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====== Optimal Preview Control Simulation on Webots ======

Simulation on Webots is does using the generated trajectories. Trajectory points are generated for each joint. 

These trajectories are imported to variables in the controller program on Webots. 

Here is a video link of the Darwin-OP walking used the generated trajectory points. 

{{youtube>gFjKknJiKXo?large}}\\ 

The controller program that does this is : 

<code c++>
#include "Symmetry.hpp"
#include <webots/Servo.hpp>

#include <cstdlib>
#include <cmath>
#include <iostream>
#include <fstream>

using namespace webots;
using namespace std;

static const char *servoNames[NSERVOS] = {
  "ShoulderR" /*ID1 */, "ShoulderL" /*ID2 */, "ArmUpperR" /*ID3 */, "ArmUpperL" /*ID4 */,
  "ArmLowerR" /*ID5 */, "ArmLowerL" /*ID6 */, "PelvYR"    /*ID7 */, "PelvYL"    /*ID8 */,
  "PelvR"     /*ID9 */, "PelvL"     /*ID10*/, "LegUpperR" /*ID11*/, "LegUpperL" /*ID12*/,
  "LegLowerR" /*ID13*/, "LegLowerL" /*ID14*/, "AnkleR"    /*ID15*/, "AnkleL"    /*ID16*/,
  "FootR"     /*ID17*/, "FootL"     /*ID18*/, "Neck"      /*ID19*/, "Head"      /*ID20*/
};

//Constructor
Symmetry::Symmetry():
    Robot()
{
  //Get time step
//  mTimeStep = getBasicTimeStep();
    mTimeStep = 1;
  
  //Get the two RGB_LEDs
  mEyeLED = getLED("EyeLed");
  mHeadLED = getLED("HeadLed");
  
  //Get all the 20 Servos and enable them
  for(int i= 0; i < NSERVOS; i++)
  {
    mServos[i] = getServo(servoNames[i]);
    mServos[i]->enablePosition(mTimeStep);
  }
  

}

//Destructor
Symmetry::~Symmetry() {
}

//Step function
void Symmetry::myStep() {
  int ret = step(mTimeStep);
  if (ret == -1)
    exit(EXIT_SUCCESS);
}

//Wait function
void Symmetry::wait(int ms) {
  double startTime = getTime();
  double s = (double) ms / 1000.0;
  while (s + startTime >= getTime())
    myStep();
}

