├── RunMe.m ├── ampl.exe ├── ipopt.exe ├── libhsl.dll ├── GenerateAIM.p ├── ampltabl_64.dll ├── fingerprint.exe ├── libipoptfort.dll ├── DrawIntersection.p ├── ResampleProfile.p ├── EvaluateThroughput.p ├── ShowDynamicResults.p ├── SpecifyInitialGuess.p ├── ipopt.opt ├── ShowDynamicsInitialGuess.p ├── SearchTrajectoryInXYTGraph.p ├── ampl.lic ├── GenerateOriginalObstacleLayers.m ├── SpecifyRanklist.m ├── rr.run ├── rr0.run ├── WriteBoundaryValuesAndBasicParams.m ├── CheckCollisions.m ├── NLP0.mod ├── NLP.mod └── LICENSE /RunMe.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/RunMe.m -------------------------------------------------------------------------------- /ampl.exe: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ampl.exe -------------------------------------------------------------------------------- /ipopt.exe: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ipopt.exe -------------------------------------------------------------------------------- /libhsl.dll: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/libhsl.dll -------------------------------------------------------------------------------- /GenerateAIM.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/GenerateAIM.p -------------------------------------------------------------------------------- /ampltabl_64.dll: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ampltabl_64.dll -------------------------------------------------------------------------------- /fingerprint.exe: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/fingerprint.exe -------------------------------------------------------------------------------- /libipoptfort.dll: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/libipoptfort.dll -------------------------------------------------------------------------------- /DrawIntersection.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/DrawIntersection.p -------------------------------------------------------------------------------- /ResampleProfile.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ResampleProfile.p -------------------------------------------------------------------------------- /EvaluateThroughput.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/EvaluateThroughput.p -------------------------------------------------------------------------------- /ShowDynamicResults.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ShowDynamicResults.p -------------------------------------------------------------------------------- /SpecifyInitialGuess.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/SpecifyInitialGuess.p -------------------------------------------------------------------------------- /ipopt.opt: -------------------------------------------------------------------------------- 1 | max_iter 5000 2 | tol 1e-6 3 | bound_push 0.0001 4 | mu_strategy adaptive 5 | linear_solver ma57 6 | print_level 5 -------------------------------------------------------------------------------- /ShowDynamicsInitialGuess.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/ShowDynamicsInitialGuess.p -------------------------------------------------------------------------------- /SearchTrajectoryInXYTGraph.p: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/libai2020/Autonomous_Intersection_Management/HEAD/SearchTrajectoryInXYTGraph.p -------------------------------------------------------------------------------- /ampl.lic: -------------------------------------------------------------------------------- 1 | # Demo AMPL, BARON, CONOPT, CPLEX, GUROBI, KNITRO, LGO, LOQO, MINOS, 2 | # SNOPT & XPRESS license with maintenance expiring 20191227 3 | 5c24ede5 60219ae4 15d418f6 c52ef0b1 43529e59 4c74b8ad c434e8d2 66eab5f8 4 | 12718a8c bc649644 34619f70 f1442a57 9c8b54bd 9c71aa7c a3f4a734 8050c706 5 | 69ec1020 6f6426ec 13dfcc81 d0e33670 ef92c54b d7436b04 e55a34d4 6707028d 6 | 4da28867 bde4d83b 642ccf22 6041a680 4cd1cb07 e361df4d 81841234 1121c43b 7 | 94e14505 e9a4e073 129fc5e7 a7cb9772 7a3ba07b 46614b47 ef 8 | 9 | -------------------------------------------------------------------------------- /GenerateOriginalObstacleLayers.m: -------------------------------------------------------------------------------- 1 | function original_obstacle_layers = GenerateOriginalObstacleLayers() 2 | global xyt_graph_search_ obstacles_ 3 | original_obstacle_layers = cell(1, xyt_graph_search_.num_nodes_t); 4 | ang = linspace(0, 2 * pi, 200); 5 | cos_ang = cos(ang); 6 | sin_ang = sin(ang); 7 | for ii = 1 : xyt_graph_search_.num_nodes_t 8 | x_obs = []; 9 | y_obs = []; 10 | for jj = 1 : size(obstacles_, 2) 11 | obs = obstacles_{1, jj}; 12 | xc = obs{1, ii}.x; yc = obs{1, ii}.y; R = obs{1, ii}.radius; 13 | x = xc + R .* cos_ang; 14 | y = yc + R .* sin_ang; 15 | x_obs = [x_obs, x]; 16 | y_obs = [y_obs, y]; 17 | end 18 | temp.x = x_obs; temp.y = y_obs; 19 | original_obstacle_layers{1,ii} = temp; 20 | end 21 | end -------------------------------------------------------------------------------- /SpecifyRanklist.m: -------------------------------------------------------------------------------- 1 | function [index_flag, ranklist] = SpecifyRanklist(Nv) 2 | distance_to_origin = zeros(1, Nv); 3 | index_flag = zeros(1, Nv); 4 | global A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 boundary_configs_ 5 | for ii = 1 : (A1 + A2 + A3) 6 | distance_to_origin(ii) = 10 * abs(boundary_configs_{1,ii}.x0) + abs(boundary_configs_{1,ii}.y0); 7 | index_flag(ii) = 1; 8 | end 9 | 10 | for ii = (A1 + A2 + A3 + 1) : (A1 + A2 + A3 + B1 + B2 + B3) 11 | distance_to_origin(ii) = abs(boundary_configs_{1,ii}.x0) + 10 * abs(boundary_configs_{1,ii}.y0); 12 | index_flag(ii) = 2; 13 | end 14 | 15 | for ii = (A1 + A2 + A3 + B1 + B2 + B3 + 1) : (A1 + A2 + A3 + B1 + B2 + B3 + C1 + C2 + C3) 16 | distance_to_origin(ii) = 10 * abs(boundary_configs_{1,ii}.x0) + abs(boundary_configs_{1,ii}.y0); 17 | index_flag(ii) = 