Active Exploitation of Redundancies in Reconfigurable Multi-Robot Systems

While traditional robotic systems come with a monolithic system design, reconfigurable multi-robot systems can share and shift physical resources in an on-demand fashion. Multi-robot operations can benefit from this flexibility by actively managing system redundancies depending on current tasks and having more options to respond to failure events. To support this active exploitation of redundancies in robotic systems, this paper details an organization model as basis for planning with reconfigurable multi-robot systems. The model allows to exploit redundancies when optimizing a multi-robot system's probability of survival with respect to a desired mission. The resulting planning approach trades safety against efficiency in robotic operations and thereby offers a new perspective and tool to design and improve multi-robot missions. We use a simulated multi-robot planetary exploration mission to evaluate this approach and highlight an exemplary performance landscape.


I. INTRODUCTION
R ECONFIGURABLE multi-robot systems introduce a new dimension to the design of future robot missions since they permit robots to exchange physical subsystems. This flexibility to shift subsystems can be exploited to actively manage the level of redundancy of individual robots. This is especially interesting costly planetary space operations, which require highly redundant robots. The state of the art in planetary space missions are, however, single robotic systems. Despite the fact that international space agencies operate with multiple rovers on the same planet, cooperation between these system has not been targeted. With the consideration of building up infrastructure, creating habitats to prepare human presence and supporting safe operations, this paradigm will have to shift.
Current planetary space operations have to rely on ground operators for adaptations and repair, which leads to a very slow and costly process. The dependency on earth-based maintenance, or even hardware deliveries should be minimized for future long-term space mission to achieve a An incremental mission design offers an alternative and the concept is depicted in Figure 1. Here, not only software, but also hardware subsystems can evolve with the experience made in previous missions and incrementally improve already operating multi-agent systems. The possibility to extend or refurbish existing hardware is a significant advantage, even more when a team of robots can perform this process autonomously. The autonomous exploitation of features of a reconfigurable multi-robot system is, however, a significant challenge including practical issues regarding distributed communication and planning approaches. Additionally, an application in a space context requires risk mitigation strategies and high safety standards. Therefore, enabling planning approaches that permit to exploit redundancy and sharing of resources between robotic systems will be one step forward towards safe long-term operations of autonomous multi-robot systems. By introducing a Model for Reconfigurable Multi-Robot Organisations (More-Org) in this paper, we offer a modelling approach with focus on (physically) reconfigurable multi-robot systems, although the model can embed classical non-reconfigurable robots. This enables a planning approach which exploits reconfigurability as described in Section IV. The focus of this paper is, however, on the design and role of the organization model in this context.
The organization modeling and planning approach for reconfigurable multi-robot systems finds its initial motivation in space applications. In this paper we also refer to this context to provide an exemplary use of our suggested modelling approach. Meanwhile, the organization model builds on ontologies and is therefore extensible , so that users can add new subsystems, functionalities, robots, custom properties and inference rules by extending the ontological description.

