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eyesClosedInvarianceKernel.m
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eyesClosedInvarianceKernel.m
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%% Generate Eyes-closed invariance kernel
clear; clc; close all;
save_file = true;
timestamp = now;
compTraj = true;
% Setup Grids
x_min = -15;
y_min = -15;
v_min = -0.2;
theta_min = -pi;
x_max = 15;
y_max = 15;
v_max = 5.0;
theta_max = pi;
N_x = 41;
N_y = 41;
N_theta = 21;
N_v = 31;
grid_pursuer_min = [x_min; y_min; theta_min]; % Lower corner of computation domain
grid_pursuer_max = [x_max; y_max; theta_max]; % Upper corner of computation domain
grid_evader_min = [x_min; y_min; v_min; theta_min];
grid_evader_max = [x_max; y_max; v_max; theta_max];
N_pursuer = [N_x; N_y; N_theta]; % Number of grid points per dimension
pdDims_pursuer = 3; % 3rd dimension is periodic
N_evader = [N_x; N_y; N_v; N_theta];
pdDims_evader = 4;
g_pursuer = createGrid(grid_pursuer_min, grid_pursuer_max, N_pursuer, pdDims_pursuer);
g_evader = createGrid(grid_evader_min, grid_evader_max, N_evader, pdDims_evader);
%% Generate Initial Set of Pursuer
R = 0.75; % Uncertainty in initial position ((x-x0)^2 + (y-y0)^2 <= R)
W = 0.6; % Uncertainty in initial heading (theta0 +/- W/2)
x0 = [0; 0; 0];
% data0 = shapeCylinder(grid,ignoreDims,center,radius)
cylinder0 = shapeCylinder(g_pursuer, 3, x0, R);
box0 = shapeRectangleByCenter(g_pursuer, x0, [Inf; Inf; W]);
initialPursuerState = shapeIntersection(box0, cylinder0);
%% Time vector for game
t0 = 0;
tMax = 3.0;
dt = 0.10;
tau = t0:dt:tMax;
%% Pursuer params
speed = [0, 2];
wMax = 1;
uModePursuer = 'max';
minWithPursuer = 'none';
dCarPursuer = DubinsCarVControl(x0, wMax, speed); % Puruser system
schemeDataPursuer.grid = g_pursuer;
schemeDataPursuer.dynSys = dCarPursuer;
schemeDataPursuer.accuracy = 'high'; %set accuracy
schemeDataPursuer.uMode = uModePursuer;
schemeDataPursuer.tMode = 'forward';
HJIextraArgsPursuer.visualize = true; %show plot
HJIextraArgsPursuer.fig_num = 1; %set figure number
HJIextraArgsPursuer.deleteLastPlot = true; %delete previous plot as you update
%[data, tau, extraOuts] = ...f
% HJIPDE_solve(data0, tau, schemeData, minWith, extraArgs)
[forward_reach_set, ~, ~] = ...
HJIPDE_solve(initialPursuerState, tau, schemeDataPursuer, minWithPursuer, HJIextraArgsPursuer);
%% Project and Extrude Forward Reach Set Into Heading and Velocity Dims
extruded_frs = projectExtrudeSet(forward_reach_set, g_evader, 3, [3,4]);
% extruded_frs = projectExtrudeSet(forward_reach_set, g_pursuer, 3, 3);
%% Modify set to allow for collisions at very low ego velocity.
low_vel = 0.25; % Velocity at which colision is acceptable
high_velocity_region = shapeHyperplane(g_evader,[0,0,-1,0]',[0,0,low_vel,0]');
negative_velocity_region = shapeHyperplane(g_evader, [0,0,1,0]', [0,0,-0.2,0]');
for t = 1:length(tau)
extruded_frs(:,:,:,:,t) = shapeUnion(shapeIntersection(extruded_frs(:,:,:,:,t), high_velocity_region), negative_velocity_region);
end
extruded_frs(:,:,:,:,end) = shapeUnion(high_velocity_region, negative_velocity_region);
%% Evader Parameters
avoidSets = flip(extruded_frs,5);
terminalAvoidSet = avoidSets(:,:,:,:,1);
x0 = [0;0;0;0];
% input bounds
accel = [-1.5, 1.5];
rMin = 12.0;
wMax = 1.0;
% control trying to min or max value function?
