Topology preserving approximation of free configuration space

We present a simple algorithm for approximating the free configuration space of robots with low degrees of freedom (DOFs). We represent the free space as an arrangement of contact surfaces. We approximate the free space using an adaptive volumetric grid that is computed by performing simple geometric tests on the contact surfaces. We use an isosurface extraction algorithm to compute a piecewise-linear approximation to the boundary of the free space. We prove that our approximation is topologically equivalent to the exact free space boundary. We also ensure that our approximation is geometrically close to the exact free space boundary by bounding its two-sided Hausdorff error. We have applied our algorithm to compute the free configuration space for the following instances: (1) a 2D polygonal robot with translational and rotational DOFs navigating among polygonal obstacles, and (2) a 3D polyhedral robot translating among polyhedral obstacles. In practice, our algorithm works well on robots with three DOFs