base/rrtbase.cc

   1 /*
   2 This file is part of I am car.
   3
   4 I am car is free software: you can redistribute it and/or modify
   5 it under the terms of the GNU General Public License as published by
   6 the Free Software Foundation, either version 3 of the License, or
   7 (at your option) any later version.
   8
   9 I am car is distributed in the hope that it will be useful,
  10 but WITHOUT ANY WARRANTY; without even the implied warranty of
  11 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  12 GNU General Public License for more details.
  13
  14 You should have received a copy of the GNU General Public License
  15 along with I am car. If not, see <http://www.gnu.org/licenses/>.
  16 */
  17
  18 #include <algorithm>
  19 #include <cmath>
  20 #include <omp.h>
  21 #include <queue>
  22 #include "bcar.h"
  23 #include "rrtbase.h"
  24 // OpenGL
  25 #include <GL/gl.h>
  26 #include <GL/glu.h>
  27 #include <SDL2/SDL.h>
  28 // RRT
  29 #include "sample.h"
  30 #include "cost.h"
  31 #include "steer.h"
  32 #include "nn.h"
  33 #include "nv.h"
  34
  35 extern SDL_Window* gw;
  36 extern SDL_GLContext gc;
  37
  38 RRTBase::~RRTBase()
  39 {
  40         for (auto n: this->nodes_)
  41                 if (n != this->root_)
  42                         delete n;
  43         for (auto n: this->dnodes_)
  44                 if (n != this->root_ && n != this->goal_)
  45                         delete n;
  46         for (auto s: this->samples_)
  47                 if (s != this->goal_)
  48                         delete s;
  49         for (auto edges: this->rlog_)
  50                 for (auto e: edges)
  51                         delete e;
  52         delete this->root_;
  53         delete this->goal_;
  54 }
  55
  56 RRTBase::RRTBase():
  57         root_(new RRTNode()),
  58         goal_(new RRTNode())
  59 {
  60         this->nodes_.push_back(this->root_);
  61         this->add_iy(this->root_);
  62 }
  63
  64 RRTBase::RRTBase(RRTNode *init, RRTNode *goal):
  65         root_(init),
  66         goal_(goal)
  67 {
  68         this->nodes_.push_back(init);
  69         this->add_iy(init);
  70 }
  71
  72 // getter
  73 RRTNode *RRTBase::root()
  74 {
  75         return this->root_;
  76 }
  77
  78 RRTNode *RRTBase::goal()
  79 {
  80         return this->goal_;
  81 }
  82
  83 std::vector<RRTNode *> &RRTBase::nodes()
  84 {
  85         return this->nodes_;
  86 }
  87
  88 std::vector<RRTNode *> &RRTBase::dnodes()
  89 {
  90         return this->dnodes_;
  91 }
  92
  93 std::vector<RRTNode *> &RRTBase::samples()
  94 {
  95         return this->samples_;
  96 }
  97
  98 std::vector<CircleObstacle> *RRTBase::co()
  99 {
 100         return this->cobstacles_;
 101 }
 102
 103 std::vector<SegmentObstacle> *RRTBase::so()
 104 {
 105         return this->sobstacles_;
 106 }
 107
 108 std::vector<float> &RRTBase::clog()
 109 {
 110         return this->clog_;
 111 }
 112
 113 std::vector<float> &RRTBase::nlog()
 114 {
 115         return this->nlog_;
 116 }
 117
 118 std::vector<std::vector<RRTEdge *>> &RRTBase::rlog()
 119 {
 120         return this->rlog_;
 121 }
 122
 123 std::vector<float> &RRTBase::slog()
 124 {
 125         return this->slog_;
 126 }
 127
 128 std::vector<std::vector<RRTNode *>> &RRTBase::tlog()
 129 {
 130         return this->tlog_;
 131 }
 132
 133 bool RRTBase::goal_found()
 134 {
 135         return this->goal_found_;
 136 }
 137
 138 float RRTBase::elapsed()
 139 {
 140         std::chrono::duration<float> dt;
 141         dt = std::chrono::duration_cast<std::chrono::duration<float>>(
 142                         this->tend_ - this->tstart_);
 143         return dt.count();
 144 }
 145
 146 // setter
 147 void RRTBase::root(RRTNode *node)
 148 {
 149         this->root_ = node;
 150 }
 151
 152 void RRTBase::goal(RRTNode *node)
 153 {
 154         this->goal_ = node;
 155 }
 156
 157 bool RRTBase::logr(RRTNode *root)
 158 {
 159         std::vector<RRTEdge *> e; // Edges to log
 160         std::vector<RRTNode *> s; // DFS stack
 161         std::vector<RRTNode *> r; // reset visited_
 162         RRTNode *tmp;
 163         s.push_back(root);
 164         while (s.size() > 0) {
 165                 tmp = s.back();
 166                 s.pop_back();
 167                 if (!tmp->visit()) {
 168                         r.push_back(tmp);
 169                         for (auto ch: tmp->children()) {
