I have two points in 2D space (A and B) and some sort of obstacle between them, I need to find a path to avoid colliding with an obstacle.
Hi, you can indesd model your problem as a linear optimal control problem. First you can use linear dynamics equatiobs:
dy/dx =u (t)
Where u (t) is the control variable.
The lenght of the path which has to be minimized is int (sqrt (1 +u (t)^2)) between x0 and xf whith initial and final conditions in y.
The obstacle avoidance can be written as an iniqualty constraint involving x and y.
The problem can be solve usind optimal control theory
Hello, Thank's Sir @Richard Epenoy, yes is that correctly what i want, to discute all available cases, to find an optimal path.... Can you recommand me a good articles and references ? for more explication.
Hi, the model is simple. The derivative of y as a function of x is the control. Then the length of the path is int ds where ds is the small increment of length along the path. We have:
ds^2 = du^2 + dy^2 = ds^2(1+(dy/dx)^2)
that leads to the model.
Than You can apply model your avoidance constraint and try to solve this problem.
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