The Weighted Markov-Dubins Problem

In this letter, a variation of the classical Markov-Dubins problem is considered, which deals with curvature-constrained least-cost paths in plane prescribed initial and final configurations, different bounds for sinistral dextral curvatures, penalties $\mu _{L}$ _{R}$ turns, respectively. The addressed generalizes asymmetric sinistral/dextral problem. proposed formulation can be used to model an Unmanned Aerial Vehicle (UAV) penalty associated turn due required additional thrust maintain altitude airspeed while turning, or UAV curvature costs turns hardware failures. Using optimal control theory, main result letter shows that path belongs set at most 21 candidate paths, each comprising five segments. Unlike problem, notation="LaTeX">$CCC$ path, not weighted Moreover, obtained list reduces standard notation="LaTeX">$CSC$ corresponding degenerate when approach zero.