Minimum-Time Escape from the Conic Field of View of a Reeds--Shepp Pursuer: the Faster Evader
Abstract
We continue the study of minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds--Shepp pursuer, now for a faster evader, and solve the game for every speed ratio ν>1 and every half-angle 0<α<π/2: the escape time is characterized by explicit characteristics and the selection of roots of a scalar equation, and it is the value of the game in nonanticipative strategies at every state. Above the end E of the evader's dispersal line on the front axis, the evader chases the reversing pursuer along a universal line fed by tributaries. The characteristic from the boundary of the usable part is an involute of a circle of radius ν ending at a cusp, and two explicit thresholds decide whether it reaches the axis before the cusp and whether the jump of the escape time across it ends before the cusp or runs to it; in the latter case primaries fold back next to the barrier. The pursuer's optimal strategy is the relay of the slower case. The evader follows the tributaries and switches once to a primary, or commits in advance to a heading certified by the scalar equation of the primaries. Level-set and semi-Lagrangian computations are compared with the value.
Related
- Minimum-Time Escape from the Conic Field of View of a Reeds-Shepp Pursuer: Classification and Game Value for a Slower or Equally Fast Evader
- Finite-Time Tracking Success or Failure in the Pursuer--Evader Model
- Localic Esakia Duality via Conic Frames
- An atomic approach to Shokurov's conic-bundle conjecture
- On wall-crossing invariant combinations of Welschinger numbers for rational surfaces with a conic bundle
BibTeX
@misc{ruiz2026minimumtime,
title = {{Minimum-Time Escape from the Conic Field of View of a Reeds--Shepp Pursuer: the Faster Evader}},
author = {Ubaldo Ruiz},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38125},
eprint = {2610.38125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38125},
}
RIS
TY - UNPB
TI - Minimum-Time Escape from the Conic Field of View of a Reeds--Shepp Pursuer: the Faster Evader
AU - Ubaldo Ruiz
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38125
UR - https://arxiv.org/abs/2610.38125
AB - We continue the study of minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds--Shepp pursuer, now for a faster evader, and solve the game for every speed ratio ν>1 and every half-angle 0<α<π/2: the escape time is characterized by explicit characteristics and the selection of roots of a scalar equation, and it is the value of the game in nonanticipative strategies at every state. Above the end E of the evader's dispersal line on the front axis, the evader chases the reversing pursuer along a universal line fed by tributaries. The characteristic from the boundary of the usable part is an involute of a circle of radius ν ending at a cusp, and two explicit thresholds decide whether it reaches the axis before the cusp and whether the jump of the escape time across it ends before the cusp or runs to it; in the latter case primaries fold back next to the barrier. The pursuer's optimal strategy is the relay of the slower case. The evader follows the tributaries and switches once to a primary, or commits in advance to a heading certified by the scalar equation of the primaries. Level-set and semi-Lagrangian computations are compared with the value.
ER -