Interaction in Human-Robot Societies

As robots evolve into an integral part of the human ecosystem, humans and robots are getting involved in a multitude of collaborative tasks that require complex coordination and cooperation. Indeed there has been extensive work in the robotics, planning as well as the human-robot interaction communities to understand and facilitate such seamless teaming. However, it has been argued that their increasing participation as independent autonomous agents in hitherto human-habited environments has introduced many new challenges to classical human-robot teaming scenarios. When robots are deployed with independent and often self-sufficient tasks in a shared workspace, teams are often not formed explicitly and multiple teams cohabiting an environment interact like colleagues rather than traditional teammates. In this paper, we formalize these differences and analyze metrics to characterize autonomous behavior in such human-robot cohabitation settings. Robots are increasingly becoming capable of performing daily tasks with accuracy and reliability, and are thus getting integrated into different fields of work that were until now traditionally limited to humans only. This has made the dream of human-robot cohabitation a not so distant reality. We are now witnessing the development of autonomous agents that are especially designed to operate in predominantly human-inhabited environments often with completely independent tasks and goals. Examples of such agents would include robotic security guards like Knightscope, virtual presence platforms like Double and iRobot Ava, and even autonomous assistance in hospitals such as Aethon TUG. Indeed there has been a lot of work recently in the context of “human-aware” planning, both from a point of view of path planning (Sisbot et al. 2007; Kuderer et al. 2012) and task planning (Koeckemann, Pecora, and Karlsson 2014; Cirillo, Karlsson, and Saffiotti 2010), with the intention of making the robot’s plans socially acceptable, e.g. resolving conflicts with the plans of fellow humans. Even though all of these scenarios involve significantly different levels of autonomy from the robotic agent, the underlying theme of autonomy in such settings involve the robot achieving some sense of independence of purpose in so much as its existence is not just defined by the goals of the humans around it but are rather contingent on tasks it is supposed to be achieving on its own. Thus the robots in a way become colleagues rather than teammates. This becomes even more prominent when we consider interactions between multiple independent teams in a human-robot cohabited environment. We thus postulate that the notions of coordination and cooperation between the humans and their robotic colleagues is inherently different from those investigated in existing literature on interaction in human-robot teams, and should rather reflect the kind of interaction we have come to expect from human colleagues themselves. Indeed recent work (Chakraborti et al. 2015a; Chakraborti et al. 2015b; Talamadupula et al. 2014) hints at these distinctions, but has neither made any attempt at formalizing these ideas, nor provided methods to quantify behavior is such settings. To this end, we propose a formal framework for studying inter-team and intra-team interactions in human-robot societies, and outline metrics that are useful for evaluating performance of autonomous agents in such environments. 1 Human Robot Cohabitation At some abstracted level, agents in any environment can be seen as part of a team achieving a high level goal. Consider, for example, your university or organization. At a micro level, it consists of many individual labs or groups that work independently on their specific tasks. But when taken as a whole, the entire institute is a team trying to achieve some higher order tasks like increasing its relative standing among its peers or competitors. So in the discussion that follows, we talk about environments, and teams or colleagues acting within it, in the context of the goals they achieve. 