commit fc9514494f5114c66c0a5386aab2127d5e1fe2ee Author: Jun Zeng Date: Thu Sep 24 14:24:22 2020 -0700 Initial commit diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..5f528d0 --- /dev/null +++ b/.gitignore @@ -0,0 +1,163 @@ +# MATLAB +# Windows default autosave extension +*.asv + +# OSX / *nix default autosave extension +*.m~ + +# Compiled MEX binaries (all platforms) +*.mex* + +# Packaged app and toolbox files +*.mlappinstall +*.mltbx + +# Generated helpsearch folders +helpsearch*/ + +# Simulink code generation folders +slprj/ +sccprj/ + +# Matlab code generation folders +codegen/ + +# Simulink autosave extension +*.autosave + +# Simulink cache files +*.slxc + +# Octave session info +octave-workspace + +# PYTHON +# Byte-compiled / optimized / DLL files +__pycache__/ +*.py[cod] +*$py.class + +# C extensions +*.so + +# Distribution / packaging +.Python +build/ +develop-eggs/ +dist/ +downloads/ +eggs/ +.eggs/ +lib/ +lib64/ +parts/ +sdist/ +var/ +wheels/ +pip-wheel-metadata/ +share/python-wheels/ +*.egg-info/ +.installed.cfg +*.egg +MANIFEST + +# PyInstaller +# Usually these files are written by a python script from a template +# before PyInstaller builds the exe, so as to inject date/other infos into it. +*.manifest +*.spec + +# Installer logs +pip-log.txt +pip-delete-this-directory.txt + +# Unit test / coverage reports +htmlcov/ +.tox/ +.nox/ +.coverage +.coverage.* +.cache +nosetests.xml +coverage.xml +*.cover +*.py,cover +.hypothesis/ +.pytest_cache/ + +# Translations +*.mo +*.pot + +# Django stuff: +*.log +local_settings.py +db.sqlite3 +db.sqlite3-journal + +# Flask stuff: +instance/ +.webassets-cache + +# Scrapy stuff: +.scrapy + +# Sphinx documentation +docs/_build/ + +# PyBuilder +target/ + +# Jupyter Notebook +.ipynb_checkpoints + +# IPython +profile_default/ +ipython_config.py + +# pyenv +.python-version + +# pipenv +# According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control. +# However, in case of collaboration, if having platform-specific dependencies or dependencies +# having no cross-platform support, pipenv may install dependencies that don't work, or not +# install all needed dependencies. +#Pipfile.lock + +# PEP 582; used by e.g. github.com/David-OConnor/pyflow +__pypackages__/ + +# Celery stuff +celerybeat-schedule +celerybeat.pid + +# SageMath parsed files +*.sage.py + +# Environments +.env +.venv +env/ +venv/ +ENV/ +env.bak/ +venv.bak/ + +# Spyder project settings +.spyderproject +.spyproject + +# Rope project settings +.ropeproject + +# mkdocs documentation +/site + +# mypy +.mypy_cache/ +.dmypy.json +dmypy.json + +# Pyre type checker +.pyre/ diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..ab4bdb9 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2020 Jun Zeng + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..45ce77c --- /dev/null +++ b/README.md @@ -0,0 +1,48 @@ +# MPC-CBF +Model Predictive Control with Control Barrier Functions + +![](car-racing/demo.gif) + +# Prerequisites +## Matlab +The packages needed for running the code are [Yalmip](https://yalmip.github.io/) and [IPOPT](https://projects.coin-or.org/Ipopt/wiki/MatlabInterface). + +We also provide the zipped version of precompiled .mex files for IPOPT in the folder `packages` in case you don't have it. Unzip that file and add those .mex files into your MATLAB path. + +# Description +## 2D double integrator +The 2D double integrator is assigned to reach the target position at origin while avoiding obstacles. We have three classes for different controllers: `DCLF_DCBF.m` (DCLF-DCBF), `MPC_CBF.m` (MPC-CBF) and `MPC_DC` (MPC-DC), respectively. + +Moreover, to illustrate the performance among them, we have: +* `main.m`: Run DCLF-DCBF/MPC-CBF/MPC-DC respectively. +* `analysis_gamma.m`: Run analysis for different hyperparameter $\gamma$. +* `analysis_horizon.m`: Run analysis for different horizon. + +We illustrate the performance between DCLF-DCBF/MPC-DC/MPC-CBF +| DCLF-DCBF | MPC-DC (N=8) | +| --- | --- | +| | | + +| MPC-CBF (N=1) | MPC-CBF (N=8) | +| --- | --- | +| | | + +and also the safety performance for different numbers of horizon and hyperparameters +| Different hyperparameter | Different horizon | +| --- | --- | +| | | + +## Car racing competition +We have the speed profile and control input shown as follow, + + + + + + + +The animation can be found on the top of this readme, we will release full code after the paper is accepted. + +# References +This repository is based on the following: +* Jun Zeng, Bike Zhang and Koushil Sreenath. "Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function." [[PDF]](http://arxiv.org/abs/2007.11718) diff --git a/car-racing/demo.gif b/car-racing/demo.gif new file mode 100644 index 0000000..ed9cb18 Binary files /dev/null and b/car-racing/demo.gif differ diff --git a/car-racing/lmpc-deviation-profile.png b/car-racing/lmpc-deviation-profile.png new file mode 100644 index 0000000..b4d177a Binary files /dev/null and b/car-racing/lmpc-deviation-profile.png differ diff --git a/car-racing/lmpc-input-profile.png b/car-racing/lmpc-input-profile.png new file mode 100644 index 0000000..e3a21b9 Binary files /dev/null and b/car-racing/lmpc-input-profile.png differ diff --git a/car-racing/lmpc-speed-norm-profile.png b/car-racing/lmpc-speed-norm-profile.png new file mode 100644 index 0000000..c79fe05 Binary files /dev/null and b/car-racing/lmpc-speed-norm-profile.png differ diff --git a/car-racing/lmpc-speed-profile.png b/car-racing/lmpc-speed-profile.png new file mode 100644 index 0000000..cb9a32d Binary files /dev/null and b/car-racing/lmpc-speed-profile.png differ diff --git a/double-integrator-2D/DCLF_DCBF.m b/double-integrator-2D/DCLF_DCBF.m new file mode 100644 index 0000000..2e8e0d8 --- /dev/null +++ b/double-integrator-2D/DCLF_DCBF.m @@ -0,0 +1,105 @@ +classdef DCLF_DCBF < handle + properties + system + params + x0 + x_curr + time_curr = 0.0 + xlog = [] + ulog = [] + u_cost = 0 + obs + end + + methods + function self = DCLF_DCBF(x0, system, params) + % Define DCLF-DCBF controller + self.x0 = x0; + self.x_curr = x0; + self.system = system; + self.params = params; + end + + function sim(self, time) + % Simulate the system until a given time + xk = self.x_curr; + while self.time_curr <= time + % Solve DCLF-DCBF + uk = self.solve_dclf_dcbf(); + xk = self.system.A * xk + self.system.B * uk; + % update system + self.x_curr = xk; + self.time_curr = self.time_curr + self.system.dt; + self.xlog = [self.xlog, xk]; + self.ulog = [self.ulog, uk]; + self.u_cost = self.u_cost + uk'*uk*self.system.dt; + end + end + + function uopt = solve_dclf_dcbf(self) + % Solve DCLF-DCBF + x = self.x_curr; + u = sdpvar(2,1); + delta = sdpvar(1,1); + constraints = []; + % add DCLF constraints + x_next = self.system.A * x + self.system.B * u; + v = x' * self.params.P * x; + v_next = x_next' * self.params.P * x_next; + constraints = [constraints; v_next - v + self.params.alpha * v <= delta]; + % add DCBF constraints + pos = self.obs.pos; + r = self.obs.r; + b = (x(1:2)-pos)'*(x(1:2)-pos) - r^2; + b_next = (x_next(1:2)-pos)'*(x_next(1:2)-pos) - r^2; + constraints = [constraints; b_next - b + self.params.gamma*b >= 0]; + % input constraints + constraints = [constraints; self.system.ul <= u <= self.system.uu]; + % cost + cost = u'*self.params.H*u + delta'*self.params.p*delta; + % solve optimization + ops = sdpsettings('solver','ipopt','verbose',0); + diagnostics = optimize(constraints, cost, ops); + if diagnostics.problem == 0 + feas = true; + uopt = value(u); + else + feas = false; + uopt = []; + end + fprintf('solver time: %f\n', diagnostics.solvertime); + end + + function plot(self,figure_name) + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot trajectory + plot(self.xlog(1,:), self.xlog(2,:), 'ko-',... + 'LineWidth', 1.0,'MarkerSize',4); + % plot obstacle + pos = self.obs.pos; + r = self.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980], 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(self.x0(1), self.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'DCLF-DCBF'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf,strcat('figures/',figure_name), '-depsc'); + end + end +end \ No newline at end of file diff --git a/double-integrator-2D/MPC_CBF.m b/double-integrator-2D/MPC_CBF.m new file mode 100644 index 0000000..45299ee --- /dev/null +++ b/double-integrator-2D/MPC_CBF.m @@ -0,0 +1,145 @@ +classdef MPC_CBF < handle + % MPC with distance constraints + properties + system + params + x0 + x_curr + time_curr = 0.0 + xlog = [] + ulog = [] + distlog = [] + solvertime = [] + xopenloop = {} + uopenloop = {} + u_cost = 0 + obs + end + methods + function self = MPC_CBF(x0, system, params) + % Define MPC_CBF controller + self.x0 = x0; + self.x_curr = x0; + self.system = system; + self.params = params; + end + + function sim(self, time) + % Simulate the system until a given time + xk = self.x_curr; + while self.time_curr <= time + % Solve CFTOC + [~, uk] = self.solve_mpc_dc(self.x_curr); + xk = self.system.A * xk + self.system.B * uk; + % update system + self.x_curr = xk; + self.time_curr = self.time_curr + self.system.dt; + self.xlog = [self.xlog, xk]; + self.ulog = [self.ulog, uk]; + self.u_cost = self.u_cost + uk'*uk*self.system.dt; + end + end + + function [xopt, uopt] = solve_mpc_dc(self, xk) + % Solve MPC-CBF + [feas, x, u, J] = self.solve_cftoc(xk); + if ~feas + xopt = []; + uopt = []; + return + else + xopt = x(:,2); + uopt = u(:,1); + end + end + + function [feas, xopt, uopt, Jopt] = solve_cftoc(self, xk) + % Solve CFTOC + % extract variables + N = self.params.N; + % define variables and cost + x = sdpvar(4, N+1); + u = sdpvar(2, N); + constraints = []; + cost = 0; + % initial constraint + constraints = [constraints; x(:,1) == xk]; + % add constraints and costs + for i = 1:N + constraints = [constraints; + self.system.xl <= x(:,i) <= self.system.xu; + self.system.ul <= u(:,i) <= self.system.uu + x(:,i+1) == self.system.A * x(:,i) + self.system.B * u(:,i)]; + cost = cost + x(:,i)'*self.params.Q*x(:,i) + u(:,i)'*self.params.R*u(:,i); + end + % add CBF constraints + for i = 1:N + pos = self.obs.pos; + r = self.obs.r ; + b = (x([1:2],i)-pos)'*((x([1:2],i)-pos)) - r^2; + b_next = (x([1:2],i+1)-pos)'*((x([1:2],i+1)-pos)) - r^2; + constraints = [constraints; b_next - b + self.params.gamma * b >= 0]; + end + % add terminal cost + cost = cost + x(:,N+1)'*self.params.P*x(:,N+1); + ops = sdpsettings('solver','ipopt','verbose',0); + % solve optimization + diagnostics = optimize(constraints, cost, ops); + if diagnostics.problem == 0 + feas = true; + xopt = value(x); + uopt = value(u); + Jopt = value(cost); + else + feas = false; + xopt = []; + uopt = []; + Jopt = []; + end + self.distlog = [self.distlog, sqrt((xk(1:2)-pos)'*(xk(1:2)-pos)-r^2)]; + self.xopenloop{size(self.xopenloop,2)+1} = xopt; + self.uopenloop{size(self.uopenloop,2)+1} = uopt; + self.solvertime = [self.solvertime, diagnostics.solvertime]; + fprintf('solver time: %f\n', diagnostics.solvertime); + end + + function plot(self, figure_name) + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot closed-loop trajectory + plot(self.xlog(1,:), self.xlog(2,:), 'ko-',... + 'LineWidth', 1.0, 'MarkerSize', 4); + % plot open-loop trajectory + for i = 1:size(self.xopenloop, 2) + plot(self.xopenloop{i}(1,:), self.xopenloop{i}(2,:),... + 'k*-.', 'LineWidth', 0.5,'MarkerSize',0.5) + end + % plot obstacle + pos = self.obs.pos; + r = self.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980],... + 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980],... + 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(self.x0(1), self.