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I am working on a similar problem. I have a dynamical model of a boat (Nomoto turn-rate model, with side-slip and linear speed dynamics added) that I am trying to use to generate motion primitives. As I understand, ideally I should choose primitives that end up in specific grid cells. However, as mentioned by Martin, it is not necessarily easily possible with the non-holonomic model I am using.

In my case, currently I am applying certain control actions for a specific period of time to forward propagate the dynamic model. Then whatever end-pose I end up with, I map it into its corresponding grid cell. Depending on discretization used, this approach will result in discontinuities at end grid points.

I was wondering if anyone else has come across such a scenario. I would certainly appreciate an input. Thank you very much for your help!