  Forward complete systems are guaranteed to have solutions that exist globally
for all positive time. In this paper, a relaxed Lyapunov-like condition for
forward completeness is presented for finite-dimensional systems defined on
open sets that does not require boundedness of the Lyapunov-like function along
the solutions of the system. The corresponding condition is then exploited for
the design of autonomous two-dimensional movement, with focus on lane-free
cruise controllers for automated vehicles described by the bicycle kinematic
model. The derived feedback laws (cruise controllers) are decentralized and can
account for collision avoidance, roads of variable width, on-ramps and
off-ramps as well as different desired speed for each vehicle.
