Page - 36 - in Joint Austrian Computer Vision and Robotics Workshop 2020

`i = wi@L occurs in some #minimize statement inP and `i holds w.r.t.X. We also call ΣXL the util- ity ofX at priority levelL. An answer setX ofP is dominated if there is an answer setY ofP such that ΣYL <Σ X L and Σ Y L′ = Σ X L′ for allL ′>L, and optimalotherwise. 3.ASPandLogistics: TwoCases-Studies To evaluate ASP in an industrial environment, we discovered two interesting case-studies. Both are re- lated to Fleet Management Systems (FMS) - one at IncubedIT, the other one at the BMWGroup. In bothcases, the imperativelydescribedtaskallocation strategywas replacedbyanASP-basedprogram. 3.1. TheBMWUseCase: TaskAssignment and ChargingManagement By the following, the requirements for the FMS at the BMWGroup are described. Here, two ele- mental decisions have to be made. These are on one hand the assignment of tasks to the vehicles and on the other hand the assignment of charging and park- ing stations to the same vehicles. Both decisions are made online, which means that neither tasks nor the needs for charging (and parking) are known before- hand. With task we mean a transportation job of a container, accomplished by a vehicle, from a station to another one. The required time is estimated from the Euclideandistance. For the task assignment, the standard C# sched- uler applies a trivial first-in-first-out (FIFO) strategy, which means that earlier created tasks have to be ex- ecuted first. By that, the criterion for the selection of tasks, formulated as a constraint, is not to assign a task if there is anotherappropriate taskwithearlier creation time assignable. Vehicles on the field must haveabatterylevelataminimumof25%,andcharg- ing vehicles a battery level of 40% to be assigned to tasks. The optimal assignment of vehicles to tasks is based on the traveling costs that are set to be the Euclidean distance between robots and the first goal of the assigned task. The used optimization criterion ensures the lowest traveling cost for the tasks with earliest time ofcreation. In ASP a different optimization criterion is used, in order to achieve a better overall quality of the so- lution. The Euclidean distance for all assignments is summed up and minimized, in order to have a better make-spanandsavemoreenergy. ConsideringT and Ras the set of tasks and robots respectively, task as- signment isencodedbythefollowinglogicformulas: ∀t∈T(|{r∈R|(assign(t, )}|≤1) ∀t1,t2∈T,∀r∈R (assign(t1,r)∧assign(t2,r)∧ t1 6= t2⇒⊥) The first formula may (non-deterministically) as- sign each task to one robot at most. The second one makes sure that two different tasks are not assigned to the same robot. The non-deterministic choice is driven by the optimization algorithm. In ASP, above formulasareencodedas follows (:- stands for← ): Listing1ASPencodingof the taskassignment 0{assign (T,R) : robot (R, , , )}1:− task (T, , ) . :− assign (T,R) , assign (T2,R) , T != T2. The first rule makes use of both a conditional lit- eralandacardinalityconstraint. Aconditional literal a : b1, .. . ,bn is a nested implication, where a and b1, .. . ,bn can be seen as the head and the body of a rule respectively. The cardinality constraint is used to ensure that each task is assigned to one robot at most. Givenx{head}y :-body, the meaning is that, for each different body instantiation (for each task T in our case), the head is instantiated from x to y times (from 0 to 1 in our case). In our code this implies that, for each task T, at most one robotR is assigned inside the head. The second rule is an integrity constraint. In the case that after the task assignment was performed unassigned vehicles are remaining, these free vehicles are assigned to charg- ing stations and parking places. The rules used for this particular assignment problem are defined sepa- rately for vehicles on the field and vehicles currently in charging stations. A charging vehicle can only be assigned to a charging station if the battery level is below 90%. Vehicles on the field can be sent to charging stations any time, regardless of the current battery level. Charging vehicles can go to a park- ing place only if the battery level is above or equal 90%,whereasvehicleson thefieldcangotoparking places independently from the battery level. In the original implementation, priority is given to vehicles with the lowest battery level. Similarly to the FIFO strategy in task assignment, first we assigne the least chargedvehicle tothecloseststation, thenthesecond least charged one, and so on. However, this imple- mentation shows its limits on circumstances where multiple robots have critical battery levels that differ 36