A. History and Related Work
Implementations of reconfigurable multi-robot systems exist within a spectrum ranging from industrial robots which allow an end effector exchange to fully self-reconfigurable multirobots systems [5,16,8]. Research in the area of reconfigurable multi-robot systems has initially been driven by the latter, i.e., the concept of so-called self-reconfigurable systems. Their main design characteristic is a high-level of redundancy of mostly homogeneous modules, which can automatically restructure to establish a target structure; a broad review of self-reconfigurable multi-robot systems is provided by Chennareddy, Agrawal, and Karuppiah [6] and Liu, Zhang, and Hao [17]. Self-reconfiguration aims a providing highly resilient systems, i.e., being able to recover from disruptive (structural) changes and failures. These highly-modular systems typically suffer, however, from limited capabilities and thus lack broad applicability. Planning approaches in this context focus on the transition between two organization states, e.g., Baca et al. [1] apply coalition game theory to optimize the organizational state. They characterize coalitions, however, based on strong assumptions with a utility function which (a) has a static utility for each agent independent of the coalition it will be embedded into, and (b) cannot account for interface compatibility issues leading to constrained coalition formation. The swarm-bot system developed by Mondada et al. [18] initially takes a middle ground and uses simple structured, yet reconfigurable swarm-based system in combination with a behavior-based control approach to exploit reconfigurability. They are able to illustrate team capabilities that arise from superaddition such as gap and obstacle traversal as well as (heavy) object transport.
Similarly to the swarm-bot system, our work targets reconfigurable multi-robot systems which consist of individual agents that can already be considered capable robots. Wilcox et al. [33], for instance, developed the reconfigurable sixlegged robot ATHLETE to support infrastructure build up on planetary surfaces. Although Wilcox et al. [33] did approach automation of reconfiguration procedures, they did not develop high-level planning approaches to fully exploit reconfigurability. For similar capable robots reconfigurability focuses on the adaption of internal subsystems, e.g., the Scarab rover [2] is able to adapt its locomotion platform. Reid et al. [22] show how to exploit this kind of reconfigurability with a dedicated sampling-based (motion) planning approach after modeling the reconfiguration space of the motion planning system.
In the context of organization research outside of the robotics domain Dignum [12] looks at reconfiguration of organizational processes involving humans. According to Dignum the general need to actively organize teams aims at increasing efficiency, and she sees flexible and adaptive organizations as suitable means to deal with dynamic environments. She suggests that organizations conditionally adapt and should reorganize if this will lead to an increasing success of an organization; even a suboptimal reorganization can be better than no response at all. However, the question when to reorganize and when to accept loss is left unanswered.
In Dignum's work she points to strategic flexibility, a concept developed in the scope of managing high-technology industries by Evans [13]. Evans framework conceptualizes the strategic use of a company's or more generically a market player's flexibility. Flexibility to adapt leads to a significant competitive advantage, since it offers a market player additional means to encounter unforeseen events. Hence, adaptation can directly lead to a greater probability of survival or net monetary benefit for market players. In his work Evans [13] refers to proactive, reactive, defensive and exploitative system capabilities and relates defensive one to robustness and resilience. While robustness refers to a system which can endure impacts up to a certain degree without breaking, resilience results from the ability to recover from error and return into a functional state.
Especially resilience is a key to survival, and not only in natural systems, but for technical and social systems alike shown by examples collected from Zolli and Healy [36]. Resilient systems, however, rely on their capability to adapt. Therefore, reconfigurability can contribute to an increased resilience of robotic systems. Evans' conceptual framework is general enough to be applied to reconfigurable multi-robot systems, and his categorization of maneuvers can be similarly applied for a characterization of robotic activities: protective and corrective activities count as defensive maneuvers.
The design of a space robots is typically focusing on defensive measures by adding redundancies and preparing failure handling strategies. What the flexibility of reconfigurable multi-robot systems offers, however, is the possibility for an active management of these redundancies, for instance, to adapt the organization to respond to functional requirements or to optimize the redundancy level across all available systems. An active management with a global optimization policy will treat all resources equally. This means, that the controller of a robotic mission can influence the level of resources redundancies. As a side effect active management might even result in an overall cost-optimized system design, by reducing the mean redundancy level of the multi-robot system.
Continuous optimization of an organization structure can also be found in Model of Organisation for multI-agent SystEms (MOISE+). Hübner, Sichman, and Boissier focus on a design pattern to control the reconfiguration process and identify key components. They outline an architecture to continuously optimize an organization structure to achieve main organization's objectives. Objectives for a (sub)team can be defined as Hierarchical Task Network (HTN) in a socalled scheme, which leads to the definition of a behavioural pattern, e.g., they use playing soccer as primary example. A reconfiguration process or rather transition from one team structure to another can be planned or unplanned: planned transitions can be triggered in a top-down fashion by an external operator, or they can be scheduled for a specific time. Hübner, Sichman, and Boissier require planned transitions to follow a previously defined and therefore static reorganization pattern, while unplanned transitions have to be dynamically controlled by agents.
The reorganization process in MOISE+ itself requires forming a special, predefined group structure: one agent has to adopt the role of the so-called OrgManager in order to organize the overall reconfiguration. The reconfiguration group also requires at least one agent to take over the Designer role, in order to analyse the current status of the organizational structure, and suggest a potentially better structure.
In the area of robotics Organisation Model for Adaptive Computational Systems (OMACS) is another approach for designing an organization model presented by Deloach, Oyenan, and Matson [11] and DeLoach [10]. The main concepts in OMACS are goals, roles, agents and capabilities. OMACS uses a capability-based representation for a role, i.e., a role is defined by a set of capabilities. The quality of an agent's capability can be quantified using normalized values. In the same way DeLoach quantifies an agent's ability to fulfill a role based on its capabilities. OMACS sets the main focus on the quantification of the potential of abstract roles and agents to contribute towards an organization's success. The usage of this information allows to optimize the team structure by allowing the best suited agent to handle a task, and thereby increases the likelihood of an organization's success.
Similar to MOISE+, DeLoach suggests the use of behaviour policies to control the cooperative behaviour of agents. In OMACS an organization designer can explicitly define reorganization rules. For instance to specify if and how one agent can replace another agent once the latter becomes unable to fulfil a role. An application of runtime reorganization has been shown with three real robots, and a single laptop agent by Zhong and DeLoach [35].
OMACS assumes atomic capabilities without composition, and the value normalisation to [0, 1] restricts the quantification, e.g., for a qualification of capability, to a single dimension. The quality of an agent's capability has therefore (initially) unclear semantics, which limits the applicability of the approach in practical applications.
Our approach looks superficially very similar to MOISE+ and OMACS with respect to exploiting a mapping between structure and function. However, MOISE+ as well as OMACS do this still on a higher level: MOISE+ simply defines the suitability of an agent to fill a role, while OMACS already analyses agent capabilities. Both organization models fit loosely-coupled agent teams, but do neither take physical reconfiguration under resource constraints into account, nor can they infer functionality of newly composed agents. While MoreOrg takes a similar capability-based approach of identifying an agent's available functionality to OMACS, it (a) derives this information dynamically from the available set of hardware and software resources, and thus permits inference of properties, (b) does not (yet) characterize the quality of a function. Instead we estimate the probability of survival of a function based on the available resources. Neither MOISE+ nor OMACS offer multi-agent planning, instead they allow to control agent behaviour via predefined tasks.
The robotic framework KnowRob [29] uses a semantic modelling approach and uses ontologies to represent the structure of a robotic system to create a mapping between structure and function. Beetz, Mösenlechner, and Tenorth [4] exploit this abstraction by defining plan templates for a single robot, which can then be used to identify required functionality during plan execution.
In contrast to the existing robot modeling and planning approaches, MoreOrg can model a heterogeneous set of physically reconfigurable robots and infer agent as well as organization properties. This permits an exploitation of superadditive effects and in parallel accounts for safety. To the best of our knowledge none of the existing organization modeling and planning approaches in robotics has covered these aspects so far.

B. Relation to Previous Work & Contribution
We base the results in this paper on the practical experience gained from working with multiple teams of reconfigurable systems [7,3,24,27] 1 . Furthermore, this work is part of the planning approach developed with a special focus on reconfigurable multi-robot systems [25,23]. The contributions of this paper are: (i) detailing an organization model for reconfigurable multi-robot systems with focus on functionalitybased probability of survival, (ii) offering the open-source implementation of this model, and (iii) evaluating the trade-off between safety, efficacy and efficiency for an exemplary space mission.

C. Outline
This paper takes a bottom-up approach in describing More-Org. In Section II we first provide our revised formalization and terminology for reconfigurable multi-robot systems including atomic and composite agents. Section III extends the modeling and formalization to agent and organization properties and in particular how they can be generically inferred. Redundancy is a special properties and quantified in this context with respect to required functionality. In Section IV we provide details of our planning or rather optimization approach for reconfigurable multi-robot systems that is based on MoreOrg. In Section V we describe an exemplary planning result and in Section VI we discuss the current state, open challenges and give a critical review on our take on dealing with reconfigurable multi-robot systems.

