Tackling the Combinatorial Challenge Non-temporal and temporal classical planning ap-proaches have a limited applicability regarding planning for reconfigurable multi-robot sys-tems since they rely on an explicit and static representation of planning domains. Although very effective heuristics exist in guiding forward search, classical approaches still require op-erator instantiation which can be prohibitive when considering all feasible agents in a recon-figurable system. The planning approach implemented withTemPlinitially avoids the full in-stantiation by relying on a compact, cardinality based description of agent types. Furthermore, the mission specification is based on a resource-oriented requirement definition. Functionality constraints are combined with explicit agent type constraints to formulate mission constraints on the basis of an available mapping between functionality and agent types. This mapping is provided by the organisation model MoreOrg. The computation of the functionality map-ping has worst case computational cost ofO(2|A|) when all agent types have to be exhaustively evaluated. Knowledge about the relationship between structure and function can, however, be exploited to prune irrelevant types from the search space. This observation has led to the development of the functional saturation bound in this thesis. Eventually, the application of the functional saturation bound is the key element to efficiently identify suitable agents which can satisfy mission requirements.
Distinction toVRPsand Classical Planning Compared to existing VRPbased approaches the mission planning problem embeds most of the known properties, such as time windows, capacity, heterogeneity and fleet size, but also comes with distinctive features. While the prop-erties are mainly treated separately inVRPs,TemPloffers a combined approach. Additionally, TemPl is not only accounting for commodity demand, and hence the presence of single
sys-tems, but combines demand for commodities with the demand for functional properties of agents. For that purpose, required functionalities are resolved to actual agents Thereby a func-tionality driven mission design becomes feasible, while the set of required agents is selected from a pool of available agents.
Classical planning approaches typically define the achievable goal as a particular world state, or by one or more tasks that have to be performed. The relation to the former action based approaches exists through the organisation model which encodes the domain description into the organisation state. A relation to the task planning approaches can be established, as soon as a mapping from a task definition to functional requirements or agent roles exists. As an extension, this task model can also be embedded into the organisation model using a similar approach to modelling functionalities.
VRPs’s reason quantitatively with time and use soft and hard time constraints. This limits the options for coordination of activities; to state that two customers shall receive their goods at the exact same time hard time constraints must be used.TemPl’s usage of qualitative temporal constraints enables a partial ordering of requirements and leads to a generically applicable synchronisation for agent activities. As long as no duration constraints are involved a valid plan computed byTemPlrepresents a reusable synchronisation template. Effectively, existing solutions can then used as a whole or even in parts as synchronisation templates.
A multi-pickup multi-delivery problem is part ofTemPl’s mission planning problem. The ini-tial motivation for multi-pickup and multi-delivery is the planning for a long-term multi-robot operation where agents are reusable. Although atomic agents are reusable, in real missions they might also be stateful. This chapter has illustrated an exemplary sample-return mission with limited reusability of a sampling module. To partially address this issue TemPl allows to constrain the route of agent roles using min/max/all equal constraints. However, TemPl is, however, not a generic planner and compared toPDDL-based it cannot generically handle domain and problem descriptions. Furthermore, it does not consider temporary usage restric-tions based on an agent state, e.g., when energy level are to low.
Reconfigurable multi-robot systems have a flexibility to exchange resources and balance the resource distribution. Thereby, a organisation’s redundancy level can be maintained to serve as safety buffer. The developed planning approach accounts for the organisation’s redundancy state and characterises the safety of a plan by the lowest redundancy level. In effect, TemPl illustrates an approach to deal with inter-route constraints by enabling a mechanism to trade-offsolution efficacy, efficiency, and safety.
Scalability The planning approach embeds multi-commodity min-cost flow optimisation as local search after a (partial) plan has been generated. The multi-commodity min-cost flow optimisation is translated into a linear integer program, which can subsequently be solved with any available linear integer program solvers including GLPK (Free Software Foundation2015), coin-or/CBC, coin-or/CLP (Lougee-Heimer2003) or SCIP (Achterberg et al.2008). GLPK and SCIP use for example different solution strategies. GLPK applies the simplex algorithm to solve and optimise the multi-commodity min-cost flow problem. Without using presolving, even infeasible solutions can be inspected and used as input for a local repair approach. This is not directly possible for SCIP which uses a combination of constraint-based programming and mixed integer programming, but provides a plugin mechanism to use column generation.
The size of the multi-commodity min-cost flow problem as linear program depends upon the
size of the temporally expanded network, as well as the number of mobile and immobile agents which need to be routed. Therefore the scalability of the planning approach is currently limited by the used LP solvers. An improvement could be achieved using an implicit representation of the search space, as it has been done for the organisation model. This means that the cur-rent local optimisation strategies have to be adapted to using a column generation approach which allows for a dynamic and scalable optimisation approach. Alternatively, heuristic search approaches can be considered, e.g., such as Tabu Search, Very Large Neighbourhood Search (VLNS)or destroy-repair search algorithms in general. When these approaches require an ini-tial (feasible) solution to start from,TemPlcan still be used for boosting other algorithms.