uModeEvader = 'max';
minWithEvader = 'none';
dCarEvader = DubinsCarAControl(x0, rMin, wMax, accel); %do dStep3 here
% Put grid and dynamic systems into schemeData
schemeDataEvader.grid = g_evader;
schemeDataEvader.dynSys = dCarEvader;
schemeDataEvader.accuracy = 'high'; %set accuracy
schemeDataEvader.uMode = uModeEvader;
HJIextraArgsEvader.targets = avoidSets;
HJIextraArgsEvader.visualize = true; %show plot
HJIextraArgsEvader.fig_num = 2; %set figure number
HJIextraArgsEvader.deleteLastPlot = true; %delete previous plot as you update
HJIextraArgsEvader.visualizeLevelSet = true;
% HJIextraArgs.visualizeObstaclesFunction = true;
%[data, tau, extraOuts] = ...
% HJIPDE_solve(data0, tau, schemeData, minWith, extraArgs)
[eyes_closed_invariance_kernel, ~, ~] = ...
HJIPDE_solve(terminalAvoidSet, ...
tau, ...
schemeDataEvader, ...
minWithEvader, ...
HJIextraArgsEvader);
%% Compute optimal trajectory from some initial state
if true
%set the initial state
xinit = [5, 0, 2, -pi];
%check if this initial state is in the BRS/BRT
%value = eval_u(g, data, x)
value = eval_u(g_evader,eyes_closed_invariance_kernel(:,:,:,:,end),xinit);
if value >= 0 %if initial state is in BES/BET
% find optimal trajectory
dCarEvader.x = xinit; %set initial state of the dubins car
TrajextraArgs.uMode = uModeEvader; %set if control wants to min or max
TrajextraArgs.visualize = true; %show plot
TrajextraArgs.fig_num = 3; %figure number
%we want to see the first two dimensions (x and y)
TrajextraArgs.projDim = [1 1 0 0];
%flip data time points so we start from the beginning of time
dataTraj = flip(eyes_closed_invariance_kernel,5);
for t = 1:length(tau)
t
derivs{t} = computeGradients(g_evader, dataTraj(:,:,:,:,t));
end
else
error(['Initial state is not in the BRS/BRT! It have a value of ' num2str(value,2)])
end
end
%%
if compTraj && value >= 0
xinit = [5.0,0.0,4.0,0.0];
dCarEvader.x = xinit;
% [traj, traj_tau] = ...
% computeOptTraj(g, data, tau, dynSys, extraArgs)
[traj, traj_tau] = ...
computeOptTraj(g_evader, dataTraj, tau, dCarEvader, TrajextraArgs, derivs, flip(avoidSets,5));
end
%% Process data for saving
derivs_array = zeros([size(eyes_closed_invariance_kernel),4]);
for t = 1:length(derivs)
for d = 1:4
derivs_array(:,:,:,:,t,d) = derivs{t}{d};
end
end
eyes_closed_invariance_kernel_orig = eyes_closed_invariance_kernel;
eyes_closed_invariance_kernel_wrapped = cat(4, ...
eyes_closed_invariance_kernel, ...
eyes_closed_invariance_kernel(:,:,:,1,:));
derivs_array = cat(4, derivs_array, derivs_array(:,:,:,1,:,:));
eyes_closed_invariance_kernel_wrapped = flip(eyes_closed_invariance_kernel_wrapped, 5);
g_evader_wrapped = g_evader;
g_evader_wrapped.vs{4} = cat(1, g_evader.vs{4}, g_evader.vs{4}(end) + g_evader.dx(4));
g_vs_x = g_evader_wrapped.vs{1};
g_vs_y = g_evader_wrapped.vs{2};
g_vs_v = g_evader_wrapped.vs{3};
g_vs_theta = g_evader_wrapped.vs{4};
%% Save data
if false
save('eyesclosedV1.mat',...
'eyes_closed_invariance_kernel_wrapped',...
'derivs_array',...
'g_vs_x',...
'g_vs_y',...
'g_vs_v',...
'g_vs_theta',...
'accel',...
'rMin',...
'wMax',...
'tau',...
'timestamp',...
'-v7.3')
end
%% Validate lookup
out = eval_u(g_evader_wrapped, eyes_closed_invariance_kernel_wrapped(:,:,:,:,1), [2.12,-2.21,0.32,2.06])