  We consider the problem of finding collision-free paths for
curvature-constrained systems in the presence of obstacles while minimizing
execution time. Specifically, we focus on the setting where a planar system can
travel at some range of speeds with unbounded acceleration. This setting can
model many systems, such as fixed-wing drones. Unfortunately, planning for such
systems might require evaluating many (local) time-optimal transitions
connecting two close-by configurations, which is computationally expensive.
Existing methods either pre-compute all such transitions in a preprocessing
stage or use heuristics to speed up the search, thus foregoing any guarantees
on solution quality. Our key insight is that computing all the time-optimal
transitions is both~(i)~computationally expensive and~(ii)~unnecessary for many
problem instances. We show that by finding bounded-suboptimal solutions
(solutions whose cost is bounded by $1+\varepsilon$ times the cost of the
optimal solution for any user-provided $\varepsilon$) and not time-optimal
solutions, one can dramatically reduce the number of time-optimal transitions
used. We demonstrate using empirical evaluation that our planning framework can
reduce the runtime by several orders of magnitude compared to the
state-of-the-art while still providing guarantees on the quality of the
solution.