II. RECONFIGURABLE MULTI-ROBOT SYSTEMS
This section provides the basic notation, definitions and the underlying assumptions regarding reconfigurable multi-robot systems. The notation builds on the formalisms found in coalition games [32]. In particular, the agent-type representation is based on the representations developed by Shrot et al. [26] and Ueda et al. [31].
While reconfiguration affects hardware and software alike, the focus of this work is on handling physical reconfiguration of agents. The level of granularity is chosen correspondingly with the lowest level being a physical agent which cannot be separated further into two or more physical agents. This agent is denoted by atomic agent.
Definition (Atomic agent). An atomic agent a represents a monolithic physical robotic system. Note that a physical agent representing an atomic agent still contains subsystems. They are, however, inseparable parts of the physical agent.
Definition ((Atomic) Agent pool). An agent pool A denotes a set of atomic atomic agents, such that A = {a 1 , . . . , a |A| }, is the set of all atomic agents, and a ∈ A or equivalently {a} ⊆ A. A set of agents pools is denoted by Connection interfaces are the key elements in reconfigurable system and here, open the opportunity for combining two or more atomic agents. A composition from two or more atomic agents is referred to as composite agent. The join operator ∪ in the following definition for composite agents aligns well with the actual physical join operation of atomic agents and permits an intuitive representation.
Definition (Composite agent). A linked system of two or more atomic agents is a set CA, which is denoted by composite agent CA = a i ∪ . . . ∪ a j = {a i , . . . , a j }, where a i , . . . , a j ∈ A, |A| ≥ |CA| > 1. Figure 2 illustrates the general approach to agent composition as basis for superaddition, as explained with the following example: A mobile robot (atomic agent m) can share its power source with other robots, but it has no camera. After attaching an unpowered atomic agent c which has one camera as a subsystem, the composite agent {m, c} is equipped to take images. It can now move to any location and take images -a functionality neither of the atomic agents m or c provides. Fig. 2. An available set of atomic agents and a subset of composite agents that can be formed by combining different atomic agents (see [24,27] for details on the real counterparts). From top left to right: (1) a rover with four male and two female interfaces, (2) a payload item with one male and one female interface, (3) a base station with four male interfaces, (3) a legged robot with one male interface and (4) a star-wheeled robot with two male interfaces Combinatorial explosion is one of the main challenges to deal with when considering a reconfigurable system with a large number of atomic agents. One means to reduce the effects of combinatorial explosion is typing. Agent typing allows dealing with same typed agents using homogeneously formed partitions of an overall set of agents.
Definition (Atomic and composite agent type). The type of an atomic agent a is denoted byâ and equivalently for a composite agent CA the type is denoted by CA.
The set of all atomic agent types is denoted by and A x represents an agent pool containing only atomic agents of type x. The concept of a (general) agent wraps the concepts of atomic and composite agents. Henceforth, the term agent is equivalently used to the term general agent.
Definition (General agent). Any subset A ⊆ A, where A = ∅ forms a physical coalition is denoted by general agent. A (general) agent has a corresponding atomic agent type partitioned set of agent instances Definition (General agent type). The type of a (general) agent GA is denoted by GA. A general agent type GA is represented as a function γ GA : θ(A) → N 0 . The function γ GA maps an atomic agent typeâ to the cardinality câ of the type partition of GA, such that câ = |GAâ|. Equivalently to γ GA (â) ≥ 1 the following notation will be used:â ∈ GA, andâ ∈ GA for γ GA (â) = 0.
The reverse mapping from type GA to the general agent is denoted by i( GA) = GA.
A general agent type is also represented as a collection of tuples relating agent type and cardinality: An agent pool can now be represented in two ways: (i) as set of atomic agents as already introduced, or (ii) as general agent type A, such that ∀a ∈ A : γ A (â) = |Aâ|, where the latter offers a more compact representation and is used preferably in our implementation of the organization model.
To execute robotic missions, atomic agents from an available agent pool will be assigned to particular tasks. However, if multiple atomic agents of the same type exist and equal start conditions hold for these atomic agents, multiple equivalent assignments of atomic agents to a task are possible. For that purpose, requirements for atomic agents will be defined by so-called roles, which act as correctly typed placeholders for instances of an agent type.
Definition (Atomic agent role). An atomic agent role râ represents an anonymous agent instance of an atomic agent typeâ.
Given an overall set of atomic agents, various reconfiguration states of the overall systems are possible. These reconfiguration states result from forming different sets of composite agents, but always with the restriction of the overall available set of atomic agents. In the field of multi-agent systems and particularly characteristic function games (see [32]) this leads to so-called coalition structures. A coalition structure represents the set of active atomic and composite agents that form a reconfigurable multi-robot system. Note that we will also use the term organization in order to describe a reconfigurable multi-robot system represented by an agent pool A.

Definition (Coalition structure). A coalition structure of an agent pool A is denoted by CS A and is represented by a set of disjunct general agents CS
Composite agents result from the combination of atomic agents. We use the following definitions to separate the current (realized and physically assembled) set of general agents in a coalition structure from the (virtual) set of agents, which can be formed from the set of atomic agents.
Definition (Operative and dormant agents). Let the current state of a reconfigurable multi-robot system be described by a coalition structure CS A . Then all general agents GA ∈ CS A are referred to as operative agents, and complementary, all general agents GA ∈ P A ∧ GA ∈ CS are referred to as dormant agents, where P A is the powerset of all atomic agents.
The previous definitions look at a reconfigurable multi-robot system as a collection of agents, and consider pairing and coalitions only at this level of modularity. A reconfigurable multi-robot system can form composite agents in different ways depending upon the compatibility of interfaces. Hence, to perform a detailed reasoning on connectivity of agents, we also have to account for the physical interfaces as subsystems of an agent to analyze the feasibility of all agents. composite agent. The scope of the presented formal description so far, is based on a set-theory description and covers what is denoted agent space.
Definition (Agent space). Agent space denotes the settheory based view to a reconfigurable multi-robot system without constraining the connectivity between any two agents.
Agent space is, however, only a restricted view onto link space.
Definition (Link space). Link space denotes a graph-based structure of a reconfigurable multi-robot system. In link space a reconfigurable multi-robot system is represented by an undirected graph G = (V, E), where each vertex v ∈ V maps to an atomic agent's interface and an edge e = (u, v), u, v ∈ V represents the existing connection between two interfaces.
The current modeling approach regarding link space accounts only for edges that represent electromechanical connections between agents as precondition for sharing resource in a composite agent. Data connections between software and hardware components as well as configuration options of hardware and software components are currently left out in our modeling approach.

