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Active Exploitation of Redundancies in Reconfigurable Multi-Robot Systems

Thomas M. Roehr1

Abstract—While traditional robotic systems come with a existing hardware is a significant advantage, even more when monolithic system design, reconfigurable multi-robot systems a team of robots can perform this process autonomously. can share and shift physical resources in an on-demand fash- The autonomous exploitation of features of a reconfigurable ion. Multi-robot operations can benefit from this flexibility by actively managing system redundancies depending on cur- multi-robot system is, however, a significant challenge in- rent tasks and having more options to respond to failure cluding practical issues regarding distributed communication events. To support this active exploitation of redundancies in and planning approaches. Additionally, an application in a robotic systems, this paper details an organization model as space context requires risk mitigation strategies and high safety basis for planning with reconfigurable multi-robot systems. standards. Therefore, enabling planning approaches that permit The model allows to exploit redundancies when optimizing a multi-robot system’s probability of survival with respect to a to exploit redundancy and sharing of resources between robotic desired mission. The resulting planning approach trades safety systems will be one step forward towards safe long-term against efficiency in robotic operations and thereby offers a operations of autonomous multi-robot systems. By introducing new perspective and tool to design and improve multi-robot a Model for Reconfigurable Multi-Robot Organisations (More- missions. We use a simulated multi-robot planetary exploration Org) in this paper, we offer a modelling approach with focus mission to evaluate this approach and highlight an exemplary performance landscape. Our implementation of the organiza- on (physically) reconfigurable multi-robot systems, although tion model is open-source available (https://github.com/rock- the model can embed classical non-reconfigurable robots. This knowledge-reasoning/knowledge-reasoning-moreorg). enables a planning approach which exploits reconfigurability Index Terms—Multi-Robot Systems; Planning, Scheduling and as described in Section IV. The focus of this paper is, however, Coordination; Space Robotics and Automation; Reconfigurable on the design and role of the organization model in this Robots context. The organization modeling and planning approach for re- I.INTRODUCTION configurable multi-robot systems finds its initial motivation in space applications. In this paper we also refer to this ECONFIGURABLE multi-robot systems introduce a context to provide an exemplary use of our suggested mod- R new dimension to the design of future robot missions elling approach. Meanwhile, the organization model builds on since they permit robots to exchange physical subsystems. ontologies and is therefore extensible , so that users can add This flexibility to shift subsystems can be exploited to actively new subsystems, functionalities, robots, custom properties and manage the level of redundancy of individual robots. This inference rules by extending the ontological description. 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. A. History and Related Work Despite the fact that international space agencies operate Implementations of reconfigurable multi-robot systems exist with multiple rovers on the same planet, cooperation between within a spectrum ranging from industrial robots which allow arXiv:2106.12079v1 [cs.RO] 22 Jun 2021 these system has not been targeted. With the consideration of an end effector exchange to fully self-reconfigurable multi- building up infrastructure, creating habitats to prepare human robots systems [5, 16, 8]. Research in the area of recon- presence and supporting safe operations, this paradigm will figurable multi-robot systems has initially been driven by have to shift. the latter, i.e., the concept of so-called self-reconfigurable Current planetary space operations have to rely on ground systems. Their main design characteristic is a high-level of operators for adaptations and repair, which leads to a very redundancy of mostly homogeneous modules, which can au- slow and costly process. The dependency on earth-based tomatically restructure to establish a target structure; a broad 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 previ- ous missions and incrementally improve already operating multi-agent systems. The possibility to extend or refurbish

