Generalized Multi-Speed Dubins Motion Model
CoRR(2024)
摘要
The paper develops a novel motion model, called Generalized Multi-Speed
Dubins Motion Model (GMDM), which extends the Dubins model by considering
multiple speeds. While the Dubins model produces time-optimal paths under a
constant-speed constraint, these paths could be suboptimal if this constraint
is relaxed to include multiple speeds. This is because a constant speed results
in a large minimum turning radius, thus producing paths with longer maneuvers
and larger travel times. In contrast, multi-speed relaxation allows for slower
speed sharp turns, thus producing more direct paths with shorter maneuvers and
smaller travel times. Furthermore, the inability of the Dubins model to reduce
speed could result in fast maneuvers near obstacles, thus producing paths with
high collision risks.
In this regard, GMDM provides the motion planners the ability to jointly
optimize time and risk by allowing the change of speed along the path. GMDM is
built upon the six Dubins path types considering the change of speed on path
segments. It is theoretically established that GMDM provides full reachability
of the configuration space for any speed selections. Furthermore, it is shown
that the Dubins model is a specific case of GMDM for constant speeds. The
solutions of GMDM are analytical and suitable for real-time applications. The
performance of GMDM in terms of solution quality (i.e., time/time-risk cost)
and computation time is comparatively evaluated against the existing motion
models in obstacle-free as well as obstacle-rich environments via extensive
Monte Carlo simulations. The results show that in obstacle-free environments,
GMDM produces near time-optimal paths with significantly lower travel times
than the Dubins model while having similar computation times. In obstacle-rich
environments, GMDM produces time-risk optimized paths with substantially lower
collision risks.
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