Elongation of curvature-bounded path

The elongation of curvature-bounded paths to an expected length is fundamentally important plan missions for nonholonomic-constrained vehicles in many practical applications, such as coordinating multiple reach a destination simultaneously or performing mission with strict time window. In the paper, by applying properties reachability set paths, explicit conditions existence joining two oriented points are established. These numerically verifiable, allowing readily checking between prescribed desired length. addition, once met, strategies provided get Finally, some examples minimum-time path planning Dubins cooperatively achieve triangle-shaped formation presented, illustrating and verifying developments paper.