1DFKI GmbH Robotics Innovation Center Bremen, Robert-Hooke-Str. 1, Fig. 1. Schematic description of an incremental design of planetary space 28359 Bremen, Germany, correspondence: [email protected] missions using reconfigurable multi-robot systems. 2 review of self-reconfigurable multi-robot systems is provided can endure impacts up to a certain degree without breaking, by Chennareddy, Agrawal, and Karuppiah [6] and Liu, Zhang, resilience results from the ability to recover from error and and Hao [17]. Self-reconfiguration aims a providing highly return into a functional state. resilient systems, i.e., being able to recover from disrup- Especially resilience is a key to survival, and not only in tive (structural) changes and failures. These highly-modular natural systems, but for technical and social systems alike systems typically suffer, however, from limited capabilities shown by examples collected from Zolli and Healy [36]. and thus lack broad applicability. Planning approaches in Resilient systems, however, rely on their capability to adapt. this context focus on the transition between two organization Therefore, reconfigurability can contribute to an increased states, e.g., Baca et al. [1] apply coalition game theory to resilience of robotic systems. Evans’ conceptual framework optimize the organizational state. They characterize coalitions, is general enough to be applied to reconfigurable multi-robot however, based on strong assumptions with a utility function systems, and his categorization of maneuvers can be similarly which (a) has a static utility for each agent independent of the applied for a characterization of robotic activities: protective coalition it will be embedded into, and (b) cannot account for and corrective activities count as defensive maneuvers. interface compatibility issues leading to constrained coalition The design of a space robots is typically focusing on formation. The swarm-bot system developed by Mondada et al. defensive measures by adding redundancies and preparing fail- [18] initially takes a middle ground and uses simple structured, ure handling strategies. What the flexibility of reconfigurable yet reconfigurable swarm-based system in combination with a multi-robot systems offers, however, is the possibility for an behavior-based control approach to exploit reconfigurability. active management of these redundancies, for instance, to They are able to illustrate team capabilities that arise from adapt the organization to respond to functional requirements or superaddition such as gap and obstacle traversal as well as to optimize the redundancy level across all available systems. (heavy) object transport. An active management with a global optimization policy will Similarly to the swarm-bot system, our work targets re- treat all resources equally. This means, that the controller configurable multi-robot systems which consist of individual of a robotic mission can influence the level of resources agents that can already be considered capable robots. Wilcox redundancies. As a side effect active management might even et al. [33], for instance, developed the reconfigurable six- result in an overall cost-optimized system design, by reducing legged robot ATHLETE to support infrastructure build up on the mean redundancy level of the multi-robot system. planetary surfaces. Although Wilcox et al. [33] did approach Continuous optimization of an organization structure can automation of reconfiguration procedures, they did not develop also be found in Model of Organisation for multI-agent high-level planning approaches to fully exploit reconfigurabil- SystEms (MOISE+). Hubner,¨ Sichman, and Boissier focus ity. For similar capable robots reconfigurability focuses on the on a design pattern to control the reconfiguration process adaption of internal subsystems, e.g., the Scarab rover [2] is and identify key components. They outline an architecture able to adapt its locomotion platform. Reid et al. [22] show to continuously optimize an organization structure to achieve how to exploit this kind of reconfigurability with a dedicated main organization’s objectives. Objectives for a (sub)team can sampling-based (motion) planning approach after modeling the be defined as Hierarchical Task Network (HTN) in a so- reconfiguration space of the motion planning system. called scheme, which leads to the definition of a behavioural In the context of organization research outside of the pattern, e.g., they use playing soccer as primary example. robotics domain Dignum [12] looks at reconfiguration of orga- A reconfiguration process or rather transition from one team nizational processes involving humans. According to Dignum structure to another can be planned or unplanned: planned the general need to actively organize teams aims at increasing transitions can be triggered in a top-down fashion by an efficiency, and she sees flexible and adaptive organizations external operator, or they can be scheduled for a specific time. as suitable means to deal with dynamic environments. She Hubner,¨ Sichman, and Boissier require planned transitions to suggests that organizations conditionally adapt and should follow a previously defined and therefore static reorganization reorganize if this will lead to an increasing success of an pattern, while unplanned transitions have to be dynamically organization; even a suboptimal reorganization can be better controlled by agents. than no response at all. However, the question when to The reorganization process in MOISE+ itself requires form- reorganize and when to accept loss is left unanswered. ing a special, predefined group structure: one agent has to In Dignum’s work she points to strategic flexibility, a adopt the role of the so-called OrgManager in order to concept developed in the scope of managing high-technology organize the overall reconfiguration. The reconfiguration group industries by Evans [13]. Evans framework conceptualizes the also requires at least one agent to take over the Designer role, strategic use of a company’s or more generically a market in order to analyse the current status of the organizational player’s flexibility. Flexibility to adapt leads to a significant structure, and suggest a potentially better structure. competitive advantage, since it offers a market player addi- In the area of robotics Organisation Model for Adaptive tional means to encounter unforeseen events. Hence, adapta- Computational Systems (OMACS) is another approach for de- tion can directly lead to a greater probability of survival or signing an organization model presented by Deloach, Oyenan, net monetary benefit for market players. In his work Evans and Matson [11] and DeLoach [10]. The main concepts in [13] refers to proactive, reactive, defensive and exploitative OMACS are goals, roles, agents and capabilities. OMACS system capabilities and relates defensive one to robustness uses a capability-based representation for a role, i.e., a role and resilience. While robustness refers to a system which is defined by a set of capabilities. The quality of an agent’s 3 capability can be quantified using normalized values. In the B. Relation to Previous Work & Contribution same way DeLoach quantifies an agent’s ability to fulfill a role We base the results in this paper on the practical experience based on its capabilities. OMACS sets the main focus on the gained from working with multiple teams of reconfigurable quantification of the potential of abstract roles and agents to systems [7, 3, 24, 27]1. Furthermore, this work is part of contribute towards an organization’s success. The usage of this the planning approach developed with a special focus on information allows to optimize the team structure by allowing reconfigurable multi-robot systems [25, 23]. The contributions the best suited agent to handle a task, and thereby increases of this paper are: (i) detailing an organization model for re- the likelihood of an organization’s success. configurable multi-robot systems with focus on functionality- Similar to MOISE+, DeLoach suggests the use of behaviour based probability of survival, (ii) offering the open-source policies to control the cooperative behaviour of agents. In implementation of this model, and (iii) evaluating the trade-off OMACS an organization designer can explicitly define reorga- between safety, efficacy and efficiency for an exemplary space nization rules. For instance to specify if and how one agent can mission. replace another agent once the latter becomes unable to fulfil a role. An application of runtime reorganization has been shown C. Outline with three real robots, and a single laptop agent by Zhong and This paper takes a bottom-up approach in describing More- DeLoach [35]. Org. In Section II we first provide our revised formalization and terminology for reconfigurable multi-robot systems in- OMACS assumes atomic capabilities without composition, cluding atomic and composite agents. Section III extends the and the value normalisation to [0, 1] restricts the quantification, modeling and formalization to agent and organization proper- e.g., for a qualification of capability, to a single dimension. The ties and in particular how they can be generically inferred. quality of an agent’s capability has therefore (initially) unclear Redundancy is a special properties and quantified in this semantics, which limits the applicability of the approach in context with respect to required functionality. In Section IV practical applications. we provide details of our planning or rather optimization Our approach looks superficially very similar to MOISE+ approach for reconfigurable multi-robot systems that is based and OMACS with respect to exploiting a mapping between on MoreOrg. In Section V we describe an exemplary planning structure and function. However, MOISE+ as well as OMACS result and in Section VI we discuss the current state, open do this still on a higher level: MOISE+ simply defines challenges and give a critical review on our take on dealing the suitability of an agent to fill a role, while OMACS with reconfigurable multi-robot systems. already analyses agent capabilities. Both organization models fit loosely-coupled agent teams, but do neither take physi- II.RECONFIGURABLE MULTI-ROBOT SYSTEMS cal reconfiguration under resource constraints into account, This section provides the basic notation, definitions and the nor can they infer functionality of newly composed agents. underlying assumptions regarding reconfigurable multi-robot While MoreOrg takes a similar capability-based approach of systems. The notation builds on the formalisms found in coali- identifying an agent’s available functionality to OMACS, it tion games [32]. In particular, the agent-type representation is (a) derives this information dynamically from the available set based on the representations developed by Shrot et al. [26] of hardware and software resources, and thus permits inference and Ueda et al. [31]. of properties, (b) does not (yet) characterize the quality of a While reconfiguration affects hardware and software alike, function. Instead we estimate the probability of survival of a the focus of this work is on handling physical reconfiguration function based on the available resources. Neither MOISE+ of agents. The level of granularity is chosen correspondingly nor OMACS offer multi-agent planning, instead they allow to with the lowest level being a physical agent which cannot be control agent behaviour via predefined tasks. separated further into two or more physical agents. This agent is denoted by atomic agent. The robotic framework KnowRob [29] uses a semantic mod- elling approach and uses ontologies to represent the structure Definition (Atomic agent). An atomic agent a represents a of a robotic system to create a mapping between structure and monolithic physical robotic system. function. Beetz, Mosenlechner,¨ and Tenorth [4] exploit this Note that a physical agent representing an atomic agent still abstraction by defining plan templates for a single robot, which contains subsystems. They are, however, inseparable parts of can then be used to identify required functionality during plan the physical agent. execution. Definition ((Atomic) Agent pool). An agent pool A denotes In contrast to the existing robot modeling and planning a set of atomic atomic agents, such that A = {a1, . . . , a|A|}, approaches, MoreOrg can model a heterogeneous set of phys- is the set of all atomic agents, and a ∈ A or equiva- ically reconfigurable robots and infer agent as well as organi- lently {a} ⊆ A. A set of agents pools is denoted by zation properties. This permits an exploitation of superadditive A = {A1,...,A|A|}. effects and in parallel accounts for safety. To the best of our Connection interfaces are the key elements in reconfigurable knowledge none of the existing organization modeling and system and here, open the opportunity for combining two or planning approaches in robotics has covered these aspects so far. 1Field Trials Utah: https://www.youtube.com/watch?v=pvKIzldni68 4 more atomic agents. A composition from two or more atomic represented as a function γ : θ(A) → . The function GAd N0 agents is referred to as composite agent. The join operator γ maps an atomic agent type aˆ to the cardinality c of the GAd aˆ aˆ ∪ in the following definition for composite agents aligns well type partition of GAd, such that caˆ = |GA |. Equivalently to with the actual physical join operation of atomic agents and γ (ˆa) ≥ 1 the following notation will be used: aˆ ∈ GA, GAd d permits an intuitive representation. and aˆ 6∈ GA for γ (ˆa) = 0. d GAd Definition (Composite agent). A linked system of two or The reverse mapping from type GAd to the general agent more atomic agents is a set CA, which is denoted by is denoted by i(GAd) = GA. composite agent CA = a ∪...∪a = {a , . . . , a }, where i j i j A general agent type is also represented as a a , . . . , a ∈ A, |A| ≥ |CA| > 1. i j collection of tuples relating agent type and cardinality: Figure 2 illustrates the general approach to agent composi- {(ˆa0, caˆ ), (ˆa1, caˆ ),..., (ˆan, caˆ )}. tion as basis for superaddition, as explained with the following 0 1 n example: A mobile robot (atomic agent m) can share its power An agent pool can now be represented in two ways: (i) as set source with other robots, but it has no camera. After attaching of atomic agents as already introduced, or (ii) as general agent an unpowered atomic agent c which has one camera as a type Ab, such that ∀a ∈ A : γ (ˆa) = |Aaˆ|, where the latter subsystem, the composite agent {m, c} is equipped to take Ab offers a more compact representation and is used preferably images. It can now move to any location and take images - a in our implementation of the organization model. functionality neither of the atomic agents m or c provides. To execute robotic missions, atomic agents from an avail- able 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.

