<a href="https://github.com/shubhampaul/Real_Time_Planet_Tracking_System/tree/master/RTPT">Github</a>

Software Integration and Trajectory Prediction

Now after connecting all the hardware to the respective pins we start integrating the software for getting MPU readings.