A. Assumptions
A large spectrum of reconfigurable multi-robot systems exists. Most often, fully distributed control approaches apply, due to the use of swarm-based systems. The definition of the general agent already reflects one important design choice of this work, which relaxes this apparent requirement for distribution. Instead of enforcing distributed control approaches at all system levels, centralized control approaches for locally autonomous and self-sustained operation of agents are permitted and feasible. This implicitly allows an atomic agent to act as a temporary 'master' in a master-slave architecture. When forming a composite agent, for instance, a single atomic agent in this formation acts as master, which is able to control all other attached atomic agents. In effect, each general agent represents a single-minded (collaborative) agent. The distribution of the overall agent system is still maintained by an appropriate design of the operational infrastructure.
Assumption (Individual agent). Each atomic and composite agent comprises a central controller and thus represents an individual, single-minded agent.
Generally, two atomic agents can connect via multiple interfaces. We assume, however, limited connectivity and currently do not consider geometrical constraints. This restriction allows us to focus on the identification of essential needs for modeling and automating of reconfigurable multi-robot systems.

Assumption (Single link). A physical coupling between two
atomic agents can only be established through two and only two compatible coupling interfaces. In principle Definition II allows a single agent to have multiple types. However, we assume a single characterising agent type. Meanwhile, one agent type can still inherit the properties of a parent type.
Assumption (Single agent type). An agent can be mapped to a single agent type only.
Assumption (Agent type inheritance). An agent type can inherit the properties of another agent type.
A key assumption, when dealing with an active exploitation of resource is the possibility to join the available resources of two or more agents. Hence, when two or more atomic agents form a composite agent, they join their set of resources. In principle, geometrical restrictions might apply to reuse the set of resources effectively. However, we initially assume that resources are shared without restriction within a composite agent.
Assumption (Resource usage). A composite agent can reuse the subsystems of its composing atomic agents.
To enable resource sharing in a composite agent, various ways of coupling two or more atomic agents can be considered, e.g., electromechanical or thermo-electromechanical. We currently assume, however, that composite agents establish links between their composing atomic agents which permit data, energy and power transmission.
Assumption (Agent Linkage). Links which connect atomic agents in a composite agent permit transfer of data, energy and power.
To effectively exploit resources in redundant structure, the following assumption is made: Assumption (Component substitution). To maintain the functionality of an agent, one component can replace another if it is an instance of the other's class, which also includes instances of subclasses. This seems like a strong assumption, since even if components are instances of the same concept, e.g., a camera, it might not be possible to substitute one with the other without loosing functionality. However, this is a matter of modeling equivalence as part of the ontological design in MoreOrg.

III. ORGANIZATION MODELLING
We have developed the organization model MoreOrg 2 to quantify the properties of a reconfigurable multi-robot system and provide cost measures for a reconfigurable multi-robot system. The organization model permits a quantification of system properties at different granularity levels and can characterize the active set of agents, i.e., the coalition structure of the organization by using a bottom-up approach. Figure 3 depicts the hierarchical decomposition of an organization which serves as baseline for MoreOrg's reasoning approach. The coalition structure of a reconfigurable multi-robot system can change on-demand, which might involve creating and/or removing one or more connection between atomic agents, but all agents can be characterized by their set of associated resources, i.e., hardware and software components.
MoreOrg relies on ontologies to describe resources in general and more specifically atomic agents and their associated functionalities and subsystems. All subsystems and atomic agents are characterized by data properties, e.g., MoreOrg focuses on a set of numeric data properties to enable mobile transport agents (cf. [23] where we relate planning for reconfigurable multi-robot systems to Vehicle Routing Problems). As a benefit of this ontological representation, Description Logic (DL)-based reasoning can be applied and an agent's available functionalities and properties can be inferred from its composing set of resources or rather subsystems. Additional reasoning mechanisms are applied to finally describe the organizational properties, where our focus is set on efficacy and safety. The following subsections detail the organization model and its reasoning approach.

A. Subsystem Properties
Subsystems are tightly bound to atomic agents and come with statically defined properties. All subsystems are at least associated with a probability of survival to define their reliability. This is the basis for computing a safety measure for the overall multi-robot organization. The details of this computation are provided in Section III-D.