aˆ Fig. 2. An available set of atomic agents and a subset of composite agents Definition (Atomic agent role). An atomic agent role r that can be formed by combining different atomic agents (see [24, 27] for represents an anonymous agent instance of an atomic agent details on the real counterparts). From top left to right: (1) a rover with four type aˆ. 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 Given an overall set of atomic agents, various reconfig- robot with one male interface and (4) a star-wheeled robot with two male interfaces uration states of the overall systems are possible. These reconfiguration states result from forming different sets of Combinatorial explosion is one of the main challenges to composite agents, but always with the restriction of the overall deal with when considering a reconfigurable system with a available set of atomic agents. In the field of multi-agent large number of atomic agents. One means to reduce the systems and particularly characteristic function games (see effects of combinatorial explosion is typing. Agent typing [32]) this leads to so-called coalition structures. A coalition allows dealing with same typed agents using homogeneously structure represents the set of active atomic and composite formed partitions of an overall set of agents. agents that form a reconfigurable multi-robot system. Note that we will also use the term organization in order to describe Definition (Atomic and composite agent type). The type a reconfigurable multi-robot system represented by an agent of an atomic agent a is denoted by aˆ and equivalently pool A. for a composite agent CA the type is denoted by CAd. The set of all atomic agent types is denoted by θ(A) = Definition (Coalition structure). A coalition structure of an {1,..., |θ(A)|}, with the corresponding type-partitioned agent pool A is denoted by CSA and is represented by a 1 |θ(A)| 1 A sets of agent instances A ,...,A , where A = A ∪ set of disjunct general agents CS = {GA0, . . . , GAn}, |θ(A)| x ... ∪ A and A represents an agent pool containing where GA0 ∪ ... ∪ GAn = A, and i, j = 0, . . . , n, ∀i, j, i 6= only atomic agents of type x. j : GAi ∩ GAj = ∅. The concept of a (general) agent wraps the concepts of Composite agents result from the combination of atomic atomic and composite agents. Henceforth, the term agent is agents. We use the following definitions to separate the current equivalently used to the term general agent. (realized and physically assembled) set of general agents in a Definition (General agent). Any subset A0 ⊆ A, where coalition structure from the (virtual) set of agents, which can A0 6= ∅ forms a physical coalition is denoted by general be formed from the set of atomic agents. agent. A (general) agent has a corresponding atomic agent Definition (Operative and dormant agents). Let the current type partitioned set of agent instances A1,...,A|θ(A)|, state of a reconfigurable multi-robot system be described where A = A1 ∪ ... ∪ A|θ(A)|. by a coalition structure CSA. Then all general agents Definition (General agent type). The type of a (general) GA ∈ CSA are referred to as operative agents, and com- agent GA is denoted by GAd. A general agent type GAd is plementary, all general agents GA ∈ PA ∧ GA 6∈ CS are 5

referred to as dormant agents, where PA is the powerset Generally, two atomic agents can connect via multiple inter- of all atomic agents. faces. We assume, however, limited connectivity and currently The previous definitions look at a reconfigurable multi-robot do not consider geometrical constraints. This restriction allows system as a collection of agents, and consider pairing and us to focus on the identification of essential needs for modeling coalitions only at this level of modularity. A reconfigurable and automating of reconfigurable multi-robot systems. multi-robot system can form composite agents in different Assumption (Single link). A physical coupling between two ways depending upon the compatibility of interfaces. Hence, atomic agents can only be established through two and only to perform a detailed reasoning on connectivity of agents, we two compatible coupling interfaces. also have to account for the physical interfaces as subsystems In principle Definition II allows a single agent to have of an agent to analyze the feasibility of all agents. composite multiple types. However, we assume a single characterising agent. The scope of the presented formal description so far, is agent type. Meanwhile, one agent type can still inherit the based on a set-theory description and covers what is denoted properties of a parent type. agent space. Assumption (Single agent type). An agent can be mapped Definition (Agent space). Agent space denotes the set- to a single agent type only. theory based view to a reconfigurable multi-robot system without constraining the connectivity between any two Assumption (Agent type inheritance). An agent type can agents. inherit the properties of another agent type. Agent space is, however, only a restricted view onto link A key assumption, when dealing with an active exploitation space. of resource is the possibility to join the available resources of two or more agents. Hence, when two or more atomic agents Definition (Link space). Link space denotes a graph-based form a composite agent, they join their set of resources. In structure of a reconfigurable multi-robot system. In link principle, geometrical restrictions might apply to reuse the space a reconfigurable multi-robot system is represented by set of resources effectively. However, we initially assume that an undirected graph G = (V,E), where each vertex v ∈ V resources are shared without restriction within a composite maps to an atomic agent’s interface and an edge e = (u, v), agent. u, v ∈ V represents the existing connection between two interfaces. Assumption (Resource usage). A composite agent can reuse the subsystems of its composing atomic agents. The current modeling approach regarding link space ac- counts only for edges that represent electromechanical con- To enable resource sharing in a composite agent, various nections between agents as precondition for sharing resource ways of coupling two or more atomic agents can be con- in a composite agent. Data connections between software sidered, e.g., electromechanical or thermo-electromechanical. and hardware components as well as configuration options of We currently assume, however, that composite agents establish hardware and software components are currently left out in links between their composing atomic agents which permit our modeling approach. data, energy and power transmission. Assumption (Agent Linkage). Links which connect atomic agents in a composite agent permit transfer of data, energy A. Assumptions and power. A large spectrum of reconfigurable multi-robot systems To effectively exploit resources in redundant structure, the exists. Most often, fully distributed control approaches apply, following assumption is made: due to the use of swarm-based systems. The definition of the Assumption (Component substitution). To maintain the general agent already reflects one important design choice of functionality of an agent, one component can replace an- this work, which relaxes this apparent requirement for distri- other if it is an instance of the other’s class, which also bution. Instead of enforcing distributed control approaches at includes instances of subclasses. all system levels, centralized control approaches for locally autonomous and self-sustained operation of agents are per- This seems like a strong assumption, since even if com- mitted and feasible. This implicitly allows an atomic agent ponents are instances of the same concept, e.g., a camera, it to act as a temporary ’master’ in a master-slave architecture. might not be possible to substitute one with the other without When forming a composite agent, for instance, a single atomic loosing functionality. However, this is a matter of modeling agent in this formation acts as master, which is able to equivalence as part of the ontological design in MoreOrg. control all other attached atomic agents. In effect, each general agent represents a single-minded (collaborative) agent. The III.ORGANIZATION MODELLING distribution of the overall agent system is still maintained by We have developed the organization model MoreOrg2 to an appropriate design of the operational infrastructure. quantify the properties of a reconfigurable multi-robot system and provide cost measures for a reconfigurable multi-robot Assumption (Individual agent). Each atomic and composite agent comprises a central controller and thus represents an 2http://github.com/rock-knowledge-reasoning/ individual, single-minded agent. knowledge-reasoning-moreorg 6

