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Classification and Game Value of Minimum-Time Escape from the Cone Field of View of a Reeds-Shepp Pursuer

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Ubaldo Ruiz published a research paper on arXiv studying how an omnidirectional evader escapes in minimum time from the forward cone field of view of a Reeds-Shepp pursuer with minimum turning radius r. For slower or equal-speed evaders with speed ratio sinα<ν≤1, a feedback solution is constructed using Isaacs characteristic lines, and a scalar equation for the finite escape time is given. The paper proves a global escape/hold classification: when ν≤sinα, straight-line reversing can hold the entire cone field of view; when sinα<ν≤1, escape is confined to the region bounded by obstacle boundaries; when ν>1, escape is possible from any state. A sample-and-hold counter-control shows that, except at corner points, this escape time is the game value under nonanticipative strategies; an independent level-set solver agrees with the closed-form solution under the tested parameters and reproduces the holding region.