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'MPC-CBF'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf,strcat('figures/',figure_name), '-depsc'); + end + end +end \ No newline at end of file diff --git a/double-integrator-2D/MPC_DC.m b/double-integrator-2D/MPC_DC.m new file mode 100644 index 0000000..738b24b --- /dev/null +++ b/double-integrator-2D/MPC_DC.m @@ -0,0 +1,144 @@ +classdef MPC_DC < handle + % MPC with distance constraints + properties + system + params + x0 + x_curr + time_curr = 0.0 + xlog = [] + ulog = [] + distlog = [] + solvertime = [] + xopenloop = {} + uopenloop = {} + u_cost = 0 + obs + end + methods + function self = MPC_DC(x0, system, params) + % Define MPC_DC controller + self.x0 = x0; + self.x_curr = x0; + self.system = system; + self.params = params; + end + + function sim(self, time) + % Simulate the system until a given time + xk = self.x_curr; + while self.time_curr <= time + % Solve CFTOC + [~, uk] = self.solve_mpc_dc(self.x_curr); + xk = self.system.A * xk + self.system.B * uk; + % update system + self.x_curr = xk; + self.time_curr = self.time_curr + self.system.dt; + self.xlog = [self.xlog, xk]; + self.ulog = [self.ulog, uk]; + self.u_cost = self.u_cost + uk'*uk*self.system.dt; + end + end + + function [xopt, uopt] = solve_mpc_dc(self, xk) + % Solve MPC-DC + [feas, x, u, J] = self.solve_cftoc(xk); + if ~feas + xopt = []; + uopt = []; + return + else + xopt = x(:,2); + uopt = u(:,1); + end + end + + function [feas, xopt, uopt, Jopt] = solve_cftoc(self, xk) + % Solve CFTOC + % extract variables + N = self.params.N; + % define variables and cost + x = sdpvar(4, N+1); + u = sdpvar(2, N); + constraints = []; + cost = 0; + % initial constraint + constraints = [constraints; x(:,1) == xk]; + % add constraints and costs + for i = 1:N + constraints = [constraints; + self.system.xl <= x(:,i) <= self.system.xu; + self.system.ul <= u(:,i) <= self.system.uu + x(:,i+1) == self.system.A * x(:,i) + self.system.B * u(:,i)]; + cost = cost + x(:,i)'*self.params.Q*x(:,i) + u(:,i)'*self.params.R*u(:,i); + end + % add CBF constraints + for i = 1:N + pos = self.obs.pos; + r = self.obs.r ; + b = (x([1:2],i)-pos)'*((x([1:2],i)-pos)) - r^2; + constraints = [constraints; b >= 0]; + end + % add terminal cost + cost = cost + x(:,N+1)'*self.params.P*x(:,N+1); + ops = sdpsettings('solver','ipopt','verbose',0); + % solve optimization + diagnostics = optimize(constraints, cost, ops); + if diagnostics.problem == 0 + feas = true; + xopt = value(x); + uopt = value(u); + Jopt = value(cost); + else + feas = false; + xopt = []; + uopt = []; + Jopt = []; + end + self.distlog = [self.distlog, sqrt((xk(1:2)-pos)'*(xk(1:2)-pos)-r^2)]; + self.xopenloop{size(self.xopenloop,2)+1} = xopt; + self.uopenloop{size(self.uopenloop,2)+1} = uopt; + self.solvertime = [self.solvertime, diagnostics.solvertime]; + fprintf('solver time: %f\n', diagnostics.solvertime); + end + + function plot(self, figure_name) + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot closed-loop trajectory + plot(self.xlog(1,:), self.xlog(2,:), 'ko-',... + 'LineWidth', 1.0, 'MarkerSize', 4); + % plot open-loop trajectory + for i = 1:size(self.xopenloop, 2) + plot(self.xopenloop{i}(1,:), self.xopenloop{i}(2,:),... + 'k*-.', 'LineWidth', 0.5,'MarkerSize',0.5) + end + % plot obstacle + pos = self.obs.pos; + r = self.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980],... + 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980],... + 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(self.x0(1), self.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'MPC-DC'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf,strcat('figures/',figure_name), '-depsc'); + end + end +end \ No newline at end of file diff --git a/double-integrator-2D/analysis_benchmark.m b/double-integrator-2D/analysis_benchmark.m new file mode 100644 index 0000000..816f219 --- /dev/null +++ b/double-integrator-2D/analysis_benchmark.m @@ -0,0 +1,66 @@ +close all +clear + +%% Setup and Parameters +x0 = [-5; -5; 0; 0]; +time_total = 20.0; +dt = 0.2; +P = 100*eye(4); +Q = 10*eye(4); +R = eye(2); +N = 8; +umin = [-1; -1]; +umax = [1; 1]; +xmin = [-5; -5; -5; -5]; +xmax = [5; 5; 5; 5]; + +%% Discrete-time double integrator 2D +system.dt = dt; +system.A = [1 0 dt 0; + 0 1 0 dt; + 0 0 1 0; + 0 0 0 1]; +system.B = [0.5*dt^2 0; + 0 0.5*dt^2; + dt 0; + 0 dt]; +system.xl = xmin; +system.xu = xmax; +system.ul = umin; +system.uu = umax; + +%% MPC-CBF parameters +params.Q = Q; +params.R = R; +params.P = P; +params.N = N; +params.gamma = 0.5; + +%% Obstacle +obs.pos = [-2; -2.25]; +obs.r = 1.5; + +%% Simulate MPC-CBF +gamma_list = linspace(0.1, 0.5, 5); +controller_mpc_cbf_list = {}; +for i = 1:size(gamma_list, 2) + new_params = params; + new_params.N = 5; + new_params.gamma = gamma_list(i); + controller_mpc_cbf = MPC_CBF(x0, system, new_params); + controller_mpc_cbf.obs = obs; + controller_mpc_cbf.sim(time_total); + controller_mpc_cbf_list{i} = controller_mpc_cbf; +end + +%% Computational time benchmark +for i = 1:size(gamma_list, 2) + controller_mpc_cbf = controller_mpc_cbf_list{i}; + fprintf('Computational time for MPC-CBF3: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_cbf.solvertime),... + std(controller_mpc_cbf.solvertime),... + min(controller_mpc_cbf.solvertime),... + max(controller_mpc_cbf.solvertime),... + controller_mpc_cbf.u_cost,... + min(controller_mpc_cbf.distlog)]); +end \ No newline at end of file diff --git a/double-integrator-2D/analysis_gamma.m b/double-integrator-2D/analysis_gamma.m new file mode 100644 index 0000000..e081b75 --- /dev/null +++ b/double-integrator-2D/analysis_gamma.m @@ -0,0 +1,95 @@ +close all +clear + +%% Setup and Parameters +x0 = [-5; -5; 0; 0]; +time_total = 20.0; +dt = 0.2; +P = 100*eye(4); +Q = 10*eye(4); +R = eye(2); +N = 8; +umin = [-1; -1]; +umax = [1; 1]; +xmin = [-5; -5; -5; -5]; +xmax = [5; 5; 5; 5]; + +%% Discrete-time double integrator 2D +system.dt = dt; +system.A = [1 0 dt 0; + 0 1 0 dt; + 0 0 1 0; + 0 0 0 1]; +system.B = [0.5*dt^2 0; + 0 0.5*dt^2; + dt 0; + 0 dt]; +system.xl = xmin; +system.xu = xmax; +system.ul = umin; +system.uu = umax; + +%% MPC-CBF parameters +params_mpc_cbf.Q = Q; +params_mpc_cbf.R = R; +params_mpc_cbf.P = P; +params_mpc_cbf.N = N; +params_mpc_cbf.gamma = 0.5; + +%% Obstacle +obs.pos = [-2; -2.25]; +obs.r = 1.5; + +%% Simulate MPC-CBF +gamma_list = [0.1, 0.2, 0.3, 1.0]; +for ind = 1:size(gamma_list, 2) + fprintf('Run MPC-CBF with gamma %f\n', gamma_list(ind)); + params_mpc_cbf.gamma = gamma_list(ind); + controller_mpc_cbf_list{ind} = MPC_CBF(x0, system, params_mpc_cbf); + controller_mpc_cbf_list{ind}.obs = obs; + controller_mpc_cbf_list{ind}.sim(time_total); +end + +%% Simulate MPC-DC +params_mpc_dc = params_mpc_cbf; +controller_mpc_dc = MPC_DC(x0, system, params_mpc_cbf); +controller_mpc_dc.obs = obs; +controller_mpc_dc.sim(time_total); + +%% Visualization benchmark +figure('Renderer', 'painters', 'Position', [0 0 400 400]); +set(gca,'LooseInset',get(gca,'TightInset')); +hold on +for ind = 1:size(gamma_list, 2) + plot(controller_mpc_cbf_list{ind}.xlog(1,:), controller_mpc_cbf_list{ind}.xlog(2,:),... + '-', 'LineWidth', 1.0, 'MarkerSize', 4); +end +plot(controller_mpc_dc.xlog(1,:), controller_mpc_dc.xlog(2,:),... + 'k--', 'LineWidth', 1.0, 'MarkerSize', 4); +% plot obstacle +pos = obs.pos; +r = obs.r; +th = linspace(0,2*pi*100); +x = cos(th) ; y = sin(th) ; +plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980],... + 'LineWidth', 2); +plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980],... + 'MarkerSize', 5, 'LineWidth', 2); +% plot target position +plot(x0(1), x0(2), 'db', 'LineWidth', 1); +plot(0.0, 0.0, 'dr', 'LineWidth', 1); +h=get(gca,'Children'); +h_legend = legend(h([end, end-1, end-2, end-3, end-4]),... + {'MPC-CBF ($\gamma=0.1$)', 'MPC-CBF ($\gamma=0.2$)',... + 'MPC-CBF ($\gamma=0.3$)', 'MPC-CBF ($\gamma=1.0$)', 'MPC-DC'}, 'Location', 'SouthEast'); +set(h_legend, 'Interpreter','latex'); +set(gca,'LineWidth', 0.2, 'FontSize', 15); +grid on +xlabel('$x (m)$','interpreter','latex','FontSize',20); +ylabel('$y (m)$','interpreter','latex','FontSize',20); +xticks(-5:1); +yticks(-5:1); +xlim([-5,0.2]); +ylim([-5,0.2]); +print(gcf,'figures/benchmark-gamma.eps', '-depsc'); +print(gcf,'figures/benchmark-gamma.png', '-dpng', '-r800'); \ No newline at end of file diff --git a/double-integrator-2D/analysis_horizon.m b/double-integrator-2D/analysis_horizon.m new file mode 100644 index 0000000..e937723 --- /dev/null +++ b/double-integrator-2D/analysis_horizon.m @@ -0,0 +1,198 @@ +close all +clear + +%% Setup and Parameters +x0 = [-5; -5; 0; 0]; +time_total = 20.0; +dt = 0.2; +P = 100*eye(4); +Q = 10*eye(4); +R = eye(2); +N = 8; +umin = [-1; -1]; +umax = [1; 1]; +xmin = [-5; -5; -5; -5]; +xmax = [5; 5; 5; 5]; + +%% Discrete-time double integrator 2D +system.dt = dt; +system.A = [1 0 dt 0; + 0 1 0 dt; + 0 0 1 0; + 0 0 0 1]; +system.B = [0.5*dt^2 0; + 0 0.5*dt^2; + dt 0; + 0 dt]; +system.xl = xmin; +system.xu = xmax; +system.ul = umin; +system.uu = umax; + +%% MPC-CBF parameters +params.Q = Q; +params.R = R; +params.P = P; +params.N = N; +params.gamma = 0.5; + +%% Obstacle +obs.pos = [-2; -2.25]; +obs.r = 1.5; + +%% Simulate MPC-CBF +params.N = 5; +params.gamma = 0.25; +controller_mpc_cbf_1 = MPC_CBF(x0, system, params); +controller_mpc_cbf_1.obs = obs; +controller_mpc_cbf_1.sim(time_total); + +%% Simulate MPC-CBF with lower gamma +params.gamma = 0.20; +controller_mpc_cbf_2 = MPC_CBF(x0, system, params); +controller_mpc_cbf_2.obs = obs; +controller_mpc_cbf_2.sim(time_total); + +params.gamma = 0.15; +controller_mpc_cbf_3 = MPC_CBF(x0, system, params); +controller_mpc_cbf_3.obs = obs; +controller_mpc_cbf_3.sim(time_total); + +%% Simulate MPC-DC +params.N = 7; +controller_mpc_dc_1 = MPC_DC(x0, system, params); +controller_mpc_dc_1.obs = obs; +controller_mpc_dc_1.sim(time_total); + +%% Simulate MPC-DC with larger horizon +params.N = 15; +controller_mpc_dc_2 = MPC_DC(x0, system, params); +controller_mpc_dc_2.obs = obs; +controller_mpc_dc_2.sim(time_total); + +%% +params.N = 30; +controller_mpc_dc_3 = MPC_DC(x0, system, params); +controller_mpc_dc_3.obs = obs; +controller_mpc_dc_3.sim(time_total); + +%% Visualization benchmark +figure('Renderer', 'painters', 'Position', [0 0 400 400]); +set(gca,'LooseInset',get(gca,'TightInset')); +hold on +plot(controller_mpc_cbf_3.xlog(1,:), controller_mpc_cbf_3.xlog(2,:),... + '-', 'Color', [0, 0.4470, 0.7410], 'LineWidth', 1.0, 'MarkerSize', 4); +plot(controller_mpc_cbf_2.xlog(1,:), controller_mpc_cbf_2.xlog(2,:),... + '-', 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 1.0, 'MarkerSize', 4); +plot(controller_mpc_cbf_1.xlog(1,:), controller_mpc_cbf_1.xlog(2,:),... + '-', 'Color', [0.9290, 0.6940, 0.1250], 'LineWidth', 1.0, 'MarkerSize', 4); +plot(controller_mpc_dc_1.xlog(1,:), controller_mpc_dc_1.xlog(2,:),... + '--', 'Color', [0.4940, 0.1840, 0.5560], 'LineWidth', 1.0, 'MarkerSize', 4); +plot(controller_mpc_dc_2.xlog(1,:), controller_mpc_dc_2.xlog(2,:),... + '--', 'Color', [0.4660, 0.6740, 0.1880], 'LineWidth', 1.0, 'MarkerSize', 4); +plot(controller_mpc_dc_3.xlog(1,:), controller_mpc_dc_3.xlog(2,:),... + '--', 'Color', [0.3010, 0.7450, 0.9330], 'LineWidth', 1.0, 'MarkerSize', 4); +% plot obstacle +pos = obs.pos; +r = obs.r; +th = linspace(0,2*pi*100); +x = cos(th) ; y = sin(th) ; +plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980],... + 'LineWidth', 