Recall that using normalized vector fields does not alter the existence of solutions. This is convenient because needs to be bounded to approximate it with a finite set of samples. It is useful to restrict the action set to obtain

(8.60) |

To improve performance, it is sometimes possible to use only those for which or ; however, numerical instability problems may arise. A finite sample set for should have low dispersion and always include .

Steven M LaValle 2020-08-14