3; 18 | end 19 | 20 | for ii = (A1 + A2 + A3 + B1 + B2 + B3 + C1 + C2 + C3 + 1) : Nv 21 | distance_to_origin(ii) = abs(boundary_configs_{1,ii}.x0) + 10 * abs(boundary_configs_{1,ii}.y0); 22 | index_flag(ii) = 4; 23 | end 24 | 25 | [~, ranklist] = sort(distance_to_origin,'descend'); 26 | end -------------------------------------------------------------------------------- /rr.run: -------------------------------------------------------------------------------- 1 | reset; 2 | model NLP.mod; 3 | include IG.INIVAL; 4 | option solver ipopt; 5 | 6 | shell ("del " & ("opti_flag.txt")); 7 | printf "0">>("opti_flag.txt"); 8 | close ("opti_flag.txt"); 9 | 10 | solve; 11 | 12 | shell ("del " & ("opti_flag.txt")); 13 | if match (solve_message, "Optimal") > 0 then { 14 | printf "1">>("opti_flag.txt"); 15 | } else{ 16 | printf "0">>("opti_flag.txt"); 17 | } 18 | close ("opti_flag.txt"); 19 | 20 | shell ("del " & ("x.txt")); 21 | shell ("del " & ("y.txt")); 22 | shell ("del " & ("theta.txt")); 23 | shell ("del " & ("phy.txt")); 24 | 25 | for {i in {1..Nv}} { 26 | for {j in {1..Nfe}} { 27 | printf "%5.4f;", x[i,j]>>("x.txt"); 28 | printf "%5.4f;", y[i,j]>>("y.txt"); 29 | printf "%5.4f;", theta[i,j]>>("theta.txt"); 30 | printf "%5.4f;", phy[i,j]>>("phy.txt"); 31 | } 32 | } 33 | close ("x.txt"); 34 | close ("y.txt"); 35 | close ("theta.txt"); 36 | close ("phy.txt"); 37 | 38 | if match (solve_message, "Optimal") > 0 then { 39 | shell ("del " & ("IG.INIVAL")); 40 | for {k in {1..Nv}} { 41 | for {i in {1..Nfe}} { 42 | printf "let x[%d,%d]:=%5.3f;\n", k, i, x[k,i]>>("IG.INIVAL"); 43 | printf "let y[%d,%d]:=%5.3f;\n", k, i, y[k,i]>>("IG.INIVAL"); 44 | printf "let xr[%d,%d]:=%5.3f;\n", k, i, xr[k,i]>>("IG.INIVAL"); 45 | printf "let yr[%d,%d]:=%5.3f;\n", k, i, yr[k,i]>>("IG.INIVAL"); 46 | printf "let xf[%d,%d]:=%5.3f;\n", k, i, xf[k,i]>>("IG.INIVAL"); 47 | printf "let yf[%d,%d]:=%5.3f;\n", k, i, yf[k,i]>>("IG.INIVAL"); 48 | printf "let theta[%d,%d]:=%5.3f;\n", k, i, theta[k,i]>>("IG.INIVAL"); 49 | printf "let v[%d,%d]:=%5.3f;\n", k, i, v[k,i]>>("IG.INIVAL"); 50 | printf "let a[%d,%d]:=%5.3f;\n", k, i, a[k,i]>>("IG.INIVAL"); 51 | printf "let phy[%d,%d]:=%5.3f;\n", k, i, phy[k,i]>>("IG.INIVAL"); 52 | printf "let w[%d,%d]:=%5.3f;\n", k, i, w[k,i]>>("IG.INIVAL"); 53 | } 54 | } 55 | close ("IG.INIVAL"); 56 | } 57 | -------------------------------------------------------------------------------- /rr0.run: -------------------------------------------------------------------------------- 1 | reset; 2 | model NLP0.mod; 3 | include IG.INIVAL; 4 | option solver ipopt; 5 | 6 | shell ("del " & ("opti_flag.txt")); 7 | printf "0">>("opti_flag.txt"); 8 | close ("opti_flag.txt"); 9 | 10 | solve; 11 | 12 | shell ("del " & ("opti_flag.txt")); 13 | if match (solve_message, "Optimal") > 0 then { 14 | printf "1">>("opti_flag.txt"); 15 | } else{ 16 | printf "0">>("opti_flag.txt"); 17 | } 18 | close ("opti_flag.txt"); 19 | 20 | shell ("del " & ("x.txt")); 21 | shell ("del " & ("y.txt")); 22 | shell ("del " & ("theta.txt")); 23 | shell ("del " & ("phy.txt")); 24 | 25 | for {i in {1..Nv}} { 26 | for {j in {1..Nfe}} { 27 | printf "%5.4f;", x[i,j]>>("x.txt"); 28 | printf "%5.4f;", y[i,j]>>("y.txt"); 29 | printf "%5.4f;", theta[i,j]>>("theta.txt"); 30 | printf "%5.4f;", phy[i,j]>>("phy.txt"); 31 | } 32 | } 33 | close ("x.txt"); 34 | close ("y.txt"); 35 | close ("theta.txt"); 36 | close ("phy.txt"); 37 | 38 | if match (solve_message, "Optimal") > 0 then { 39 | shell ("del " & ("IG.INIVAL")); 40 | for {k in {1..Nv}} { 41 | for {i in {1..Nfe}} { 42 | printf "let x[%d,%d]:=%5.3f;\n", k, i, x[k,i]>>("IG.INIVAL"); 43 | printf "let y[%d,%d]:=%5.3f;\n", k, i, y[k,i]>>("IG.INIVAL"); 44 | printf "let xr[%d,%d]:=%5.3f;\n", k, i, xr[k,i]>>("IG.INIVAL"); 45 | printf "let yr[%d,%d]:=%5.3f;\n", k, i, yr[k,i]>>("IG.INIVAL"); 46 | printf "let xf[%d,%d]:=%5.3f;\n", k, i, xf[k,i]>>("IG.INIVAL"); 47 | printf "let yf[%d,%d]:=%5.3f;\n", k, i, yf[k,i]>>("IG.INIVAL"); 48 | printf "let theta[%d,%d]:=%5.3f;\n", k, i, theta[k,i]>>("IG.INIVAL"); 49 | printf "let v[%d,%d]:=%5.3f;\n", k, i, v[k,i]>>("IG.INIVAL"); 50 | printf "let a[%d,%d]:=%5.3f;\n", k, i, a[k,i]>>("IG.INIVAL"); 51 | printf "let phy[%d,%d]:=%5.3f;\n", k, i, phy[k,i]>>("IG.INIVAL"); 52 | printf "let w[%d,%d]:=%5.3f;\n", k, i, w[k,i]>>("IG.INIVAL"); 53 | } 54 | } 55 | close ("IG.INIVAL"); 56 | } 57 | -------------------------------------------------------------------------------- /WriteBoundaryValuesAndBasicParams.m: -------------------------------------------------------------------------------- 1 | function WriteBoundaryValuesAndBasicParams(Nv, Nfe) 2 | warning off 3 | global boundary_configs_ 4 | delete('BV'); 5 | fid = fopen('BV', 'w'); 6 | for ii = 1 : size(boundary_configs_,2) 7 | fprintf(fid, '%g 1 %f\r\n', ii, boundary_configs_{1,ii}.x0); 8 | fprintf(fid, '%g 2 %f\r\n', ii, boundary_configs_{1,ii}.y0); 9 | fprintf(fid, '%g 3 %f\r\n', ii, boundary_configs_{1,ii}.theta0); 10 | fprintf(fid, '%g 4 %f\r\n', ii, boundary_configs_{1,ii}.xtf); 11 | fprintf(fid, '%g 5 %f\r\n', ii, boundary_configs_{1,ii}.ytf); 12 | fprintf(fid, '%g 6 %f\r\n', ii, boundary_configs_{1,ii}.thetatf); 13 | end 14 | fclose(fid); 15 | 16 | global vehicle_geometrics_ vehicle_kinematics_ xyt_graph_search_ 17 | delete('BP'); 18 | fid = fopen('BP', 'w'); 19 | fprintf(fid, '1 %f\r\n', vehicle_geometrics_.wheelbase); 20 | fprintf(fid, '2 %f\r\n', vehicle_geometrics_.radius); 21 | fprintf(fid, '3 %f\r\n', vehicle_geometrics_.r2p); 22 | fprintf(fid, '4 %f\r\n', vehicle_geometrics_.f2p); 23 | 24 | fprintf(fid, '5 %f\r\n', vehicle_kinematics_.v_max); 25 | fprintf(fid, '6 %f\r\n', vehicle_kinematics_.a_max); 26 | fprintf(fid, '7 %f\r\n', vehicle_kinematics_.phy_max); 27 | fprintf(fid, '8 %f\r\n', vehicle_kinematics_.w_max); 28 | 29 | fprintf(fid, '9 %f\r\n', xyt_graph_search_.t_max); 30 | fprintf(fid, '10 %g\r\n', Nv); 31 | fprintf(fid, '11 %g\r\n', Nfe); 32 | fprintf(fid, '12 %g\r\n', vehicle_kinematics_.v_common); 33 | fclose(fid); 34 | 35 | global A1 A2 A3 B1 B2 B3 C1 C2 C3 D1 D2 D3 36 | cav_group = [A1, A2, A3, B1, B2, B3, C1, C2, C3, D1, D2, D3]; 37 | index_start = zeros(1, length(cav_group)); 38 | index_end = zeros(1, length(cav_group)); 39 | index_start(1,1) = 1; 40 | for ii = 2 : length(cav_group) 41 | index_start(ii) = sum(cav_group(1,1:ii-1)) + 1; 42 | end 43 | for ii = 1 : length(cav_group) 44 | index_end(ii) = index_start(ii) + cav_group(ii) - 1; 45 | end 46 | delete('cav_index_start'); 47 | delete('cav_index_end'); 48 | fid1 = fopen('cav_index_start', 'w'); 49 | fid2 = fopen('cav_index_end', 'w'); 50 | for ii = 1 : length(cav_group) 51 | fprintf(fid1, '%g %g \r\n', ii, index_start(ii)); 52 | fprintf(fid2, '%g %g \r\n', ii, index_end(ii)); 53 | end 54 | fclose(fid1); 55 | fclose(fid2); 56 | end -------------------------------------------------------------------------------- /CheckCollisions.m: -------------------------------------------------------------------------------- 1 | function is_collided = CheckCollisions() 2 | is_collided = 1; 3 | global NLP_ 4 | Nfe = NLP_.Nfe; 5 | load x.txt 6 | load y.txt 7 | load theta.txt 8 | Nv = length(x) / Nfe; 9 | x = reshape(x',Nfe,Nv)'; 10 | y = reshape(y',Nfe,Nv)'; 11 | theta = reshape(theta',Nfe,Nv)'; 12 | global NLP_ 13 | number_of_frame = NLP_.Nfe; 14 | Nv = size(x,1); 15 | global vehicle_geometrics_ 16 | lw = vehicle_geometrics_.wheelbase; 17 | hlb = vehicle_geometrics_.width / 2; 18 | global obstacles_ xyt_graph_search_ 19 | Nobs = size(obstacles_,2); 20 | index_list = round(linspace(1, xyt_graph_search_.num_nodes_t, number_of_frame)); 21 | for ii = 1 : number_of_frame 22 | for kk = 1 : Nobs 23 | cur_obs = obstacles_{1,kk}; 24 | xc = cur_obs{1,index_list(ii)}.x; 25 | yc = cur_obs{1,index_list(ii)}.y; 26 | rc = cur_obs{1,index_list(ii)}.radius; 27 | 28 | for jj = 1 : Nv 29 | xv = x(jj,ii); 30 | yv = y(jj,ii); 31 | tv = theta(jj,ii); 32 | 33 | xr = xv + vehicle_geometrics_.r2p * cos(tv); 34 | yr = yv + vehicle_geometrics_.r2p * sin(tv); 35 | xf = xv + vehicle_geometrics_.f2p * cos(tv); 36 | yf = yv + vehicle_geometrics_.f2p * sin(tv); 37 | 38 | if (norm([xr - xc, yr - yc]) - rc - vehicle_geometrics_.radius < -0.001) 39 | return; 40 | end 41 | if (norm([xf - xc, yf - yc]) - rc - vehicle_geometrics_.radius < -0.001) 42 | return; 43 | end 44 | end 45 | end 46 | 47 | for jj = 1 : (Nv - 1) 48 | for kk = (jj + 1) : Nv 49 | xv1 = x(jj,ii); 50 | yv1 = y(jj,ii); 51 | tv1 = theta(jj,ii); 52 | xv2 = x(kk,ii); 53 | yv2 = y(kk,ii); 54 | tv2 = theta(kk,ii); 55 | if (IsConfig1CollidingWithConfig2([xv1, yv1, tv1], [xv2, yv2, tv2])) 56 | return; 57 | end 58 | end 59 | end 60 | end 61 | is_collided = 0; 62 | end 63 | 64 | function is_colliding = IsConfig1CollidingWithConfig2(vec1, vec2) 65 | global vehicle_geometrics_ 66 | xr = [vec1(1), vec2(1)] + vehicle_geometrics_.r2p * cos([vec1(3), vec2(3)]); 67 | yr = [vec1(2), vec2(2)] + vehicle_geometrics_.r2p * sin([vec1(3), vec2(3)]); 68 | xf = [vec1(1), vec2(1)] + vehicle_geometrics_.f2p * cos([vec1(3), vec2(3)]); 69 | yf = [vec1(2), vec2(2)] + vehicle_geometrics_.f2p * sin([vec1(3), vec2(3)]); 70 | P11 = [xr(1), yr(1)]; 71 | P12 = [xf(1), yf(1)]; 72 | P21 = [xr(2), yr(2)]; 73 | P22 = [xf(2), yf(2)]; 74 | distance = min([norm(P11 - P21), norm(P11 - P22), norm(P12 - P21), norm(P12 - P22)]) - 2 * vehicle_geometrics_.radius; 75 | 76 | if (distance <= -0.001) 77 | is_colliding = 1; 78 | else 79 | is_colliding = 0; 80 | end 81 | end -------------------------------------------------------------------------------- /NLP0.mod: -------------------------------------------------------------------------------- 1 | param cav_index_start{i in {1..12}}; 2 | param cav_index_end{i in {1..12}}; 3 | set A1 := {cav_index_start[1]..cav_index_end[1]}; 4 | set A2 := {cav_index_start[2]..cav_index_end[2]}; 5 | set A3 := {cav_index_start[3]..cav_index_end[3]}; 6 | set B1 := {cav_index_start[4]..cav_index_end[4]}; 7 | set B2 := {cav_index_start[5]..cav_index_end[5]}; 8 | set B3 := {cav_index_start[6]..cav_index_end[6]}; 9 | set C1 := {cav_index_start[7]..cav_index_end[7]}; 10 | set C2 := {cav_index_start[8]..cav_index_end[8]}; 11 | set C3 := {cav_index_start[9]..cav_index_end[9]}; 12 | set D1 := {cav_index_start[10]..cav_index_end[10]}; 13 | set D2 := {cav_index_start[11]..cav_index_end[11]}; 14 | set D3 := {cav_index_start[12]..cav_index_end[12]}; 15 | 16 | param BP{i in {1..12}}; 17 | param wheelbase == BP[1]; 18 | param FourSqR == 4 * ((BP[2])^2); 19 | param R == BP[2]; 20 | param r2p == BP[3]; 21 | param f2p == BP[4]; 22 | param vmax == BP[5]; 23 | param amax == BP[6]; 24 | param phymax == BP[7]; 25 | param wmax == BP[8]; 26 | param tf == BP[9]; 27 | param Nv == BP[10]; 28 | param Nfe == BP[11]; 29 | param vcommon == BP[12]; 30 | param hi = tf / Nfe; 31 | 32 | param BV{i in {1..Nv}, j in {1..6}}; 33 | set IPmnt := {1..Nfe}; 34 | set IP := {1..Nfe}; 35 | 36 | var x{i in {1..Nv}, j in {1..Nfe}}; 37 | var y{i in {1..Nv}, j in {1..Nfe}}; 38 | var xf{i in {1..Nv}, j in {1..Nfe}}; 39 | var yf{i in {1..Nv}, j in {1..Nfe}}; 40 | var xr{i in {1..Nv}, j in {1..Nfe}}; 41 | var yr{i in {1..Nv}, j in {1..Nfe}}; 42 | var theta{i in {1..Nv}, j in {1..Nfe}}; 43 | var v{i in {1..Nv}, j in {1..Nfe}}; 44 | var a{i in {1..Nv}, j in {1..Nfe}}; 45 | var phy{i in {1..Nv}, j in {1..Nfe}}; 46 | var w{i in {1..Nv}, j in {1..Nfe}}; 47 | 48 | minimize cost_function: 49 | sum{k in A1}(x[k,Nfe]) + sum{k in A2}(-y[k,Nfe]) + sum{k in A3}(-x[k,Nfe]) + sum{k in B1}(y[k,Nfe]) + sum{k in B2}(x[k,Nfe]) + sum{k in B3}(-y[k,Nfe]) + sum{k in C1}(-x[k,Nfe]) + sum{k in C2}(y[k,Nfe]) + sum{k in C3}(x[k,Nfe]) + sum{k in D1}(-y[k,Nfe]) + sum{k in D2}(-x[k,Nfe]) + sum{k in D3}(y[k,Nfe]); 50 | 51 | 52 | s.t. DIFF_dxdt {k in {1..Nv}, i in {2..Nfe}}: 53 | x[k,i] = x[k,i-1] + hi * v[k,i] * cos(theta[k,i]); 54 | s.t. DIFF_dydt {k in {1..Nv}, i in {2..Nfe}}: 55 | y[k,i] = y[k,i-1] + hi * v[k,i] * sin(theta[k,i]); 56 | s.t. DIFF_dvdt {k in {1..Nv}, i in {2..Nfe}}: 57 | v[k,i] = v[k,i-1] + hi * a[k,i]; 58 | s.t. DIFF_dthetadt {k in {1..Nv}, i in {2..Nfe}}: 59 | theta[k,i] = theta[k,i-1] + hi * tan(phy[k,i]) * v[k,i] / wheelbase; 60 | s.t. DIFF_dphydt {k in {1..Nv}, i in {2..Nfe}}: 61 | phy[k,i] = phy[k,i-1] + hi * w[k,i]; 62 | 63 | s.t. RELATIONSHIP_XF {k in {1..Nv}, i in IPmnt}: 64 | xf[k,i] = x[k,i] + f2p * cos(theta[k,i]); 65 | s.t. RELATIONSHIP_YF {k in {1..Nv}, i in IPmnt}: 66 | yf[k,i] = y[k,i] + f2p * sin(theta[k,i]); 67 | s.t. RELATIONSHIP_XR {k in {1..Nv}, i in IPmnt}: 68 | xr[k,i] = x[k,i] + r2p * cos(theta[k,i]); 69 | s.t. RELATIONSHIP_YR {k in {1..Nv}, i in IPmnt}: 70 | yr[k,i] = y[k,i] + r2p * sin(theta[k,i]); 71 | 72 | s.t. Bonds_phy {k in {1..Nv}, i in {1..Nfe}}: 73 | -phymax <= phy[k,i] <= phymax; 74 | s.t. Bonds_a {k in {1..Nv}, i in {1..Nfe}}: 75 | -amax <= a[k,i] <= amax; 76 | s.t. Bonds_v {k in {1..Nv}, i in {1..Nfe}}: 77 | 0 <= v[k,i] <= vmax; 78 | s.t. Bonds_w {k in {1..Nv}, i in {1..Nfe}}: 79 | -wmax <= w[k,i] <= wmax; 80 | 81 | ### D1 ### 82 | s.t. L1argeCircle_for_D1 {i in D1, j in IP}: 83 | ((xr[i,j]+100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 84 | s.t. M1iddleCircle_for_D1 {i in D1, j in IP}: 85 | ((xr[i,j]+56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 86 | s.t. S1mallCircle_for_D1 {i in D1, j in IP}: 87 | ((xr[i,j]+34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 88 | s.t. L2argeCircle_for_D1 {i in D1, j in IP}: 89 | ((xf[i,j]+100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 90 | s.t. M2iddleCircle_for_D1 {i in D1, j in IP}: 91 | ((xf[i,j]+56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 92 | s.t. S2mallCircle_for_D1 {i in D1, j in IP}: 93 | ((xf[i,j]+34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 94 | s.t. limit_xr_D1 {i in D1, j in IP}: 95 | xr[i,j] + R <= 12; 96 | s.t. limit_xf_D1 {i in D1, j in IP}: 97 | xf[i,j] + R <= 12; 98 | s.t. limit_yr_D1 {i in D1, j in IP}: 99 | yr[i,j] - R >= -12; 100 | s.t. limit_yf_D1 {i in D1, j in IP}: 101 | yf[i,j] - R >= -12; 102 | s.t. terminal_x_D1 {m in D1}: 103 | yr[m,Nfe] - R >= 12; 104 | s.t. terminal_xr_D1 {m in D1}: 105 | xr[m,Nfe] - R >= 0; 106 | s.t. terminal_xf_D1 {m in D1}: 107 | xf[m,Nfe] - R >= 0; 108 | s.t. interval_theta_D1 {i in D1, j in IPmnt}: 109 | -1 <= theta[i,j] <= 2; 110 | ### D2 ### 111 | s.t. limit_yr_D2 {i in D2, j in IP}: 112 | -12 + R <= yr[i,j] <= -R; 113 | s.t. limit_yf_D2 {i in D2, j in IP}: 114 | -12 + R <= yf[i,j] <= -R; 115 | s.t. terminal_x_D2 {m in D2}: 116 | xr[m,Nfe] - R >= 12; 117 | s.t. interval_theta_D2 {i in D2, j in IPmnt}: 118 | -1 <= theta[i,j] <= 1; 119 | ### D3 ### 120 | s.t. L1argeCircle_for_D3 {i in D3, j in IP}: 121 | ((xr[i,j]+100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 122 | s.t. M1iddleCircle_for_D3 {i in D3, j in IP}: 123 | ((xr[i,j]+56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 124 | s.t. S1mallCircle_for_D3 {i in D3, j in IP}: 125 | ((xr[i,j]+34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 126 | s.t. L2argeCircle_for_D3 {i in D3, j in IP}: 127 | ((xf[i,j]+100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 128 | s.t. M2iddleCircle_for_D3 {i in D3, j in IP}: 129 | ((xf[i,j]+56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 130 | s.t. S2mallCircle_for_D3 {i in D3, j in IP}: 131 | ((xf[i,j]+34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 132 | s.t. limit_xr_D3 {i in D3, j in IP}: 133 | xr[i,j] + R <= 0; 134 | s.t. limit_xf_D3 {i in D3, j in IP}: 135 | xf[i,j] + R <= 0; 136 | s.t. limit_yr_D3 {i in D3, j in IP}: 137 | yr[i,j] + R <= 0; 138 | s.t. limit_yf_D3 {i in D3, j in IP}: 139 | yf[i,j] + R <= 0; 140 | s.t. terminal_x_D3 {m in D3}: 141 | yr[m,Nfe] + R <= -12; 142 | s.t. interval_theta_D3 {i in D3, j in IPmnt}: 143 | -2 <= theta[i,j] <= 1; 144 | ### A1 ### 145 | s.t. L1argeCircle_for_A1 {i in A1, j in IP}: 146 | ((xr[i,j]+100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 147 | s.t. M1iddleCircle_for_A1 {i in A1, j in IP}: 148 | ((xr[i,j]+56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 149 | s.t. S1mallCircle_for_A1 {i in A1, j in IP}: 150 | ((xr[i,j]+34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 151 | s.t. L2argeCircle_for_A1 {i in A1, j in IP}: 152 | ((xf[i,j]+100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 153 | s.t. M2iddleCircle_for_A1 {i in A1, j in IP}: 154 | ((xf[i,j]+56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 155 | s.t. S2mallCircle_for_A1 {i in A1, j in IP}: 156 | ((xf[i,j]+34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 157 | s.t. limit_xr_A1 {i in A1, j in IP}: 158 | xr[i,j] + R <= 12; 159 | s.t. limit_xf_A1 {i in A1, j in IP}: 160 | xf[i,j] + R <= 12; 161 | s.t. limit_yr_A1 {i in A1, j in IP}: 162 | yr[i,j] + R <= 12; 163 | s.t. limit_yf_A1 {i in A1, j in IP}: 164 | yf[i,j] + R <= 12; 165 | s.t. terminal_x_A1 {m in A1}: 166 | xr[m,Nfe] + R <= -12; 167 | s.t. terminal_yr_A1 {m in A1}: 168 | yr[m,Nfe] - R >= 0; 169 | s.t. terminal_yf_A1 {m in A1}: 170 | yf[m,Nfe] - R >= 0; 171 | s.t. interval_theta_A1 {i in A1, j in IPmnt}: 172 | 1 <= theta[i,j] <= 4; 173 | ### A2 ### 174 | s.t. limit_xr_A2 {i in A2, j in IP}: 175 | R <= xr[i,j] <= 12 - R; 176 | s.t. limit_xf_A2 {i in A2, j in IP}: 177 | R <= xf[i,j] <= 12 - R; 178 | s.t. terminal_x_A2 {m in A2}: 179 | yr[m,Nfe] - R >= 12; 180 | s.t. interval_theta_A2 {i in A2, j in IPmnt}: 181 | 1 <= theta[i,j] <= 2; 182 | ### A3 ### 183 | s.t. L1argeCircle_for_A3 {i in A3, j in IP}: 184 | ((xr[i,j]-100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 185 | s.t. M1iddleCircle_for_A3 {i in A3, j in IP}: 186 | ((xr[i,j]-56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 187 | s.t. S1mallCircle_for_A3 {i in A3, j in IP}: 188 | ((xr[i,j]-34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 189 | s.t. L2argeCircle_for_A3 {i in A3, j in IP}: 190 | ((xf[i,j]-100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 191 | s.t. M2iddleCircle_for_A3 {i in A3, j in IP}: 192 | ((xf[i,j]-56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 193 | s.t. S2mallCircle_for_A3 {i in A3, j in IP}: 194 | ((xf[i,j]-34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 195 | s.t. limit_xr_A3 {i in A3, j in IP}: 196 | xr[i,j] - R >= 0; 197 | s.t. limit_xf_A3 {i in A3, j in IP}: 198 | xf[i,j] - R >= 0; 199 | s.t. limit_yr_A3 {i in A3, j in IP}: 200 | yr[i,j] + R <= 0; 201 | s.t. limit_yf_A3 {i in A3, j in IP}: 202 | yf[i,j] + R <= 0; 203 | s.t. terminal_x_A3 {m in A3}: 204 | xr[m,Nfe] - R >= 12; 205 | s.t. interval_theta_A3 {i in A3, j in IPmnt}: 206 | -1 <= theta[i,j] <= 2; 207 | ### B1 ### 208 | s.t. L1argeCircle_for_B1 {i in B1, j in IP}: 209 | ((xr[i,j]-100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 210 | s.t. M1iddleCircle_for_B1 {i in B1, j in IP}: 211 | ((xr[i,j]-56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 212 | s.t. S1mallCircle_for_B1 {i in B1, j in IP}: 213 | ((xr[i,j]-34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 214 | s.t. L2argeCircle_for_B1 {i in B1, j in IP}: 215 | ((xf[i,j]-100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 216 | s.t. M2iddleCircle_for_B1 {i in B1, j in IP}: 217 | ((xf[i,j]-56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 218 | s.t. S2mallCircle_for_B1 {i in B1, j in IP}: 219 | ((xf[i,j]-34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 220 | s.t. limit_xr_B1 {i in B1, j in IP}: 221 | xr[i,j] - R >= -12; 222 | s.t. limit_xf_B1 {i in B1, j in IP}: 223 | xf[i,j] - R >= -12; 224 | s.t. limit_yr_B1 {i in B1, j in IP}: 225 | yr[i,j] + R <= 12; 226 | s.t. limit_yf_B1 {i in B1, j in IP}: 227 | yf[i,j] + R <= 12; 228 | s.t. terminal_x_B1 {m in B1}: 229 | yr[m,Nfe] + R <= -12; 230 | s.t. terminal_xr_B1 {m in B1}: 231 | xr[m,Nfe] + R <= 0; 232 | s.t. terminal_xf_B1 {m in B1}: 233 | xf[m,Nfe] + R <= 0; 234 | s.t. interval_theta_B1 {i in B1, j in IPmnt}: 235 | 2 <= theta[i,j] <= 6; 236 | ### B2 ### 237 | s.t. limit_yr_B2 {i in B2, j in IP}: 238 | R <= yr[i,j] <= 12 - R; 239 | s.t. limit_yf_B2 {i in B2, j in IP}: 240 | R <= yf[i,j] <= 12 - R; 241 | s.t. terminal_x_B2 {m in B2}: 242 | xr[m,Nfe] + R <= -12; 243 | s.t. interval_theta_B2 {i in B2, j in IPmnt}: 244 | 2 <= theta[i,j] <= 4; 245 | ### B3 ### 246 | s.t. L1argeCircle_for_B3 {i in B3, j in IP}: 247 | ((xr[i,j]-100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 248 | s.t. M1iddleCircle_for_B3 {i in B3, j in IP}: 249 | ((xr[i,j]-56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 250 | s.t. S1mallCircle_for_B3 {i in B3, j in IP}: 251 | ((xr[i,j]-34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 252 | s.t. L2argeCircle_for_B3 {i in B3, j in IP}: 253 | ((xf[i,j]-100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 254 | s.t. M2iddleCircle_for_B3 {i in B3, j in IP}: 255 | ((xf[i,j]-56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 256 | s.t. S2mallCircle_for_B3 {i in B3, j in IP}: 257 | ((xf[i,j]-34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 258 | s.t. limit_xr_B3 {i in B3, j in IP}: 259 | xr[i,j] - R >= 0; 260 | s.t. limit_xf_B3 {i in B3, j in IP}: 261 | xf[i,j] - R >= 0; 262 | s.t. limit_yr_B3 {i in B3, j in IP}: 263 | yr[i,j] - R >= 0; 264 | s.t. limit_yf_B3 {i in B3, j in IP}: 265 | yf[i,j] - R >= 0; 266 | s.t. terminal_x_B3 {m in B3}: 267 | yr[m,Nfe] - R >= 12; 268 | s.t. interval_theta_B3 {i in B3, j in IPmnt}: 269 | 1 <= theta[i,j] <= 4; 270 | ### C1 ### 271 | s.t. L1argeCircle_for_C1 {i in C1, j in IP}: 272 | ((xr[i,j]-100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 273 | s.t. M1iddleCircle_for_C1 {i in C1, j in IP}: 274 | ((xr[i,j]-56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 275 | s.t. S1mallCircle_for_C1 {i in C1, j in IP}: 276 | ((xr[i,j]-34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 277 | s.t. L2argeCircle_for_C1 {i in C1, j in IP}: 278 | ((xf[i,j]-100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 279 | s.t. M2iddleCircle_for_C1 {i in C1, j in IP}: 280 | ((xf[i,j]-56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 281 | s.t. S2mallCircle_for_C1 {i in C1, j in IP}: 282 | ((xf[i,j]-34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 283 | s.t. limit_xr_C1 {i in C1, j in IP}: 284 | xr[i,j] - R >= -12; 285 | s.t. limit_xf_C1 {i in C1, j in IP}: 286 | xf[i,j] - R >= -12; 287 | s.t. limit_yr_C1 {i in C1, j in IP}: 288 | yr[i,j] - R >= -12; 289 | s.t. limit_yf_C1 {i in C1, j in IP}: 290 | yf[i,j] - R >= -12; 291 | s.t. terminal_x_C1 {m in C1}: 292 | xr[m,Nfe] - R >= 12; 293 | s.t. terminal_xr_C1 {m in C1}: 294 | yr[m,Nfe] + R <= 0; 295 | s.t. terminal_xf_C1 {m in C1}: 296 | yf[m,Nfe] + R <= 0; 297 | s.t. interval_theta_C1 {i in C1, j in IPmnt}: 298 | -2 <= theta[i,j] <= 1; 299 | ### C2 ### 300 | s.t. limit_xr_C2 {i in C2, j in IP}: 301 | -12 + R <= xr[i,j] <= -R; 302 | s.t. limit_xf_C2 {i in C2, j in IP}: 303 | -12 + R <= xf[i,j] <= -R; 304 | s.t. terminal_x_C2 {m in C2}: 305 | yr[m,Nfe] + R <= -12; 306 | s.t. interval_theta_C2 {i in C2, j in IPmnt}: 307 | -2 <= theta[i,j] <= -1; 308 | ### C3 ### 309 | s.t. L1argeCircle_for_C3 {i in C3, j in IP}: 310 | ((xr[i,j]+100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 311 | s.t. M1iddleCircle_for_C3 {i in C3, j in IP}: 312 | ((xr[i,j]+56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 313 | s.t. S1mallCircle_for_C3 {i in C3, j in IP}: 314 | ((xr[i,j]+34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 315 | s.t. L2argeCircle_for_C3 {i in C3, j in IP}: 316 | ((xf[i,j]+100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 317 | s.t. M2iddleCircle_for_C3 {i in C3, j in IP}: 318 | ((xf[i,j]+56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 