Guaranteed Plans for Multi-Robot Systems via Optimization Modulo Theories

Industries are on the brink of widely accepting a new paradigm for organizing production by having autonomous robots manage in-factory processes. This transition from static process chains towards more automation and autonomy poses new challenges in terms of, e.g., efficiency of production processes. The RoboCup Logistics League (RCLL) has been proposed as a realistic testbed to study the above mentioned problem at a manageable scale. In RCLL, teams of robots manage and optimize the material flow according to dynamic orders in a simplified factory environment. In particular, robots have to transport workpieces among several machines scattered around the factory shop floor. Each machine performs a specific processing step, orders that denote the products which must be assembled with these operations are posted at run-time and require quick planning and scheduling. Orders also come with a delivery time window, therefore introducing a temporal component into the problem. Though there exist successful heuristic approaches to solve the underlying planning and scheduling problems, a disadvantage of these methods is that they provide no guarantees about the quality of the solution. A promising solution to this problem is offered by the recently emerging field of Optimization Modulo Theories (OMT), where Satisfiability Modulo Theories (SMT) solving is extended with optimization functionalities. In this paper, we present an approach that combines bounded model checking and optimization to generate optimal controllers for multi-robot systems. In particular, using the RoboCup Logistics League as a testbed, we build formal models for robot motions, production processes, and for order schedules, deadlines and rewards. We then encode the synthesis problem as a linear mixed-integer problem and employ Optimization Modulo Theories to synthesize controllers with optimality guarantees.