 170                                 s.push_back(ch);
 171                                 e.push_back(new RRTEdge(tmp, ch));
 172                         }
 173                 }
 174         }
 175         for (auto n: r)
 176                 n->visit(false);
 177         this->rlog_.push_back(e);
 178         return true;
 179 }
 180
 181 float RRTBase::ocost(RRTNode *n)
 182 {
 183         float dist = 9999;
 184         for (auto o: *this->cobstacles_)
 185                 if (o.dist_to(n) < dist)
 186                         dist = o.dist_to(n);
 187         for (auto o: *this->sobstacles_)
 188                 if (o.dist_to(n) < dist)
 189                         dist = o.dist_to(n);
 190         return n->ocost(dist);
 191 }
 192
 193 bool RRTBase::tlog(std::vector<RRTNode *> t)
 194 {
 195         if (t.size() > 0) {
 196                 this->slog_.push_back(this->elapsed());
 197                 this->clog_.push_back(t.front()->ccost() - t.back()->ccost());
 198                 this->nlog_.push_back(this->nodes_.size());
 199                 this->tlog_.push_back(t);
 200                 return true;
 201         } else {
 202                 return false;
 203         }
 204 }
 205
 206 void RRTBase::tstart()
 207 {
 208         this->tstart_ = std::chrono::high_resolution_clock::now();
 209 }
 210
 211 void RRTBase::tend()
 212 {
 213         this->tend_ = std::chrono::high_resolution_clock::now();
 214 }
 215
 216 bool RRTBase::link_obstacles(
 217                 std::vector<CircleObstacle> *cobstacles,
 218                 std::vector<SegmentObstacle> *sobstacles)
 219 {
 220         this->cobstacles_ = cobstacles;
 221         this->sobstacles_ = sobstacles;
 222         if (!this->cobstacles_ || !this->sobstacles_) {
 223                 return false;
 224         }
 225         return true;
 226 }
 227
 228 bool RRTBase::add_iy(RRTNode *n)
 229 {
 230         int i = IYI(n->y());
 231         if (i < 0)
 232                 i = 0;
 233         if (i >= IYSIZE)
 234                 i = IYSIZE - 1;
 235         this->iy_[i].push_back(n);
 236         return true;
 237 }
 238
 239 bool RRTBase::goal_found(bool f)
 240 {
 241         this->goal_found_ = f;
 242         return f;
 243 }
 244
 245 // other
 246 bool RRTBase::glplot()
 247 {
 248         glClear(GL_COLOR_BUFFER_BIT);
 249         glLineWidth(1);
 250         glPointSize(1);
 251         // Plot obstacles
 252         glBegin(GL_LINES);
 253         for (auto o: *this->sobstacles_) {
 254                 glColor3f(0, 0, 0);
 255                 glVertex2f(GLVERTEX(o.init()));
 256                 glVertex2f(GLVERTEX(o.goal()));
 257         }
 258         glEnd();
 259         // Plot root, goal
 260         glPointSize(8);
 261         glBegin(GL_POINTS);
 262         glColor3f(1, 0, 0);
 263         glVertex2f(GLVERTEX(this->root_));
 264         glVertex2f(GLVERTEX(this->goal_));
 265         glEnd();
 266         // Plot last sample
 267         if (this->samples_.size() > 0) {
 268                 glPointSize(8);
 269                 glBegin(GL_POINTS);
 270                 glColor3f(0, 1, 0);
 271                 glVertex2f(GLVERTEX(this->samples_.back()));
 272                 glEnd();
 273         }
 274         // Plot nodes
 275         std::vector<RRTNode *> s; // DFS stack
 276         std::vector<RRTNode *> r; // reset visited_
 277         RRTNode *tmp;
 278         glBegin(GL_LINES);
 279         s.push_back(this->root_);
 280         while (s.size() > 0) {
 281                 tmp = s.back();
 282                 s.pop_back();
 283                 if (!tmp->visit()) {
 284                         r.push_back(tmp);
 285                         for (auto ch: tmp->children()) {
 286                                 s.push_back(ch);
 287                                 glColor3f(0.5, 0.5, 0.5);
 288                                 glVertex2f(GLVERTEX(tmp));
 289                                 glVertex2f(GLVERTEX(ch));
 290                         }
 291                 }
 292         }
 293         glEnd();
 294         // Plot nodes (from goal)
 295         glBegin(GL_LINES);
 296         s.push_back(this->goal_);
 297         while (s.size() > 0) {
 298                 tmp = s.back();
 299                 s.pop_back();
 300                 if (!tmp->visit()) {
 301                         r.push_back(tmp);
 302                         for (auto ch: tmp->children()) {