B. Generic Agent Type Properties
MoreOrg provides a mechanism to defined agent properties in a general way, such that composite agent properties can be derived from the atomic agents that form the agent.
Definition (Agent Type Property Value). The value function for an agent type A and a numeric property named np is denoted by pvalue( A, np).
Some atomic agent type properties as listed in Table I are statically defined and required to implement the planning approach. Note that other uses of the organization model can lead to the use of a completely different set of properties. Hence, the listed properties are examples only and have been added to support the operation of a logistics chain as targeted reconfigurable multi-robot planning problem in space exploration (see Section IV). Nevertheless, the already defined properties will likely be sufficient and needed for many standard robotic scenarios. Any missing properties can easily be added to the ontology if needed.
While many properties of atomic agent types are directly set, some atomic agents' properties and all properties of composite agents have to be inferred. Here, MoreOrg distinguishes between boolean and numeric properties (cf. Table II).
1) Boolean Properties: Boolean properties map to the availability of particular capabilities and they can be inferred from available combinations of functionalities and subsystems, e.g., the functionality AutonomousNavigation is inferred from the availability of other capabilities and subsystems, here Locomotion, Mapping, MotionPlanning, SelfLocalization and a subsystem PowerSource. The boolean property has f ( A, f ) defines whether an agent A supports a functionality f or not. This boolean property enables selection mechanisms, e.g., to identify agents which have the functionalities to perform a particular tasks.
For atomic agents the inference of available functionality is based on ontological reasoning and exploits available DLbased reasoners, here Fact++ [30]. For composite agents, we allow to quantify the support for a functionality by an agent's resources, so that the boolean property depends on the amount of support: , where A is the agent type, f a functionality and support is defined in the following. Support for an agent's functionality is based on a single resource concept c, e.g., where c can represent a subsystem type such as Camera, as follows (see also [25]): where card min and card max return the minimum required and maximum available cardinality of resource instances (including instances of derived resource concepts), respectively. Accordingly, support of a functionality f with respect to a resource class c can be categorized as follows: full support > 0 and < 1 partial support  Support for a single functionality and subsequently for a set of functionalities F is then defined as: where C is a set of resource concepts and ∀c ∈ C : card min (c, f ) ≥ 1 to account only for relevant resource concepts, and 2) Numeric Properties: Not all static numeric properties of atomic agents need to be directly assigned, since they can be inferred from other properties, e.g., due to laws of physics. As an example available energy capacity (Wh) can be derived from the capacity of the power source (Ah) and the supply voltage (V): pvalue(A, ecap) = pvalue(A, esourcecap) · pvalue(A, esupply) , where |A| = 1. MoreOrg allows to define these mathematical relationships between properties. This is done by annotating properties in the ontology and by using a simple Domainspecific Language (DSL) in combination with a math parser library 3 .
To infer the value of numeric properties for composite agents, MoreOrg permits the definition of custom inference rules. These rules are defined as higher-order functions, which can be constructed from selection policies and composition operations. c) Inference Rule: Both, composition operators and selection policies can be combined to form an inference rule for composite agents, e.g., for all properties relating to locomotion, such as nominal velocity: pvalue( A, v nom ) = c(sel TransportProvider (i( A)), v nom , +) , which maps to the v nom property value of the only available TransportProvider or 0 if there is none.
Inference rules are defined in the ontology, so that users can add their own rules.

C. Special Agent Type Properties
Some special agent properties exist, where in contrast to the generic agent type properties the reasoning mechanisms are hard-coded into the model. 1) Safety: In MoreOrg the computation of safety of an agent is a special property motivated through the space application context. Safety is based on resource redundancy under the assumption of possible component substitution (see Section II-A). The measure for redundancy is the central part of our safety heuristic and it is based on the standard modeling approach for parallel and serial component-based systems (see [21]). Each resource can be associated with a probability of survival, so that an overall probability of survival can be computed using a function decomposition tree approach. Information about the probability of survival of components should be derived from an initial system identification and is ideally updated with performance and degradation information from the real system.
The reliability R f , also referred to as probability of survival, of a single functionality f can be computed by accounting Fig. 4. Schematic of a system composition consisting of three resource types: a,b,c, where the ratio from required to available is for a 1:3, for b 1:1, and for c 2:8.
for parallel components, i.e., resources that are not strictly required but which can serve as replacement: where p i (t) is the time-dependent probability of survival with 0 ≤ p i (t) ≤ 1. While component degrading can be one reason for a change of the probability of survival, MoreOrg leaves the use of time-dependence as future improvement and instead uses a static probability of survival with t = 0.
Definition (Functional reliability). R( A, F) denotes the reliability of a set of required functionalities F which is provided by an agent A.
The computation of R( A, F) is based on the functional decomposition of the agent type A into atomic resources. For each resource a redundancy at component level (cf. [21]) is assumed. As a heuristic the redundancy is computed based on a type partitioning considering all resources which have no further dependencies. All resources of the same type are modeled as subsystems, which again form a serial system. Figure 4 illustrates this modeling approach.
For each subsystem which is composed of a single resource type the redundancy is computed for r required instances, n available instances and the probability of survival p for the resource type: The function req maps a set of functionalities F to the required number of instances for each resource type: where req i represents the minimum cardinality of a resource type i to fulfill all functionalities in F. The function avl maps an agent type to the number of maximum available resources with respect to a functionality set F. Only resources that can contribute to the provision of F need to be considered: where avl i represents the maximum cardinality of a resource type i available in the general agent type A. Resources lead to a heuristic system structure as shown in Figure 4 using serial and parallel systems. Based on this structure, an agent's reliability with respect to a set of functionalities is defined as: where p i represents the probability of survival for a resource type i. Example: Before introducing this example note that functionalities can dependent upon other functionalities or resources. Hence, an availability of functionality f 1 might imply the availability of a functionality set F 1 = {f 1 , f 2 , f 3 }, where f 2 and f 3 are direct dependencies of f 1 . In this example a functionality LocationImageProvider depends on a functionality ImageProvider and a functionality MoveTo. The requirements for the ImageProvider are one of each resource: Camera and PowerSource. MoveTo requires one of each resource: Localization, Locomotion, Mapping, PowerSource. Table III lists the cardinalities and probabilities of survival for an atomic agent type SherpaTT with relevant resources. This agent type provides the functionality LocationImage-Provider with a redundant camera system, and otherwise a series system. According to Equation 11 the probability of survival for the functionality LocationImageProvider is: A composite agent which has an additional atomic agent PayloadBattery can increase the redundancy of the resource PowerSource by 1. This leads to an increase of the probability of survival for the functionality LocationImageProvider, since now two redundant subsystems exist: 2) Efficacy: Efficacy in the context of MoreOrg describes the ability of a reconfigurable multi-robot system to provide a particular functionality. To measure an agent's efficacy an objective has to be given, here as a set of required functionalities. The identification of efficacy leads only to a binary result: either the organization supports the given functionality or not.
The definition of support can be viewed as an analysis of the redundancy level of components with respect to a required set of functionalities. The bottom-up definition of functionality support, eventually leads to the definition of an agent's efficacy: This definition of efficacy illustrates our approach to use resource summation to actively exploit redundancies for the creation of functional systems. For efficacy only a sufficient component count is relevant, while the computation of the safety objective will take into account any excess resources.
3) Operation Cost: Typically, robotic systems consume electrical energy and MoreOrg additionally expects a definition of all agents nominal power consumption. Since we do not assume a homogeneous set of robots and might also operate in varying coalitions agents will have a varying power consumption. Therefore, operation time only is not an accurate cost measure. Instead, MoreOrg uses the total energy consumption of a reconfigurable multi-robot system as cost measure.
Power consumption can vary over time with the type of activity, but MoreOrg assumes a constant power consumption of all operative atomic agents and leaves a more sophisticated estimation, e.g., based on a functionality-based power consumption model, as future enhancement. MoreOrg estimates the operation cost as total consumed energy for all agents based on the nominal power consumption:

