  A vector-based any-angle path planner, R2, is evolved in to R2+ in this
paper. By delaying line-of-sight, R2 and R2+ search times are largely
unaffected by the distance between the start and goal points, but are
exponential in the worst case with respect to the number of collisions during
searches. To improve search times, additional discarding conditions in the
overlap rule are introduced in R2+. In addition, R2+ resolves interminable
chases in R2 by replacing ad hoc points with limited occupied-sector traces
from target nodes, and simplifies R2 by employing new abstract structures and
ensuring target progression during a trace. R2+ preserves the speed of R2 when
paths are expected to detour around few obstacles, and searches significantly
faster than R2 in maps with many disjoint obstacles.