 303                                 s.push_back(ch);
 304                                 glColor3f(0.5, 0.5, 0.5);
 305                                 glVertex2f(GLVERTEX(tmp));
 306                                 glVertex2f(GLVERTEX(ch));
 307                         }
 308                 }
 309         }
 310         glEnd();
 311         std::vector<RRTNode *> cusps;
 312         // Plot last trajectory
 313         if (this->tlog().size() > 0) {
 314                 glLineWidth(2);
 315                 glBegin(GL_LINES);
 316                 for (auto n: this->tlog().back()) {
 317                         if (n->parent()) {
 318                                 glColor3f(0, 0, 1);
 319                                 glVertex2f(GLVERTEX(n));
 320                                 glVertex2f(GLVERTEX(n->parent()));
 321                                 if (sgn(n->s()) != sgn(n->parent()->s()))
 322                                         cusps.push_back(n);
 323                         }
 324                 }
 325                 glEnd();
 326         }
 327         // Plot cusps
 328         glPointSize(8);
 329         glBegin(GL_POINTS);
 330         for (auto n: cusps) {
 331                 glColor3f(0, 0, 1);
 332                 glVertex2f(GLVERTEX(n));
 333         }
 334         glEnd();
 335         SDL_GL_SwapWindow(gw);
 336         for (auto n: r)
 337                 n->visit(false);
 338         return true;
 339 }
 340
 341 bool RRTBase::goal_found(
 342                 RRTNode *node,
 343                 float (*cost)(RRTNode *, RRTNode* ))
 344 {
 345         float xx = pow(node->x() - this->goal_->x(), 2);
 346         float yy = pow(node->y() - this->goal_->y(), 2);
 347         float dh = std::abs(node->h() - this->goal_->h());
 348         if (IS_NEAR(node, this->goal_)) {
 349                 if (this->goal_found_) {
 350                         if (node->ccost() + (*cost)(node, this->goal_) <
 351                                         this->goal_->ccost()) {
 352                                 RRTNode *op; // old parent
 353                                 float oc; // old cumulative cost
 354                                 float od; // old direct cost
 355                                 op = this->goal_->parent();
 356                                 oc = this->goal_->ccost();
 357                                 od = this->goal_->dcost();
 358                                 node->add_child(this->goal_,
 359                                                 (*cost)(node, this->goal_));
 360                                 if (this->collide(node, this->goal_)) {
 361                                         node->children().pop_back();
 362                                         this->goal_->parent(op);
 363                                         this->goal_->ccost(oc);
 364                                         this->goal_->dcost(od);
 365                                 } else {
 366                                         op->rem_child(this->goal_);
 367                                         return true;
 368                                 }
 369                         } else {
 370                                 return false;
 371                         }
 372                 } else {
 373                         node->add_child(
 374                                         this->goal_,
 375                                         (*cost)(node, this->goal_));
 376                         if (this->collide(node, this->goal_)) {
 377                                 node->children().pop_back();
 378                                 this->goal_->remove_parent();
 379                                 return false;
 380                         }
 381                         this->goal_found_ = true;
 382                         return true;
 383                 }
 384         }
 385         return false;
 386 }
 387
 388 bool RRTBase::collide(RRTNode *init, RRTNode *goal)
 389 {
 390         std::vector<RRTEdge *> edges;
 391         RRTNode *tmp = goal;
 392         volatile bool col = false;
 393         unsigned int i;
 394         while (tmp != init) {
 395                 BicycleCar bc(tmp->x(), tmp->y(), tmp->h());
 396                 std::vector<RRTEdge *> bcframe = bc.frame();
 397                 #pragma omp parallel for reduction(|: col)
 398                 for (i = 0; i < (*this->cobstacles_).size(); i++) {