Definition (Agent Type Property Value). The value function for an agent type Ab and a numeric property named np is denoted by pvalue(A,b 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 Fig. 3. The organization model is based on a hierarchical view and defined properties will likely be sufficient and needed for many corresponding property generation. Atomic agents come with (mainly) static properties assignments, while composite agents and overall organization standard robotic scenarios. Any missing properties can easily properties have to be dynamically derived from the active coalition structure. 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 com- system. The organization model permits a quantification of posite agents have to be inferred. Here, MoreOrg distinguishes system properties at different granularity levels and can char- between boolean and numeric properties (cf. Table II). acterize the active set of agents, i.e., the coalition structure 1) Boolean Properties: Boolean properties map to the of the organization by using a bottom-up approach. Figure 3 availability of particular capabilities and they can be inferred depicts the hierarchical decomposition of an organization from available combinations of functionalities and subsystems, which serves as baseline for MoreOrg’s reasoning approach. e.g., the functionality AutonomousNavigation is inferred from The coalition structure of a reconfigurable multi-robot system the availability of other capabilities and subsystems, here can change on-demand, which might involve creating and/or Locomotion, Mapping, MotionPlanning, SelfLocalization and removing one or more connection between atomic agents, a subsystem PowerSource. The boolean property has f(A,b f) but all agents can be characterized by their set of associated defines whether an agent A supports a functionality f or not. resources, i.e., hardware and software components. This boolean property enables selection mechanisms, e.g., to MoreOrg relies on ontologies to describe resources in gen- identify agents which have the functionalities to perform a eral and more specifically atomic agents and their associated particular tasks. functionalities and subsystems. All subsystems and atomic For atomic agents the inference of available functionality agents are characterized by data properties, e.g., MoreOrg is based on ontological reasoning and exploits available DL- focuses on a set of numeric data properties to enable mobile based reasoners, here Fact++ [30]. For composite agents, we transport agents (cf. [23] where we relate planning for recon- allow to quantify the support for a functionality by an agent’s figurable multi-robot systems to Vehicle Routing Problems). resources, so that the boolean property depends on the amount As a benefit of this ontological representation, Description of support: Logic (DL)-based reasoning can be applied and an agent’s ( available functionalities and properties can be inferred from its true if support(A,ˆ f) ≥ 1 has f(A,b f) = (1) composing set of resources or rather subsystems. Additional false otherwise reasoning mechanisms are applied to finally describe the organizational properties, where our focus is set on efficacy , where Ab is the agent type, f a functionality and support is and safety. The following subsections detail the organization defined in the following. model and its reasoning approach. 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]): A. Subsystem Properties ( 0 if cardmin(c, f) = 0 Subsystems are tightly bound to atomic agents and come support(A,b c, f) = , cardmax(c,Ab) otherwise with statically defined properties. All subsystems are at least cardmin(c,f) associated with a probability of survival to define their re- (2) liability. This is the basis for computing a safety measure where card and card return the minimum required for the overall multi-robot organization. The details of this min max and maximum available cardinality of resource instances (in- computation are provided in Section III-D. cluding instances of derived resource concepts), respectively. Accordingly, support of a functionality f with respect to a resource class c can be categorized as follows: B. Generic Agent Type Properties  0 no support MoreOrg provides a mechanism to defined agent properties  in a general way, such that composite agent properties can be support(A,b c, f) = ≥ 1 full support (3) derived from the atomic agents that form the agent. > 0 and < 1 partial support 7

TABLE I STATIC ATOMIC AGENT TYPE PROPERTIES (ADAPTEDFROM [23])

Property Syntax Description

velocity vnom(ba) nominal velocity of an agent type ba, |vnom| > 0 for mobile atomic agent types and vnom = 0 for immobile transport capacity tcap(ˆa) maximum total capacity of an agent of type aˆ to transport other agents transport consumption tcon(ˆa) number of storage units an agent of type aˆ consumes, when being transported by another agent (tcon is set to 1 for all agent types if not mentioned otherwise) transport load tload(a) current load transported by an atomic agent a, i.e., represents the consumed transport capacity of an agent power source capacity esourcecap(ˆa) power source capacity of an atomic agent in Ah supply voltage esupply(ˆa) electrical supply voltage of an atomic agent in V power consumption pw(ˆa) (electrical) power consumption of an agent of type aˆ

TABLE II INFERREDAGENTTYPEPROPERTIES

Property Syntax Description

has functionality has f(A,b f) boolean property, defines whether an agent of type Aˆ has functionality f. The truth value is inferred from the resource dependencies that are defined for f in the ontology. efficacy efficacy(A,b F) boolean property, defines whether an agent type Ab supports all function- alities in F or not

numeric property pvalue(A,b np) numeric property, value for an agent of type Ab and a property np reliability R(A,b F) numeric property, reliability ([0,1]) of an agent type Ab with respect to functionalities in F, based on resource redundancies operation cost ocost(A,b t) numeric property, here: total consumed power for an agent type Ab over time t

Support for a single functionality and subsequently for a set a) Selection Policy: A selection policy A0 = sel(A) of functionalities F is then defined as: permits to identify a subselection of atomic agents A0 from a (general) agent A according to defined criteria. It is built from support(A,b f) = min support(A,b c, f) , (4) 0 c∈C subselection policies which take the form: A = sel(A,... ). MoreOrg offers three basic subselection policies, which to where C is a set of resource concepts and ∀c ∈ C : build custom selection policies: cardmin(c, f) ≥ 1 to account only for relevant resource concepts, and 1. agent size-based selection: A0 = size sel(A, op, β), where support(A,b F) = min support(A,b f) (5) ∀A ∈ A0 : |A| op β with op ∈ {<, <=, >, >=, =} f∈F 2. functionality-based selection: A0 = func sel(A, f), where 2) Numeric Properties: Not all static numeric properties of ∀A ∈ A0 : has f(A,b f) atomic agents need to be directly assigned, since they can be 3. property-based selection: A0 = prop sel(A, op, np), where inferred from other properties, e.g., due to laws of physics. 0 ∀A ∈ A : A = opA∈A pvalue(A,b np), where op ∈ As an example available energy capacity (Wh) can be derived {argmax, argmin} from the capacity of the power source (Ah) and the supply voltage (V): By chaining basic selection policies according to f(A) ◦ pvalue(A, ecap) = g(A) = f(g(A)), custom selection policies can be defined pvalue(A, esourcecap) · pvalue(A, esupply) , in the ontology. The following example illustrates the policy where |A| = 1. MoreOrg allows to define these mathematical to identify all transport providers with maximum transport relationships between properties. This is done by annotating capacity in a composite agent: properties in the ontology and by using a simple Domain- specific Language (DSL) in combination with a math parser library 3. selTransportProvider(A) = To infer the value of numeric properties for composite random sel(A) agents, MoreOrg permits the definition of custom inference ◦ prop sel(A, argmax, tcap) rules. These rules are defined as higher-order functions, which ◦ size sel(A, =, 1) can be constructed from selection policies and composition ◦ func sel(A,TransportProvider) A operations. ◦ P , where PA is the powerset of all atomic agents in A and 3muParser: https://beltoforion.de/en/muparser random sel a tie-breaker function: 8

