Optimizing nonlinear system, difficult objective function

Hi, I am trying to write a MATLAB script that optimizes a ball throwing robot where the objective is to throw the ball as far as possible.

The equations of motion are of the form: M(q)d2q + C(q,dq)dq + G(q) + K(q) = T

The ball is released from the robots grip when it crosses the y-axis, and the distance thrown is calculated. The objective function is then: F = -d^2

Now, since the distance is only computed after a simulated pitching motion of the robot, the objective function is not a smooth and nice-to-work with objective function. Inside the objective function, I must simulate the pitching and give a function evaluation back to fmincon.

What I am wondering about is how to go about this problem, just point me in the right direction... How can I simulate the robot with the input sequence that fmincon gives me? ODE solver?

Answer 1

[Alan Weiss]

There is a similar but simpler example in the documentation of Global Optimization Toolbox, but the example works for fmincon as well (interior-point algorithm for sure).

Alan Weiss

MATLAB mathematical toolbox documentation