Provably Constant-time Planning and Replanning for Real-time Grasping Objects off a Conveyor Belt

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.