Re-Organize Files Again

- Deliverables folder holds final files for submission
- Experimentation holds scripts and things related to our development of
  a final solution
- Simulation holds the provided files
- Added template for part 2 submission with comments

Simulation/forwardIntegrateControlInput.m

@@ -0,0 +1,114 @@
+function [Y,T]=forwardIntegrateControlInput(U,x0)
+% function [Y] = forwardIntegrateControlInput(U,x0)
+% 
+% Given a set of inputs and an initial condition, returns the vehicles
+% trajectory. If no initial condition is specified the default for the track
+% is used.
+% 
+%  INPUTS:
+%    U           an N-by-2 vector of inputs, where the first column is the
+%                steering input in radians, and the second column is the 
+%                longitudinal force in Newtons.
+%    
+%    x0          a 1-by-6 vector of the initial state of the vehicle.
+%                If not specified, the default is used
+% 
+%  OUTPUTS:
+%    Y           an N-by-6 vector where each column is the trajectory of the
+%                state of the vehicle
+%
+%    T           a 1-by-N vector of time stamps for each of the rows of Y.
+% 
+%  Written by: Sean Vaskov
+%  Created: 31 Oct 2018
+%  Modified: 6 Nov 2018
+%
+%   Revision notes:
+%   - Sid Dey (6 Dec 2019)
+
+    %  if initial condition not given use default
+    if nargin < 2
+        x0 = [287,5,-176,0,2,0] ;
+    end
+
+    %generate time vector
+    T=0:0.01:(size(U,1)-1)*0.01;
+
+    if (length(T) == 1)
+        % in case U is a 1x2 vector, meaning T would be a 1x1 scalar, 
+        % we return the initial condition.
+        Y = x0;
+        
+    else
+        %Solve for trajectory
+        options = odeset('MaxStep',0.01);
+        [~,Y]=ode45(@(t,x)bike(t,x,T,U),T,x0,options);
+        
+        % in case U is a 2x2 vector, meaning T would be a 1x2 vector [t0 tf],
+        % ode45 would provide the solution at its own integration timesteps
+        % (in between t0 and tf). To avoid this, we simply take the first
+        % and last value of Y (which should correspond with t0 and tf).
+        
+        if ( size(U,1) ~= size(Y,1) )
+            % Take first and last value of Y.
+            Y = [Y(1, :); Y(end, :)];
+        end
+        
+    end
+    
+end
+
+function dzdt=bike(t,x,T,U)
+%constants
+Nw=2;
+f=0.01;
+Iz=2667;
+a=1.35;
+b=1.45;
+By=0.27;
+Cy=1.2;
+Dy=0.7;
+Ey=-1.6;
+Shy=0;
+Svy=0;
+m=1400;
+g=9.806;
+
+
+%generate input functions
+delta_f=interp1(T,U(:,1),t,'previous','extrap');
+F_x=interp1(T,U(:,2),t,'previous','extrap');
+
+%slip angle functions in degrees
+a_f=rad2deg(delta_f-atan2(x(4)+a*x(6),x(2)));
+a_r=rad2deg(-atan2((x(4)-b*x(6)),x(2)));
+
+%Nonlinear Tire Dynamics
+phi_yf=(1-Ey)*(a_f+Shy)+(Ey/By)*atan(By*(a_f+Shy));
+phi_yr=(1-Ey)*(a_r+Shy)+(Ey/By)*atan(By*(a_r+Shy));
+
+F_zf=b/(a+b)*m*g;
+F_yf=F_zf*Dy*sin(Cy*atan(By*phi_yf))+Svy;
+
+F_zr=a/(a+b)*m*g;
+F_yr=F_zr*Dy*sin(Cy*atan(By*phi_yr))+Svy;
+
+F_total=sqrt((Nw*F_x)^2+(F_yr^2));
+F_max=0.7*m*g;
+
+if F_total>F_max
+    
+    F_x=F_max/F_total*F_x;
+  
+    F_yr=F_max/F_total*F_yr;
+end
+
+%vehicle dynamics
+dzdt= [x(2)*cos(x(5))-x(4)*sin(x(5));...
+          (-f*m*g+Nw*F_x-F_yf*sin(delta_f))/m+x(4)*x(6);...
+          x(2)*sin(x(5))+x(4)*cos(x(5));...
+          (F_yf*cos(delta_f)+F_yr)/m-x(2)*x(6);...
+          x(6);...
+          (F_yf*a*cos(delta_f)-F_yr*b)/Iz];
+end
+