D. Organization Properties
In contrast to atomic and composite agents, an organization property can differ in its structure, i.e., might change its coalition structures over time. Therefore we describe here the coalition structure properties of a reconfigurable multirobot system, as well as the cost to change between coalition structures.
1) Coalition Structure Properties: a) Goal Dependant Reliability: The organizational structure intends to support activities of its member agents that help to achieve and maximize the shared organizational goals. Agents can operate in parallel at different physical locations. The objective for an active coalition structure CS = {GA 1 , . . . , GA |CS| } of an organization is therefore described by a corresponding set of functionality sets denoted F S = {F 1 , . . . F |CS| }, and a2f : CS → F S allows to map each operative agent GA i to the required functionality set F i . The current redundancy of the organization is then the minimum achievable level of redundancy: Note that this computation is not used in the planning approach, but will be used in the future to identify coalition structures with critically unbalanced resource distribution. b) Efficacy: The efficacy of an organization's current coalition structure is computed from all operative agents' efficacy: Here, all operative agents in a coalition structure need to support the functionalities in F. Note, that MoreOrg implements the optimal coalition structure generation algorithm developed by Rahwan et al. [20] to search for a coalition structure where efficacy(CS, F) = 1. This optimisation approach is used, e.g., to validate the feasibility of a transition of a set of agents between two locations. Since only mobile agents can relocate, a coalition structure is required such that efficacy(CS, {M oveT o}) = 1.
2) Operation Cost: Reconfiguration of an organization contributes to operation cost, since transitions between coalition structures require time and energy. The time to transition from one coalition structure CS A i to another CS A j when CS A i = CS A j is therefore estimated with a heuristic function. The heuristic firstly assumes basic cost for the number of atomic agents which are involved in the reconfiguration. Secondly, additional and significantly higher cost arise from the need to coordinate multiple agents to exchange atomic agents or to merge. Therefore, the reconfiguration cost function to form a single agent from an existing coalition structure takes into account the number of general agents, equal to the partitions of the coalition structure CS, and the total number of involved atomic agents: where t a and t b are heuristic time constants. Robotic experiments are required to establish a realistic estimate for the magnitude of these parameters. Our real world experiments give an indication for these parameters for small teams, so that a default setting of t a = 600 s and t b = 100 s applies. The values are estimates which consider time for additional error handling. The overall reconfiguration cost to transition from a coalition structure CS A i to another CS A j is defined as: Note that the reconfiguration cost heuristic does not account for relocation cost. Instead we assume that all agents taking part in a reconfiguration process operate in direct proximity. Thus, this heuristic penalizes an involvement of an increasing number of agents to extract a new one. The first term penalizes the total number of involved independent agents to form a new agent with; each additional agent increases communication and coordination cost, as well as the likelihood for failures. The second term accounts for the fact, that only a selected set of atomic agents is involved in a reconfiguration -the fewer the better.

IV. EXPLOITATION OF REDUNDANCIES
To exploit reconfigurable multi-robot systems we use a constraint-based mission planning approach. Constraints allow to define the essential characteristics of a potential solution, by letting a user specify task requirements. The collected constraints then define a partial-ordered plan for which a suitable full solution has to be found by translating the mission requirements to an agent allocation and constellation problem. Agent allocation here means, that the exact organization structure and its development over time throughout a mission is initially unknown. What is known apart from the given constraints, however, are the total available atomic agents, their associated resources and the model to combine atomic agents to composite agents in order to support required functionalities.
We implemented the planner Temporal Planning for Reconfigurable Multi-Robot Systems (TemPl) [23] to address the constraint-based planning problem for reconfigurable multirobot systems. This planner uses MoreOrg as organization model, but adds a temporal and spatial dimension to problem definitions.
Definition (Spatio-temporal requirement). A spatiotemporal requirement is represented as a spatio-temporally qualified expression s, which describes the functional requirements and agent instance requirements for a time-interval and a location: where F is a set of functionality constants, A s is the general agent type representing the required agent type cardinalities, l ∈ L is a location variable, and t s , t e ∈ T are temporal variables describing a temporal interval with the implicit constraint t s < t e .
Each spatio-temporal requirement represents a persistence constraint, i.e., the requirements have to hold throughout the time interval. The mission specification allows to relate spatiotemporal requirements to the organization model which defines agent types and functionalities along with the associated properties.

Definition (Mission). A robotic mission is a tuple M =
A, ST R, X , OM, T, L , where the general agent type A describes the available agent types, ST R is a set of spatiotemporally qualified expressions, X is a set of constraints, OM represents the organization model (here MoreOrg as described in Section III), T is the set of timepoints and L the set of locations.

