  For robotic arms to operate in arbitrary environments, especially near
people, it is critical to certify the safety of their motion planning
algorithms. However, there is often a trade-off between safety and real-time
performance; one can either carefully design safe plans, or rapidly generate
potentially-unsafe plans. This work presents a receding-horizon, real-time
trajectory planner with safety guarantees, called ARMTD (Autonomous
Reachability-based Manipulator Trajectory Design). The method first computes
(offline) a reachable set of parameterized trajectories for each joint of an
arm. Each trajectory includes a fail-safe maneuver (braking to a stop). At
runtime, in each receding-horizon planning iteration, ARMTD constructs a
parameterized reachable set of the full arm in workspace and intersects it with
obstacles to generate sub-differentiable, provably-conservative
collision-avoidance constraints on the trajectory parameters. ARMTD then
performs trajectory optimization over the parameters, subject to these
constraints. On a 6 degree-of-freedom arm, ARMTD outperforms CHOMP in
simulation, never crashes, and completes a variety of real-time planning tasks
on hardware.
