Estimating and optimizing throughput of a robotic part feeder using queueing theory

We study a programmable robotic part feeder that relies on a sequence of three conveyor belts to singulate and re-circulate parts. In industrial practice, belt speeds are set in an ad-hoc fashion. Experience with real feeders reveals that throughput can suffer due to (1) starvation where no parts are visible to the camera and (2) saturation, where too many parts are visible, which prevents identifying part pose or grasping due to obstruction by nearby parts. This motivates our search for a systematic approach to setting belt speeds. This paper introduces models based on a 2D Poisson process for both intermittent and continuous motion feeding. For intermittent motion feeding we apply renewal theory to approximate and optimize the theoretical throughput. For continuous motion feeding we use a M/G/1 queue with customer impatience to approximate and optimize the theoretical throughput. We show that the analytic theory compares very well with simulation studies. For both models we show how to optimize the throughput when there is a constraint on the expected number of times a part should go through the system.