 399                         if ((*this->cobstacles_)[i].collide(tmp)) {
 400                                 col = true;
 401                         }
 402                         for (auto &e: bcframe) {
 403                                 if ((*this->cobstacles_)[i].collide(e)) {
 404                                         col = true;
 405                                 }
 406                         }
 407                 }
 408                 if (col) {
 409                         for (auto e: bcframe) {
 410                                 delete e->init();
 411                                 delete e->goal();
 412                                 delete e;
 413                         }
 414                         for (auto e: edges) {
 415                                 delete e;
 416                         }
 417                         return true;
 418                 }
 419                 #pragma omp parallel for reduction(|: col)
 420                 for (i = 0; i < (*this->sobstacles_).size(); i++) {
 421                         for (auto &e: bcframe) {
 422                                 if ((*this->sobstacles_)[i].collide(e)) {
 423                                         col = true;
 424                                 }
 425                         }
 426                 }
 427                 if (col) {
 428                         for (auto e: bcframe) {
 429                                 delete e->init();
 430                                 delete e->goal();
 431                                 delete e;
 432                         }
 433                         for (auto e: edges) {
 434                                 delete e;
 435                         }
 436                         return true;
 437                 }
 438                 if (!tmp->parent()) {
 439                         break;
 440                 }
 441                 edges.push_back(new RRTEdge(tmp, tmp->parent()));
 442                 tmp = tmp->parent();
 443                 for (auto e: bcframe) {
 444                         delete e->init();
 445                         delete e->goal();
 446                         delete e;
 447                 }
 448         }
 449         for (auto &e: edges) {
 450                 #pragma omp parallel for reduction(|: col)
 451                 for (i = 0; i < (*this->cobstacles_).size(); i++) {
 452                         if ((*this->cobstacles_)[i].collide(e)) {
 453                                 col = true;
 454                         }
 455                 }
 456                 if (col) {
 457                         for (auto e: edges) {
 458                                 delete e;
 459                         }
 460                         return true;
 461                 }
 462                 #pragma omp parallel for reduction(|: col)
 463                 for (i = 0; i < (*this->sobstacles_).size(); i++) {
 464                         if ((*this->sobstacles_)[i].collide(e)) {
 465                                 col = true;
 466                         }
 467                 }
 468                 if (col) {
 469                         for (auto e: edges) {
 470                                 delete e;
 471                         }
 472                         return true;
 473                 }
 474         }
 475         for (auto e: edges) {
 476                 delete e;
 477         }
 478         return false;
 479 }
 480
 481 class RRTNodeDijkstra {
 482         public:
 483                 RRTNodeDijkstra(int i):
 484                         ni(i),
 485                         pi(0),
 486                         c(9999),
 487                         v(false)
 488                 {};
 489                 RRTNodeDijkstra(int i, float c):
 490                         ni(i),
 491                         pi(0),
 492                         c(c),
 493                         v(false)
 494                 {};
 495                 RRTNodeDijkstra(int i, int p, float c):
 496                         ni(i),
 497                         pi(p),
 498                         c(c),
 499                         v(false)
 500                 {};
 501                 unsigned int ni;
 502                 unsigned int pi;
 503                 float c;
 504                 bool v;
 505                 bool vi()
 506                 {
 507                         if (this->v)
 508                                 return true;