 ∅ if A = ∅  random sel(A) = randomly picked otherwise (6)  element from A The inverse selection policy is denoted by ¬sel(A) = A \ sel(A). 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 b) Composition operator: A composition operator for c 2:8. c(A, np, op) combines the numeric property values of all atomic agents that form an agent. Note that composition for parallel components, i.e., resources that are not strictly operators currently need to be hard-coded into the model. The required but which can serve as replacement: default supported operator is defined as: ( Qn X 1 − i=1(1 − pi(t)) parallel system c(A, np, +) = pvalue({aˆ}, np) , Rf (t) = Qn , (7) i=1 pi(t) serial system a∈A , where np is a numeric property. where pi(t) is the time-dependent probability of survival with c) Inference Rule: Both, composition operators and se- 0 ≤ pi(t) ≤ 1. While component degrading can be one reason lection policies can be combined to form an inference rule for for a change of the probability of survival, MoreOrg leaves composite agents, e.g., for all properties relating to locomo- the use of time-dependence as future improvement and instead tion, such as nominal velocity: uses a static probability of survival with t = 0. pvalue(A,b vnom) = Definition (Functional reliability). R(A,b F) denotes the c(selTransportProvider(i(Ab)), vnom, +) , which reliability of a set of required functionalities F which is maps to the vnom property value of the only available provided by an agent Ab. TransportProvider or 0 if there is none. The computation of R(A,b F) is based on the functional More complex inference is required to compute the (remain- decomposition of the agent type Ab into atomic resources. For ing) transport capacity: each resource a redundancy at component level (cf. [21]) is pvalue(A,b tcap) = assumed. As a heuristic the redundancy is computed based c(selTransportProvider(i(Ab)), tcap, +) on a type partitioning considering all resources which have - c(¬selTransportProvider(i(Ab)), tcon, +) no further dependencies. All resources of the same type are , where i(Ab) represents the reverse mapping from type to modeled as subsystems, which again form a serial system. agent. Figure 4 illustrates this modeling approach. For each subsystem which is composed of a single resource Inference rules are defined in the ontology, so that users can type the redundancy is computed for r required instances, n add their own rules. available instances and the probability of survival p for the resource type: C. Special Agent Type Properties ( n 1 − [1 − pr] r , where n ≥ r Some special agent properties exist, where in contrast to rsub(r, n, p) = (8) the generic agent type properties the reasoning mechanisms 0 otherwise are hard-coded into the model. The function req maps a set of functionalities F to the 1) Safety: In MoreOrg the computation of safety of an required number of instances for each resource type: agent is a special property motivated through the space ap- plication context. Safety is based on resource redundancy req(F) = {req1, . . . , req|req(F)|} , (9) under the assumption of possible component substitution (see Section II-A). The measure for redundancy is the central part where reqi represents the minimum cardinality of a resource of our safety heuristic and it is based on the standard modeling type i to fulfill all functionalities in F. approach for parallel and serial component-based systems (see The function avl maps an agent type to the number of [21]). Each resource can be associated with a probability maximum available resources with respect to a functionality of survival, so that an overall probability of survival can set F. Only resources that can contribute to the provision of be computed using a function decomposition tree approach. F need to be considered: Information about the probability of survival of components avl(A,b F) = {avl1, . . . , avl|req(F)|} , (10) should be derived from an initial system identification and is ideally updated with performance and degradation information where avli represents the maximum cardinality of a resource from the real system. type i available in the general agent type Ab. The reliability Rf , also referred to as probability of survival, Resources lead to a heuristic system structure as shown of a single functionality f can be computed by accounting in Figure 4 using serial and parallel systems. Based on 9

