I found that a configuration-space approach is a elegant way to describe problems in motion planning. However, I was not able to find a known general way to construct configuration-spaces. By general I mean: arbitrarily shaped object, arbitrary amount of degrees of freedom.
To give an example: Lets assume I can parameterise an object and a space which includes obstacles. Assuming that this object is rigid we have 6 degress of freedom. (Idealy I would like to also include non-rigid object, i.e. with additional joints). This object now moves in a space which is partially blocked by arbitrary obstacles
Now: How can I construct the configuration space which only includes allowed configurations (not reachable, but allowed)?
For simple problems, one can construct them "by hand". However, I expect there to be a general way how to do this.
My best idea, so far, was to sample all possible (discretised and hence finite) configurations and check whether they are overlapping with any obstacle i.e. with the help of point clouds. However, I feel like there should be a better way.
How is this handled in modern robotics?