Abstract
In this article, three-dimensional (3D) stacking problem, as a mandatory task in the warehouse distribution centers, is smartly represented by a new mathematical formulation. A model predictive control (MPC) scheme is proposed to optimally solve the problem. The MPC cost function consists of several sequential criteria to suitably put the incoming packages on the dedicated cart and fully use up the cart capacity as much as possible. The practical and hard constraints are taken into consideration without confronting with a complicated optimization problem. A theorem is presented to guarantee the constraints satisfaction. Regarding the burden of computations, the proposed strategy is efficiently applicable to large carts by introducing the adaptive window (AW) idea. The efficacy of the proposed AW-MPC framework is shown by a numerical case study.
Highlights
Recent years have witnessed an accelerating demand for E-commerce driven by the lifestyle change and, most recently, the COVID-19 pandemic
Remark 5: If it happens that constrained optimization problem (45-a)-(45-e) gives more than one optimal solution at time point t, one of the possibilities could be arbitrarily selected without causing any obstacle to the exploitation of the adaptive window (AW)-model predictive control (MPC) scheme
We mathematically described the stacking problem taking into account several important practical and intrinsic constraints
Summary
Recent years have witnessed an accelerating demand for E-commerce driven by the lifestyle change and, most recently, the COVID-19 pandemic. In such settings, for an inexpensive practical robotic automation, it is mostly assumed that the previously settled items cannot be readjusted, and a new incoming package cannot be put under the previous packages since such locations are usually difficult and expensive for robots to access – which we refer to as practical-robotic constraint. Model predictive control (MPC) as a well-known effective approach can potentially provide benefits to online stacking problems It can solve high-dimensional problems and deal with various types of constraints in obtaining an optimal solution while taking into consideration of the future predicted states.
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