TABLE III This definition of efficacy illustrates our approach to use RESOURCESOFTHEAGENTTYPE SherpaTT WHICH ARE RELEVANT TO resource summation to actively exploit redundancies for the PROVISIONTHEFUNCTIONALITY LocationImageProvider. creation of functional systems. For efficacy only a sufficient component count is relevant, while the computation of the Resource reqi avli pi safety objective will take into account any excess resources. Localization 1 1 0.95 3) Operation Cost: Typically, robotic systems consume Locomotion 1 1 0.95 Mapping 1 1 0.95 electrical energy and MoreOrg additionally expects a definition PowerSource 1 1 0.95 of all agents nominal power consumption. Since we do not Camera 1 2 0.95 assume a homogeneous set of robots and might also operate in varying coalitions agents will have a varying power consump- tion. Therefore, operation time only is not an accurate cost this structure, an agent’s reliability with respect to a set of measure. Instead, MoreOrg uses the total energy consumption functionalities is defined as: of a reconfigurable multi-robot system as cost measure. |req(F)| Power consumption can vary over time with the type of Y R(A,b F) = rsub(reqi, avli, pi) , (11) activity, but MoreOrg assumes a constant power consumption i=1 of all operative atomic agents and leaves a more sophisticated where pi represents the probability of survival for a resource estimation, e.g., based on a functionality-based power con- type i. sumption model, as future enhancement. MoreOrg estimates Example: Before introducing this example note that func- the operation cost as total consumed energy for all agents tionalities can dependent upon other functionalities or re- based on the nominal power consumption: sources. Hence, an availability of functionality f1 might imply X ocost(A,b t) = γ (ˆa)(pw(ˆa) · t) the availability of a functionality set F1 = {f1, f2, f3}, where Ab aˆ∈A f2 and f3 are direct dependencies of f1. In this example a func- b tionality LocationImageProvider depends on a functionality ImageProvider and a functionality MoveTo. The requirements D. Organization Properties for the ImageProvider are one of each resource: Camera In contrast to atomic and composite agents, an organization and PowerSource. MoveTo requires one of each resource: property can differ in its structure, i.e., might change its Localization, Locomotion, Mapping, PowerSource. coalition structures over time. Therefore we describe here Table III lists the cardinalities and probabilities of survival the coalition structure properties of a reconfigurable multi- for an atomic agent type SherpaTT with relevant resources. robot system, as well as the cost to change between coalition This agent type provides the functionality LocationImage- structures. Provider with a redundant camera system, and otherwise a 1) Coalition Structure Properties: series system. According to Equation 11 the probability of a) Goal Dependant Reliability: The organizational struc- survival for the functionality LocationImageProvider is: ture intends to support activities of its member agents that P = (1 − (1 − 0.95)2) · 0.954 ≈ 0.81 help to achieve and maximize the shared organizational goals. Agents can operate in parallel at different physical loca- A composite agent which has an additional atomic agent tions. The objective for an active coalition structure CS = PayloadBattery can increase the redundancy of the resource {GA1, . . . , GA|CS|} of an organization is therefore described PowerSource by 1. This leads to an increase of the probability by a corresponding set of functionality sets denoted FS = of survival for the functionality LocationImageProvider, since {F1,... F|CS|}, and a2f : CS → FS allows to map each now two redundant subsystems exist: operative agent GAi to the required functionality set Fi. The P = (1 − (1 − 0.95)2)2 · 0.953 ≈ 0.85 current redundancy of the organization is then the minimum achievable level of redundancy: 2) Efficacy: Efficacy in the context of MoreOrg describes the ability of a reconfigurable multi-robot system to provide R(CS, F S) = min R(A,b a2f(A)) (13) A∈CS a particular functionality. To measure an agent’s efficacy an objective has to be given, here as a set of required function- Note that this computation is not used in the planning alities. The identification of efficacy leads only to a binary approach, but will be used in the future to identify coalition result: either the organization supports the given functionality structures with critically unbalanced resource distribution. or not. b) Efficacy: The efficacy of an organization’s current The definition of support can be viewed as an analysis coalition structure is computed from all operative agents’ of the redundancy level of components with respect to a efficacy: required set of functionalities. The bottom-up definition of efficacy(CS, F) = min efficacy(A,b F) (14) functionality support, eventually leads to the definition of an A∈CS agent’s efficacy: Here, all operative agents in a coalition structure need to ( support the functionalities in F. 1 support(A,b F) ≥ 1 efficacy(A,b F) = (12) Note, that MoreOrg implements the optimal coalition struc- 0 otherwise ture generation algorithm developed by Rahwan et al. [20] to 10 search for a coalition structure where efficacy(CS, F) = 1. atomic agents to composite agents in order to support required This optimisation approach is used, e.g., to validate the feasi- functionalities. bility of a transition of a set of agents between two locations. We implemented the planner Temporal Planning for Recon- Since only mobile agents can relocate, a coalition structure is figurable Multi-Robot Systems (TemPl) [23] to address the required such that efficacy(CS, {MoveT o}) = 1. constraint-based planning problem for reconfigurable multi- 2) Operation Cost: Reconfiguration of an organization con- robot systems. This planner uses MoreOrg as organization tributes to operation cost, since transitions between coalition model, but adds a temporal and spatial dimension to problem structures require time and energy. The time to transition from definitions. one coalition structure CSA to another CSA when CSA 6= i j i Definition (Spatio-temporal requirement). A spatio- CSA is therefore estimated with a heuristic function. The j temporal requirement is represented as a spatio-temporally heuristic firstly assumes basic cost for the number of atomic qualified expression s, which describes the functional agents which are involved in the reconfiguration. Secondly, requirements and agent instance requirements for a additional and significantly higher cost arise from the need time-interval and a location: to coordinate multiple agents to exchange atomic agents or to merge. Therefore, the reconfiguration cost function to form s = (F, Abs)@(l, [ts, te]), a single agent from an existing coalition structure takes into account the number of general agents, equal to the partitions where F is a set of functionality constants, Abs is the general of the coalition structure CS, and the total number of involved agent type representing the required agent type cardinalities, atomic agents: l ∈ L is a location variable, and ts, te ∈ T are temporal variables describing a temporal interval with the implicit ρ(GA, CS) = ta · |CS| + tb · |GA| , (15) constraint ts < te. Each spatio-temporal requirement represents a persistence where ta and tb are heuristic time constants. Robotic exper- iments are required to establish a realistic estimate for the constraint, i.e., the requirements have to hold throughout the magnitude of these parameters. Our real world experiments time interval. The mission specification allows to relate spatio- give an indication for these parameters for small teams, so temporal requirements to the organization model which defines agent types and functionalities along with the associated that a default setting of ta = 600 s and tb = 100 s applies. The values are estimates which consider time for additional properties. error handling. The overall reconfiguration cost to transition Definition (Mission). A robotic mission is a tuple M = A A from a coalition structure CSi to another CSj is defined as: hA,b ST R, X , OM,T,Li, where the general agent type Ab X describes the available agent types, STR is a set of spatio- ρ(CSA,CSA) = ρ(GA, CSA) (16) i j i temporally qualified expressions, X is a set of constraints, GA∈CSA j OM represents the organization model (here MoreOrg as Note that the reconfiguration cost heuristic does not account described in Section III), T is the set of timepoints and L for relocation cost. Instead we assume that all agents taking the set of locations. part in a reconfiguration process operate in direct proximity. Thus, this heuristic penalizes an involvement of an increasing A. Mission Constraints number of agents to extract a new one. The first term penalizes Constraints in X can refer to spatio-temporally qualified the total number of involved independent agents to form a new expressions and the initial state of a mission is defined by the agent with; each additional agent increases communication and earliest timepoint and binds available agents to their starting coordination cost, as well as the likelihood for failures. The depot. The earliest timepoint is t ∈ T and ∀t ∈ T, t 6= second term accounts for the fact, that only a selected set of 0 t : t > t . Note that this planning approach neither requires atomic agents is involved in a reconfiguration - the fewer the 0 0 a single starting location for all agents nor a single final better. destination. An example for a mission is given in Table VIII. a) Temporal Constraints: Temporal constraints are listed IV. EXPLOITATION OF REDUNDANCIES in Table IV. They allow to defined the temporal relation To exploit reconfigurable multi-robot systems we use a between spatio-temporal constraints in a relative and absolute constraint-based mission planning approach. Constraints allow manner. to define the essential characteristics of a potential solution, b) Model Constraints: TemPl implements a subset of by letting a user specify task requirements. The collected feasible (meta-)constraints (see Table V). Model constraints constraints then define a partial-ordered plan for which a set requirements for agent types and agent roles. They al- suitable full solution has to be found by translating the low bounding the cardinality of agent types so that the mission requirements to an agent allocation and constellation combinatorial search problem can be limited according to problem. Agent allocation here means, that the exact orga- a least-commitment principle. Equality constraints allow to nization structure and its development over time throughout restrict agent routes partially or even completely. Requiring a mission is initially unknown. What is known apart from the minimum equality of a single agent type over the full the given constraints, however, are the total available atomic mission defines the full route for a single atomic agent of this agents, their associated resources and the model to combine type. Thereby, modelling constraints allow to detail a mission. 11

TABLE IV TEMPORALCONSTRAINTSFORAMISSION M = hA,b ST R, X , OM,T,Li.

Name Syntax Description

temporal relation htn, REL, tmi tn and tm are qualitative timepoints and REL is the set of permitted relations, so that REL ⊆ {<, >, =} [9] min duration minDuration(tn, tm, d) sets a lower bound for the duration of a time interval: tn − tm ≥ d, + where tn and tm are two qualitative timepoints d ∈ R ; implies the qualitative relationship tn > tm max duration maxDuration(tn, tm, d) sets an upper bound for the duration of a time interval: tn − tm ≤ d, + where tn and tm are two qualitative timepoints d ∈ R ; implies the qualitative relationship tn > tm

