commit 7442cd91ba7eb02b16d819d519fa57d22a607ead Author: Steffen Vogel Date: Sat Jun 4 09:26:58 2016 +0200 first commit for Patti diff --git a/Animation.gif b/Animation.gif new file mode 100644 index 0000000..4fc9d64 Binary files /dev/null and b/Animation.gif differ diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..b188d59 --- /dev/null +++ b/Makefile @@ -0,0 +1,16 @@ +CXX = clang++ + +CXXFLAGS = -I/opt/local/include/eigen3/ + +.PHONY: plot all + +all: collision_probabilty + +collision_probabilty: collision_probabilty.cpp + $(CXX) $(CXXFLAGS) collision_probabilty.cpp -o collision_probabilty + +samples.dat: collision_probabilty + ./collision_probabilty > samples.dat + +plot: samples.dat + gnuplot -c gnuplot.script \ No newline at end of file diff --git a/collision_probabilty b/collision_probabilty new file mode 100755 index 0000000..c77f18b Binary files /dev/null and b/collision_probabilty differ diff --git a/collision_probabilty.cpp b/collision_probabilty.cpp new file mode 100755 index 0000000..921d69c --- /dev/null +++ b/collision_probabilty.cpp @@ -0,0 +1,200 @@ +#include +#include +#include +#include +#include +#include +#include + +#include +#include + +using namespace std; +using namespace Eigen; + +typedef Matrix VertexList; + +#define N 1000 + +typedef bool(*CollisionFunction)(const Vector3d &a, const Vector3d &b); + +/* Generate N-dimensional normal distributed samples */ +class MultivariateNormalDistribution : normal_distribution { + +protected: + mt19937 gen; + + Matrix covar; + Matrix transform; + Matrix mean; + + // drawback: this creates a useless eigenSolver when using Cholesky decomposition, but it yields access to eigenvalues and vectors + + +public: + MultivariateNormalDistribution(const Matrix &m, const Matrix &c, const mt19937 &g) : + gen(g), + mean(m), + covar(c), + normal_distribution(0, 1) + { + LLT > cholSolver(covar); + // We can only use the cholesky decomposition if + // the covariance matrix is symmetric, pos-definite. + // But a covariance matrix might be pos-semi-definite. + // In that case, we'll go to an EigenSolver + if (cholSolver.info() == Success) { + // Use cholesky solver + transform = cholSolver.matrixL(); + } + else { + SelfAdjointEigenSolver > eigenSolver(covar); + transform = eigenSolver.eigenvectors() * eigenSolver.eigenvalues().cwiseMax(0).cwiseSqrt().asDiagonal(); + } + } + + Vector3d randc() + { + Vector3d p, q; + + /* Get vector of standard normal distributed samples */ + for (int i = 0; i < p.rows(); i++) + p[i] = operator()(gen); + + return transform * p + mean; + } +}; + +/* Is point "t" in polygon "v"? + * From: https://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html */ +bool pnpoly(const VertexList &v, const Vector2d &t) +{ + int i, j; + bool c = false; + + for (i = 0, j = v.cols()-1; i < v.cols(); j = i++) { + if ( + ((v(1,i) > t(1)) != (v(1,j) > t(1))) && + (t(0) < (v(0,j) - v(0,i)) * (t(1) - v(1,i)) / (v(1,j) - v(1,i)) + v(0,i)) + ) + c = !c; + } + + return c; +} + +/* Calculate vertices of car polygon + * vertx, verty will be filled */ +VertexList poly_vehicle(const Vector3d &car) +{ + Rotation2D rot(car[2]); + + VertexList vertices(2, 4); + Vector2d offset = car.head(2); + + double scale = 1.5; + + vertices.col(0) << 2*scale, 1*scale; + vertices.col(1) << -2*scale, 1*scale; + vertices.col(2) << -2*scale, -1*scale; + vertices.col(3) << 2*scale, -1*scale; + + for (int i = 0; i < vertices.cols(); i++) + vertices.col(i) = rot * vertices.col(i) + offset; + return vertices; +} + +bool collision_vehicle(const Vector3d &vehicle, const Vector3d &obstacle) +{ + /* Create list of X/Y