2); +plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980],... + 'MarkerSize', 5, 'LineWidth', 2); +% plot target position +plot(x0(1), x0(2), 'db', 'LineWidth', 1); +plot(0.0, 0.0, 'dr', 'LineWidth', 1); +h=get(gca,'Children'); +h_legend = legend(h([end, end-1, end-2, end-3, end-4, end-5]),... + {'MPC-CBF ($N = 5, \gamma = 0.15$)', 'MPC-CBF ($N = 5, \gamma = 0.20$)',... + 'MPC-CBF ($N = 5, \gamma = 0.25$)', 'MPC-DC ($N = 7$)', 'MPC-DC ($N = 15$)',... + 'MPC-DC ($N = 30$)'}, 'Location', 'SouthEast'); +set(h_legend, 'Interpreter','latex', 'FontSize', 10); +set(gca,'LineWidth', 0.2, 'FontSize', 15); +grid on +xlabel('$x (m)$','interpreter','latex','FontSize',20); +ylabel('$y (m)$','interpreter','latex','FontSize',20); +xticks(-5:0); +yticks(-5:0); +xlim([-5,0.2]); +ylim([-5,0.2]); +print(gcf,'figures/benchmark-horizon.eps', '-depsc'); +print(gcf,'figures/benchmark-horizon.png', '-dpng', '-r800'); + +%% Computational time benchmark +figure('Renderer', 'painters', 'Position', [0 0 800 400]); +xlabel('Computational time (s)', 'interpreter', 'latex', 'FontSize', 16); +ylabel('Percentage', 'interpreter', 'latex', 'FontSize', 16); +hold on +% [N_mpc_3, edges_mpc_3] = histcounts(controller_mpc_cbf_3.solvertime, 10, 'Normalization', 'probability'); +% plot(edges_mpc_3(1:end-1), N_mpc_3, '-', 'Color', [0, 0.4470, 0.7410], 'LineWidth', 1); +% [N_mpc_2, edges_mpc_2] = histcounts(controller_mpc_cbf_2.solvertime, 10, 'Normalization', 'probability'); +% plot(edges_mpc_2(1:end-1), N_mpc_2, '-', 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 1); +[N_mpc_1, edges_mpc_1] = histcounts(controller_mpc_cbf_1.solvertime, 10, 'Normalization', 'probability'); +plot(edges_mpc_1(1:end-1), N_mpc_1, '-', 'Color', [0.9290, 0.6940, 0.1250], 'LineWidth', 1); +[N_dc_1, edges_dc_1] = histcounts(controller_mpc_dc_1.solvertime, 10, 'Normalization', 'probability'); +plot(edges_dc_1(1:end-1), N_dc_1, '--', 'Color', [0.4940, 0.1840, 0.5560], 'LineWidth', 1); +[N_dc_2, edges_dc_2] = histcounts(controller_mpc_dc_2.solvertime, 10, 'Normalization', 'probability'); +plot(edges_dc_2(1:end-1), N_dc_2, '--', 'Color', [0.4660, 0.6740, 0.1880], 'LineWidth', 1); +[N_dc_3, edges_dc_3] = histcounts(controller_mpc_dc_3.solvertime, 10, 'Normalization', 'probability'); +plot(edges_dc_3(1:end-1), N_dc_3, '--', 'Color', [0.3010, 0.7450, 0.9330], 'LineWidth', 1); +h=get(gca,'Children'); +h_legend = legend(h([end, end-1, end-2, end-3]),... + {'MPC-CBF ($N = 5, \gamma = 0.25$)',... + 'MPC-DC ($N = 7$)',... + 'MPC-DC ($N = 15$)',... + 'MPC-DC ($N = 30$)'}, 'Location', 'NorthEast'); +set(h_legend, 'Interpreter','latex'); +set(gca,'LineWidth', 0.2, 'FontSize', 15); +print(gcf,'figures/benchmark-horizon-computational-time.eps', '-depsc'); +print(gcf,'figures/benchmark-horizon-computational-time.png', '-dpng', '-r800'); +%% Computational time table +fprintf('Computational time for MPC-CBF3: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_cbf_3.solvertime),... + std(controller_mpc_cbf_3.solvertime),... + min(controller_mpc_cbf_3.solvertime),... + max(controller_mpc_cbf_3.solvertime),... + controller_mpc_cbf_3.u_cost,... + min(controller_mpc_cbf_3.distlog)]); + +fprintf('Computational time for MPC-CBF2: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_cbf_2.solvertime),... + std(controller_mpc_cbf_2.solvertime),... + min(controller_mpc_cbf_2.solvertime),... + max(controller_mpc_cbf_2.solvertime),... + controller_mpc_cbf_2.u_cost,... + min(controller_mpc_cbf_2.distlog)]); + +fprintf('Computational time for MPC-CBF1: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_cbf_1.solvertime),... + std(controller_mpc_cbf_1.solvertime),... + min(controller_mpc_cbf_1.solvertime),... + max(controller_mpc_cbf_1.solvertime),... + controller_mpc_cbf_1.u_cost,... + min(controller_mpc_cbf_1.distlog)]); + +fprintf('Computational time for MPC-DC1: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_dc_1.solvertime),... + std(controller_mpc_dc_1.solvertime),... + min(controller_mpc_dc_1.solvertime),... + max(controller_mpc_dc_1.solvertime),... + controller_mpc_dc_1.u_cost,... + min(controller_mpc_dc_1.distlog)]); + +fprintf('Computational time for MPC-DC2: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_dc_2.solvertime),... + std(controller_mpc_dc_2.solvertime),... + min(controller_mpc_dc_2.solvertime),... + max(controller_mpc_dc_2.solvertime),... + controller_mpc_dc_2.u_cost,... + min(controller_mpc_dc_2.distlog)]); + +fprintf('Computational time for MPC-DC3: mean %.3f, std %.3f, min %.3f, max %.3f, input cost %.3f, min dist %f\n',... + [mean(controller_mpc_dc_3.solvertime),... + std(controller_mpc_dc_3.solvertime),... + min(controller_mpc_dc_3.solvertime),... + max(controller_mpc_dc_3.solvertime),... + controller_mpc_dc_3.u_cost,... + min(controller_mpc_dc_3.distlog)]); \ No newline at end of file diff --git a/double-integrator-2D/figures/benchmark-gamma.eps b/double-integrator-2D/figures/benchmark-gamma.eps new file mode 100644 index 0000000..48d8079 --- /dev/null +++ b/double-integrator-2D/figures/benchmark-gamma.eps @@ -0,0 +1,3297 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: (MATLAB, The Mathworks, Inc. 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+f-2068629528 +f +GR +GS +[0.75 0 0 0.75 69.04322 226.1797] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 73.40985 222.008] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 77.68999 217.91894] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 81.8854 213.91083] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 85.99773 209.98209] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 90.02862 206.13113] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 93.97967 202.35648] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 97.85251 198.65654] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 101.64865 195.02986] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 105.36962 191.47501] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 109.01691 187.99054] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 112.59198 184.57508] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 116.09625 181.22725] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.53114 177.94571] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.89799 174.72915] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.19819 171.57628] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.43302 168.48586] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.7118 166.13683] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.01192 164.53664] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.68249 163.39719] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.95915 162.53785] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.98606 161.83706] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.85953 161.22733] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.6324 160.65902] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.34366 160.11038] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.01024 159.55897] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 132.64942 159.00027] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 132.26453 158.42134] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.86511 157.8242] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.44941 157.1988] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.0243 156.54984] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.58619 155.86781] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.14114 155.15878] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.68489 154.41283] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.22351 153.63698] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 128.75246 152.82059] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 128.27805 151.97152] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.79573 151.07827] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.31215 150.14949] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.82288 149.17277] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.3349 148.1577] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.84405 147.09081] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.35767 145.98276] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.87197 144.81901] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.39458 143.61135] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.92221 142.34416] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.4628 141.03055] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.01368 139.6538] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.58297 138.22844] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.16884 136.73671] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.77946 135.19474] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.414 133.58373] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.08051 131.92159] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.7793 130.1886] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.51819 128.40459] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.29873 126.54901] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.12821 124.6438] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.0096 122.66776] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.94933 120.64498] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.95188 118.55384] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.02242 116.42073] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.16704 114.22371] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.3892 111.9915] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.69654 109.70213] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.09036 107.38651] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.57982 105.02287] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.16347 102.64409] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.85191 100.22881] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.64047 97.81158] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.541 95.37155] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.54511 92.94445] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.66577 90.51008] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.89052 88.1047] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.23324 85.70882] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.6772 83.35849] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 132.23703 81.03489] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.89174 78.77309] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 135.65658 76.55487] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 137.50648 74.41349] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 139.45731 72.33132] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 141.48032 70.33899] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 143.59198 68.41942] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 145.7605 66.6] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 148.00302 64.86417] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 150.2854 63.2356] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 152.6256 61.6983] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 154.98794 60.27198] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 157.39118 58.94128] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 159.79072 57.7062] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 