On the Length of Dubins Path with Any Initial and Terminal Configurations
Li Dai · Pure and Applied Mathematics Journal · 2015
Dubins has proved in 1957 that the minimum length path between an initial and a terminal configuration can be found among the six paths {LSL, RSR, LSR, RSL, RLR, LRL}. Skel and Lumelsky have studied the length of Dubins path with the initial configuration (0, 0; α) and the terminal configuration (d, 0; β) and the minimal turning radius ρ=1 in 2001. We extended the Skel and Lumelsky’s results to the case that the initial and terminal configuration is(x0, y0, α), (x1, y1, β), respectively (where x0, y0, x1, y1ϵℝ), and the minimal turning radius is ρ>0.