In general, constraints apply to the dimensions space, time, approach used by Wurm et al. [34] to estimate the cost based agent types, and roles. on the travel time between two locations. We suggest to use c) Functionality & Property Constraints: Agents either nominal speed vnom as default property for atomic agents, so comprise a functionality or they do not. In effect, functionality that based on this information a duration estimate for location is requested with a maximum cardinality of one, which makes changes of mobile agents can be computed. As long as no the introduction of a maximum function constraint unneces- better estimation or other routing constraints are available, the sary. Note that this is a limitation of the current modelling line-of-sight distance between two locations is still the basis approach. However, the property of a agent providing a for the cost computation. particular functionality can be of importance, and the use of Parameter β controls the penalty for missions that can only property constraints allows to narrow applicable agents. be partially fulfilled, here the heuristic assumes that each requirement is of equal importance. Future approaches should also take a priority into account. B. Planning and Optimization The preference of safer operations and thus agents with The (high-level) optimization problem for a given mission higher redundancy is control via . In principle, a high negative M can be stated as: value of  leads to a preference for a solution with a single, minimize cost(M∗, M) yet highly redundant agent that can solve the mission. M∗ For the search for an optimal transition between coalition subject to STR and X structures it has to be considered, that due to a high degree of redundancy a safer coalition structure might lead to lower , where efficiency. Therefore, any optimization has to trade safety and STR spatio-temporal requirements efficiency against each other and can lead only to a pareto- X mission constraints optimal solution. ∗ M solution to mission M C. Algorithm ∗ ∗ cost(M , M) = αE(M ) To tackle the given optimization problem one or more solu- + βSAT (M∗, M) tions for a given mission have to be identified. Due to the need + SAF (M∗, M) for various possible mappings between required functionality and satisfying agents, the problem cannot be directly solved in The multi-objective cost function is based on the heuristics a classical form, e.g., with Linear Programming. The problem listed in Table VII, and can be evaluated as soon as a solution needs to be transformed with the help of the MoreOrg, so that for a mission exists. existing optimization approaches can be combined to perform The three objectives are presented in the cost function: local optimization, here combinatorial optimization, coalition efficiency through the energy cost function, efficacy through structure optimization and min-cost flow multi-commodity checking the level of fulfillment, and safety as a redundancy flow via Linear Programming. dependent survival metric; for balancing the parameters α, β The basic algorithm that we are currently using is illustrated and  can be used. Note that safety and fulfillment have a in Figure 5. We will outline the general approach and refer to value range [0, 1], so that α should account for normalization [23] for further details. The algorithm involves a generation to [0, 1] for the energy cost; α therefore comprises a factor candidate generation, which accounts for major constraints −1 Emax, where Emax is the maximum energy cost which is but not all required ones. Only after candidate optimization either the allowed one or is extracted from existing mission and subsequent characterization it will be known whether solutions. The latter is done for our evaluation in Section V. the suggested solution candidate is feasible, i.e., whether The importance of operation cost is controlled via α, a the resulting quantitative temporal network is consistent and higher value will lead a preference of missions which require whether required reconfigurations and location transitions can less energy. The time of an agent’s operation depends upon be performed. Since we also permit partial solutions, i.e. effi- estimated travel cost, time for the actual requested operation cacy < 1, feasibility does not necessarily imply that all spatio- or task, and time for reconfiguration. Our approach extends an temporal requirements of a mission are satisfied, but only that 12

TABLE V MODELCONSTRAINTS, WHERE S ⊆ STR AND Abs REPRESENTSTHEGENERALAGENTTYPEREQUIREMENTOF s ∈ S.

Name Syntax Description min cardinality minCard(S, a,ˆ c) Minimum cardinality constraint ∀s ∈ S : γ (ˆa) ≥ c, where c ≥ 0 Abs max cardinality maxCard(S, a,ˆ c) maximum cardinality constraint corresponding to minCard so that ∀s ∈ S : γ ≤ c, where c ≥ 0 Abs all distinct allDistinct(S, aˆ) ∀s ∈ S : T Aaˆ = ∅ s min distinct minDistinct(S, a,ˆ n) ∀s , s ∈ S, i 6= j : |Aaˆ | − |Aaˆ | ≥ n, where n > 0 i j si sj max distinct maxDistinct(S, a,ˆ n) the equivalent maximum constraint to minDistinct, so that

∀s , s ∈ S, i 6= j : |Aaˆ | − |Aaˆ | ≤ n, where n ≥ 0 i j si sj min equal minEqual(S, Ar) minimum existence of the same agent roles so that Aeq = T 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 = T 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)

TABLE VI FUNCTIONALITYANDPROPERTYCONSTRAINTS.

Name Syntax Description min function minF unc(s, f) functionality f to be available at spatio-temporal requirement (str) s ∈ STR, so that f ∈ F s, where F represents the functionality requirements associated with s min property minP rop(s, f, p, n) constrain the numeric property pf of a functionality f to be pf ≥ n, where n ∈ R and minP rop(s, f, p, n) implies that minF unc(s, f) holds max property maxP rop(s, f, p, n) equivalent maximum property value constraint to minP rop(s, f, p, n), so that property pf ≤ n, n ∈ R

and ψ¬m. The default is ψm = 0 and ψ¬m = 0, which means, that a set of mutually-exclusive requirements only get the min- imum needed resources to resolve their conflict: the parameters ψm 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

Fig. 5. Planning with TemPl uses a constraint-based solution candidate For an experimental evaluation of the planning approach we generation, where each candidate is characterized according to the mission look at a simulated space mission, which has been outlined by objectives. 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 the activities that are part of the suggested solution can be cast into a respective mission specification which is listed in performed. Generating solution candidates with an efficacy Table VIII. Note that each location is defined by longitude and < 1 (a) accounts for a future prioritization of requirements, latitude in the specification; TemPl uses Mercator projection and (b) permits the identification of pareto-optimal solutions to convert these into Cartesian coordinates. A corresponding with respect to safety, efficacy and efficiency. subsection of a solution found by TemPl is shown in Figure 6. Initially the planner aims at generating a resource efficient With respect to the safety measure the starting assignment is solution, by reducing the number of involved agents. It does ignored by assuming a probability of survival of 1.0. This is so by bounding the number of agents that are assigned to done to avoid an initial bias of the safety objective. To compute mutually-exclusive requirements through two parameters: ψm the safety objective only relevant spatio-temporal requirements 13

TABLE VII HEURISTIC COST COMPUTATION ON THE SOLUTION M∗ FORAMISSION M (ADAPTEDFROM [23])

Name Syntax Description distance d(a, M∗) traveled distance of an agent a in M∗ operation time op(a, M∗) time horizon of the mission; any location change introduces a lower bound ∆tmin for time intervals by assuming a traversal with the d(a,M∗) mobile agent’s nominal velocity vnom(ˆa), i.e., ∆tmin ≥ vnom(ˆa) ∗ ∗ P ∗ energy E(M ) E(M ) = a∈A ocost(ˆa, op(a, M )) as overall consumed energy per mission, by summing the consumed energy per agent a to perform M∗; ∗ ∗ ∗ safety SAF (M , M) SAF (M , M) = mins∈STR R(As , Fs), where R denotes the functional reliability function (see Section III-C) , Fs is the required ∗ functionality to satisfy s and As the available and assigned agent in mission solution M∗. ∗ ∗ 1 P ∗ fulfilment SAT (M , M) SAT (M , M) = |STR| s∈STR sat(s, M ) represents the ratio of fulfilled requirements, where ( 0 if constraint s is not satisfied in M∗ sat(s, M∗) = 1 if constraint s is satisfied in M∗

