Abstract
Path planning for Automated Guided Vehicles (AGVs) is crucial for transportation efficiency in modern ware-houses. This paper focuses on the problem of simultaneously planning minimum-time paths for a fleet of AGVs on a two-dimensional grid. The dynamics of each AGV is modeled as a double integrator with finite acceleration and limited maximum speed. Since analytic solution of this optimal control problem does not exist, we transform it into a parametric optimization by applying the Zero-Order-Hold (ZOH) control. Due to the continuous AGV dynamics and the nonlinear constraints, the obtained parametric optimization problem belongs to the class of Nonlinear Programming (NLP) problems which are very difficult to solve. In order to circumvent the pitfalls of the NLP-problem formulation, we reformulate this problem as a Mixed Integer Linear Programming (MILP) problem by introducing a necessary number of discrete variables while keeping the control variables continuous. The MILP problem formulation, if feasible, always leads to an optimal solution. The application of MILP optimization problem to path planning of several AGVs is illustrated on an appropriate example.
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