Conflict-Free Routing of Mobile Robots

Doctoral thesis, 2022

The recent advances in perception have enabled the development of more autonomous mobile robots in the sense that they can operate in a more dynamic environment where obstacles surrounding the robot emerge, disappear, and move. The increased perception of Autonomous Mobile Robots (AMRs) allows them to plan detailed on-line trajectories in order to avoid previously unforeseen obstacles, making AMRs useful in dynamic environments where humans, traditional fork-lifts, and also other mobile robots operate. These abilities contributed to increase automation in logistic applications. This thesis discusses how to efficiently operate a fleet of AMRs and make sure that all tasks are successfully completed.

Assigning robots to specific delivery tasks and deciding the routes they have to travel can be modelled as a variant of the classical Vehicle Routing Problem (VRP), the combinatorial optimization problem of designing routes for vehicles. In related research it has been extended to scheduling routes for vehicles to serve customers according to predetermined specifications, such as arrival time at a customer, amount of goods to deliver, etc.

In this thesis we consider to schedule a fleet of robots such that areas avoid being congested, delivery time-windows are met, the need for robots to recharge is considered, while at the same time the robots have freedom to use alternative paths to handle changes in the environment. This particular version of the VRP, called CF-EVRP (Conflict-free Electrical Vehicle Routing Problem) is motivated by an industrial need. In this work we consider using optimizing general purpose solvers, in particular, MILP and SMT solvers are investigated. We run extensive computational analysis over well-known combinatorial optimization problems, such as job shop scheduling and bin-packing problems, to evaluate modeling techniques and the relative performance of state-of-the-art MILP and SMT solvers.

We propose a monolithic model for the CF-EVRP as well as a compositional approach that decomposes the problem into sub-problems and formulate them as either MILP or SMT problems depending on what fits each particular problem best. The performance of the two approaches is evaluated on a set of CF-EVRP benchmark problems, showing the feasibility of using a compositional approach for solving practical fleet scheduling problems.