Existence of an admissible corridor sequence for sliver obstacles

Determine whether an admissible sequence of convex corridors exists for the sliver-obstacle configuration in which Phase I fails, particularly when the heading-aligned boxes and independently selected separating half-planes leave insufficient room for the vehicle to turn.

Background

The planner fails on cluttered case 101 because long, thin obstacles near the start and goal cause the heading-aligned box to meet the obstacles at a small angle, while the independently selected half-planes leave too little room for turning. Phase I therefore terminates with positive infeasibility, even though OBCA-CT solves the case with a longer time limit.

The unresolved issue is whether the specific corridor-generation strategy can produce any admissible corridor sequence for such a configuration. The discussion identifies joint half-plane selection and region-growing methods such as FIRI as possible directions, but does not establish existence or provide a construction.