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working pds, though differential_lift_x is _quite_ bad
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,47 @@ | ||
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| clear all | ||
| clc | ||
| close all | ||
| import casadi.* | ||
| %% discretization parameters | ||
| N_sim = 100; | ||
| T_sim = 10; | ||
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| %% NOSNOC settings | ||
| problem_options = nosnoc.Options(); | ||
| solver_options = nosnoc.solver.Options(); | ||
| problem_options.n_s = 2; | ||
| settings.homotopy_update_slope = 0.1; | ||
| %problem_options.rk_scheme = RKSchemes.GAUSS_LEGENDRE; | ||
| problem_options.rk_scheme = RKSchemes.RADAU_IIA; | ||
| problem_options.rk_representation= 'differential_lift_x'; | ||
| %problem_options.rk_representation= 'integral'; | ||
| problem_options.N_sim = N_sim; | ||
| problem_options.N_finite_elements = 2; | ||
| problem_options.T_sim = T_sim; | ||
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| %solver_options.homotopy_steering_strategy = 'ELL_INF'; | ||
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| model = nosnoc.model.Pds(); | ||
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| model.x0 = [0;pi-2;0]; | ||
| x = SX.sym('x',2); | ||
| t = SX.sym('t'); | ||
| model.x = [x;t]; | ||
| model.c = [-norm(x - [sin(t);cos(t)])^2+(1-0.5)^2]; | ||
| model.f_x = [0; 0; 1]; | ||
| model.E = diag([1,1,0]); | ||
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| integrator = nosnoc.Integrator(model, problem_options, solver_options); | ||
| [t_grid, x_res] = integrator.simulate(); | ||
| % | ||
| figure | ||
| plot(x_res(1,:), x_res(2,:)) | ||
| grid on | ||
| xlabel('$t$','Interpreter','latex') | ||
| ylabel('$x(t)$','Interpreter','latex') | ||
| grid on | ||
|
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| fig = figure('Position', [10 10 1600 800]); | ||
| plot_moving_set([],x_res,[0.5], ["circle"], fig, 'moving_set'); |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,44 @@ | ||
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| clear all | ||
| clc | ||
| close all | ||
| import casadi.* | ||
| %% discretization parameters | ||
| N_sim = 100; | ||
| T_sim = 10; | ||
|
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||
| %% NOSNOC settings | ||
| problem_options = nosnoc.Options(); | ||
| solver_options = nosnoc.solver.Options(); | ||
| problem_options.n_s = 2; | ||
| settings.homotopy_update_slope = 0.1; | ||
| %problem_options.rk_scheme = RKSchemes.GAUSS_LEGENDRE; | ||
| problem_options.rk_scheme = RKSchemes.RADAU_IIA; | ||
| problem_options.rk_representation= 'differential_lift_x'; | ||
| %problem_options.rk_representation= 'integral'; | ||
| problem_options.N_sim = N_sim; | ||
| problem_options.N_finite_elements = 2; | ||
| problem_options.T_sim = T_sim; | ||
| solver_options.homotopy_steering_strategy = 'ELL_INF'; | ||
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| model = nosnoc.model.Pds(); | ||
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| model.x0 = [sqrt(2)/2;sqrt(2)/2]; | ||
| x = SX.sym('x',2); | ||
| model.x = x; | ||
| model.c = x(2)+0.2; | ||
| model.f_x = [x(2);-x(1)]; | ||
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| model.x0 = [0;pi-2;0]; | ||