Expressiveness of the Mission Specification TemPl’s mission specification is a combination of constraints which are typically tackled by special variants ofVRP formulations. As a re-sult a mission specification allows to define: spatio-temporal requirements for functionality and agent presence, partial or full paths of atomic agents, and high-level synchronisation be-tween multiple atomic agents. The presented constraints are only a subset of applicable (meta-)constraints and they limited to persistence constraints. The current mission specification like-wise model event constraints as follows: Assuming a mission M which uses a time interval [t0, t1]; the requirement of an agent type ˆa0to appear at location lat any time within this in-terval requires the addition of the following constraints: ST R′ =ST R∪(∅,{( ˆa0,1)})@(l,[ts, te]) andX′=X ∪t0≤ts, te≤t1. The mission specification can currently not express transition con-straints, so that the provisioning of functionality is not guaranteed throughout a transition.
The current constraint-based mission representation does not support the definition of coali-tion structure constraints for a single locacoali-tion. For instance, limiting the cardinality of the functionality to maximum one results from this limitation. Instead such constraints have to be modelled with additional locations at the cost of a larger space-time network.
The planner TemPl considers a subset of the intra-route and intra-route constraints as pre-sented in Section4.1.1mainly focusing on resource limitations and synchronisation. Efficiency and safety are non-functional properties and used as optimisation criteria. They could also be considered for use as spatio-temporal, intra-route, or inter-route constraints. Such an exten-sion would permit an more detailed problem representation with respect to non-functional requirements.
Usage of the Organisation Model The organisation model MoreOrg and its ability to dy-namically represent agents are the basis for the mission planning approach. The organisation model serves as knowledge base to describe agents and resource models. It also serves as domain specific reasoner for composite systems. Although MoreOrg uses a generic resource representation, the mission specification uses two subconcepts: agent and functionality. This separation is not strictly necessary and could be further generalised by permitting resources in general in spatio-temporal requirements.
The special needs of reconfigurable multi-robot systems have been accounted for by introduc-ing heuristics and policies, e.g., to select the transport provider in a composite agent. TemPl uses the defined heuristics and policies to compute the cost of a solution. While the current set of heuristics and policies is clearly domain specific and based on some strong assumptions, it points to further research opportunities to improve generalisation.
Multi-objective Optimisation TemPlhas been developed to serve as basis for a safe, effective and efficient operation of reconfigurable multi-robot systems. As such, the mission planning problem turns out to be a multi objective optimisation problem where specialised optimisation strategies could be applied. The safety target competes with the target of efficiency, and hence requires balancing, where the primal objective remains effectiveness. Future research requires a detailed evaluation of the multi-objective optimisation problem, where this thesis provides a basis to study reconfigurable multi-robot system and develop new application strategies.
A safety analysis of a timeline which is discretised and evaluated only at given timepoints neglects the transition, which take a big share in the overall mission. A team of agents which always (including transitions) operates in a closer range, will be quicker to help each other, e.g., to exchange failing components (cf. Chapter3). Thus, such state should be honoured with a higher safety level. For this reason, the overall state progression of the organisation model has to be considered and interpolated for a better computation of a safety estimate for the mission.
Transferability The mission specification and overall organisation model has been developed with a focus on reconfigurable multi-robot systems. TemPloffers a generic solution approach which contains several challenges of classicVRPsincludingCVRP. Most of these problems use restrictions, which have to be explicitly encoded into a mission specification forTemPl. The CVRP, for instance, can be modelled as described in the following.
The definition of theCVRPrequires an organisation model which describes two atomic agent types ˆavand ˆac, where ˆavrepresentsvehiclesand ˆaccommodities. The ability to link vehicles and commodities is encoded through two interface classes. The concepts of male and female inter-facesEmiActiveandEmiPassiveare reused. While a vehicle has only one interface EmiPas-sive, each commodity has oneEmiActiveand oneEmiPassive. This setup prevents coalitions of two or more vehicles, but (initially) allows to attach an arbitrary number of commodities to a vehicle. A vehicle type has, however, a problem specific transport capacitytcap(aˆc)< U Btcap. The mission specification assigns all available agents defined by the agent poolGAˆ to an initial depot location, so thatsinit= (∅,GA)@(lˆ depot,[t0, t1]), wheret0represents a setup vertex. The ve-hicles are also assigned to a final depot accordingly. Since no time windows are given, synchro-nisation of vehicles is not needed. The standardTSPconstraints also demand that each vehicle visits a customer/location only once. Hence, to translate the standard CVRP into a mission description forTemPlrequires the addition of the following constraints:allDistinct(S,aˆc) and themaxAccess(lx,aˆv,1), wheremaxAccessrepresents a location access constraint only for mobile agents. Note that location access restriction can also be encountered inVRPMSs(Drexl2013).
Solving aCVRP with the more generic mission planning approach is less efficient compared to a specialised solution approach. The use of the temporally expanded network introduces unnecessary side constraints and idle times for vehicles. Additionally, for a comparison with existing benchmarks the cost function needs to use covered distance of the vehicles instead of the here suggested energy consumption.