vertex points of car */ + VertexList vertices_vehicle, vertices_obstacle; + + vertices_vehicle = poly_vehicle(vehicle); + vertices_obstacle = poly_vehicle(obstacle); + + /* Check if any of the vertices of the obstacle car is inside the vehicle polygon */ + for (int i = 0; i < vertices_obstacle.cols(); i++) { + if (pnpoly(vertices_vehicle, vertices_obstacle.col(i)) > 0) + return true; + } + + return false; +} + +bool collision_circle(const Vector3d &vehicle, const Vector3d &obstacle) +{ + const double minDistance = 5; + + Vector3d delta = vehicle - obstacle; + + return delta.norm() < minDistance; /* Collision occured if distance (r) is smaller than 1 */ +} + +double collision_probability(CollisionFunction cfunc, MultivariateNormalDistribution &vehicle, MultivariateNormalDistribution &obstacle) +{ + unsigned collisions = 0; + + for (unsigned j = 0; j < N; j++) { + Vector3d sample_vehicle, sample_obstacle; + VertexList vertices_vehicle, vertices_obstacle; + + sample_vehicle = vehicle.randc(); + sample_obstacle = obstacle.randc(); + + vertices_vehicle = poly_vehicle(sample_vehicle); + vertices_obstacle = poly_vehicle(sample_obstacle); + + bool coll = cfunc(sample_vehicle, sample_obstacle); + + /* Print vehicle centers */ + cout << ((coll) ? 1 : 0) << " " + << sample_vehicle.transpose() << " " + << sample_obstacle.transpose(); + + /* Print vertices of vehicles */ + for (int i = 0; i < 4; i++) + cout << " " << vertices_vehicle.col(i).transpose(); + for (int i = 0; i < 4; i++) + cout << " " << vertices_obstacle.col(i).transpose(); + + cout << endl; + + if (coll) + collisions++; + } + + cout << "# collisions = " << collisions << endl; + + return (double) collisions / N; +} + +int main(int argc, char *argv[]) { + /* Initialize PRNG */ + random_device rd; + mt19937 gen(rd()); + + Vector3d mean_vehicle, mean_obstacle; + Matrix3d covar_vehicle, covar_obstacle; + + mean_vehicle << 5, 0, 3.0/4.0 * M_PI; // x, y, heading + mean_obstacle << 0, 0, 1.0/4.0 * M_PI; // x, y, heading + + covar_vehicle << 5, -4, 0, + -4, 9, 0, + 0, 0, 1.0/16.0*M_PI; + + covar_obstacle << 3, 2, 0, + 2, 3, 0, + 0, 0, 1.0/16.0*M_PI; + + CollisionFunction cfunc = collision_vehicle; + + MultivariateNormalDistribution vehicle(mean_vehicle, covar_vehicle, gen); + MultivariateNormalDistribution obstacle(mean_obstacle, covar_obstacle, gen); + + cout << "# Collision Vehicle_x Vehicle_y Obstacle_x Obstacle_y" << endl; + + double prob = collision_probability(cfunc, vehicle, obstacle); + + cout << "# collision probability is: " << prob << endl; +} \ No newline at end of file diff --git a/gnuplot.script b/gnuplot.script new file mode 100644 index 0000000..ffefcdc --- /dev/null +++ b/gnuplot.script @@ -0,0 +1,45 @@ +#reset +#set term gif animate +#set output "animate.gif" + + +unset key +set size ratio -1 +s = 0.4 + +samples = `egrep -v ^# samples.dat | wc -l` +collisions = `egrep ^1 samples.dat | wc -l` + +do for [tt=1:10] { + system "./collision_probabilty > samples.dat" + reread + + do for [pp=1:1] { + do for [ii=1:collisions-1] { + plot \ + "samples.dat" using 2:3 t "Vehicle" lc rgb "red" lt 7, \ + "samples.dat" using 5:6 t "Obstacle" lc rgb "blue" lt 7, \ + "samples.dat" using 2:3:(s*cos($4)):(s*sin($4)) with vectors nohead lc rgb "red", \ + "samples.dat" using 5:6:(s*cos($7)):(s*sin($7)) with vectors nohead lc rgb "blue", \ + "< egrep ^1 samples.dat" using 2:3:($5-$2):($6-$3) every ::ii::ii with vectors nohead lw 2 lc rgb "green" t "Collisions", \ + \ + "< egrep ^1 samples.dat" using 8:9:($10-$8):($11-$9) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 