162.22521 56.59021] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 164.61148 55.49632] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 167.05032 54.61464] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 169.44088 53.75041] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 171.81942 52.99317] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 174.15088 52.25092] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 176.43616 51.52337] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 178.67618 50.81023] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 180.87187 50.1112] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 183.02407 49.42602] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 185.13364 48.75441] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 187.20144 48.0961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 189.2283 47.45082] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 191.21502 46.81832] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 193.1624 46.19835] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 195.07121 45.59065] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 196.94222 44.99499] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 198.77621 44.41112] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 200.57387 43.83881] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 202.33591 43.27784] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 204.06308 42.72797] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 205.75605 42.18899] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 207.41547 41.66069] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 209.04206 41.14284] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 210.63643 40.63526] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 212.19921 40.13772] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 213.73107 39.65004] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 215.23258 39.17201] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 216.70436 38.70344] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 218.14703 38.24416] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 219.56108 37.79397] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 220.94717 37.3527] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 222.30579 36.92016] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 223.63751 36.49619] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 224.94285 36.08061] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 226.22237 35.67327] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 227.47652 35.27399] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 228.70585 34.88261] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 229.91084 34.49899] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 231.09196 34.12296] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 232.24969 33.75438] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 233.38451 33.3931] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 234.49686 33.03897] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 235.58716 32.69185] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 236.6559 32.35161] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 237.70345 32.01811] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 238.73026 31.69121] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 239.73676 31.37078] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 240.72331 31.0567] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 241.69032 30.74883] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 242.63818 30.44707] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 243.56728 30.15127] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 244.47798 29.86134] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 245.37067 29.57715] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 246.24566 29.29858] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 247.10332 29.02554] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 247.94398 28.75789] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 0 0.25] CT +0.851 0.325 0.098 RC +1 LJ +2.667 LW +N +353.769 159.24 M +353.574 153.368 L +352.989 147.518 L +352.018 141.716 L +350.663 135.985 L +348.93 130.347 L +346.826 124.826 L +344.361 119.443 L +341.542 114.22 L +338.383 109.179 L +334.895 104.339 L +331.094 99.721 L +326.993 95.342 L +322.609 91.22 L +317.961 87.372 L +313.067 83.814 L +307.946 80.559 L +302.62 77.621 L +297.109 75.012 L +291.437 72.742 L +285.625 70.82 L +279.697 69.254 L +273.677 68.051 L +267.589 67.215 L +261.458 66.749 L +255.308 66.656 L +249.165 66.935 L +243.053 67.587 L +236.996 68.607 L +231.019 69.992 L +225.146 71.737 L +219.4 73.834 L +213.806 76.275 L +208.385 79.05 L +203.159 82.148 L +198.149 85.556 L +193.375 89.261 L +188.857 93.248 L +184.613 97.5 L +180.659 102.001 L +177.013 106.733 L +173.688 111.676 L +170.697 116.81 L +168.054 122.116 L +165.768 127.571 L +163.849 133.153 L +162.304 138.84 L +161.141 144.61 L +160.362 150.439 L +159.972 156.303 L +159.972 162.178 L +160.362 168.042 L +161.141 173.871 L +162.304 179.64 L +163.849 185.328 L +165.768 190.91 L +168.054 196.365 L +170.697 201.67 L +173.688 206.805 L 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-17.131 QT +6.824 -10.194 L +6.746 -9.819 6.418 -9.561 QT +6.09 -9.303 5.699 -9.303 QT +5.387 -9.303 5.137 -9.514 QT +4.887 -9.725 4.887 -10.069 QT +4.887 -10.225 4.918 -10.303 QT +6.652 -17.178 L +6.918 -18.288 6.918 -19.022 QT +6.918 -19.772 6.613 -20.303 QT +6.309 -20.834 5.559 -20.834 QT +4.574 -20.834 3.746 -20.397 QT +2.918 -19.959 2.301 -19.241 QT +1.684 -18.522 1.168 -17.538 QT +-0.676 -10.194 L +-0.769 -9.819 -1.09 -9.561 QT +-1.41 -9.303 -1.801 -9.303 QT +-2.129 -9.303 -2.371 -9.514 QT +-2.613 -9.725 -2.613 -10.069 QT +cp +f +GR +GS +[0 -0.75 0.75 0 23.99999 128.99989] CT +0.149 GC +N +20.472 -2.85 M +20.238 -2.85 20.238 -3.084 QT +20.238 -3.209 20.285 -3.256 QT +24.91 -7.772 24.91 -16.35 QT +24.91 -24.928 20.347 -29.381 QT +20.238 -29.459 20.238 -29.616 QT +20.238 -29.709 20.308 -29.78 QT +20.379 -29.85 20.472 -29.85 QT +20.722 -29.85 L +20.8 -29.85 20.863 -29.803 QT +22.8 -28.272 24.09 -26.084 QT +25.379 -23.897 25.98 -21.413 QT +26.582 -18.928 26.582 -16.35 QT +26.582 -14.444 26.261 -12.592 QT +25.941 -10.741 25.23 -8.936 QT +24.519 -7.131 23.441 -5.608 QT +22.363 -4.084 20.863 -2.897 QT +20.8 -2.85 20.722 -2.85 QT +20.472 -2.85 L +cp +f +GR +GS +[0.75 0 0 0.75 0 0] CT +1 LJ +1.333 LW +N +64.254 334.738 M +68.015 330.954 L +73.449 325.487 L +79.336 319.563 L +85.221 313.643 L +91.011 307.817 L +96.691 302.102 L +102.259 296.5 L +107.716 291.01 L +113.065 285.628 L +118.307 280.354 L +123.445 275.185 L +128.48 270.118 L +133.415 265.153 L +138.253 260.286 L +142.993 255.516 L +147.64 250.841 L +152.194 246.259 L +156.657 241.768 L +161.032 237.367 L +165.319 233.053 L +169.521 228.825 L +172.428 225.746 L +174.108 223.677 L +174.953 222.168 L +175.296 221.024 L +175.323 220.087 L +175.158 219.274 L +174.865 218.514 L +174.496 217.782 L +174.07 217.045 L +173.611 216.3 L +173.12 215.528 L +172.611 214.732 L +172.081 213.898 L +171.54 213.034 L +170.982 212.126 L +170.415 211.183 L +169.833 210.189 L +169.245 209.158 L +168.643 208.072 L +168.038 206.944 L +167.422 205.756 L +166.804 204.524 L +166.177 203.226 L +165.553 201.879 L +164.923 200.462 L +164.298 198.993 L +163.673 197.447 L +163.058 195.846 L +162.447 194.164 L +161.852 192.422 L +161.268 190.594 L +160.706 188.705 L +160.163 186.724 L +159.65 184.679 L +159.164 182.539 L +158.717 180.334 L +158.308 178.03 L +157.947 175.661 L +157.637 173.192 L +157.385 170.66 L +157.197 168.026 L +157.08 165.333 L +157.038 162.542 L +157.081 159.697 L +157.214 156.758 L +157.443 153.774 L +157.777 150.704 L +158.218 147.599 L +158.779 144.42 L +159.457 141.22 L +160.267 137.96 L +161.202 134.696 L +162.281 131.389 L +163.49 128.098 L +164.85 124.784 L +166.341 121.507 L +167.988 118.229 L +169.764 115.01 L +171.695 111.814 L +173.748 108.699 L +175.95 105.63 L +178.263 102.663 L +180.716 99.765 L +183.265 96.987 L +185.939 94.297 L +188.689 91.744 L +191.547 89.295 L +194.46 86.993 L +197.461 84.808 L +200.443 82.695 L +203.557 80.825 L +206.649 79.032 L +209.813 77.45 L +212.941 75.935 L +216.11 74.638 L +219.236 73.404 L +222.352 72.322 L +225.417 71.286 L +228.422 70.276 L +231.369 69.288 L +234.256 68.319 L +237.086 67.37 L +239.86 66.439 L +242.579 65.527 L +245.243 64.633 L +247.855 63.757 L +250.414 62.899 L +252.923 62.057 L +255.382 61.232 L +257.791 60.424 L +260.153 59.632 L +262.468 58.855 L +264.737 58.094 L +266.96 57.348 L +269.14 56.617 L +271.275 55.901 L +273.369 55.198 L +275.421 54.51 L +277.432 53.836 L +279.402 53.174 L +281.334 52.526 L +283.227 51.891 L +285.083 51.269 L +286.901 50.659 L +288.684 50.061 L +290.431 49.475 L +292.143 48.901 L +293.821 48.338 L +295.466 47.786 L +297.078 47.245 L +298.658 46.715 L +300.206 46.196 L +301.724 45.687 L +303.211 45.188 L +304.669 44.699 L +306.098 44.219 L +307.498 43.75 L +308.871 43.289 L +310.216 42.838 L +311.534 42.396 L +312.827 41.962 L +314.093 41.537 L +315.334 41.121 L +316.551 40.713 L +317.743 40.313 L +318.912 39.921 L +320.057 39.537 L +321.18 39.16 L +322.28 38.791 L +S +GR +GS +[0.75 0 0 0.75 48.19038 251.05385] CT +N +0 -2 M +1.105 -2 2 -1.105 2 0 C +2 0 L +2 1.105 1.105 2 0 2 C +-1.105 2 -2 1.105 -2 0 C +-2 -1.105 -1.105 -2 0 -2 C +cp +0 -3.333 M +-1.841 -3.333 -3.333 -1.841 -3.333 0 C +-3.333 1.841 -1.841 3.333 0 3.333 C +1.841 3.333 3.333 1.841 3.333 0 C +3.333 0 L +3.333 -1.841 1.841 -3.333 0 -3.333 C +cp +f +GR +GS +[0.75 0 0 0.75 51.01154 248.21539] CT +N +/f-2068629528{0 -2 M +1.105 -2 2 -1.105 2 0 C +2 0 L +2 1.105 1.105 2 0 2 C +-1.105 2 -2 1.105 -2 0 C +-2 -1.105 -1.105 -2 0 -2 C +cp +0 -3.333 M +-1.841 -3.333 -3.333 -1.841 -3.333 0 C +-3.333 1.841 -1.841 3.333 0 3.333 C +1.841 3.333 3.333 1.841 3.333 0 C +3.333 0 L +3.333 -1.841 1.841 -3.333 0 -3.333 C +cp}def +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 55.08653 244.11539] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 59.50237 239.67247] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 63.91573 235.23203] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 68.25854 230.86258] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 72.51844 226.57654] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 76.69423 222.37511] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 80.7871 218.25714] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 84.79851 214.22113] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 88.73011 210.26541] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 92.58345 206.38843] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 96.36012 202.58858] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 100.06161 198.8644] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 103.68945 195.2143] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 107.24507 191.63686] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 110.72994 188.13062] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 114.14544 184.69415] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.49298 181.32608] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.7739 178.02505] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.9895 174.78971] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.14111 171.61876] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.32067 