I am doing a project related to robotics where I am using fmincon function from matlab to minimize the distance between the points x_0 and x_f. Basically task is to make manipulator move from x_0 to x_f such that it never goes out of torus region. So I think it is a constrained optimization problem. I am having difficulty in figuring out what is the strategy to find the two intermediate points (as shown in figure below) so that given x_0 and x_f, it gives us two points [x1,y1,z1] and [x2,y2,z2] to use as via points.
Can you please figure out how should I write the objective function.
The distance cost function I wrote is below, but I cannot figure out what's strategy to find the two points (via points) :
function z = objfun(x,p)
z = sqrt((p(1)-x(1))^2+(p(2)-x(2))^2+(p(3)-x(3))^2);
end
Hi, if I understand well you have simply to formulate your constraint mathematically : the trajectory must remain inside the torus. Then, when calling fmincon the trajectory will certainly exhibits contact points with the torus (where the constraint is active). So, the contact points will be an output of the optimizer and you don't have to add them as additional unknowns I think.
Dear Talha,
I suggest you to see links on subject.
-Initialization of 3D pose graph optimization using Lagrangian duality ...
ieeexplore.ieee.org/document/7989600
-Applications of Evolutionary Computation: 17th European Conference, ...
https://books.google.dz/books?isbn=3662455234
Best regards
You mention a manipulator, but it is not really clear your problem is about path planning in workspace or jointspace (I would guess workspace based on your notation).
The problem is easier in taskspace since then you just travel along geodesics of the torus, see
http://www.rdrop.com/~half/math/torus/torus.geodesics.pdf
In workspace you can follow the circle of the torus, assuming it shaped exactly like a torus. If it is a curved tube of some kind, then read up on the 'path planning' problem. There are many methods.
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