I will begin by describing a situation. I work in laser machining control company. The essence of the problem, to which I would like to try to apply AI based tool is this:
Say I have a analytically described trajectory in 3D space. It can consist of lines, arcs, circles, NURB curves etc, anything that can be parametricaly described. I have a machine which can move at limited speed, limited acceleration, limited Jerk. In short, a machine which has real kinematic limits. I would like that machine to follow the parametric curve at some prescribed speed. As machine has real kinematic limits, it wont be able to follow trajectory exactly. For example, one cannot execute continuous corner motion. The machine should either stop, change direction of movement, and start moving again, or it can "smooth" the corned, by moving in a curve some distance $d$ away from the prescribed parametric curve. If $d$ is smaller then some prescribed constant, I am ok with that.
So let me restate the problem. I have a corridor in 3D Euclidean space which has a analytical description. I would like my magical AI tool to generate a parametric curve in that corridor which would satisfy some prescribed analytical constrains and minimize some analytical parameters.
EDIT: Maybe it could be helpful to imagine it as a game. Say it is a race game in space. The track is a round corridor in a 3D space. My goal is to stay as close to the middle of the corridor as possible. My motion is governed by some equation and objective and analytical limitations. At any point, I can change my motion equation, to adapt to the trajectory of corridor. Another rule is, that I would like to make as little of those changes of trajectory as possible. I want to find out, when I should make those choices to change my motion and how should I change my motion. The winner is the one who stayed as close to the middle as possible and who used as little changes of motion as possible. If at any point I would end up being outside the corridor, it's and instant loose
Could such tool be created? How difficult it would be? How efficient and reliable such tool could be? How one should start making such tool? How one should ensure its reliability? Is anyone aware of work which was already be done in this field?
Thank you very much for your answers and help,
Very happy to be a part of this community!
Donatas
