  To operate with limited sensor horizons in unpredictable environments,
autonomous robots use a receding-horizon strategy to plan trajectories, wherein
they execute a short plan while creating the next plan. However, creating safe,
dynamically-feasible trajectories in real time is challenging; and, planners
must ensure persistent feasibility, meaning a new trajectory is always
available before the previous one has finished executing. Existing approaches
make a tradeoff between model complexity and planning speed, which can require
sacrificing guarantees of safety and dynamic feasibility. This work presents
the Reachability-based Trajectory Design (RTD) method for trajectory planning.
RTD begins with an offline Forward Reachable Set (FRS) computation of a robot's
motion when tracking parameterized trajectories; the FRS provably bounds
tracking error. At runtime, the FRS is used to map obstacles to parameterized
trajectories, allowing RTD to select a safe trajectory at every planning
iteration. RTD prescribes an obstacle representation to ensure that obstacle
constraints can be created and evaluated in real time while maintaining safety.
Persistent feasibility is achieved by prescribing a minimum sensor horizon and
a minimum duration for the planned trajectories. A system decomposition
approach is used to improve the tractability of computing the FRS, allowing RTD
to create more complex plans at runtime. RTD is compared in simulation with
Rapidly-Exploring Random Trees and Nonlinear Model-Predictive Control. RTD is
also demonstrated in randomly-crafted environments on two hardware platforms: a
differential-drive Segway, and a car-like Rover. The proposed method is safe
and persistently feasible across thousands of simulations and dozens of
real-world hardware demos.