A. Mission Constraints
Constraints in X can refer to spatio-temporally qualified expressions and the initial state of a mission is defined by the earliest timepoint and binds available agents to their starting depot. The earliest timepoint is t 0 ∈ T and ∀t ∈ T, t = t 0 : t > t 0 . Note that this planning approach neither requires a single starting location for all agents nor a single final destination. An example for a mission is given in Table VIII. a) Temporal Constraints: Temporal constraints are listed in Table IV. They allow to defined the temporal relation between spatio-temporal constraints in a relative and absolute manner.
b) Model Constraints: TemPl implements a subset of feasible (meta-)constraints (see Table V). Model constraints set requirements for agent types and agent roles. They allow bounding the cardinality of agent types so that the combinatorial search problem can be limited according to a least-commitment principle. Equality constraints allow to restrict agent routes partially or even completely. Requiring the minimum equality of a single agent type over the full mission defines the full route for a single atomic agent of this type. Thereby, modelling constraints allow to detail a mission. In general, constraints apply to the dimensions space, time, agent types, and roles. c) Functionality & Property Constraints: Agents either comprise a functionality or they do not. In effect, functionality is requested with a maximum cardinality of one, which makes the introduction of a maximum function constraint unnecessary. Note that this is a limitation of the current modelling approach. However, the property of a agent providing a particular functionality can be of importance, and the use of property constraints allows to narrow applicable agents.

B. Planning and Optimization
The (high-level) optimization problem for a given mission M can be stated as: The multi-objective cost function is based on the heuristics listed in Table VII, and can be evaluated as soon as a solution for a mission exists.
The three objectives are presented in the cost function: efficiency through the energy cost function, efficacy through checking the level of fulfillment, and safety as a redundancy dependent survival metric; for balancing the parameters α, β and can be used. Note that safety and fulfillment have a value range [0, 1], so that α should account for normalization to [0, 1] for the energy cost; α therefore comprises a factor E −1 max , where E max is the maximum energy cost which is either the allowed one or is extracted from existing mission solutions. The latter is done for our evaluation in Section V.
The importance of operation cost is controlled via α, a higher value will lead a preference of missions which require less energy. The time of an agent's operation depends upon estimated travel cost, time for the actual requested operation or task, and time for reconfiguration. Our approach extends an approach used by Wurm et al. [34] to estimate the cost based on the travel time between two locations. We suggest to use nominal speed v nom as default property for atomic agents, so that based on this information a duration estimate for location changes of mobile agents can be computed. As long as no better estimation or other routing constraints are available, the line-of-sight distance between two locations is still the basis for the cost computation.
Parameter β controls the penalty for missions that can only be partially fulfilled, here the heuristic assumes that each requirement is of equal importance. Future approaches should also take a priority into account.
The preference of safer operations and thus agents with higher redundancy is control via . In principle, a high negative value of leads to a preference for a solution with a single, yet highly redundant agent that can solve the mission.
For the search for an optimal transition between coalition structures it has to be considered, that due to a high degree of redundancy a safer coalition structure might lead to lower efficiency. Therefore, any optimization has to trade safety and efficiency against each other and can lead only to a paretooptimal solution.

C. Algorithm
To tackle the given optimization problem one or more solutions for a given mission have to be identified. Due to the need for various possible mappings between required functionality and satisfying agents, the problem cannot be directly solved in a classical form, e.g., with Linear Programming. The problem needs to be transformed with the help of the MoreOrg, so that existing optimization approaches can be combined to perform local optimization, here combinatorial optimization, coalition structure optimization and min-cost flow multi-commodity flow via Linear Programming.
The basic algorithm that we are currently using is illustrated in Figure 5. We will outline the general approach and refer to [23] for further details. The algorithm involves a generation candidate generation, which accounts for major constraints but not all required ones. Only after candidate optimization and subsequent characterization it will be known whether the suggested solution candidate is feasible, i.e., whether the resulting quantitative temporal network is consistent and whether required reconfigurations and location transitions can be performed. Since we also permit partial solutions, i.e. efficacy < 1, feasibility does not necessarily imply that all spatiotemporal requirements of a mission are satisfied, but only that

Name
Syntax Description min cardinality minCard(S,â, c) Minimum cardinality constraint ∀s ∈ S : γ As (â) ≥ c, where c ≥ 0 max cardinality maxCard(S,â, c) maximum cardinality constraint corresponding to minCard so that ∀s ∈ S : γ As ≤ c, where c ≥ 0 all distinct allDistinct(S,â) ∀s ∈ S : Aâ s = ∅ min distinct minDistinct(S,â, n) ∀s i , s j ∈ S, i = j : |Aâ s i | − |Aâ s j | ≥ n, where n > 0 max distinct maxDistinct(S,â, n) the equivalent maximum constraint to minDistinct, so that ∀s i , s j ∈ S, i = j : |Aâ s i | − |Aâ s j | ≤ n, where n ≥ 0 min equal minEqual(S, Ar) minimum existence of the same agent roles so that Aeq = s∈S r(As) and Ar ⊂ Aeq, where Ar ⊂ r(A), A is the available agent pool for a mission, and As is the agent pool that fulfils s ∈ S max equal maxEqual(S, Ar) maximum existence of the same agent roles so that Aeq = s∈S r(As) and Aeq ⊂ Ar, where Ar ⊂ r(A), A is the available agent pool for a mission, and As is the agent pool that fulfils s ∈ S all equal allEqual(S, Ar) the constraint conjunction: minEqual(S, Ar) ∧ maxEqual(S, Ar) the activities that are part of the suggested solution can be performed. Generating solution candidates with an efficacy < 1 (a) accounts for a future prioritization of requirements, and (b) permits the identification of pareto-optimal solutions with respect to safety, efficacy and efficiency.
Initially the planner aims at generating a resource efficient solution, by reducing the number of involved agents. It does so by bounding the number of agents that are assigned to mutually-exclusive requirements through two parameters: ψ m and ψ ¬m . The default is ψ m = 0 and ψ ¬m = 0, which means, that a set of mutually-exclusive requirements only get the minimum needed resources to resolve their conflict: the parameters ψ m and ψ ¬m refer to the number of additionally permitted mobile and immobile agents respectively to be assigned to mutually-exclusive requirements. In effect, these parameters can increase the resource usage and level of redundancy for a solution, and at the same time increase the options to find a solution that satisfies all requirements. A resulting increase of the number of agents can come, however, at a price: (a) higher complexity of the problem since additional agents allow for exponentially more reconfiguration options, and (b) higher operational cost, i.e., lower efficiency.