169.30959] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.58086 167.75767] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.21484 166.62622] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.47197 165.76774] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.49215 165.06561] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.36821 164.45514] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.14891 163.88541] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.87222 163.33636] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.55271 162.78389] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.20798 162.22525] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.83981 161.64568] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.45851 161.04913] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 129.06102 160.42355] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 128.65521 159.77578] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 128.23619 159.09413] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.8112 158.38693] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.37463 157.64194] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.93371 156.86868] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.48259 156.05392] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 126.02877 155.20825] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.56629 154.31733] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.103 153.39283] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.63305 152.41921] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.16461 151.40933] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.69205 150.34633] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.22387 149.24438] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.75475 148.08524] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.29353 146.88455] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.83532 145.62266] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.38919 144.31677] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.9509 142.94579] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.52964 141.52873] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.12199 140.043] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.73713 138.50955] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.37267 136.90437] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.03756 135.25052] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.73066 133.52261] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.46052 131.74604] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.22738 129.89409] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.03912 127.99464] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.89758 126.01982] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.80964 124.00012] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.77885 121.90671] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.81067 119.77275] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 117.91058 117.56869] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.08211 115.33035] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.33277 113.02774] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 118.66358 110.69926] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.08414 108.31472] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.59249 105.9149] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.20019 103.46966] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 120.90175 101.02185] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 121.71069 98.54164] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 122.61739 96.07336] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 123.63725 93.58777] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.75612 91.13] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 125.99107 88.67157] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 127.32318 86.25758] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 128.77104 83.86042] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.31084 81.52431] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 131.96254 79.22258] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 133.69761 76.99757] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 135.53725 74.82362] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 137.44857 72.74031] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 139.45395 70.72301] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 141.5167 68.80773] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 143.66036 66.97096] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 145.84522 65.24445] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 148.0959 63.6059] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 150.33192 62.02151] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 152.66786 60.61872] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 154.98655 59.27422] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 157.35943 58.08776] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 159.7054 56.95148] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 162.08216 55.97848] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 164.42729 55.05332] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 166.76432 54.24132] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 169.06265 53.46465] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 171.31682 52.70733] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 173.52644 51.96586] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 175.69216 51.23931] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 177.81477 50.52726] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 179.89517 49.82937] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 181.93414 49.14539] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 183.93256 48.47501] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 185.89118 47.81797] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 187.81082 47.17402] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 189.69228 46.54287] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 191.53627 45.92429] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 193.34356 45.31802] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 195.1149 44.72382] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 196.85097 44.14144] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 198.5525 43.57065] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 200.22015 43.01123] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 201.85464 42.46293] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 203.45659 41.92555] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 205.02665 41.39886] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 206.56544 40.88266] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 208.07364 40.37672] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 209.55183 39.88086] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 211.00056 39.39487] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 212.42049 38.91855] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 213.81214 38.4517] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 215.17612 37.99415] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 216.51295 37.54571] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 217.82316 37.10619] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 219.10728 36.67542] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 220.36588 36.25322] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 221.59941 35.83942] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 222.80839 35.43386] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 223.99331 35.03637] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 225.15466 34.64679] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 226.29286 34.26497] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 227.40845 33.89074] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 228.50182 33.52396] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 229.57343 33.16449] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 230.62372 32.81216] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 231.65309 32.46685] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 232.66198 32.12841] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 233.65079 31.79671] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 234.61993 31.4716] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 235.56979 31.15297] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 236.50072 30.84068] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 237.41313 30.53461] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 238.3074 30.23462] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 239.18385 29.94061] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 240.04287 29.65244] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 240.88479 29.37001] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 241.70995 29.09321] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 0 0] CT +0.851 0.325 0.098 RC +1 LJ +2.667 LW +N +345.115 162.538 M +344.926 156.538 L +344.359 150.561 L +343.416 144.632 L +342.101 138.776 L +340.42 133.015 L +338.379 127.373 L +335.987 121.873 L +333.252 116.537 L +330.187 111.386 L +326.803 106.44 L +323.115 101.721 L +319.136 97.246 L +314.883 93.035 L +310.373 89.103 L +305.625 85.467 L +300.656 82.141 L +295.489 79.139 L +290.142 76.473 L +284.638 74.154 L +278.999 72.19 L +273.247 70.59 L +267.407 69.36 L +261.5 68.506 L +255.551 68.03 L +249.585 67.935 L +243.624 68.221 L +237.694 68.886 L +231.817 69.929 L +226.018 71.344 L +220.32 73.127 L +214.746 75.27 L +209.318 77.764 L +204.058 80.599 L +198.987 83.765 L +194.126 87.247 L +189.495 91.033 L +185.111 95.107 L +180.993 99.452 L +177.158 104.051 L +173.62 108.886 L +170.393 113.937 L +167.492 119.183 L +164.927 124.604 L +162.71 130.178 L +160.848 135.882 L +159.349 141.694 L +158.22 147.589 L +157.464 153.545 L +157.086 159.537 L +157.086 165.54 L +157.464 171.532 L +158.22 177.488 L +159.349 183.383 L +160.848 189.195 L +162.71 194.899 L +164.927 200.473 L +167.492 205.894 L +170.393 211.14 L +173.62 216.191 L +177.158 221.026 L +180.993 225.625 L +185.111 229.97 L +189.495 234.044 L +194.126 237.83 L +198.987 241.312 L +204.058 244.478 L +209.318 247.313 L +214.746 249.807 L +220.32 251.95 L +226.018 253.733 L +231.817 255.148 L +237.694 256.191 L +243.624 256.856 L +249.585 257.142 L +255.551 257.047 L +261.5 256.571 L +267.407 255.716 L +273.247 254.487 L +278.999 252.887 L +284.638 250.923 L +290.142 248.604 L +295.489 245.938 L +300.656 242.936 L +305.625 239.61 L +310.373 235.974 L +314.883 232.042 L +319.136 227.831 L +323.115 223.356 L +326.803 218.637 L +330.187 213.691 L +333.252 208.54 L +335.987 203.204 L +338.379 197.703 L +340.42 192.062 L +342.101 186.301 L +343.416 180.445 L +344.359 174.516 L +344.926 168.539 L +345.115 162.538 L +S +GR +GS +[0.75 0 0 0.75 47.25 252] CT +0 0 1 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +1 0 0 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 0 0] CT +1 GC +N +378 325 M +378 300 L +173 300 L +173 325 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +0.641 4.32 M +0.641 3.679 L +2.484 3.679 2.484 2.617 QT +2.484 -6.774 L +2.484 -7.336 0.641 -7.336 