Energy reduction of stochastic time-constrained robot stations

Abstract

This paper looks at the problem of reducing the energy use of robot movements in a robot station with stochastic execution times, while keeping the productivity of the station. The problem is formulated as a stochastic optimization problem, that constrains the makespan of the station to meet a deadline with a high probability. The energy use of the station is a function of the execution times of the robot operations, and the goal is to reduce this energy use by finding the optimal execution times and operation order. A theoretical motivation to why the stochastic variables in the problem, under some conditions, can be approximated as independent and normally distributed is presented, together with a derivation of the max function of stochastic variables. This allows the stochastic optimization problem to be approximated with a deterministic version, that can be solved with a commercial solver. The accuracy of the deterministic approximation is evaluated on multiple numerical examples, which show that the method successfully reduces the energy use, while the deadlines of the stations are met with high probabilities.