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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;
xmin = [-5; -5; -5; -5];
xmax = [5; 5; 5; 5];
umin = [-1; -1];
umax = [1; 1];
%% 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 = DCLFDCBF(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 = MPCCBF(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 = MPCCBF(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 = MPCDC(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