 509                         this->v = true;
 510                         return false;
 511                 };
 512 };
 513
 514 class RRTNodeDijkstraComparator {
 515         public:
 516                 int operator() (
 517                                 const RRTNodeDijkstra& n1,
 518                                 const RRTNodeDijkstra& n2)
 519                 {
 520                         return n1.c > n2.c;
 521                 }
 522 };
 523
 524 bool RRTBase::optp_dijkstra(
 525                 std::vector<RRTNode *> &cusps,
 526                 std::vector<int> &npi)
 527 {
 528         std::vector<RRTNodeDijkstra> dnodes;
 529         for (unsigned int i = 0; i < cusps.size(); i++)
 530                 if (i > 0)
 531                         dnodes.push_back(RRTNodeDijkstra(
 532                                                 i,
 533                                                 i - 1,
 534                                                 cusps[i]->ccost()));
 535                 else
 536                         dnodes.push_back(RRTNodeDijkstra(
 537                                                 i,
 538                                                 cusps[i]->ccost()));
 539         dnodes[0].vi();
 540         std::priority_queue<
 541                 RRTNodeDijkstra,
 542                 std::vector<RRTNodeDijkstra>,
 543                 RRTNodeDijkstraComparator> pq;
 544         RRTNodeDijkstra tmp = dnodes[0];
 545         pq.push(tmp);
 546         float ch_cost = 9999;
 547         std::vector<RRTNode *> steered;
 548         while (!pq.empty()) {
 549                 tmp = pq.top();
 550                 pq.pop();
 551                 for (unsigned int i = tmp.ni + 1; i < cusps.size(); i++) {
 552                         ch_cost = dnodes[tmp.ni].c +
 553                                 this->cost(cusps[tmp.ni], cusps[i]);
 554                         steered = this->steer(cusps[tmp.ni], cusps[i]);
 555                         for (unsigned int j = 0; j < steered.size() - 1; j++)
 556                                 steered[j]->add_child(steered[j + 1], 1);
 557                         if (this->collide(
 558                                         steered[0],
 559                                         steered[steered.size() - 1]))
 560                                 continue;
 561                         if (ch_cost < dnodes[i].c) {
 562                                 dnodes[i].c = ch_cost;
 563                                 dnodes[i].pi = tmp.ni;
 564                                 if (!dnodes[i].vi())
 565                                         pq.push(dnodes[i]);
 566                         }
 567                         for (auto n: steered)
 568                                 delete n;
 569                 }
 570         }
 571         unsigned int tmpi = 0;
 572         for (auto n: dnodes) {
 573                 if (n.v && n.ni > tmpi)
 574                         tmpi = n.ni;
 575         }
 576         while (tmpi > 0) {
 577                 npi.push_back(tmpi);
 578                 tmpi = dnodes[tmpi].pi;
 579         }
 580         npi.push_back(tmpi);
 581         std::reverse(npi.begin(), npi.end());
 582         return true;
 583 }
 584
 585 bool RRTBase::optp_rrp(
 586                 std::vector<RRTNode *> &cusps,
 587                 std::vector<int> &npi)
 588 {
 589         std::vector<RRTNode *> steered;
 590         std::vector<int> candidates;
 591         RRTNode *x_j = nullptr;
 592         RRTNode *x_i = nullptr;
 593         int j = cusps.size() - 1;
 594         int i_min = 0;
 595         float c_min = 0;
 596         float cost = 0;
 597         float dx = 0;
 598         float dy = 0;
 599         float ed = 0;
 600         float th_i = 0;
 601         float th_j = 0;
 602         while (j > 0) {
 603                 npi.push_back(j);
 604                 steered.clear();
 605                 candidates.clear();
 606                 x_j = cusps[j];
 607                 for (int i = 0; i < j; i++) {
 608                         steered = this->steer(cusps[i], x_j);
 609                         for (unsigned int k = 0; k < steered.size() - 1; k++)
 610                                 steered[k]->add_child(steered[k + 1], 1);
 611                         if (!this->collide(
 612                                         steered[0],
 613                                         steered[steered.size() - 1]))
