Motion planning with planar geometric models

We present algebraic algorithms for collision-avoidance robot motion planning problems with planar geometric models. By decomposing the collision-free space into horizontal vertex visibility cells and connecting these cells into a connectivity graph, we represent the global topological structure of collision-free space. Using the C-space obstacle boundaries and this connectivity graph we generate exact (non-heuristic) compliant and gross motion paths of planar curved objects moving with a fixed orientation amidst similar obstacles. The gross motion planning algorithm is further extended (though using approximations) to the case of objects moving with both translational and rotational degrees of freedom by taking slices of the overall orientations into finite segments.