319 | s.t. S2mallCircle_for_C3 {i in C3, j in IP}: 320 | ((xf[i,j]+34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 321 | s.t. limit_xr_C3 {i in C3, j in IP}: 322 | xr[i,j] + R <= 0; 323 | s.t. limit_xf_C3 {i in C3, j in IP}: 324 | xf[i,j] + R <= 0; 325 | s.t. limit_yr_C3 {i in C3, j in IP}: 326 | yr[i,j] - R >= 0; 327 | s.t. limit_yf_C3 {i in C3, j in IP}: 328 | yf[i,j] - R >= 0; 329 | s.t. terminal_x_C3 {m in C3}: 330 | xr[m,Nfe] + R <= -12; 331 | s.t. interval_theta_C3 {i in C3, j in IPmnt}: 332 | -4 <= theta[i,j] <= -1; 333 | 334 | s.t. EQ_init_x {m in {1..Nv}}: 335 | x[m,1] = BV[m,1]; 336 | s.t. EQ_init_y {m in {1..Nv}}: 337 | y[m,1] = BV[m,2]; 338 | s.t. EQ_init_theta {m in {1..Nv}}: 339 | theta[m,1] = BV[m,3]; 340 | s.t. EQ_init_v {m in {1..Nv}}: 341 | v[m,1] = vcommon; 342 | s.t. EQ_init_a {m in {1..Nv}}: 343 | a[m,1] = 0; 344 | s.t. EQ_init_phy {m in {1..Nv}}: 345 | phy[m,1] = 0; 346 | s.t. EQ_init_w {m in {1..Nv}}: 347 | w[m,1] = 0; 348 | s.t. EQ_end_theta {m in {1..Nv}}: 349 | theta[m,Nfe] = BV[m,6]; 350 | s.t. EQ_end_v {m in {1..Nv}}: 351 | v[m,Nfe] = vcommon; 352 | s.t. EQ_end_a {m in {1..Nv}}: 353 | a[m,Nfe] = 0; 354 | s.t. EQ_end_phy {m in {1..Nv}}: 355 | phy[m,Nfe] = 0; 356 | s.t. EQ_end_w {m in {1..Nv}}: 357 | w[m,Nfe] = 0; 358 | 359 | data; 360 | param: cav_index_start := include cav_index_start; 361 | param: cav_index_end := include cav_index_end; 362 | param: BV := include BV; 363 | param: BP := include BP; -------------------------------------------------------------------------------- /NLP.mod: -------------------------------------------------------------------------------- 1 | param cav_index_start{i in {1..12}}; 2 | param cav_index_end{i in {1..12}}; 3 | set A1 := {cav_index_start[1]..cav_index_end[1]}; 4 | set A2 := {cav_index_start[2]..cav_index_end[2]}; 5 | set A3 := {cav_index_start[3]..cav_index_end[3]}; 6 | set B1 := {cav_index_start[4]..cav_index_end[4]}; 7 | set B2 := {cav_index_start[5]..cav_index_end[5]}; 8 | set B3 := {cav_index_start[6]..cav_index_end[6]}; 9 | set C1 := {cav_index_start[7]..cav_index_end[7]}; 10 | set C2 := {cav_index_start[8]..cav_index_end[8]}; 11 | set C3 := {cav_index_start[9]..cav_index_end[9]}; 12 | set D1 := {cav_index_start[10]..cav_index_end[10]}; 13 | set D2 := {cav_index_start[11]..cav_index_end[11]}; 14 | set D3 := {cav_index_start[12]..cav_index_end[12]}; 15 | 16 | param BP{i in {1..12}}; 17 | param wheelbase == BP[1]; 18 | param FourSqR == 4 * ((BP[2])^2); 19 | param R == BP[2]; 20 | param r2p == BP[3]; 21 | param f2p == BP[4]; 22 | param vmax == BP[5]; 23 | param amax == BP[6]; 24 | param phymax == BP[7]; 25 | param wmax == BP[8]; 26 | param tf == BP[9]; 27 | param Nv == BP[10]; 28 | param Nfe == BP[11]; 29 | param vcommon == BP[12]; 30 | param hi = tf / Nfe; 31 | 32 | param BV{i in {1..Nv}, j in {1..6}}; 33 | param TimeLine{i in {1..1}}; 34 | param Nt == TimeLine[1]; 35 | set I := {1..Nt}; 36 | set IPmnt := {1..Nfe}; 37 | set IP := {1..Nfe}; 38 | 39 | var x{i in {1..Nv}, j in {1..Nfe}}; 40 | var y{i in {1..Nv}, j in {1..Nfe}}; 41 | var xf{i in {1..Nv}, j in {1..Nfe}}; 42 | var yf{i in {1..Nv}, j in {1..Nfe}}; 43 | var xr{i in {1..Nv}, j in {1..Nfe}}; 44 | var yr{i in {1..Nv}, j in {1..Nfe}}; 45 | var theta{i in {1..Nv}, j in {1..Nfe}}; 46 | var v{i in {1..Nv}, j in {1..Nfe}}; 47 | var a{i in {1..Nv}, j in {1..Nfe}}; 48 | var phy{i in {1..Nv}, j in {1..Nfe}}; 49 | var w{i in {1..Nv}, j in {1..Nfe}}; 50 | 51 | minimize cost_function: 52 | hi * sum{i in {1..Nv}, j in I}(a[i,j]^2 + w[i,j]^2) + sum{k in A1}(x[k,Nfe]) + sum{k in A2}(-y[k,Nfe]) + sum{k in A3}(-x[k,Nfe]) + sum{k in B1}(y[k,Nfe]) + sum{k in B2}(x[k,Nfe]) + sum{k in B3}(-y[k,Nfe]) + sum{k in C1}(-x[k,Nfe]) + sum{k in C2}(y[k,Nfe]) + sum{k in C3}(x[k,Nfe]) + sum{k in D1}(-y[k,Nfe]) + sum{k in D2}(-x[k,Nfe]) + sum{k in D3}(y[k,Nfe]); 53 | 54 | 55 | s.t. DIFF_dxdt {k in {1..Nv}, i in {2..Nfe}}: 56 | x[k,i] = x[k,i-1] + hi * v[k,i] * cos(theta[k,i]); 57 | s.t. DIFF_dydt {k in {1..Nv}, i in {2..Nfe}}: 58 | y[k,i] = y[k,i-1] + hi * v[k,i] * sin(theta[k,i]); 59 | s.t. DIFF_dvdt {k in {1..Nv}, i in {2..Nfe}}: 60 | v[k,i] = v[k,i-1] + hi * a[k,i]; 61 | s.t. DIFF_dthetadt {k in {1..Nv}, i in {2..Nfe}}: 62 | theta[k,i] = theta[k,i-1] + hi * tan(phy[k,i]) * v[k,i] / wheelbase; 63 | s.t. DIFF_dphydt {k in {1..Nv}, i in {2..Nfe}}: 64 | phy[k,i] = phy[k,i-1] + hi * w[k,i]; 65 | 66 | s.t. RELATIONSHIP_XF {k in {1..Nv}, i in IPmnt}: 67 | xf[k,i] = x[k,i] + f2p * cos(theta[k,i]); 68 | s.t. RELATIONSHIP_YF {k in {1..Nv}, i in IPmnt}: 69 | yf[k,i] = y[k,i] + f2p * sin(theta[k,i]); 70 | s.t. RELATIONSHIP_XR {k in {1..Nv}, i in IPmnt}: 71 | xr[k,i] = x[k,i] + r2p * cos(theta[k,i]); 72 | s.t. RELATIONSHIP_YR {k in {1..Nv}, i in IPmnt}: 73 | yr[k,i] = y[k,i] + r2p * sin(theta[k,i]); 74 | 75 | s.t. Bonds_phy {k in {1..Nv}, i in {1..Nfe}}: 76 | -phymax <= phy[k,i] <= phymax; 77 | s.t. Bonds_a {k in {1..Nv}, i in {1..Nfe}}: 78 | -amax <= a[k,i] <= amax; 79 | s.t. Bonds_v {k in {1..Nv}, i in {1..Nfe}}: 80 | 0 <= v[k,i] <= vmax; 81 | s.t. Bonds_w {k in {1..Nv}, i in {1..Nfe}}: 82 | -wmax <= w[k,i] <= wmax; 83 | 84 | ### D1 ### 85 | s.t. L1argeCircle_for_D1 {i in D1, j in IP}: 86 | ((xr[i,j]+100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 87 | s.t. M1iddleCircle_for_D1 {i in D1, j in IP}: 88 | ((xr[i,j]+56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 89 | s.t. S1mallCircle_for_D1 {i in D1, j in IP}: 90 | ((xr[i,j]+34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 91 | s.t. L2argeCircle_for_D1 {i in D1, j in IP}: 92 | ((xf[i,j]+100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 93 | s.t. M2iddleCircle_for_D1 {i in D1, j in IP}: 94 | ((xf[i,j]+56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 95 | s.t. S2mallCircle_for_D1 {i in D1, j in IP}: 96 | ((xf[i,j]+34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 97 | s.t. limit_xr_D1 {i in D1, j in IP}: 98 | xr[i,j] + R <= 12; 99 | s.t. limit_xf_D1 {i in D1, j in IP}: 100 | xf[i,j] + R <= 12; 101 | s.t. limit_yr_D1 {i in D1, j in IP}: 102 | yr[i,j] - R >= -12; 103 | s.t. limit_yf_D1 {i in D1, j in IP}: 104 | yf[i,j] - R >= -12; 105 | s.t. terminal_x_D1 {m in D1}: 106 | yr[m,Nfe] - R >= 12; 107 | s.t. terminal_xr_D1 {m in D1}: 108 | xr[m,Nfe] - R >= 0; 109 | s.t. terminal_xf_D1 {m in D1}: 110 | xf[m,Nfe] - R >= 0; 111 | s.t. interval_theta_D1 {i in D1, j in IPmnt}: 112 | -1 <= theta[i,j] <= 2; 113 | ### D2 ### 114 | s.t. limit_yr_D2 {i in D2, j in IP}: 115 | -12 + R <= yr[i,j] <= -R; 116 | s.t. limit_yf_D2 {i in D2, j in IP}: 117 | -12 + R <= yf[i,j] <= -R; 118 | s.t. terminal_x_D2 {m in D2}: 119 | xr[m,Nfe] - R >= 12; 120 | s.t. interval_theta_D2 {i in D2, j in IPmnt}: 121 | -1 <= theta[i,j] <= 1; 122 | ### D3 ### 123 | s.t. L1argeCircle_for_D3 {i in D3, j in IP}: 124 | ((xr[i,j]+100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 125 | s.t. M1iddleCircle_for_D3 {i in D3, j in IP}: 126 | ((xr[i,j]+56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 127 | s.t. S1mallCircle_for_D3 {i in D3, j in IP}: 128 | ((xr[i,j]+34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 129 | s.t. L2argeCircle_for_D3 {i in D3, j in IP}: 130 | ((xf[i,j]+100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 131 | s.t. M2iddleCircle_for_D3 {i in D3, j in IP}: 132 | ((xf[i,j]+56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 133 | s.t. S2mallCircle_for_D3 {i in D3, j in IP}: 134 | ((xf[i,j]+34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 135 | s.t. limit_xr_D3 {i in D3, j in IP}: 136 | xr[i,j] + R <= 0; 137 | s.t. limit_xf_D3 {i in D3, j in IP}: 138 | xf[i,j] + R <= 0; 139 | s.t. limit_yr_D3 {i in D3, j in IP}: 140 | yr[i,j] + R <= 0; 141 | s.t. limit_yf_D3 {i in D3, j in IP}: 142 | yf[i,j] + R <= 0; 143 | s.t. terminal_x_D3 {m in D3}: 144 | yr[m,Nfe] + R <= -12; 145 | s.t. interval_theta_D3 {i in D3, j in IPmnt}: 146 | -2 <= theta[i,j] <= 1; 147 | ### A1 ### 148 | s.t. L1argeCircle_for_A1 {i in A1, j in IP}: 149 | ((xr[i,j]+100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 150 | s.t. M1iddleCircle_for_A1 {i in A1, j in IP}: 151 | ((xr[i,j]+56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 152 | s.t. S1mallCircle_for_A1 {i in A1, j in IP}: 153 | ((xr[i,j]+34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 154 | s.t. L2argeCircle_for_A1 {i in A1, j in IP}: 155 | ((xf[i,j]+100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 156 | s.t. M2iddleCircle_for_A1 {i in A1, j in IP}: 157 | ((xf[i,j]+56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 158 | s.t. S2mallCircle_for_A1 {i in A1, j in IP}: 159 | ((xf[i,j]+34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 160 | s.t. limit_xr_A1 {i in A1, j in IP}: 161 | xr[i,j] + R <= 12; 162 | s.t. limit_xf_A1 {i in A1, j in IP}: 163 | xf[i,j] + R <= 12; 164 | s.t. limit_yr_A1 {i in A1, j in IP}: 165 | yr[i,j] + R <= 12; 166 | s.t. limit_yf_A1 {i in A1, j in IP}: 167 | yf[i,j] + R <= 12; 168 | s.t. terminal_x_A1 {m in A1}: 169 | xr[m,Nfe] + R <= -12; 170 | s.t. terminal_yr_A1 {m in A1}: 171 | yr[m,Nfe] - R >= 0; 172 | s.t. terminal_yf_A1 {m in A1}: 173 | yf[m,Nfe] - R >= 0; 174 | s.t. interval_theta_A1 {i in A1, j in IPmnt}: 175 | 1 <= theta[i,j] <= 4; 176 | ### A2 ### 177 | s.t. limit_xr_A2 {i in A2, j in IP}: 178 | R <= xr[i,j] <= 12 - R; 179 | s.t. limit_xf_A2 {i in A2, j in IP}: 180 | R <= xf[i,j] <= 12 - R; 181 | s.t. terminal_x_A2 {m in A2}: 182 | yr[m,Nfe] - R >= 12; 183 | s.t. interval_theta_A2 {i in A2, j in IPmnt}: 184 | 1 <= theta[i,j] <= 2; 185 | ### A3 ### 186 | s.t. L1argeCircle_for_A3 {i in A3, j in IP}: 187 | ((xr[i,j]-100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 188 | s.t. M1iddleCircle_for_A3 {i in A3, j in IP}: 189 | ((xr[i,j]-56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 190 | s.t. S1mallCircle_for_A3 {i in A3, j in IP}: 191 | ((xr[i,j]-34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 192 | s.t. L2argeCircle_for_A3 {i in A3, j in IP}: 193 | ((xf[i,j]-100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 194 | s.t. M2iddleCircle_for_A3 {i in A3, j in IP}: 195 | ((xf[i,j]-56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 196 | s.t. S2mallCircle_for_A3 {i in A3, j in IP}: 197 | ((xf[i,j]-34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 198 | s.t. limit_xr_A3 {i in A3, j in IP}: 199 | xr[i,j] - R >= 0; 200 | s.t. limit_xf_A3 {i in A3, j in IP}: 201 | xf[i,j] - R >= 0; 202 | s.t. limit_yr_A3 {i in A3, j in IP}: 203 | yr[i,j] + R <= 0; 204 | s.t. limit_yf_A3 {i in A3, j in IP}: 205 | yf[i,j] + R <= 0; 206 | s.t. terminal_x_A3 {m in A3}: 207 | xr[m,Nfe] - R >= 12; 208 | s.t. interval_theta_A3 {i in A3, j in IPmnt}: 209 | -1 <= theta[i,j] <= 2; 210 | ### B1 ### 211 | s.t. L1argeCircle_for_B1 {i in B1, j in IP}: 212 | ((xr[i,j]-100)^2 + (yr[i,j]+100)^2) / 8014.224 >= 1; 213 | s.t. M1iddleCircle_for_B1 {i in B1, j in IP}: 214 | ((xr[i,j]-56)^2 + (yr[i,j]+56)^2) / 2072.271 >= 1; 215 | s.t. S1mallCircle_for_B1 {i in B1, j in IP}: 216 | ((xr[i,j]-34)^2 + (yr[i,j]+34)^2) / 553.294 >= 1; 217 | s.t. L2argeCircle_for_B1 {i in B1, j in IP}: 218 | ((xf[i,j]-100)^2 + (yf[i,j]+100)^2) / 8014.224 >= 1; 219 | s.t. M2iddleCircle_for_B1 {i in B1, j in IP}: 220 | ((xf[i,j]-56)^2 + (yf[i,j]+56)^2) / 2072.271 >= 1; 221 | s.t. S2mallCircle_for_B1 {i in B1, j in IP}: 222 | ((xf[i,j]-34)^2 + (yf[i,j]+34)^2) / 553.294 >= 1; 223 | s.t. limit_xr_B1 {i in B1, j in IP}: 224 | xr[i,j] - R >= -12; 225 | s.t. limit_xf_B1 {i in B1, j in IP}: 226 | xf[i,j] - R >= -12; 227 | s.t. limit_yr_B1 {i in B1, j in IP}: 228 | yr[i,j] + R <= 12; 229 | s.t. limit_yf_B1 {i in B1, j in IP}: 230 | yf[i,j] + R <= 12; 231 | s.t. terminal_x_B1 {m in B1}: 232 | yr[m,Nfe] + R <= -12; 233 | s.t. terminal_xr_B1 {m in B1}: 234 | xr[m,Nfe] + R <= 0; 235 | s.t. terminal_xf_B1 {m