// function containing the main feedback loop
void Symmetry::run() {

  
  double position = 0;
  float xp [802] = {0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801};
  float footl_loc [] = 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  float footr_loc [] = 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  float anklel_loc [] = 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  float ankler_loc [] = 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  float kneel_loc [] = 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  float kneer_loc [] = 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  float hipPl_loc [] = 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// 
  float hipPr_loc [] = 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  float hipRl_loc [] 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  float hipRr_loc [] = {0,0,0,0,0,7.2125e-11,5.8885e-10,2.0211e-09,4.7374e-09,8.9419e-09,1.47e-08,2.1997e-08,3.08e-08,4.109e-08,5.2878e-08,6.6207e-08,8.1145e-08,9.7771e-08,1.1617e-07,1.3645e-07,1.5869e-07,1.83e-07,2.095e-07,2.3832e-07,2.6958e-07,3.0343e-07,3.4004e-07,3.7957e-07,4.2222e-07,4.6818e-07,5.1768e-07,5.7094e-07,6.2821e-07,6.8929e-07,7.5292e-07,8.2094e-07,8.9513e-07,9.7621e-07,1.0643e-06,1.1594e-06,1.2614e-06,1.3706e-06,1.4875e-06,1.6124e-06,1.7463e-06,1.8896e-06,2.0432e-06,2.2078e-06,2.3841e-06,2.5731e-06,2.7755e-06,2.9924e-06,3.2248e-06,3.4736e-06,3.7402e-06,4.0258e-06,4.3317e-06,4.6594e-06,5.0104e-06,5.3864e-06,5.7892e-06,6.2206e-06,6.6791e-06,7.1557e-06,7.6638e-06,8.2165e-06,8.8192e-06,9.4728e-06,1.0177e-05,1.0932e-05,1.1739e-05,1.2601e-05,1.3523e-05,1.451e-05,1.5565e-05,1.6696e-05,1.7907e-05,1.9204e-05,2.0593e-05,2.2081e-05,2.3674e-05,2.538e-05,2.7208e-05,2.9165e-05,3.1261e-05,3.3507e-05,3.5911e-05,3.8487e-05,4.1245e-05,4.4199e-05,4.7364e-05,5.0753e-05,5.4383e-05,5.8272e-05,6.2436e-05,6.6897e-05,7.1674e-05,7.6792e-05,8.2272e-05,8.8143e-05,9.4431e-05,0.00010117,0.00010838,0.00011611,0.00012438,0.00013325,0.00014274,0.0001529,0.00016379,0.00017545,0.00018793,0.0002013,0.00021562,0.00023095,0.00024737,0.00026496,0.0002838,0.00030397,0.00032558,0.00034872,0.00037331,0.00039887,0.00042612,0.00045576,0.00048807,0.00052311,0.00056086,0.00060133,0.00064459,0.00069081,0.00074022,0.00079308,0.00084966,0.00091025,0.00097514,0.0010446,0.0011191,0.0011988,0.0012841,0.0013756,0.0014735,0.0015783,0.0016906,0.0018109,0.0019397,0.0020776,0.0022254,0.0023836,0.0025531,0.0027346,0.002929,0.0031372,0.0033602,0.0035991,0.0038549,0.0041289,0.0044224,0.0047367,0.0050733,0.0054339,0.00582,0.0062337,0.0066766,0.0071511,0.0076593,0.0082035,0.0087865,0.0094108,0.01008,0.010796,0.011563,0.012384,0.013264,0.014207,0.015216,0.016297,0.017455,0.018695,0.020023,0.021446,0.022969,0.024601,0.026348,0.028218,0.030221,0.032365,0.03466,0.037117,0.039747,0.042563,0.045579,0.048811,0.052276,0.055996,0.059991,0.064285,0.068904,0.073869,0.079199,0.084904,0.090979,0.097401,0.10412,0.11107,0.11816,0.12528,0.13222,0.13881,0.14493,0.15056,0.15572,0.16047,0.16487,0.16897,0.17279,0.17637,0.17971,0.18282,0.18571,0.18841,0.19092,0.19325,0.19541,0.19743,0.19929,0.20103,0.20264,0.20413,0.20552,0.20679,0.20798,0.20906,0.21007,0.21099,0.21183,0.2126,0.2133,0.21394,0.21452,0.21504,0.21549,0.21589,0.21623,0.21652,0.21675,0.21694,0.21708,0.21718,0.21722,0.21722,0.21717,0.21707,0.21693,0.21673,0.21649,0.21619,0.21584,0.21544,0.21498,0.21447,0.21389,0.21325,0.21255,0.21177,0.21092,0.20999,0.20898,0.20789,0.2067,0.20541,0.20402,0.20252,0.2009,0.19915,0.19727,0.19525,0.19307,0.19073,0.18821,0.1855,0.1826,0.17947,0.17612,0.17252,0.16865,0.1645,0.16005,0.15527,0.15014,0.14464,0.13873,0.13239,0.12556,0.11822,0.11032,0.1018,0.092614,0.082712,0.072054,0.060618,0.048408,0.03547,0.021896,0.0078303,-0.0065455,-0.020977,-0.034995,-0.048198,-0.060389,-0.071553,-0.081781,-0.091208,-0.099954,-0.10811,-0.11574,-0.12287,-0.12953,-0.13574,-0.14153,-0.14691,-0.15192,-0.15657,-0.16091,-0.16494,-0.1687,-0.17219,-0.17543,-0.17845,-0.18126,-0.18386,-0.18628,-0.18852,-0.1906,-0.19252,-0.1943,-0.19594,-0.19745,-0.19885,-0.20012,-0.20129,-0.20236,-0.20333,-0.20421,-0.205,-0.20571,-0.20633,-0.20688,-0.20735,-0.20775,-0.20808,-0.20833,-0.20852,-0.20865,-0.2087,-0.20869,-0.20861,-0.20847,-0.20825,-0.20797,-0.20762,-0.2072,-0.2067,-0.20613,-0.20548,-0.20474,-0.20392,-0.20302,-0.20201,-0.20091,-0.19971,-0.19839,-0.19696,-0.1954,-0.19372,-0.19189,-0.18992,-0.18779,-0.18549,-0.18301,-0.18034,-0.17747,-0.17438,-0.17105,-0.16748,-0.16363,-0.15951,-0.15507,-0.15031,-0.1452,-0.13971,-0.13382,-0.12748,-0.12067,-0.11333,-0.10544,-0.096923,-0.087742,-0.077845,-0.067192,-0.055759,-0.043554,-0.03062,-0.017052,-0.0029928,0.011375,0.02578,0.039682,0.052666,0.064566,0.075411,0.085333,0.094483,0.10299,0.11093,0.11837,0.12533,0.13183,0.13789,0.14353,0.14878,0.15366,0.1582,0.16243,0.16636,0.17002,0.17342,0.17658,0.17952,0.18226,0.18479,0.18715,0.18933,0.19135,0.19323,0.19496,0.19655,0.19803,0.19938,0.20062,0.20176,0.2028,0.20374,0.20459,0.20535,0.20605,0.20666,0.20719,0.20765,0.20803,0.20834,0.20857,0.20875,0.20885,0.20889,0.20887,0.20878,0.20862,0.2084,0.20811,0.20775,0.20732,0.20681,0.20623,0.20557,0.20483,0.204,0.20309,0.20208,0.20098,0.19982,0.19856,0.19717,0.19562,0.19393,0.19208,0.19009,0.18793,0.18562,0.18313,0.18045,0.17757,0.17447,0.17113,0.16755,0.1637,0.15956,0.15512,0.15035,0.14523,0.13973,0.13383,0.12749,0.12067,0.11339,0.10579,0.097632,0.088698,0.078888,0.068194,0.056651,0.044317,0.03127,0.017615,0.0034929,-0.010921,-0.025366,-0.03931,-0.052339,-0.064289,-0.075187,-0.08516,-0.094359,-0.10291,-0.1109,-0.11838,-0.12538,-0.13192,-0.13802,-0.14371,-0.14899,-0.15392,-0.1585,-0.16276,-0.16674,-0.17044,-0.17389,-0.1771,-0.18009,-0.18288,-0.18547,-0.18788,-0.19012,-0.1922,-0.19414,-0.19594,-0.19761,-0.19916,-0.20059,-0.20192,-0.20315,-0.20429,-0.20533,-0.2063,-0.20718,-0.20799,-0.20872,-0.20939,-0.21,-0.21055,-0.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  float x = 0;
  float anklel; 
  float ankler; 
  float footl; 
  float footr;
  float kneel; 
  float kneer;
  float hipPl; 
  float hipPr;
  float hipRl; 
  float hipRr;
//  for(int i= 0; i < 50; i++)
//  {
//    anklel_loc[i] = -anklel_loc[i];
//    ankler_loc[i] = -ankler_loc[i];
//    hipRl_loc[i] = -hipRl_loc[i];
//    hipRr_loc[i] = -hipRr_loc[i];
//    }
  myStep();
  for(int i= 0; i < NSERVOS; i++)
  {
    position = mServos[i]->getPosition();
    cout << i ;
    cout << "[" << position << "]\n";
  }
   
