Updating parameters in a function being called by Octave's fsolve - octave

Question

I am working on modeling the motion of a single actuated leg in Octave. The leg has 3 points: a stationary hip (point A), a foot (point B) that moves along a known path, and a knee (point C) whose location and angle I am trying to solve for.
Using the code below I can successfully solve for the knee's XYZ position and relevant angles for a single value of the parameters s0 and Theta_H.
Now I want to be able to loop through multiple s0 and Theta_H values and run the solver. My problem is that I can't figure out how to pass new values for those variables into the equations function.
The reason this is tricky is that the function format necessary to use Octave's fsolve prevents entering inputs other than the unknowns into the function. I've tried updating a global variable as an indexer but to do that I would need to clear all workspace variables which causes other problems.
Any ideas on how to update the parameters in this function while still being able to input it into fsolve would be really appreciated!
The code below calls the solver:
global AC = 150; % length of the thigh limb
global CB = 150; % length of the shin limb
global lspan = 75; % width span of the foot touch down wrt the hip
global bob = 10; % height of the hip joint off the ground during a step
inits = [ .75; 2.35; 37; 0; 125]; % initial guesses at horizontal step position
% x(1): hip joint - guessing a 45 deg (.75 rad) angle for hip joint
% x(2): knee joint - guessing a 135 deg (2.35 rad) angle (wrt to vert)
% x(3): X position of the knee joint - guessing middle of the leg span in mm
% x(4): Y position of the knee joint - know it is 0 mm at the horizontal step position
% x(5): Z position of the knee joint - guessing the height to be ~80% of the height of a limb
[x, fval, info] = fsolve(#Rug_Bug_Leg, inits); % when running fsolve for the first time often have to remove the output suppress
The code below shows the function containing the system of equations to be solved by Octave's fsolve function:
function y = Rug_Bug_Leg(x)
global AC;
global CB;
global lspan;
global bob;
s0 = 0; % fore/aft (Y) position of the foot during the step. Trying to iterate this
Theta_H = 0; % hip angle during the step. Trying to iterate this
y = zeros(6,1); % zeros for left side of each equation
% First set of equations, Joint C wrt to Joint A
y(1) = -1*x(3)+AC*sin(x(1))*cos(Theta_H);
y(2) = -1*x(4)+AC*sin(x(1))*sin(Theta_H);
y(3) = -1*bob - x(5)+AC*cos(x(1));
% Second set of equations, Joint B wrt to Joint C
y(4) = x(3)-lspan +CB*sin(x(2))*cos(Theta_H);
y(5) = x(4) - s0 +sin(x(2))*sin(Theta_H);
y(6) = x(5) + bob + CB*cos(x(2));
end function

Answer 1

You can definitely do that!
All you need to do is create a function that returns a function.
First have your Rug_Bug_Leg function take s0 and Theta_H as inputs:
function y = Rug_Bug_Leg(x, s0, Theta_H)
% ...
endfunction
Then, you can write a "wrapper" function around Rug_Bug_Leg like this:
rbl = #(s0, Theta_H) #(x) Rug_Bug_Leg(x, s0, Theta_H)
Now, if you call rbl with some values (s0,Theta_H), it will return a function that takes x as input and returns Rug_Bug_Leg(x,s0,Theta_H).
For instance, rbl(0,0) returns the function:
#(x) Rug_Bug_Leg(x,0,0)
Here's a sample usage:
for s0=1:10
for Theta_H=1:10
[x, fval, info] = fsolve( rbl(s0,Theta_H), inits );
endfor
endfor