in B1}: 236 | xf[m,Nfe] + R <= 0; 237 | s.t. interval_theta_B1 {i in B1, j in IPmnt}: 238 | 2 <= theta[i,j] <= 6; 239 | ### B2 ### 240 | s.t. limit_yr_B2 {i in B2, j in IP}: 241 | R <= yr[i,j] <= 12 - R; 242 | s.t. limit_yf_B2 {i in B2, j in IP}: 243 | R <= yf[i,j] <= 12 - R; 244 | s.t. terminal_x_B2 {m in B2}: 245 | xr[m,Nfe] + R <= -12; 246 | s.t. interval_theta_B2 {i in B2, j in IPmnt}: 247 | 2 <= theta[i,j] <= 4; 248 | ### B3 ### 249 | s.t. L1argeCircle_for_B3 {i in B3, j in IP}: 250 | ((xr[i,j]-100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 251 | s.t. M1iddleCircle_for_B3 {i in B3, j in IP}: 252 | ((xr[i,j]-56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 253 | s.t. S1mallCircle_for_B3 {i in B3, j in IP}: 254 | ((xr[i,j]-34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 255 | s.t. L2argeCircle_for_B3 {i in B3, j in IP}: 256 | ((xf[i,j]-100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 257 | s.t. M2iddleCircle_for_B3 {i in B3, j in IP}: 258 | ((xf[i,j]-56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 259 | s.t. S2mallCircle_for_B3 {i in B3, j in IP}: 260 | ((xf[i,j]-34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 261 | s.t. limit_xr_B3 {i in B3, j in IP}: 262 | xr[i,j] - R >= 0; 263 | s.t. limit_xf_B3 {i in B3, j in IP}: 264 | xf[i,j] - R >= 0; 265 | s.t. limit_yr_B3 {i in B3, j in IP}: 266 | yr[i,j] - R >= 0; 267 | s.t. limit_yf_B3 {i in B3, j in IP}: 268 | yf[i,j] - R >= 0; 269 | s.t. terminal_x_B3 {m in B3}: 270 | yr[m,Nfe] - R >= 12; 271 | s.t. interval_theta_B3 {i in B3, j in IPmnt}: 272 | 1 <= theta[i,j] <= 4; 273 | ### C1 ### 274 | s.t. L1argeCircle_for_C1 {i in C1, j in IP}: 275 | ((xr[i,j]-100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 276 | s.t. M1iddleCircle_for_C1 {i in C1, j in IP}: 277 | ((xr[i,j]-56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 278 | s.t. S1mallCircle_for_C1 {i in C1, j in IP}: 279 | ((xr[i,j]-34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 280 | s.t. L2argeCircle_for_C1 {i in C1, j in IP}: 281 | ((xf[i,j]-100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 282 | s.t. M2iddleCircle_for_C1 {i in C1, j in IP}: 283 | ((xf[i,j]-56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 284 | s.t. S2mallCircle_for_C1 {i in C1, j in IP}: 285 | ((xf[i,j]-34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 286 | s.t. limit_xr_C1 {i in C1, j in IP}: 287 | xr[i,j] - R >= -12; 288 | s.t. limit_xf_C1 {i in C1, j in IP}: 289 | xf[i,j] - R >= -12; 290 | s.t. limit_yr_C1 {i in C1, j in IP}: 291 | yr[i,j] - R >= -12; 292 | s.t. limit_yf_C1 {i in C1, j in IP}: 293 | yf[i,j] - R >= -12; 294 | s.t. terminal_x_C1 {m in C1}: 295 | xr[m,Nfe] - R >= 12; 296 | s.t. terminal_xr_C1 {m in C1}: 297 | yr[m,Nfe] + R <= 0; 298 | s.t. terminal_xf_C1 {m in C1}: 299 | yf[m,Nfe] + R <= 0; 300 | s.t. interval_theta_C1 {i in C1, j in IPmnt}: 301 | -2 <= theta[i,j] <= 1; 302 | ### C2 ### 303 | s.t. limit_xr_C2 {i in C2, j in IP}: 304 | -12 + R <= xr[i,j] <= -R; 305 | s.t. limit_xf_C2 {i in C2, j in IP}: 306 | -12 + R <= xf[i,j] <= -R; 307 | s.t. terminal_x_C2 {m in C2}: 308 | yr[m,Nfe] + R <= -12; 309 | s.t. interval_theta_C2 {i in C2, j in IPmnt}: 310 | -2 <= theta[i,j] <= -1; 311 | ### C3 ### 312 | s.t. L1argeCircle_for_C3 {i in C3, j in IP}: 313 | ((xr[i,j]+100)^2 + (yr[i,j]-100)^2) / 8014.224 >= 1; 314 | s.t. M1iddleCircle_for_C3 {i in C3, j in IP}: 315 | ((xr[i,j]+56)^2 + (yr[i,j]-56)^2) / 2072.271 >= 1; 316 | s.t. S1mallCircle_for_C3 {i in C3, j in IP}: 317 | ((xr[i,j]+34)^2 + (yr[i,j]-34)^2) / 553.294 >= 1; 318 | s.t. L2argeCircle_for_C3 {i in C3, j in IP}: 319 | ((xf[i,j]+100)^2 + (yf[i,j]-100)^2) / 8014.224 >= 1; 320 | s.t. M2iddleCircle_for_C3 {i in C3, j in IP}: 321 | ((xf[i,j]+56)^2 + (yf[i,j]-56)^2) / 2072.271 >= 1; 322 | s.t. S2mallCircle_for_C3 {i in C3, j in IP}: 323 | ((xf[i,j]+34)^2 + (yf[i,j]-34)^2) / 553.294 >= 1; 324 | s.t. limit_xr_C3 {i in C3, j in IP}: 325 | xr[i,j] + R <= 0; 326 | s.t. limit_xf_C3 {i in C3, j in IP}: 327 | xf[i,j] + R <= 0; 328 | s.t. limit_yr_C3 {i in C3, j in IP}: 329 | yr[i,j] - R >= 0; 330 | s.t. limit_yf_C3 {i in C3, j in IP}: 331 | yf[i,j] - R >= 0; 332 | s.t. terminal_x_C3 {m in C3}: 333 | xr[m,Nfe] + R <= -12; 334 | s.t. interval_theta_C3 {i in C3, j in IPmnt}: 335 | -4 <= theta[i,j] <= -1; 336 | 337 | s.t. VehicleItoJfr {i in {1..(Nv-1)}, j in {(i+1)..Nv}, kk in I}: 338 | (xf[i,kk] - xr[j,kk])^2 + (yf[i,kk] - yr[j,kk])^2 >= FourSqR; 339 | s.t. VehicleItoJrf {i in {1..(Nv-1)}, j in {(i+1)..Nv}, kk in I}: 340 | (xr[i,kk] - xf[j,kk])^2 + (yr[i,kk] - yf[j,kk])^2 >= FourSqR; 341 | s.t. VehicleItoJff {i in {1..(Nv-1)}, j in {(i+1)..Nv}, kk in I}: 342 | (xf[i,kk] - xf[j,kk])^2 + (yf[i,kk] - yf[j,kk])^2 >= FourSqR; 343 | s.t. VehicleItoJrr {i in {1..(Nv-1)}, j in {(i+1)..Nv}, kk in I}: 344 | (xr[i,kk] - xr[j,kk])^2 + (yr[i,kk] - yr[j,kk])^2 >= FourSqR; 345 | 346 | s.t. EQ_init_x {m in {1..Nv}}: 347 | x[m,1] = BV[m,1]; 348 | s.t. EQ_init_y {m in {1..Nv}}: 349 | y[m,1] = BV[m,2]; 350 | s.t. EQ_init_theta {m in {1..Nv}}: 351 | theta[m,1] = BV[m,3]; 352 | s.t. EQ_init_v {m in {1..Nv}}: 353 | v[m,1] = vcommon; 354 | s.t. EQ_init_a {m in {1..Nv}}: 355 | a[m,1] = 0; 356 | s.t. EQ_init_phy {m in {1..Nv}}: 357 | phy[m,1] = 0; 358 | s.t. EQ_init_w {m in {1..Nv}}: 359 | w[m,1] = 0; 360 | s.t. EQ_end_theta {m in {1..Nv}}: 361 | theta[m,Nfe] = BV[m,6]; 362 | s.t. EQ_end_v {m in {1..Nv}}: 363 | v[m,Nfe] = vcommon; 364 | s.t. EQ_end_a {m in {1..Nv}}: 365 | a[m,Nfe] = 0; 366 | s.t. EQ_end_phy {m in {1..Nv}}: 367 | phy[m,Nfe] = 0; 368 | s.t. EQ_end_w {m in {1..Nv}}: 369 | w[m,Nfe] = 0; 370 | 371 | data; 372 | param: cav_index_start := include cav_index_start; 373 | param: cav_index_end := include cav_index_end; 374 | param: BV := include BV; 375 | param: BP := include BP; 376 | param: TimeLine := include TimeLine; -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------