How to optimize trajectory of bipedal robot using Genetic algorithm

I am trying to optimize the trjaectory of bipedal robot by minimizing the energy consumed. I want to find the suitable hip-height and maximum height swing leg can take. My fitness function is energy consumed plus some penalty for constraint voilation.

In matlab example , the variable that needs to be optimized directly comes in fitness function. But in my case the variable which i want to optimize donot appear in fitness function but they affect the fitness function. Energy consumed is calculated by solving the dynamic equation which is influed by hip hieght and height taken by swing leg.

In such case how do i apply genetic algorithm where the variable directly do not comes in fitness function but they infulence it.

its like,, i want to find optimum x1 and x2 which minimizes f = z1+z2 , where z1 and z2 are also related to x1 and x2 but in very compicated way.

thank you.

Answer 1

[Walter Roberson]

function cost = energy(x)
   x1 = x(1); x2 = x(2);
   cost = z1(x1, x2) + z2(x1, x2);
end

ga() does not care how complicated z1 and z2 are. It does not care if, for example,

function z1cost = z1(hip,swing)
   tspan = linspace(0, 20, 3);   %not a vector of length 2!
   boundary = [0 0];
   [t, y] = ode45(@(t,y) z1ode(t, y, hip, swing), tspan, boundary);
   z1cost = y(end,1);
end

It does not care if there is a direct formula involving the inputs: it only cares that there is a deterministic calculation in which they are the inputs and there is a scalar output.