10:11:($12-$10):($13-$11) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 12:13:($14-$12):($15-$13) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 14:15:($8-$14):($9-$15) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + \ + "< egrep ^1 samples.dat" using 16:17:($18-$16):($19-$17) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 18:19:($20-$18):($21-$19) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 20:21:($22-$20):($23-$21) every ::ii::ii with vectors nohead lw 2 lc rgb "black", \ + "< egrep ^1 samples.dat" using 22:23:($16-$22):($17-$23) every ::ii::ii with vectors nohead lw 2 lc rgb "black" + + unset label 1 + unset label 2 + unset label 3 + set label 1 "Total Samples = " . samples at graph 0.1,0.1 + set label 2 "Total Collisions = " . collisions at graph 0.1,0.15 + set label 3 "Showing Collision = " . ii at graph 0.1,0.2 + } + } +} +set output \ No newline at end of file diff --git a/samples.dat b/samples.dat new file mode 100644 index 0000000..4e4466b --- /dev/null +++ b/samples.dat @@ -0,0 +1,1003 @@ +# Collision Vehicle_x Vehicle_y Obstacle_x Obstacle_y +0 2.64656 4.66815 2.48626 -1.82296 0.277819 0.91546 -0.646105 5.30716 4.11095 1.6506 5.93923 4.02913 1.18217 7.68569 -1.18395 3.57049 -4.84051 -1.18657 -2.46198 -3.01485 1.19458 1.74221 +1 3.36456 -0.649255 2.85855 -1.2668 -1.89392 1.28775 0.0650147 -1.25174 5.82628 -2.9274 6.66411 -0.0467737 0.902849 1.62889 -1.86929 1.40563 -3.54495 -4.35564 -0.664323 -5.19347 1.01135 0.567791 +0 6.12973 0.614787 1.78024 0.875086 1.39743 0.209445 4.03876 3.23735 5.28626 -2.63153 8.2207 -2.00778 6.9732 3.8611 3.49765 3.4884 -2.37123 2.2409 -1.74748 -0.69354 4.1214 0.553962 +0 1.85829 3.49847 2.15017 -2.43356 -1.0943 0.579371 -1.03941 5.18765 2.24557 0.166802 4.756 1.8093 1.47101 6.83014 -0.74438 1.8034 -5.76522 -1.48158 -4.12273 -3.992 0.898112 -0.707017 +0 6.2934 -6.02191 2.07498 1.00186 -2.00551 0.504185 3.53076 -4.11984 6.42933 -9.37325 9.05603 -7.92397 6.15747 -2.67056 2.90392 0.757129 -2.34949 -2.14144 -0.900202 -4.76814 4.35321 -1.86958 +1 6.00283 4.03988 2.5594 0.776787 3.11352 0.988608 2.67226 4.43655 7.68383 1.13743 9.33339 3.64322 4.32182 6.94233 1.17345 6.44408 -2.12566 1.43251 0.380121 -0.217045 3.67924 4.79453 +0 3.80009 2.8076 2.16468 -0.929446 0.370826 0.593879 0.878185 4.45456 4.23567 -0.518097 6.72199 1.16064 3.36451 6.1333 0.717512 3.29273 -4.25515 -0.0647501 -2.5764 -2.55108 2.39625 0.806403 +0 5.13126 2.16976 1.99974 0.101673 1.28719 0.428944 2.51942 4.27411 5.01488 -1.18232 7.7431 0.065411 5.24764 5.52184 2.20602 3.89903 -3.25041 1.40356 -2.00268 -1.32465 3.45376 1.17081 +0 3.20783 0.308539 2.23947 -1.38821 -1.52864 0.668679 0.171016 1.73254 3.89071 -2.97531 6.24464 -1.11546 2.52494 3.59239 0.0357889 1.50817 -4.67206 -2.21153 -2.81221 -4.56546 1.89564 -0.845758 +0 9.0003 -4.02582 1.62926 3.09862 1.62319 0.0584636 7.32758 -1.11859 7.67816 -7.10834 10.673 -6.93305 10.3225 -0.9433 6.00585 3.29592 0.016102 2.94534 0.191393 -0.0495361 6.18114 0.301046 +1 6.08152 1.49765 2.33045 0.83774 1.82512 0.759654 2.92789 2.63986 7.05992 -1.71058 9.23514 0.355431 5.10312 4.70588 1.97996 4.97874 -2.37049 0.846718 -0.304476 -1.3285 4.04597 2.80352 +0 8.09789 0.283804 3.06003 2.39962 3.08039 1.48923 4.98566 -0.96679 10.9657 -1.45563 11.2101 1.5344 5.23007 2.02324 1.14902 6.19263 0.660184 0.212577 3.65021 -0.0318418 4.13905 5.94821 +0 2.6024 -1.116 3.32024 -1.85717 -2.86455 1.74945 -0.0833022 -3.12523 5.8212 -2.05902 5.2881 0.893232 -0.616406 -0.172975 -3.8664 -0.178851 -2.8002 -6.08336 0.152057 -5.55025 -0.914151 0.354253 +0 3.99771 2.43373 2.38938 -0.776373 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