  Consider a robot operating in an uncertain environment with stochastic,
dynamic obstacles. Despite the clear benefits for trajectory optimization, it
is often hard to keep track of each obstacle at every time step due to sensing
and hardware limitations. We introduce the Safely motion planner, a
receding-horizon control framework, that simultaneously synthesizes both a
trajectory for the robot to follow as well as a sensor selection strategy that
prescribes trajectory-relevant obstacles to measure at each time step while
respecting the sensing constraints of the robot. We perform the motion planning
using sequential quadratic programming, and prescribe obstacles to sense based
on the duality information associated with the convex subproblems. We guarantee
safety by ensuring that the probability of the robot colliding with any of the
obstacles is below a prescribed threshold at every time step of the planned
robot trajectory. We demonstrate the efficacy of the Safely motion planner
through software and hardware experiments.