 614                                 candidates.push_back(i);
 615                 }
 616                 if (candidates.size() <= 0)
 617                         return false;
 618                 i_min = candidates[0];
 619                 x_i = cusps[i_min];
 620                 c_min = 9999;
 621                 for (auto c: candidates) {
 622                         x_i = cusps[c];
 623                         dx = x_j->x() - x_i->x();
 624                         dy = x_j->y() - x_i->y();
 625                         ed = EDIST(x_i, x_j);
 626                         th_i = (cos(x_i->h()) * dx + sin(x_i->h()) * dy) / ed;
 627                         th_j = (cos(x_j->h()) * dx + sin(x_j->h()) * dy) / ed;
 628                         cost = th_i + th_j;
 629                         if (cost < c_min) {
 630                                 i_min = c;
 631                                 c_min = cost;
 632                         }
 633                 }
 634                 j = i_min;
 635
 636         }
 637         npi.push_back(j);
 638         std::reverse(npi.begin(), npi.end());
 639         return true;
 640 }
 641
 642 bool RRTBase::optp_smart(
 643                 std::vector<RRTNode *> &cusps,
 644                 std::vector<int> &npi)
 645 {
 646         std::vector<RRTNode *> steered;
 647         int li = cusps.size() - 1;
 648         int ai = li - 1;
 649         npi.push_back(li);
 650         while (ai > 1) {
 651                 steered = this->steer(cusps[ai - 1], cusps[li]);
 652                 for (unsigned int j = 0; j < steered.size() - 1; j++)
 653                         steered[j]->add_child(steered[j + 1], 1);
 654                 if (this->collide(steered[0], steered[steered.size() - 1])) {
 655                         npi.push_back(ai);
 656                         li = ai;
 657                 }
 658                 ai--;
 659                 for (auto n: steered)
 660                         delete n;
 661         }
 662         npi.push_back(0);
 663         std::reverse(npi.begin(), npi.end());
 664         return true;
 665 }
 666
 667 bool RRTBase::opt_path()
 668 {
 669         if (this->tlog().size() == 0)
 670                 return false;
 671         float oc = this->tlog().back().front()->ccost();
 672         std::vector<RRTNode *> tmp_cusps;
 673         for (auto n: this->tlog().back()) {
 674                 if (sgn(n->s()) == 0) {
 675                         tmp_cusps.push_back(n);
 676                 } else if (n->parent() &&
 677                                 sgn(n->s()) != sgn(n->parent()->s())) {
 678                         tmp_cusps.push_back(n);
 679                         tmp_cusps.push_back(n->parent());
 680                 }
 681                 //tmp_cusps.push_back(n);
 682         }
 683         if (tmp_cusps.size() < 2)
 684                 return false;
 685         std::vector<RRTNode *> cusps;
 686         for (unsigned int i = 0; i < tmp_cusps.size(); i++) {
 687                 if (tmp_cusps[i] != tmp_cusps[(i + 1) % tmp_cusps.size()])
 688                         cusps.push_back(tmp_cusps[i]);
 689         }
 690         std::reverse(cusps.begin(), cusps.end());
 691         std::vector<int> npi; // new path indexes
 692         if (!this->optp_dijkstra(cusps, npi))
 693                 return false;
 694         RRTNode *pn = cusps[npi[0]];
 695         RRTNode *tmp = nullptr;
 696         bool en_add = true;
 697         for (unsigned int i = 0; i < npi.size() - 1; i++) {
 698                 pn = cusps[npi[i]];
 699                 for (auto ns: this->steer(cusps[npi[i]], cusps[npi[i + 1]])) {
 700                         if (!en_add) {
 701                                 delete ns;
 702                         } else if (IS_NEAR(cusps[npi[i]], ns)) {
 703                                 tmp = ns;
 704                                 while (tmp && tmp != cusps[npi[i]]) {
 705                                         pn = tmp->parent();
 706                                         delete tmp;
 707                                         tmp = pn;
 708                                 }
 709                                 pn = cusps[npi[i]];
 710                         } else if (IS_NEAR(ns, cusps[npi[i + 1]])) {
 711                                 delete ns;
 712                                 cusps[npi[i + 1]]->parent()->rem_child(
 713                                                 cusps[npi[i + 1]]);
