Solving Linear Differential Equations for Path Following ; I am getting difficulties in implementing the coding with variable psi_e, let's say if I want to run it for psi_e going from 0 to pi/2, how can it be done?

function [dydt] = MyFun(t,y,w1_x,w1_y,w2_x,w2_y)
dydt = zeros(3,1);
S = 15  ;
psi_e = pi/2 ;

k = 10 ;
Tau = 135 ;
alpha = 10 ;
S_x = y(1) ;
S_y = y(2) ;
psi = y(3) ;

p = [S_x , S_y]' ;
w1 = [w1_x , w1_y]' ;
w2 = [w2_x , w2_y]' ;

psi_f  = atan2((w2_y - w1_y),(w2_x - w1_x)) ;
S_star = ((p - w1)'*(w2 - w1))/((norm(w2 - w1))^2) ;
Epsilon = norm( p - (S_star*(w2 - w1) + w1) ) ;
Rho = sign((w2 - w1).*(p - w1)) ;

if( abs(Epsilon) > Tau )
    psi_d = psi_f + psi_e ;
    psi_c = psi_d ;    
else 
    psi_d = psi_f - psi_e*((Epsilon/Tau)^k) ;
    psi_c = psi_d -(k*psi_e*S*(Epsilon^(k-1))*sin(psi))/(alpha*(Tau^k)) ;
end

u = k*(psi_d - psi) ;
psi_dot = u ;

dydt(1) = S*cos(psi) ;
dydt(2) = S*sin(psi) ;
dydt(3) = psi_dot ;
end



%%%%%%%%%%%%%%%%% FUNCTION'S USED IN THE BELOW CODE %%%%%%%%%%%%%%%%%%


clc;
clear all;

wps = [[0, 0];[400, 400];];
wp_1 = wps(1,:);
w1_x = wp_1(1); w1_y = wp_1(2);

wp_2 = wps(2,:);
w2_x = wp_2(1); w2_y = wp_2(2); 

tspan = 0:0.1:50;
current_x = 125;
current_y = 0;
current_X = pi/2;
tau = 45;

fprintf("Trajectories\n");

arr_x = (0:1:300);  
arr_y = (0:1:300);
plot(arr_x(1,:),arr_y(1,:),'--b'); 

    y0 = [current_x current_y current_X] ;
    [t,y] = ode45(@(t,y) MyFun(t,y,w1_x,w1_y,w2_x,w2_y), tspan, y0);
    current_x = y(end,1);
    current_y = y(end,2);
    current_X = y(end,3);
    hold on 
    grid on

for i = 1:length(y(:,1))-1
    plot(y(i:i+1,1),y(i:i+1,2),'y','LineWidth',1.2);
    pause(0.001)
end

xlabel('X(m)') 
ylabel('Y(m)') 

[J. Alex Lee]

can you reformat using the "code view" functionality of the editor

[Milan Chavda]

Done !

Answer 1

[J. Alex Lee]

To change value of psi_e (make it variable) seems straightforward:

make psi_e an input in your odefun, then loop over psi_e:

function [dydt] = MyFun(t,y,w1_x,w1_y,w2_x,w2_y , psi_e)
dydt = zeros(3,1);
S = 15  ;
%psi_e = pi/2 ;
...
end

Then in your script

N = 11
psi_e_list = linspace(0.1,2,N)

for i = 1:N
    psi_e = psi_e_list(i)
    
    ...
    
end

It's not clear the rest of your objective...