Motion planning with planar geometric models

Algebraic algorithms for collision-avoidance robot motion planning problems with planar geometric models are presented. By decomposing the collision-free space into horizontal vertex visibility cells and connecting these cells into a connectivity graph, the global topological structure of collision-free space is represented. Using the C-space obstacle boundaries and this connectivity graph, exact (nonheuristic) compliant and gross motion paths of planar curved objects moving with a fixed orientation amidst similar obstacles are generated. The gross motion planning algorithm is further, extended (using approximations) to the case of objects moving with both translations and rotations by using the conventional slicing method