Changing a parameter in a differential equation according to a condition ?

I am trying to change the input wheel velocities of a mobile robot according to a position condition ?

if d > 0 & d < 0.4
        p.WR = 0.51;
        p.WL = 0.5;
    elseif d > 0.4 & d < 0.8 
        p.WR = 0.5;
        p.WL = 0.51;
    elseif d == 0.4
        p.WR = 0.5;
        p.WL = 0.5;
    end 

function dt = mydglw9(t,c,p)

     x = c(1);y = c(2);th = c(3);
      dx = (((p.r*p.WL)+(p.r*p.WR))/2) * cos(th);
      dy = (((p.r*p.WL)+(p.r*p.WR))/2) * sin(th);
      dth= ((p.r*p.WL)-(p.r*p.WR))/p.L;
      dt = [dx;dy;dth];
      pose = [x y th];
  end

however i always get the error [ Reference to non-existent field 'WL' ], is there a way to make the solver check the condition before solving the differential equations ?

Answer 1

[Star Strider]

What values does ‘d’* have?

Note that in this if block, if ‘d<=0’ or ‘d>=0.8’, the if block will not execute and the values within it will not be assigned.

[Moustafa Aboubakr]

the d is the distance between the intersection of the robot sensor line and the trajectory

%trajectory drawing as a set of straight line functions

                for j = 1:length(traj)-1
                    x = linspace(traj(1,j),traj(1,j+1),1000); 
                    m = (traj(2,j+1)-traj(2,j))/(traj(1,j+1)-traj(1,j)); 
                    y = m*(x - traj(1,j)) + traj(2,j);
                    plot(x,y,'b','linewidth',2); 
                    axis([-1.5 3 -0.5 4]);

                    %Intersection detector 

                    [xi, yi] = polyxpoly(x,y,s1,y1);

                    z = plot(xi,yi,'ko','linewidth',1.5);

                    d = sqrt((xi - xt).^2 + (yt - yi).^2)
                end

file attached for whole code clarification

[Star Strider]

You will have to add logic to be certain that ‘d’ is within the limits of the closed interval [0,0.8]. Since I am not certain how you want to do that, I leave it to you.

One option is to ‘hard-limit’ ‘d’ with a simple function.

This works to keep ‘d’ within the limits of your if block:

dscale = @(d) ((d<=0) & (d<=eps))*eps + d.*((d>0) & (d<0.8)) + (d>=0.8-eps)*(0.8-eps);

Use it before your if block as:

d = dscale(d);

This assumes that the reason your structure fields are undefined is that the if block is not executing.

[Moustafa Aboubakr]

thanks for you help but what i am trying to do is to make the odesolver check the value of 'd' and deciding which value of WR & WL to choose using the if statement and then solve the equations. can the 'events' option in odeset solve this problem ?

[Star Strider]

Your differential equation can check the value of ‘d’ and define the values of the other parameters. Your ‘p’ structure first must limit ‘d’ to an appropriate range, and my ‘dscale’ function does that.

One option is to put my ‘dscale’ function and your if block inside your ODE function, and pass ‘d’ as a parameter.

I doubt an event function would be the correct approach here. You have a continuous, bounded variable ‘d’, not an actual event.

[Moustafa Aboubakr]

yeah you're right thanks a lot :) , however i am facing another problem with polyxpoly function which returns the intersection between sensor and path and stores the value in 'd' but then overwrites it. so 'd' returns always 0 , thats why the error [ Reference to non-existent field 'WL' ] occurs

[Star Strider]

My pleasure. Thank you.

I’m not certain what you’re doing with ‘d’. If you want to store the values rather than overwrite them, you can store them separately as, for example, ‘dv’ as a vector, or matrix of ‘d’ and time, position, and other values.

I don’t know how you’re calculating ‘d’, but if it is only with respect to (x,y) coordinates, you can use the hypot function.

[Moustafa Aboubakr]

Thank you so much I used the beautiful mapshow function :) :) to draw the path instead of the long for loop and it worked great.

file attached for trial if u like, use mydglcallw10(1000,0,0.2,0) in command window

[Star Strider]

As always, my pleasure!

I’ll take a look.