Queuing theory based part-flow estimation in a pick-and-place task with a multi-robot system

Abstract

This paper addresses the problem of estimating the maximum part-flow or part feed rate for a pick-and-place task with a multi-robot system. An appropriate part-flow is important to guarantee productivity and robustness in the presence of pattern variation, that is, when the timing and position of the parts on the conveyor are presented in random. To determine the appropriate part-flow for a multi-robot system quickly, we divided the multi-robot system into several single-robot systems and estimated the part-flow for each single-robot system based on M/M/s queuing model with impatient customers. Then, the task completion rate for the ensemble of robots was computed. Simulations were used to compare the proposed method to a method based on a Monte Carlo Strategy (MCS) and a method based on an M/M/1 queuing model. The simulation results show that the proposed method can guarantee the required productivity and the task-completion success rate. The task-completion success rate determined using the proposed method reached 98.9% for 10000 randomly generated patterns. The computation time for the proposed method satisfies computation time constraints and is less than 1/10 of that for the MCS method.

Keywords

• queuing theory
• part-flow
• multi-robot system
• pick-and-place task
• pattern variation