QT +0.641 -7.977 L +4.031 -7.977 L +4.25 -7.977 4.328 -7.774 QT +8.25 2.414 L +12.172 -7.774 L +12.234 -7.977 12.453 -7.977 QT +15.859 -7.977 L +15.859 -7.336 L +14 -7.336 14 -6.774 QT +14 3.117 L +14 3.679 15.859 3.679 QT +15.859 4.32 L +10.625 4.32 L +10.625 3.679 L +12.469 3.679 12.469 3.117 QT +12.469 -7.368 L +8.047 4.117 L +7.969 4.32 7.75 4.32 QT +7.516 4.32 7.438 4.117 QT +3.063 -7.227 L +3.063 2.617 L +3.063 3.679 4.906 3.679 QT +4.906 4.32 L +0.641 4.32 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +17.094 4.32 M +17.094 3.679 L +18.953 3.679 18.953 3.117 QT +18.953 -6.774 L +18.953 -7.336 17.094 -7.336 QT +17.094 -7.977 L +23.5 -7.977 L +24.484 -7.977 25.469 -7.571 QT +26.453 -7.164 27.094 -6.391 QT +27.734 -5.618 27.734 -4.586 QT +27.734 -3.586 27.094 -2.836 QT +26.453 -2.086 25.477 -1.688 QT +24.5 -1.289 23.5 -1.289 QT +20.625 -1.289 L +20.625 3.117 L +20.625 3.679 22.484 3.679 QT +22.484 4.32 L +17.094 4.32 L +cp +20.563 -1.836 M +23.016 -1.836 L +24 -1.836 24.617 -2.118 QT +25.234 -2.399 25.523 -3 QT +25.813 -3.602 25.813 -4.586 QT +25.813 -6.055 25.164 -6.696 QT +24.516 -7.336 23.016 -7.336 QT +21.484 -7.336 L +21.156 -7.336 20.977 -7.313 QT +20.797 -7.289 20.68 -7.164 QT +20.563 -7.039 20.563 -6.774 QT +20.563 -1.836 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +32.859 2.398 M +33.469 3.179 34.391 3.632 QT +35.313 4.086 36.313 4.086 QT +37.141 4.086 37.852 3.757 QT +38.563 3.429 39.094 2.836 QT +39.625 2.242 39.914 1.5 QT +40.203 0.757 40.203 -0.071 QT +40.203 -0.211 40.359 -0.211 QT +40.578 -0.211 L +40.719 -0.211 40.719 -0.039 QT +40.719 0.898 40.359 1.773 QT +40 2.648 39.344 3.312 QT +38.688 3.976 37.828 4.343 QT +36.969 4.711 36.031 4.711 QT +34.75 4.711 33.594 4.187 QT +32.438 3.664 31.578 2.757 QT +30.719 1.851 30.242 0.656 QT +29.766 -0.539 29.766 -1.836 QT +29.766 -3.118 30.242 -4.313 QT +30.719 -5.508 31.578 -6.422 QT +32.438 -7.336 33.594 -7.852 QT +34.75 -8.368 36.031 -8.368 QT +36.953 -8.368 37.797 -7.969 QT +38.641 -7.571 39.281 -6.836 QT +40.328 -8.321 L +40.438 -8.368 40.453 -8.368 QT +40.578 -8.368 L +40.641 -8.368 40.68 -8.329 QT +40.719 -8.289 40.719 -8.227 QT +40.719 -3.368 L +40.719 -3.211 40.578 -3.211 QT +40.25 -3.211 L +40.094 -3.211 40.094 -3.368 QT +40.094 -3.883 39.883 -4.524 QT +39.672 -5.164 39.352 -5.743 QT +39.031 -6.321 38.609 -6.758 QT +37.594 -7.743 36.297 -7.743 QT +35.297 -7.743 34.391 -7.289 QT +33.484 -6.836 32.859 -6.055 QT +32.203 -5.211 31.945 -4.133 QT +31.688 -3.055 31.688 -1.836 QT +31.688 -0.618 31.945 0.468 QT +32.203 1.554 32.859 2.398 QT +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +41.953 0.992 M +41.953 -0.133 L +46.719 -0.133 L +46.719 0.992 L +41.953 0.992 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +51.859 2.398 M +52.469 3.179 53.391 3.632 QT +54.313 4.086 55.313 4.086 QT +56.141 4.086 56.852 3.757 QT +57.563 3.429 58.094 2.836 QT +58.625 2.242 58.914 1.5 QT +59.203 0.757 59.203 -0.071 QT +59.203 -0.211 59.359 -0.211 QT +59.578 -0.211 L +59.719 -0.211 59.719 -0.039 QT +59.719 0.898 59.359 1.773 QT +59 2.648 58.344 3.312 QT +57.688 3.976 56.828 4.343 QT +55.969 4.711 55.031 4.711 QT +53.75 4.711 52.594 4.187 QT +51.438 3.664 50.578 2.757 QT +49.719 1.851 49.242 0.656 QT +48.766 -0.539 48.766 -1.836 QT +48.766 -3.118 49.242 -4.313 QT +49.719 -5.508 50.578 -6.422 QT +51.438 -7.336 52.594 -7.852 QT +53.75 -8.368 55.031 -8.368 QT +55.953 -8.368 56.797 -7.969 QT +57.641 -7.571 58.281 -6.836 QT +59.328 -8.321 L +59.438 -8.368 59.453 -8.368 QT +59.578 -8.368 L +59.641 -8.368 59.68 -8.329 QT +59.719 -8.289 59.719 -8.227 QT +59.719 -3.368 L +59.719 -3.211 59.578 -3.211 QT +59.25 -3.211 L +59.094 -3.211 59.094 -3.368 QT +59.094 -3.883 58.883 -4.524 QT +58.672 -5.164 58.352 -5.743 QT +58.031 -6.321 57.609 -6.758 QT +56.594 -7.743 55.297 -7.743 QT +54.297 -7.743 53.391 -7.289 QT +52.484 -6.836 51.859 -6.055 QT +51.203 -5.211 50.945 -4.133 QT +50.688 -3.055 50.688 -1.836 QT +50.688 -0.618 50.945 0.468 QT +51.203 1.554 51.859 2.398 QT +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +61.359 4.32 M +61.359 3.679 L +63.219 3.679 63.219 3.117 QT +63.219 -6.774 L +63.219 -7.336 61.359 -7.336 QT +61.359 -7.977 L +67.984 -7.977 L +68.891 -7.977 69.828 -7.618 QT +70.766 -7.258 71.375 -6.563 QT +71.984 -5.868 71.984 -4.914 QT +71.984 -3.821 71.086 -3.079 QT +70.188 -2.336 68.984 -2.102 QT +69.766 -2.102 70.586 -1.672 QT +71.406 -1.243 71.938 -0.524 QT +72.469 0.195 72.469 1.007 QT +72.469 1.992 71.883 2.75 QT +71.297 3.507 70.367 3.914 QT +69.438 4.32 68.5 4.32 QT +61.359 4.32 L +cp +64.781 3.117 M +64.781 3.507 65 3.593 QT +65.219 3.679 65.703 3.679 QT +67.984 3.679 L +68.688 3.679 69.289 3.312 QT +69.891 2.945 70.242 2.328 QT +70.594 1.711 70.594 1.007 QT +70.594 0.32 70.305 -0.336 QT +70.016 -0.993 69.477 -1.414 QT +68.938 -1.836 68.234 -1.836 QT +64.781 -1.836 L +64.781 3.117 L +cp +64.781 -2.305 M +67.484 -2.305 L +68.031 -2.305 68.508 -2.5 QT +68.984 -2.696 69.367 -3.071 QT +69.75 -3.446 69.953 -3.914 QT +70.156 -4.383 70.156 -4.914 QT +70.156 -5.383 70.008 -5.813 QT +69.859 -6.243 69.563 -6.594 QT +69.266 -6.946 68.859 -7.141 QT +68.453 -7.336 67.984 -7.336 QT +65.703 -7.336 L +65.375 -7.336 65.195 -7.313 QT +65.016 -7.289 64.899 -7.164 QT +64.781 -7.039 64.781 -6.774 QT +64.781 -2.305 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +74.047 4.32 M +74.047 3.679 L +75.906 3.679 75.906 3.117 QT +75.906 -6.774 L +75.906 -7.336 74.047 -7.336 QT +74.047 -7.977 L +83.985 -7.977 L +84.485 -3.852 L +83.953 -3.852 L +83.844 -4.993 83.633 -5.649 QT +83.422 -6.305 83.024 -6.672 QT +82.625 -7.039 81.969 -7.188 QT +81.313 -7.336 80.141 -7.336 QT +78.5 -7.336 L +78.172 -7.336 77.992 -7.313 QT +77.813 -7.289 77.703 -7.164 QT +77.594 -7.039 77.594 -6.774 QT +77.594 -2.133 L +78.86 -2.133 L +79.781 -2.133 80.211 -2.297 QT +80.641 -2.461 80.805 -2.891 QT +80.969 -3.321 80.969 -4.243 QT +81.485 -4.243 L +81.485 0.586 L +80.969 0.586 L +80.969 -0.336 80.805 -0.766 QT +80.641 -1.196 80.211 -1.36 QT +79.781 -1.524 78.86 -1.524 QT +77.594 -1.524 L +77.594 3.117 L +77.594 3.679 79.891 3.679 QT +79.891 4.32 L +74.047 4.32 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +96.828 8.789 M +95.828 7.992 95.102 6.968 QT +94.375 5.945 93.914 4.789 QT +93.453 3.632 93.227 2.367 QT +93 1.101 93 -0.18 QT +93 -1.477 93.227 -2.743 QT +93.453 -4.008 93.922 -5.172 QT +94.391 -6.336 95.125 -7.36 QT +95.86 -8.383 96.828 -9.149 QT +96.828 -9.18 96.922 -9.18 QT +97.094 -9.18 L +97.141 -9.18 97.188 -9.133 QT +97.235 -9.086 97.235 -9.024 QT +97.235 -8.946 97.188 -8.914 QT +96.313 -8.039 95.727 -7.055 QT +95.141 -6.071 94.789 -4.961 QT +94.438 -3.852 94.274 -2.664 QT +94.11 -1.477 94.11 -0.18 QT +94.11 5.539 97.172 8.507 QT +97.235 8.57 97.235 8.664 QT +97.235 8.711 97.18 8.765 QT +97.125 8.82 97.094 8.82 QT +96.922 8.82 L +96.828 8.82 96.828 8.789 QT +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +99.094 4.32 M +98.922 4.32 98.922 4.086 QT +98.922 4.039 98.953 3.929 QT +98.985 3.82 99.031 3.75 QT +99.078 3.679 99.141 3.679 QT +100.875 3.679 101.156 2.586 QT +103.594 -7.258 L +103.094 -7.336 102.016 -7.336 QT +101.844 -7.336 101.844 -7.586 QT +101.844 -7.618 101.867 -7.735 QT +101.891 -7.852 101.946 -7.914 QT +102 -7.977 102.063 -7.977 QT +105.172 -7.977 L +105.313 -7.977 105.344 -7.868 QT +109.344 1.664 L +111.344 -6.321 L +111.375 -6.508 111.375 -6.586 QT +111.375 -7.336 109.985 -7.336 QT +109.813 -7.336 109.813 -7.586 QT +109.875 -7.805 109.906 -7.891 QT +109.938 -7.977 110.11 -7.977 QT +113.969 -7.977 L +114.141 -7.977 114.141 -7.743 QT +114.125 -7.696 114.102 -7.586 QT +114.078 -7.477 114.031 -7.407 QT +113.985 -7.336 113.906 -7.336 QT +112.188 -7.336 111.906 -6.243 QT +109.328 4.164 L +109.266 4.32 109.141 4.32 QT +108.922 4.32 L +108.797 4.32 108.766 4.195 QT +104.172 -6.696 L 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CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 235.97388 24.55914] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 245.95626 22.5978] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 254.0579 21.06054] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 260.38117 19.85512] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 265.23869 18.90961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 268.99232 18.16779] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 271.90565 17.58569] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 274.17396 17.12886] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 275.94418 16.77032] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 277.32795 16.4889] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 278.41095 16.268] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 279.2593 16.09461] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 279.92422 15.9585] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 280.44564 15.85166] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 280.85463 15.76778] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.17552 15.70194] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.42731 15.65026] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.62491 15.60969] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.78002 15.57784] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.90174 15.55284] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.9973 15.53321] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.0723 15.5178] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.13117 15.5057] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.17741 15.49621] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.21368 15.48876] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.24216 15.4829] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.26452 15.47831] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.28207 15.47471] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.29585 15.47187] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.30666 15.46965] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.31515 15.46791] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.32181 15.46654] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.32705 15.46546] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.33115 15.46462] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.33437 15.46396] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.33691 15.46344] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.33891 15.46303] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34046 15.46271] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34167 15.46246] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34264 15.46226] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34339 15.46211] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34399 15.46198] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34447 15.46189] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34481 15.46181] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34511 15.46175] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34534 15.46171] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34552 15.46167] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34566 15.46164] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34575 15.46162] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34584 15.4616] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34591 15.46159] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34595 15.46158] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.346 