 714                                 pn->add_child(
 715                                         cusps[npi[i + 1]],
 716                                         this->cost(pn, cusps[npi[i + 1]]));
 717                                 en_add = false;
 718                         } else {
 719                                 pn->add_child(ns, this->cost(pn, ns));
 720                                 pn = ns;
 721                         }
 722                 }
 723         }
 724         this->root()->update_ccost();
 725         if (this->tlog().back().front()->ccost() < oc)
 726                 return true;
 727         return false;
 728 }
 729
 730 bool RRTBase::rebase(RRTNode *nr)
 731 {
 732         if (!nr || this->goal_ == nr || this->root_ == nr)
 733                 return false;
 734         std::vector<RRTNode *> s; // DFS stack
 735         RRTNode *tmp;
 736         unsigned int i = 0;
 737         unsigned int to_del = 0;
 738         int iy = 0;
 739         s.push_back(this->root_);
 740         while (s.size() > 0) {
 741                 tmp = s.back();
 742                 s.pop_back();
 743                 for (auto ch: tmp->children()) {
 744                         if (ch != nr)
 745                                 s.push_back(ch);
 746                 }
 747                 to_del = this->nodes_.size();
 748                 #pragma omp parallel for reduction(min: to_del)
 749                 for (i = 0; i < this->nodes_.size(); i++) {
 750                         if (this->nodes_[i] == tmp)
 751                                 to_del = i;
 752                 }
 753                 if (to_del < this->nodes_.size())
 754                         this->nodes_.erase(this->nodes_.begin() + to_del);
 755                 iy = IYI(tmp->y());
 756                 to_del = this->iy_[iy].size();
 757                 #pragma omp parallel  for reduction(min: to_del)
 758                 for (i = 0; i < this->iy_[iy].size(); i++) {
 759                         if (this->iy_[iy][i] == tmp)
 760                                 to_del = i;
 761                 }
 762                 if (to_del < this->iy_[iy].size())
 763                         this->iy_[iy].erase(this->iy_[iy].begin() + to_del);
 764                 this->dnodes().push_back(tmp);
 765         }
 766         this->root_ = nr;
 767         this->root_->remove_parent();
 768         return true;
 769 }
 770
 771 std::vector<RRTNode *> RRTBase::findt()
 772 {
 773         return this->findt(this->goal_);
 774 }
 775
 776 std::vector<RRTNode *> RRTBase::findt(RRTNode *n)
 777 {
 778         std::vector<RRTNode *> nodes;
 779         if (!n || !n->parent())
 780                 return nodes;
 781         while (n) {
 782                 nodes.push_back(n);
 783                 n = n->parent();
 784         }
 785         return nodes;
 786 }
 787
 788 // RRT Framework
 789 RRTNode *RRTBase::sample()
 790 {
 791         return sa1();
 792 }
 793
 794 float RRTBase::cost(RRTNode *init, RRTNode *goal)
 795 {
 796         return co2(init, goal);
 797 }
 798
 799 RRTNode *RRTBase::nn(RRTNode *rs)
 800 {
 801         return nn4(this->iy_, rs, nullptr);
 802         //return nn3(this->iy_, rs, nullptr);
 803 }
 804
 805 std::vector<RRTNode *> RRTBase::nv(RRTNode *node, float dist)
 806 {
 807         std::vector<RRTNode *> nvs;
 808         unsigned int iy = IYI(node->y());
 809         unsigned int iy_dist = floor(dist / IYSTEP) + 1;
 810         unsigned int i = 0; // vector index
 811         unsigned int j = 0; // array index
 812         unsigned int jmin = 0; // minimal j index
 813         unsigned int jmax = 0; // maximal j index
 814         jmin = iy - iy_dist;
 815         jmin = (jmin > 0) ? jmin : 0;
 816         jmax = iy + iy_dist + 1;
 817         jmax = (jmax < IYSIZE) ? jmax : IYSIZE;
 818         #pragma omp parallel for reduction(merge: nvs)
 819         for (j = jmin; j < jmax; j++) {
 820                 #pragma omp parallel for reduction(merge: nvs)
 821                 for (i = 0; i < this->iy_[j].size(); i++) {
 822                         if (this->cost(this->iy_[j][i], node) < dist) {
 823                                 nvs.push_back(this->iy_[j][i]);
 824                         }
 825                 }
 826         }
 827         return nvs;
 828 }
 829
 830 std::vector<RRTNode *> RRTBase::steer(RRTNode *init, RRTNode *goal)
 831 {
 832         return st3(init, goal);
 833 }