{"ID":5552851,"CreatedAt":"2026-07-02T01:54:51.863792489Z","UpdatedAt":"2026-07-03T21:54:35.419828569Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.00221","arxiv_id":"2607.00221","title":"Guaranteed Escape for a Bouncing Robot in Pipe Chains","abstract":"We study the symmetric bouncing of a point robot within orthogonally-joined rectangles with equal width, which we refer to as pipes. We provide an exhaustive case analysis of every trajectory pattern inside a single rectangular pipe segment, identifying the conditions under which the robot exits. We then extend the analysis to L-shaped pipes and, more generally, to linear chains of $k$ orthogonally connected pipe segments. We prove exit guarantees for the special angle $α= π/4$. Furthermore, these results extend to pipes with curved joints.","short_abstract":"We study the symmetric bouncing of a point robot within orthogonally-joined rectangles with equal width, which we refer to as pipes. We provide an exhaustive case analysis of every trajectory pattern inside a single rectangular pipe segment, identifying the conditions under which the robot exits. We then extend the ana...","url_abs":"https://arxiv.org/abs/2607.00221","url_pdf":"https://arxiv.org/pdf/2607.00221v1","authors":"[\"Ahmad Kamaludeen\",\"Somnath Kundu\",\"Yeganeh Bahoo\"]","published":"2026-06-30T21:58:15Z","proceeding":"cs.CG","tasks":"[\"cs.CG\",\"cs.RO\"]","methods":"[]","has_code":false}