  Trajectory planning is challenging for autonomous cars since they operate in
unpredictable environments with limited sensor horizons. To incorporate new
information as it is sensed, planning is done in a loop, with the next plan
being computed as the previous plan is executed. The recent Reachability-based
Trajectory Design (RTD) is a provably safe, real-time algorithm for trajectory
planning. RTD consists of an offline component, where a Forward Reachable Set
(FRS) is computed for the vehicle tracking parameterized trajectories; and an
online part, where the FRS is used to map obstacles to constraints for
trajectory optimization in a provably-safe way. In the literature, RTD has only
been applied to small mobile robots. The contribution of this work is applying
RTD to a passenger vehicle in CarSim, with a full powertrain model, chassis and
tire dynamics. RTD produces safe trajectory plans with the vehicle traveling up
to 15 m/s on a two-lane road, with randomly-placed obstacles only known to the
vehicle when detected within its sensor horizon. RTD is compared with a
Nonlinear Model-Predictive Control (NMPC) and a Rapidly-exploring Random Tree
(RRT) approach. The experiment demonstrates RTD's ability to plan safe
trajectories in real time, in contrast to the existing state-of-the-art
approaches.