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| integrator = nosnoc.Integrator(model, problem_options, solver_options); | ||
| [t_grid, x_res] = integrator.simulate(); | ||
| % | ||
| figure | ||
| plot(x_res(1,:), x_res(2,:)) | ||
| grid on | ||
| xlabel('$t$','Interpreter','latex') | ||
| ylabel('$x(t)$','Interpreter','latex') | ||
| grid on | ||
|
|
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,101 @@ | ||
| function plot_moving_set(h,pos,r,type,fig,vidname) | ||
| n = length(r); | ||
| if ~exist('type') | ||
| type = []; | ||
| for ii=1:n | ||
| type = [type, "circle"]; | ||
| end | ||
| end | ||
| if length(type) ~= n | ||
| error('not all types specified') | ||
| end | ||
| indices = {}; | ||
| curr_idx = 1; | ||
| for ii=1:n | ||
| switch type(ii) | ||
| case "circle" | ||
| indices{ii} = curr_idx:curr_idx+1; | ||
| curr_idx = curr_idx+2; | ||
| case "square" | ||
| indices{ii} = curr_idx:curr_idx+2; | ||
| curr_idx = curr_idx+3; | ||
| end | ||
| end | ||
| if ~exist('fig') | ||
| fig = figure; | ||
| else | ||
| figure(fig) | ||
| end | ||
| axis equal | ||
| box on; | ||
| ax = gca; | ||
| set(ax,'XTick',[-10,0,10], 'YTick', [0,5,10], 'TickLength', [0.025,0.025], 'LineWidth', 4.0); | ||
| xlim([-3,3]) | ||
| ylim([-3,3]) | ||
| ax.XAxis.FontSize = 36; | ||
| ax.YAxis.FontSize = 36; | ||
| xlabel("$c_x$", "fontsize", 32) | ||
| ylabel("$c_y$", "fontsize", 32) | ||
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| %axis off | ||
| discs = {}; | ||
| tau = linspace(0, 2*pi)'; | ||
| rot = @(theta) [cos(theta) -sin(theta);... | ||
| sin(theta) cos(theta)]; | ||
| circ = @(p,r) [r*cos(tau)+p(1),r*sin(tau)+p(2)]; | ||
| sqr = @(p,r) transpose(rot(-p(3))*([r,r;r,-r;-r,-r;-r,r]') + p(1:2)); | ||
| for ii=1:n | ||
| p = pos(indices{ii},1); | ||
| switch type(ii) | ||
| case "circle" | ||
| v = circ(p,r(ii)); | ||
| case "square" | ||
| v = sqr(p,r(ii)); | ||
| end | ||
| if ii==3 | ||
| color = [0.8500 0.3250 0.0980]; | ||
| else | ||
| color = [0 0.4470 0.7410]; | ||
| end | ||
| discs{ii} = patch(v(:,1),v(:,2), color); | ||
| end | ||
| t = pos(end,1); | ||
| v_C = circ([sin(t);cos(t)],1); | ||
| C = patch(v_C(:,1),v_C(:,2), [1 0 0], 'FaceAlpha', 0.0, 'LineStyle', '--', 'EdgeColor' , [1 0 0]); | ||
| if exist('vidname') | ||
| mkdir([vidname '_frames']) | ||
| writer = VideoWriter([vidname '.avi']); | ||
| open(writer); | ||
| frame = getframe(gca); | ||
| exportgraphics(gca, [vidname '_frames/' num2str(1) '.pdf']) | ||
| writeVideo(writer,frame) | ||
| end | ||
| pause(0.1); | ||
| for jj=2:(size(pos,2)-1) | ||
| for ii=1:n | ||
| p = pos(indices{ii},jj+1); | ||
| switch type(ii) | ||
| case "circle" | ||
| v = circ(p,r(ii)); | ||
| case "square" | ||
| v = sqr(p,r(ii)); | ||
| end | ||
| discs{ii}.Vertices = v; | ||
| end | ||
| t = pos(end,jj); | ||
| v_C = circ([sin(t);cos(t)],1); | ||
| C.Vertices = v_C; | ||
| drawnow limitrate; | ||
| %pause(h(jj)); | ||
| pause(0.1) | ||
| if exist('vidname') | ||
| frame = getframe(gca); | ||
| ff=jj+1; | ||
| %exportgraphics(gca, [vidname '_frames/' num2str(jj) '.pdf']) | ||
| writeVideo(writer,frame); | ||
| end | ||
| end | ||
| if exist('vidname') | ||
| close(writer); | ||
| end | ||
| end |