Motion planning with geometric models

Robot motion planning problems are considered for boundary representation geometric models of curved planar and solid objects. We present algebraic algorithms to generate the boundary of configuration space obstacles arising from the translatory motion of objects among obstacles. To aid in the C-space generation various efficient computational geometry and algebraic geometry techniques need to be developed. We present algorithms to compute the convex hulls and various decompositions of planar curved objects. Finally, various motion planning problems are explored using these techniques