are analyzed. Hence, agents which are available at a space time of the reconfigurable system, improved solutions can be found point, but are not actually required there (represented with gray for application scenarios where safety might be an issue. colored boxes in Figure 6) do not affect the safety objective (see for instance location b6, timepoint t5). VI.CONCLUSION TemPl has been used to search for solutions to this mission This paper has outlined a modeling approach for reconfig- scenario with a setting of ψ¬m = 0 and ψm in the range of 0 urable multi-robot systems, which permits an active exploita- to 2. The search has been split into epochs with a maximum tion of redundancies in multi-robot systems through physical allowed planning time of 60 s. After 60 s search has been reconfiguration. The current approach does only moderately reinitialized in order to escape from local minima. Planning influence the level of redundancy in systems that are taking has been stopped either after memory has been exhausted or part in a robotic mission. This is mainly due to the complexity when the total planning time of 20 min was exceeded (Intel of the planning problem as result of exponentially many i7-4600Um 12 GB RAM). A higher setting of ψm requires reconfiguration options. It led us to use several heuristics additional agents to be used for the planning approach, so a and initially target resource efficient solutions. Clearly, this higher computation time per solution is to be expected. Note model might still not lead to solutions which are sufficiently that while the setting with ψm = 0 resulted in a stable range good from a safety perspective, but it offers a basis for an below 4 s per solution candidate, the required computation automated use of reconfigurable multi-robot systems and an time per solution increases for ψm = 2 to up to 12 s - in optimization strategy for organizational safety properties. Our combination with the total planning time this explains the deliberate planning approach can give an advantage compared lower number of solutions found for higher settings of ψm. to reactive reorganization strategies found in swarm-like sys- The comparison of solutions based on efficacy, efficiency and tems by avoiding dead-end configurations. Meanwhile a hybrid safety is shown in Figure 7 with additional details provided approach could be foreseen in a real application. Furthermore, in Figure 8. we plan to augment already found solutions by explicitly What can be seen is that the expected increase in redun- routing available or rather unused agents along the critical path dancy, due to the higher setting of the parameter ψm leads to of a mission. This can be done without replanning until the solution candidates with a consistently higher safety objective. known transport lines, which are established through mobile This shows that ψm is an effective control parameter. By agents, are exhausted. It comes, however, again at the cost of using an exemplary trade off setting for the cost function with efficiency. α = −1, β = 100.0, and  = 10.0 we can extract the solutions The existing heuristics are based on assumptions and a characteristics. The black star-shaped marks indicate the best limited set of practical experiments. As such they can clearly solutions according to the weights of the objective function. be interpreted as a weakness of the modelling approach. The While safety can be increased from below 0.7 to approx. 0.75 given heuristics shall, however, serve as basis and examples to for solutions with efficacy of 1, the efficiency deteriorates, develop better approaches to with reconfigurable multi-robot although only slightly for ψm = 2 compared to ψm = 0. systems. As such they firstly point to the need / benefit for a This analysis shows only an exemplary solution landscape, submodel, and secondly act as placeholders. All submodels but at the same time the working of our modeling and planning and heuristics are subject of continued improvements and approach for reconfigurable multi-robot system capabilities. efforts to detail the model further. Probability of survival, for Our evaluation confirms that by increasing the options for instance, as it is used and presented in this paper acts as a agent assignments and at the same time the level of redundancy placeholder for more sophisticated metrics, e.g., some which 14

TABLE VIII AN EXEMPLARY OUTLINE OF A SPACE EXPLORATION MISSION FOR A TEAM OF RECONFIGURABLE ROBOTS.

GAd ={(BaseCamp, 5), (CREX, 2), (CoyoteIII, 3), (P ayload, 16), (SherpaT T, 3)}  STR = ({(BaseCamp, 5), (CREX, 2), (CoyoteIII, 3), (P ayload, 16), (SherpaT T, 3)})@(lander, [t0, t1]),

(∅, {(P ayload, 3)})@(lander, [t5, t10]), ({LocationImageP rovider, EmiP owerP rovider}, {(P ayload, 3)})@(b1, [t2, t3]), (∅, {(P ayload, 1)})@(b1, [t3, t14]), ({LogisticHubP rovider, LocationImageP rovider, EmiP owerP rovider}, {(P ayload, 3)})@(b2, [t2, t3]), (∅, {(BaseCamp, 1)})@(b1, [t4, t7]), ({LocationImageP rovider}, {(P ayload, 3)})@(b4, [t6, t7]),

(∅, {(P ayload, 3)})@(b4, [t8, t9]), (∅, {(P ayload, 1)})@(b6, [t10, t14]), (∅, {(P ayload, 3)})@(b7, [t12, t14])

X ={t0 < t1, . . . , t13 < t14} OM ={¬mobile(BaseCamp), mobile(CREX), tcap(CREX) = 2, mobile(CoyoteIII), tcap(CoyoteIII) = 4, ¬mobile(P ayload), mobile(SherpaT T ), tcap(SherpaT T ) = 10,...}

T ={t0, . . . , t14} L ={lander = (lat : −83.82009, long : 87.53932, moon), b1 = (lat : −84.1812, long : 87.60494, moon),

b2 = (lat : −83.96893, long : 86.75471, moon), b3 = (lat : −83.66856, long : 87.42557, moon), b4 = (lat : −83.54570, long : 87.09851, moon), b5 = (lat : −83.82009, long : 84.66000, moon), b6 = (lat : −83.77371, long : 84.70960, moon), b7 = (lat : −83.34083, long : 84.64467, moon) }

Fig. 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). 15

Fig. 7. Solution landscape compared for different bound settings. Black star-shaped markers identify the current local best solutions where the cost function is parameterized with α = 1.0, β = −100.0,  = −10.0. The results for each setting of ψm (efficiency, safety) are: ψm = 0: (2198.25 kWh, 0.674), ψm = 1: (3489.5 kWh, 0.754), ψm = 2: (2376.11 kWh, 0.747) are based on extensive empirical studies and specifications of Ministry of Education and Research under grant agreement subsystems. Furthermore, we plan to define safety not only 01IW18003. The continued development has been supported through spatio-temporal requirements, but instead adapt the by the Federal Ministry for Economic Affairs and Energy model to reflect the risks resulting from reconfiguration, idling under grant agreement 50RA1701. The author would like to and relocation. Since a solution is characterized after all agents thank all contributors who helped to realize the multi-robot have been assigned, a dedicated models, e.g., for component team in the project TransTerrA. degradation and reconfiguration errors can be taken in account to improve the safety measure. We are also interested in using REFERENCES graph and network analysis techniques such as percolation [19] [1] Jose´ Baca et al. “ModRED: Hardware design and recon- in combination with replanning to test the options to respond figuration planning for a high dexterity modular self- to system failures. reconfigurable robot for extra-terrestrial exploration”. Reconfigurable multi-robot systems combine the benefits of In: Robotics and Autonomous Systems 62.7 (July 2014), modular robots with capable robotic systems, and we see sig- pp. 1002–1015. ISSN: 09218890. DOI: 10.1016/j.robot. nificant potential in developing further strategies and planning 2013.08.008. approaches. An automated exploitation will give designers of [2] Paul Bartlett, David Wettergreen, and William (Red) L robotic mission a new degree of freedom. Still, significant Whittaker. “Design of the Scarab Rover for Mobility practical challenges remain to exploit reconfiguration with real and Drilling in the Lunar Cold Traps”. In: 8th Inter- robots: increasing the reliability of all involved atomic agents national Symposium on Artificial Intelligence, Robotics is one challenge, and establishing reliable reconfiguration and Automation in Space (i-SAIRAS 2008). Hollywood, maneuvers is another. We do, however, outline here a feasible LA, USA, Feb. 2008. approach towards modeling and multi-objective planning for [3] Sebastian Bartsch et al. “Performance Evaluation of an such systems. Heterogeneous Multi-Robot System for Lunar Crater Exploration”. In: 10th International Symposium on Ar- ACKNOWLEDGMENT tificial Intelligence, Robotics and Automation in Space This work has been supported by the German Space Agency (i-SAIRAS). ESA, 2010, pp. 30–37. (DLR Agentur) with federal funds of the Federal Ministry [4] Michael Beetz, Lorenz Mosenlechner,¨ and Moritz of Economic Affairs and Energy for the project TransTerrA Tenorth. “CRAM: A Cognitive Robot Abstract Machine under grant agreement 50RA1301 to implement the initial for everyday manipulation in human environments”. In: planning approach. The continued evaluation and application 2010 IEEE/RSJ International Conference on Intelligent in the project Q-Rock has been supported by the Federal Robots and Systems. IEEE, Oct. 2010, pp. 1012–1017. 16

(a) Analysing efficiency with respect to efficacy.

(b) Analysing safety with respect to efficacy.

(c) Efficiency with respect to safety, where efficacy = 1.0. Fig. 8. Analysing the solution landscape of the space mission with respect to the optimization objectives. 17

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