The relaxed asymmetric Reeds-Shepp problem

The relaxed asymmetric Reeds-Shepp problem is the problem of finding a minimum-time trajectory for the Reeds-Shepp vehicle from a given initial state to a given final position, under the assumption that the backward motion of the vehicle is slower than the forward motion. This modification of the classic Reeds-Shepp problem aims at better capturing physical reality for vehicles that are less agile when moving backwards than when moving forwards - marine vehicles being a representative example - and leads to new insights into the motion planning of such vehicles. Specifically, it is shown that a family of optimal trajectories which is known to be sufficient for the relaxed Reeds-Shepp problem is also sufficient for the relaxed asymmetric Reeds-Shepp problem. It is also shown that the relaxed Reeds-Shepp problem and the relaxed asymmetric Reeds-Shepp problem cannot have the same minimum-time synthesis.