15.46157] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34605 15.46156] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34607 15.46156] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34609 15.46155] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34609 15.46155] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34612 15.46155] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34612 15.46155] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34612 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34614 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 0 0] CT +0.851 0.325 0.098 RC +1 LJ +2.667 LW +N +345.115 162.538 M +344.926 156.538 L +344.359 150.561 L +343.416 144.632 L +342.101 138.776 L +340.42 133.015 L +338.379 127.373 L +335.987 121.873 L +333.252 116.537 L +330.187 111.386 L +326.803 106.44 L +323.115 101.721 L +319.136 97.246 L +314.883 93.035 L +310.373 89.103 L +305.625 85.467 L +300.656 82.141 L +295.489 79.139 L +290.142 76.473 L +284.638 74.154 L +278.999 72.19 L +273.247 70.59 L +267.407 69.36 L +261.5 68.506 L +255.551 68.03 L +249.585 67.935 L +243.624 68.221 L +237.694 68.886 L +231.817 69.929 L +226.018 71.344 L +220.32 73.127 L +214.746 75.27 L +209.318 77.764 L +204.058 80.599 L +198.987 83.765 L +194.126 87.247 L +189.495 91.033 L +185.111 95.107 L +180.993 99.452 L +177.158 104.051 L +173.62 108.886 L +170.393 113.937 L +167.492 119.183 L +164.927 124.604 L +162.71 130.178 L +160.848 135.882 L +159.349 141.694 L +158.22 147.589 L +157.464 153.545 L +157.086 159.537 L +157.086 165.54 L +157.464 171.532 L +158.22 177.488 L +159.349 183.383 L +160.848 189.195 L +162.71 194.899 L +164.927 200.473 L +167.492 205.894 L +170.393 211.14 L +173.62 216.191 L +177.158 221.026 L +180.993 225.625 L +185.111 229.97 L +189.495 234.044 L +194.126 237.83 L +198.987 241.312 L +204.058 244.478 L +209.318 247.313 L +214.746 249.807 L +220.32 251.95 L +226.018 253.733 L +231.817 255.148 L +237.694 256.191 L +243.624 256.856 L +249.585 257.142 L +255.551 257.047 L +261.5 256.571 L +267.407 255.716 L +273.247 254.487 L +278.999 252.887 L +284.638 250.923 L +290.142 248.604 L +295.489 245.938 L +300.656 242.936 L +305.625 239.61 L +310.373 235.974 L +314.883 232.042 L +319.136 227.831 L +323.115 223.356 L +326.803 218.637 L +330.187 213.691 L +333.252 208.54 L +335.987 203.204 L +338.379 197.703 L +340.42 192.062 L +342.101 186.301 L +343.416 180.445 L +344.359 174.516 L +344.926 168.539 L +345.115 162.538 L +S +GR +GS +[0.75 0 0 0.75 47.25 252] CT +0 0 1 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 282.34616 15.46154] CT +1 0 0 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 0 0] CT +1 GC +N +378 325 M +378 300 L +173 300 L +173 325 L +cp +f +GR +GS +[0.75 0 0 0.75 164.88431 234.375] CT +N +0.641 4.32 M +0.641 3.679 L +2.484 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213.6654] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 92.80004 201.62788] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 101.72496 187.73846] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 108.71143 171.99712] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 113.75943 154.40385] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 116.86899 134.95864] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 119.6935 114.98613] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 124.17143 96.3382] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 130.58782 79.5422] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 138.94267 64.59811] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 149.23599 51.50595] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 161.46777 40.26572] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 175.63802 30.87741] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 191.59769 23.34101] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 207.89502 17.65655] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 222.80587 13.824] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 235.8436 11.84338] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 246.94286 11.28256] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 256.10365 11.43584] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 263.38852 11.88856] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 269.06644 12.4301] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 273.50082 12.95946] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 276.96909 13.4334] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 279.68456 13.83814] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 281.81223 14.17417] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 283.48025 14.44822] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 284.7884 14.6691] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 285.81461 14.8457] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 286.61982 14.98614] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 287.25169 15.09739] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 287.74761 15.1853] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 288.13683 15.25462] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 288.44234 15.30921] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 288.68216 15.35217] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 288.87039 15.38595] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.01816 15.41249] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.13416 15.43335] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.2252 15.44973] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.29668 15.4626] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.35281 15.4727] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.39684 15.48064] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.43143 15.48687] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.45857 15.49176] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.47988 15.49559] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.49661 15.49861] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.50975 15.50097] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.52005 15.50283] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.52815 15.50429] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.53449 15.50543] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.53948 15.50633] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5434 15.50704] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.54646 15.50759] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.54889 15.50803] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55077 15.50837] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55225 15.50864] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55342 15.50885] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55434 15.50901] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55507 15.50914] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55564 15.50924] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55608 15.50932] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55642 15.50939] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55669 15.50944] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5569 15.50947] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55708 15.5095] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55722 15.50953] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55731 15.50955] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5574 15.50956] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55745 15.50957] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55752 15.50958] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55754 15.50959] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55759 15.50959] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55761 15.5096] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55763 15.5096] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55763 15.5096] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.55766 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 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289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 0 0.25] CT +0.851 0.325 0.098 RC +1 LJ +2.667 LW +N +353.769 159.24 M +353.574 153.368 L +352.989 147.518 L +352.018 141.716 L +350.663 135.985 L +348.93 130.347 L +346.826 124.826 L +344.361 119.443 L +341.542 114.22 L +338.383 109.179 L +334.895 104.339 L +331.094 99.721 L +326.993 95.342 L +322.609 91.22 L +317.961 87.372 L +313.067 83.814 L +307.946 80.559 L +302.62 77.621 L +297.109 75.012 L +291.437 72.742 L +285.625 70.82 L +279.697 69.254 L +273.677 68.051 L +267.589 67.215 L +261.458 66.749 L +255.308 66.656 L +249.165 66.935 L +243.053 67.587 L +236.996 68.607 L +231.019 69.992 L +225.146 71.737 L +219.4 73.834 L +213.806 76.275 L +208.385 79.05 L +203.159 82.148 L +198.149 85.556 L +193.375 89.261 L +188.857 93.248 L +184.613 97.5 L +180.659 102.001 L +177.013 106.733 L +173.688 111.676 L +170.697 116.81 L +168.054 122.116 L +165.768 127.571 L +163.849 133.153 L +162.304 138.84 L +161.141 144.61 L +160.362 150.439 L +159.972 156.303 L +159.972 162.178 L +160.362 168.042 L +161.141 173.871 L +162.304 179.64 L +163.849 185.328 L +165.768 190.91 L +168.054 196.365 L +170.697 201.67 L +173.688 206.805 L +177.013 211.748 L +180.659 216.48 L +184.613 220.981 L +188.857 225.233 L +193.375 229.22 L +198.149 232.925 L +203.159 236.333 L +208.385 239.431 L +213.806 242.206 L +219.4 244.647 L +225.146 246.744 L +231.019 248.488 L +236.996 249.874 L +243.053 250.894 L +249.165 251.545 L +255.308 251.825 L +261.458 251.732 L +267.589 251.266 L +273.677 250.43 L +279.697 249.226 L +285.625 247.661 L +291.437 245.739 L +297.109 243.469 L +302.62 240.86 L +307.946 237.922 L +313.067 234.667 L +317.961 231.109 L +322.609 227.261 L +326.993 223.139 L +331.094 218.76 L +334.895 214.141 L +338.383 209.302 L +341.542 204.26 L +344.361 199.038 L +346.826 193.655 L +348.93 188.133 L +350.663 182.496 L +352.018 176.764 L +352.989 170.962 L +353.574 165.113 L +353.769 159.24 L +S +GR +GS +[0.75 0 0 0.75 47.25 247] CT +0 0 1 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 289.5577 15.50961] CT +1 0 0 RC +10.0 ML +1.333 LW +N +-4 0 M +0 5.32 L +4 0 L +0 -5.32 L +cp +S +GR +GS +[0.75 0 0 0.75 0 0.25] CT +1 GC +N +388 318 M +388 293 L +193 293 L +193 318 L +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +0.641 4.32 M +0.641 3.679 L +2.484 3.679 2.484 2.617 QT +2.484 -6.774 L +2.484 -7.336 0.641 -7.336 QT +0.641 -7.977 L +4.031 -7.977 L +4.25 -7.977 4.328 -7.774 QT +8.25 2.414 L +12.172 -7.774 L +12.234 -7.977 12.453 -7.977 QT +15.859 -7.977 L +15.859 -7.336 L +14 -7.336 14 -6.774 QT +14 3.117 L +14 3.679 15.859 3.679 QT +15.859 4.32 L +10.625 4.32 L +10.625 3.679 L +12.469 3.679 12.469 3.117 QT +12.469 -7.368 L +8.047 4.117 L +7.969 4.32 7.75 4.32 QT +7.516 4.32 7.438 4.117 QT +3.063 -7.227 L +3.063 2.617 L +3.063 3.679 4.906 3.679 QT +4.906 4.32 L +0.641 4.32 L +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +17.094 4.32 M +17.094 3.679 L +18.953 3.679 18.953 3.117 QT +18.953 -6.774 L +18.953 -7.336 17.094 -7.336 QT +17.094 -7.977 L +23.5 -7.977 L +24.484 -7.977 25.469 -7.571 QT +26.453 -7.164 27.094 -6.391 QT +27.734 -5.618 27.734 -4.586 QT +27.734 -3.586 27.094 -2.836 QT +26.453 -2.086 25.477 -1.688 QT +24.5 -1.289 23.5 -1.289 QT +20.625 -1.289 L +20.625 3.117 L +20.625 3.679 22.484 3.679 QT +22.484 4.32 L +17.094 4.32 L +cp +20.563 -1.836 M +23.016 -1.836 L +24 -1.836 24.617 -2.118 QT +25.234 -2.399 25.523 -3 QT +25.813 -3.602 25.813 -4.586 QT +25.813 -6.055 25.164 -6.696 QT +24.516 -7.336 23.016 -7.336 QT +21.484 -7.336 L +21.156 -7.336 20.977 -7.313 QT +20.797 -7.289 20.68 -7.164 QT +20.563 -7.039 20.563 -6.774 QT +20.563 -1.836 L +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +32.859 2.398 M +33.469 3.179 34.391 3.632 QT +35.313 4.086 36.313 4.086 QT +37.141 4.086 37.852 3.757 QT +38.563 3.429 39.094 2.836 QT +39.625 2.242 39.914 1.5 QT +40.203 0.757 40.203 -0.071 QT +40.203 -0.211 40.359 -0.211 QT +40.578 -0.211 L +40.719 -0.211 40.719 -0.039 QT +40.719 0.898 40.359 1.773 QT +40 2.648 39.344 3.312 QT +38.688 3.976 37.828 4.343 QT +36.969 4.711 36.031 4.711 QT +34.75 4.711 33.594 4.187 QT +32.438 3.664 31.578 2.757 QT +30.719 1.851 30.242 0.656 QT +29.766 -0.539 29.766 -1.836 QT +29.766 -3.118 30.242 -4.313 QT +30.719 -5.508 31.578 -6.422 QT +32.438 -7.336 33.594 -7.852 QT +34.75 -8.368 36.031 -8.368 QT +36.953 -8.368 37.797 -7.969 QT +38.641 -7.571 39.281 -6.836 QT +40.328 -8.321 L +40.438 -8.368 40.453 -8.368 QT +40.578 -8.368 L +40.641 -8.368 40.68 -8.329 QT +40.719 -8.289 40.719 -8.227 QT +40.719 -3.368 L +40.719 -3.211 40.578 -3.211 QT +40.25 -3.211 L +40.094 -3.211 40.094 -3.368 QT +40.094 -3.883 39.883 -4.524 QT +39.672 -5.164 39.352 -5.743 QT +39.031 -6.321 38.609 -6.758 QT +37.594 -7.743 36.297 -7.743 QT +35.297 -7.743 34.391 -7.289 QT +33.484 -6.836 32.859 -6.055 QT +32.203 -5.211 31.945 -4.133 QT +31.688 -3.055 31.688 -1.836 QT +31.688 -0.618 31.945 0.468 QT +32.203 1.554 32.859 2.398 QT +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +41.953 0.992 M +41.953 -0.133 L +46.719 -0.133 L +46.719 0.992 L +41.953 0.992 L +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +48.344 4.32 M +48.344 3.679 L +50.203 3.679 50.203 3.117 QT +50.203 -6.774 L +50.203 -7.336 48.344 -7.336 QT +48.344 -7.977 L +54.984 -7.977 L +56.219 -7.977 57.234 -7.446 QT +58.25 -6.914 58.969 -6.024 QT +59.688 -5.133 60.086 -4.008 QT +60.484 -2.883 60.484 -1.711 QT +60.484 -0.571 60.086 0.507 QT +59.688 1.586 58.945 2.453 QT +58.203 3.32 57.188 3.82 QT +56.172 4.32 54.984 4.32 QT +48.344 4.32 L +cp +51.813 3.117 M +51.813 3.507 52.039 3.593 QT +52.266 3.679 52.734 3.679 QT +54.516 3.679 L +55.438 3.679 56.274 3.281 QT +57.109 2.882 57.641 2.179 QT +58.219 1.414 58.414 0.484 QT +58.609 -0.446 58.609 -1.711 QT +58.609 -3.024 58.414 -4.008 QT +58.219 -4.993 57.641 -5.758 QT +57.109 -6.524 56.281 -6.93 QT +55.453 -7.336 54.516 -7.336 QT +52.734 -7.336 L +52.406 -7.336 52.227 -7.313 QT +52.047 -7.289 51.93 -7.164 QT +51.813 -7.039 51.813 -6.774 QT +51.813 3.117 L +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +65.609 2.398 M +66.219 3.179 67.141 3.632 QT +68.063 4.086 69.063 4.086 QT +69.891 4.086 70.602 3.757 QT +71.313 3.429 71.844 2.836 QT +72.375 2.242 72.664 1.5 QT +72.953 0.757 72.953 -0.071 QT +72.953 -0.211 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0.468 QT +64.953 1.554 65.609 2.398 QT +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +86.078 8.789 M +85.078 7.992 84.352 6.968 QT +83.625 5.945 83.164 4.789 QT +82.703 3.632 82.477 2.367 QT +82.25 1.101 82.25 -0.18 QT +82.25 -1.477 82.477 -2.743 QT +82.703 -4.008 83.172 -5.172 QT +83.641 -6.336 84.375 -7.36 QT +85.109 -8.383 86.078 -9.149 QT +86.078 -9.18 86.172 -9.18 QT +86.344 -9.18 L +86.391 -9.18 86.438 -9.133 QT +86.484 -9.086 86.484 -9.024 QT +86.484 -8.946 86.438 -8.914 QT +85.563 -8.039 84.977 -7.055 QT +84.391 -6.071 84.039 -4.961 QT +83.688 -3.852 83.524 -2.664 QT +83.359 -1.477 83.359 -0.18 QT +83.359 5.539 86.422 8.507 QT +86.484 8.57 86.484 8.664 QT +86.484 8.711 86.43 8.765 QT +86.375 8.82 86.344 8.82 QT +86.172 8.82 L +86.078 8.82 86.078 8.789 QT +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +88.344 4.32 M +88.172 4.32 88.172 4.086 QT +88.172 4.039 88.203 3.929 QT +88.234 3.82 88.281 3.75 QT +88.328 3.679 88.391 3.679 QT +90.125 3.679 90.406 2.586 QT 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-5.571 134.464 -6.079 QT +134.128 -6.586 133.581 -6.868 QT +133.034 -7.149 132.409 -7.149 QT +131.862 -7.149 131.308 -6.938 QT +130.753 -6.727 130.394 -6.313 QT +130.034 -5.899 130.034 -5.336 QT +130.034 -4.493 130.894 -3.914 QT +cp +f +GR +GS +[0.75 0 0 0.75 180.01358 229.375] CT +N +138.097 8.82 M +137.941 8.82 137.941 8.664 QT +137.941 8.586 137.972 8.554 QT +141.05 5.539 141.05 -0.18 QT +141.05 -5.899 138.003 -8.868 QT +137.941 -8.914 137.941 -9.024 QT +137.941 -9.086 137.987 -9.133 QT +138.034 -9.18 138.097 -9.18 QT +138.269 -9.18 L +138.316 -9.18 138.347 -9.149 QT +139.644 -8.133 140.503 -6.672 QT +141.362 -5.211 141.761 -3.555 QT +142.159 -1.899 142.159 -0.18 QT +142.159 1.101 141.948 2.336 QT +141.737 3.57 141.269 4.765 QT +140.8 5.961 140.073 6.976 QT +139.347 7.992 138.347 8.789 QT +138.316 8.82 138.269 8.82 QT +138.097 8.82 L +cp +f +GR +GS +[0.75 0 0 0.75 0 0.25] CT +1 LJ +1.333 LW +N +197.002 305.5 M +237.017 305.5 L +S +GR +GS +[0.75 0 0 0.75 162.75694 229.375] CT +N +f-2068629528 +f +GR +GS +[0.75 0 0 0.75 0 0.25] CT +0.149 GC +10.0 ML +0.267 LW +N +193 318 M +193 293 L +388 293 L +388 318 L +cp +S +GR +%%Trailer +%%Pages: 1 +%%EOF diff --git a/double-integrator-2D/figures/mpc-dc-avoidance.png b/double-integrator-2D/figures/mpc-dc-avoidance.png new file mode 100644 index 0000000..9317adf Binary files /dev/null and b/double-integrator-2D/figures/mpc-dc-avoidance.png differ diff --git a/double-integrator-2D/main.m b/double-integrator-2D/main.m new file mode 100644 index 0000000..77e874a --- /dev/null +++ b/double-integrator-2D/main.m @@ -0,0 +1,235 @@ +close all +clear + +%% General Flags +run_dclf_dcbf = true; +display_dclf_dcbf = true; +run_mpc_cbf_one = true; +display_mpc_cbf_one = true; +run_mpc_cbf_multiple = true; +run_mpc_cbf_multiple = true; +run_mpc_dc = true; +display_mpc_dc = true; + +%% Setup and Parameters +x0 = [-5; -5; 0; 0]; +time_total = 30.0; +dt = 0.2; +P = 100*eye(4); +Q = 10*eye(4); +R = eye(2); +N = 8; +umin = [-1; -1]; +umax = [1; 1]; +xmin = [-5; -5; -5; -5]; +xmax = [5; 5; 5; 5]; + +%% Discrete-time double integrator 2D +system.dt = dt; +system.A = [1 0 dt 0; + 0 1 0 dt; + 0 0 1 0; + 0 0 0 1]; +system.B = [0.5*dt^2 0; + 0 0.5*dt^2; + dt 0; + 0 dt]; +system.xl = xmin; +system.xu = xmax; +system.ul = umin; +system.uu = umax; + +%% DCLF-DCBF parameters +p = 1e3; +params_dclf_dcbf.P = P; +params_dclf_dcbf.H = R; +params_dclf_dcbf.p = p; +params_dclf_dcbf.alpha = 1.0; +params_dclf_dcbf.gamma = 0.4; + +%% MPC-CBF parameters +params_mpc_cbf.Q = Q; +params_mpc_cbf.R = R; +params_mpc_cbf.P = P; +params_mpc_cbf.N = N; +params_mpc_cbf.gamma = 0.4; + +%% MPC-DC parameters +params_mpc_dc.Q = Q; +params_mpc_dc.R = R; +params_mpc_dc.P = P; +params_mpc_dc.N = N; + +%% Obstacle +obs.pos = [-2; -2.25]; +obs.r = 1.5; + +%% Simulate DCLF-DCBF +if run_dclf_dcbf + fprintf('Run DCLF-DCBF\n'); + controller_dclf_dcbf = DCLF_DCBF(x0, system, params_dclf_dcbf); + controller_dclf_dcbf.obs = obs; + controller_dclf_dcbf.sim(time_total); +end + +%% Display DCLF-DCBF simulation +if display_dclf_dcbf + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot trajectory + plot(controller_dclf_dcbf.xlog(1,:), controller_dclf_dcbf.xlog(2,:), 'ko-',... + 'LineWidth', 1.0,'MarkerSize',4); + % plot obstacle + pos = controller_dclf_dcbf.obs.pos; + r = controller_dclf_dcbf.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980], 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(controller_dclf_dcbf.x0(1), controller_dclf_dcbf.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'DCLF-DCBF'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf,'figures/dclf-dcbf-avoidance.eps', '-depsc'); + print(gcf,'figures/dclf-dcbf-avoidance.png', '-dpng', '-r800'); +end + +%% Simulate MPC-CBF with N=1; +params_mpc_cbf.N = 1; +if run_mpc_cbf_one + fprintf('Run MPC-CBF\n'); + controller_mpc_cbf_one = MPC_CBF(x0, system, params_mpc_cbf); + controller_mpc_cbf_one.obs = obs; + controller_mpc_cbf_one.sim(time_total); +end + +%% Display MPC-CBF simulation with N=1 +if display_mpc_cbf_one + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot trajectory + plot(controller_mpc_cbf_one.xlog(1,:), controller_mpc_cbf_one.xlog(2,:), 'ko-',... + 'LineWidth', 1.0,'MarkerSize',4); + % plot obstacle + pos = controller_mpc_cbf_one.obs.pos; + r = controller_mpc_cbf_one.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980], 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(controller_mpc_cbf_one.x0(1), controller_mpc_cbf_one.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'MPC-CBF ($N=1$)'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf, 'figures/mpc-cbf-avoidance-one-step.eps', '-depsc'); + print(gcf, 'figures/mpc-cbf-avoidance-one-step.png', '-dpng', '-r800'); +end + +%% Simulate MPC-CBF with other N +params_mpc_cbf.N = 8; +if run_mpc_cbf_one + fprintf('Run MPC-CBF\n'); + controller_mpc_cbf_multiple = MPC_CBF(x0, system, params_mpc_cbf); + controller_mpc_cbf_multiple.obs = obs; + controller_mpc_cbf_multiple.sim(time_total); +end + +%% Display MPC-CBF simulation with other N +if display_mpc_cbf_one + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot trajectory + plot(controller_mpc_cbf_multiple.xlog(1,:), controller_mpc_cbf_multiple.xlog(2,:), 'ko-',... + 'LineWidth', 1.0,'MarkerSize',4); + % plot obstacle + pos = controller_mpc_cbf_multiple.obs.pos; + r = controller_mpc_cbf_multiple.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980], 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(controller_mpc_cbf_multiple.x0(1), controller_mpc_cbf_multiple.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'MPC-CBF ($N=8$)'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf, 'figures/mpc-cbf-avoidance-several-steps.eps', '-depsc'); + print(gcf, 'figures/mpc-cbf-avoidance-several-steps.png', '-dpng', '-r800'); +end + +%% Simulate MPC-DC +if run_mpc_dc + fprintf('Run MPC-DC\n'); + controller_mpc_dc = MPC_DC(x0, system, params_mpc_dc); + controller_mpc_dc.obs = obs; + controller_mpc_dc.sim(time_total); +end + +%% Display MPC-DC simulation +if display_mpc_dc + % Plot simulation + figure('Renderer', 'painters', 'Position', [0 0 400 400]); + set(gca,'LooseInset',get(gca,'TightInset')); + hold on; + % plot trajectory + plot(controller_mpc_dc.xlog(1,:), controller_mpc_dc.xlog(2,:), 'ko-',... + 'LineWidth', 1.0,'MarkerSize',4); + % plot obstacle + pos = controller_mpc_dc.obs.pos; + r = controller_mpc_dc.obs.r; + th = linspace(0,2*pi*100); + x = cos(th) ; y = sin(th) ; + plot(pos(1) + r*x, pos(2) + r*y, 'Color', [0.8500, 0.3250, 0.0980], 'LineWidth', 2); + plot(pos(1), pos(2), 'Color', [0.8500, 0.3250, 0.0980], 'MarkerSize', 5, 'LineWidth', 2); + % plot target position + plot(controller_mpc_dc.x0(1), controller_mpc_dc.x0(2), 'db', 'LineWidth', 1); + plot(0.0, 0.0, 'dr', 'LineWidth', 1); + h=get(gca,'Children'); + h_legend = legend(h([end]), {'MPC-DC ($N=8$)'}, 'Location', 'SouthEast'); + set(h_legend, 'Interpreter','latex'); + set(gca,'LineWidth', 0.2, 'FontSize', 15); + grid on + xlabel('$x (m)$','interpreter','latex','FontSize',20); + ylabel('$y (m)$','interpreter','latex','FontSize',20); + xticks(-5:0); + yticks(-5:0); + xlim([-5,0.2]); + ylim([-5,0.2]); + print(gcf, 'figures/mpc-dc-avoidance.eps', '-depsc'); + print(gcf, 'figures/mpc-dc-avoidance.png', '-dpng', '-r800'); +end \ No newline at end of file diff --git a/packages/Ipopt.zip b/packages/Ipopt.zip new file mode 100644 index 0000000..4f5f550 Binary files /dev/null and b/packages/Ipopt.zip differ