V. EVALUATION
For an experimental evaluation of the planning approach we look at a simulated space mission, which has been outlined by Sonsalla et al. [28]. The major goal of the mission is to place scientific payloads in a lunar environment at a predefined set of locations for science goals. These target science goals are cast into a respective mission specification which is listed in Table VIII. Note that each location is defined by longitude and latitude in the specification; TemPl uses Mercator projection to convert these into Cartesian coordinates. A corresponding subsection of a solution found by TemPl is shown in Figure 6. With respect to the safety measure the starting assignment is ignored by assuming a probability of survival of 1.0. This is done to avoid an initial bias of the safety objective. To compute the safety objective only relevant spatio-temporal requirements   Figure 6) do not affect the safety objective (see for instance location b6, timepoint t5).
TemPl has been used to search for solutions to this mission scenario with a setting of ψ ¬m = 0 and ψ m in the range of 0 to 2. The search has been split into epochs with a maximum allowed planning time of 60 s. After 60 s search has been reinitialized in order to escape from local minima. Planning has been stopped either after memory has been exhausted or when the total planning time of 20 min was exceeded (Intel i7-4600Um 12 GB RAM). A higher setting of ψ m requires additional agents to be used for the planning approach, so a higher computation time per solution is to be expected. Note that while the setting with ψ m = 0 resulted in a stable range below 4 s per solution candidate, the required computation time per solution increases for ψ m = 2 to up to 12 s -in combination with the total planning time this explains the lower number of solutions found for higher settings of ψ m . The comparison of solutions based on efficacy, efficiency and safety is shown in Figure 7 with additional details provided in Figure 8.
What can be seen is that the expected increase in redundancy, due to the higher setting of the parameter ψ m leads to solution candidates with a consistently higher safety objective. This shows that ψ m is an effective control parameter. By using an exemplary trade off setting for the cost function with α = −1, β = 100.0, and = 10.0 we can extract the solutions characteristics. The black star-shaped marks indicate the best solutions according to the weights of the objective function. While safety can be increased from below 0.7 to approx. 0.75 for solutions with efficacy of 1, the efficiency deteriorates, although only slightly for ψ m = 2 compared to ψ m = 0.
This analysis shows only an exemplary solution landscape, but at the same time the working of our modeling and planning approach for reconfigurable multi-robot system capabilities. Our evaluation confirms that by increasing the options for agent assignments and at the same time the level of redundancy of the reconfigurable system, improved solutions can be found for application scenarios where safety might be an issue.

VI. CONCLUSION
This paper has outlined a modeling approach for reconfigurable multi-robot systems, which permits an active exploitation of redundancies in multi-robot systems through physical reconfiguration. The current approach does only moderately influence the level of redundancy in systems that are taking part in a robotic mission. This is mainly due to the complexity of the planning problem as result of exponentially many reconfiguration options. It led us to use several heuristics and initially target resource efficient solutions. Clearly, this model might still not lead to solutions which are sufficiently good from a safety perspective, but it offers a basis for an automated use of reconfigurable multi-robot systems and an optimization strategy for organizational safety properties. Our deliberate planning approach can give an advantage compared to reactive reorganization strategies found in swarm-like systems by avoiding dead-end configurations. Meanwhile a hybrid approach could be foreseen in a real application. Furthermore, we plan to augment already found solutions by explicitly routing available or rather unused agents along the critical path of a mission. This can be done without replanning until the known transport lines, which are established through mobile agents, are exhausted. It comes, however, again at the cost of efficiency.
The existing heuristics are based on assumptions and a limited set of practical experiments. As such they can clearly be interpreted as a weakness of the modelling approach. The given heuristics shall, however, serve as basis and examples to develop better approaches to with reconfigurable multi-robot systems. As such they firstly point to the need / benefit for a submodel, and secondly act as placeholders. All submodels and heuristics are subject of continued improvements and efforts to detail the model further. Probability of survival, for instance, as it is used and presented in this paper acts as a placeholder for more sophisticated metrics, e.g., some which   6. Identified solution for the exemplary space mission after 20 min of search (ψm = 2, ψ¬m = 0) (to maintain readability only a part of the graph is placed here). Bars are annotating edges to illustrate transport capacity consumption, a green square identifies a required and available agent, while a grey square identifies an available though not required agent. Each constellation is attributed with the safety metric (probability of survival) and reconfiguration cost (in s). are based on extensive empirical studies and specifications of subsystems. Furthermore, we plan to define safety not only through spatio-temporal requirements, but instead adapt the model to reflect the risks resulting from reconfiguration, idling and relocation. Since a solution is characterized after all agents have been assigned, a dedicated models, e.g., for component degradation and reconfiguration errors can be taken in account to improve the safety measure. We are also interested in using graph and network analysis techniques such as percolation [19] in combination with replanning to test the options to respond to system failures.
Reconfigurable multi-robot systems combine the benefits of modular robots with capable robotic systems, and we see significant potential in developing further strategies and planning approaches. An automated exploitation will give designers of robotic mission a new degree of freedom. Still, significant practical challenges remain to exploit reconfiguration with real robots: increasing the reliability of all involved atomic agents is one challenge, and establishing reliable reconfiguration maneuvers is another. We do, however, outline here a feasible approach towards modeling and multi-objective planning for such systems.
ACKNOWLEDGMENT This work has been supported by the German Space Agency (DLR Agentur) with federal funds of the Federal Ministry of Economic Affairs and Energy for the project TransTerrA under grant agreement 50RA1301 to implement the initial planning approach. The continued evaluation and application in the project Q-Rock has been supported by the Federal Ministry of Education and Research under grant agreement 01IW18003. The continued development has been supported by the Federal Ministry for Economic Affairs and Energy under grant agreement 50RA1701. The author would like to thank all contributors who helped to realize the multi-robot team in the project TransTerrA.