  while (1) {
    
    if (x<2)  
    {
      footl = lip(x,xp,footl_loc);
      footr = lip(x,xp,footr_loc);
      kneel = lip(x,xp,kneel_loc);
      kneer = lip(x,xp,kneer_loc);
      hipPl = lip(x,xp,hipPl_loc);
      hipPr = lip(x,xp,hipPr_loc);
      mServos[15]->setPosition(footl);
      mServos[14]->setPosition(footr);
      mServos[13]->setPosition(kneel);
      mServos[12]->setPosition(kneer);
      mServos[11]->setPosition(hipPl);
      mServos[10]->setPosition(hipPr);
      
//    cout << y ;
//    position = mServos[0]->getPosition();
//    cout << "[" << position << "]\n";
//    if (position >= 2.1)
//          {sign = (-1);}
//        if (position <= 0)
//          {sign = (1);}
//    position = position + (sign)*0.1;
//    mServos[0]->setPosition(y);
//    x = x + 0.02;
    }
    else if (x<802)
    {
    footl = lip(x,xp,footl_loc);
    footr = lip(x,xp,footr_loc);
    kneel = lip(x,xp,kneel_loc);
    kneer = lip(x,xp,kneer_loc);
    hipPl = lip(x,xp,hipPl_loc);
    hipPr = lip(x,xp,hipPr_loc);

          // hip swing movement
    anklel = lip(x,xp,anklel_loc);
    ankler = lip(x,xp,ankler_loc);
    hipRl = lip(x,xp,hipRl_loc);
    hipRr = lip(x,xp,hipRr_loc);
    
    cout << hipRr ;
    mServos[17]->setPosition(anklel);
    mServos[16]->setPosition(ankler);
    mServos[15]->setPosition(footl);
    mServos[14]->setPosition(footr);
    mServos[13]->setPosition(kneel);
    mServos[12]->setPosition(kneer);
    mServos[11]->setPosition(hipPl);
    mServos[10]->setPosition(hipPr);
    mServos[9]->setPosition(hipRl);
    mServos[8]->setPosition(hipRr);
    }
    if (x<2)
      x = x+ 0.01;
    else if(x<501)
      x = x + 4;
    else
      x = 301;
    // step
    myStep();
  }
}

float Symmetry::lip(float x,float xp[],float yp[])
{
  float y=0;
  float xp0=0;
  float yp0=0;
  float xp1=0;
  float yp1=0;
  for (int i =0; i<=802; i++)
  {
    if (xp[i]<=x)
    {
      xp0 = xp[i];
      yp0 = yp[i];
    }
    if (xp[i]>x)
    {
      xp1 = xp[i];
      yp1 = yp[i];
      break;
    }
  }
  float m = (yp1-yp0)/(xp1-xp0);
  y = (yp0 +(m*(x-xp0)));
  return (y);
}

</code>