  In warehouse and manufacturing environments, manipulation platforms are
frequently deployed at conveyor belts to perform pick and place tasks. Because
objects on the conveyor belts are moving, robots have limited time to pick them
up. This brings the requirement for fast and reliable motion planners that
could provide provable real-time planning guarantees, which the existing
algorithms do not provide. Besides the planning efficiency, the success of
manipulation tasks relies heavily on the accuracy of the perception system
which is often noisy, especially if the target objects are perceived from a
distance. For fast moving conveyor belts, the robot cannot wait for a perfect
estimate before it starts executing its motion. In order to be able to reach
the object in time, it must start moving early on (relying on the initial noisy
estimates) and adjust its motion on-the-fly in response to the pose updates
from perception. We propose a planning framework that meets these requirements
by providing provable constant-time planning and replanning guarantees. To this
end, we first introduce and formalize a new class of algorithms called
Constant-Time Motion Planning algorithms (CTMP) that guarantee to plan in
constant time and within a user-defined time bound. We then present our
planning framework for grasping objects off a conveyor belt as an instance of
the CTMP class of algorithms.