1.1 Goal-oriented Environments Definition 1.0 A goal-oriented environment is defined as a tuple E = 〈F,O,Φ,G,Λ〉, where F is a finite set of first order predicates that describes the environment, and O is the finite set of objects in the environment, Φ ⊆ O is the set of agents, G = {g | g ⊆ FO} 1 is the finite set of goals that these agents are tasked with, and Λ ⊆ O is the set of resources in the environment that are required by these agents to achieve these goals. Each goal has a reward R(g) ∈ R associated with it. These agents, goals and resources are, of course, related to each other due to the definition of their tasks, and these SO is S ⊆ F instantiated or grounded with objects from O. relationships determine the nature of their involvement in the environment, i.e. in the form of teams or colleagues. Before we formalize such relations, however, we will like to look at the way the agent models are defined. We use PDDL (Mcdermott et al. 1998) style agent models for the rest of the discussion, as described below, but most of the discussion easily generalizes to other modes of representation. The domain model Dφ of an agent φ ∈ Φ is defined as Dφ = 〈FO, Aφ〉, where Aφ is a set of operators available to the agent. The action models a ∈ Aφ are represented as a = 〈Na,Ca,Pa,Ea〉 where Na denotes the name of the action, Ca is the cost of the action, Pa ⊆ FO is the list of pre-conditions that must hold for the action a to be applicable in a particular state S ⊆ FO of the environment; and Ea = 〈eff(a), eff−(a)〉, eff±(a) ⊆ FO is a tuple that contains the add and delete effects of applying the action to a state. The transition function δ(·) determines the next state after the application of action a in state S as δ(a, s) = (s \ eff−(a)) ∪ eff(a). A planning problem for the agent φ is given by the tuple Πα = 〈F,O, Dφ, Iφ,Gφ〉, where Iφ ⊆ FO is the initial state of the world and Gφ ⊆ FO is the goal state. The solution to the planning problem is an ordered sequence of actions or plan given by πφ = 〈a1, a2, . . . , a|πφ|〉, ai ∈ Aφ such that δ(πφ, Iφ) |= Gφ, where the cumulative transition function is given by δ(π, s) = δ(〈a2, a3, . . . , a|π|〉, δ(a1, s)). The cost of the plan is given by C(πφ) = ∑ a∈πφ Ca. We will now introduce the concept of a super-agent transformation on a set of agents that combines the capabilities of one or more agents to perform complex tasks that a single agent might not be able to do. This will help us later to formalize the nature of interactions among agents. Definition 1.1 A super-agent is a tuple Θ = 〈θ,Dθ〉 where θ ⊆ Φ is a set of agents in the environment E , and Dθ is the transformation from the individual domain models to a composite domain model given by Dθ = 〈FO, ⋃ φ∈θ Aφ〉. Definition 1.1a The planning problem of a super-agent Θ is similarly given by ΠΘ = 〈F,O, Dθ, Iθ,Gθ〉 where the composite initial and goal states are given by Iθ = ⋃ φ∈θ Iφ and Gθ = ⋃ φ∈θ Gφ respectively. The solution to the planning problem is a composite plan πθ = 〈μ1, μ2, . . . , μ|πθ|〉 where μi = {a1, . . . , a|θ|}, μ(φ) = a ∈ Aφ ∀μ ∈ πθ such that δ(Iθ, πθ) |= Gθ, where the modified transition function δ′(μ, s) = (s \ ⋃ a∈μ eff −(a)) ∪ ⋃ a∈μ eff (a). We denote the set of all such plans as πΘ. The cost of a composite plan is C(πθ) = ∑ μ∈πθ ∑ a∈μCa and π∗ θ is optimal if δ (Iθ, πθ) |= Gθ =⇒ C(π∗ θ) ≤ C(πθ). The composite plan can thus be viewed as a union of plans contributed by each agent φ ∈ θ so that φ’s component can be written as πθ(φ) = 〈a1, a2, . . . , an〉, ai = μi(φ) ∀ μi ∈ πΘ. Now we will define the relations among the components of the environment E in terms of these agent models. Definition 1.2 At any given state S ⊆ FO of the environment E , a goal-agent correspondence is defined as the relation τ : G → P(Φ); G,Φ ∈ E , that induces a set of super-agents τ(g) = {Θ | ΠΘ = 〈F,O, Dθ, S, g〉 has a solution, i.e. ∃π s.t. δ(π, S) |= g}. In other words, τ(g) gives a list of sets of agents in the environment that are capable of performing a specific task g. We will see in the next section how the notions of teammates and colleagues are derived from it. Similarly, we define a goal-resource correspondence to denote resources in the environment required to complete a given task by a specific super-agent. The discussion of interaction between teammates and colleagues will later derive from it. We use the concept of landmarks (Porteous, Sebastia, and Hoffmann 2001) in establishing this mapping. Informally, given a problem instance, landmarks are states that must be visited in order to achieve a goal. Definition 1.3 A goal-resource correspondence is a relation Γ : G × Θ → FO, such that Γ(g,Θ) = {f | f ∈ FO ∧ f ∈ L(ΠΘ)}, where L(ΠΘ) is the set of landmarks induced by ΠΘ. With these mappings from goals to resources and agents in an environment, we will now look at the types of coalitions that can be formed among the agents to achieve these goals. 1.2 Teams and Colleagues Definition 2.0 A team Tg w.r.t. a goal g ∈ G is defined as any super-agent Θ = 〈θ,Dθ〉 ∈ τ(g) iff 6 ∃φ ∈ θ such that Θ′ = 〈θ \ φ,Dθ\φ〉 and πΘ = πΘ′ . This means that any super-agent belonging to a particular goal-agent correspondence defines a team w.r.t that specific goal when every agent that forms the super-agent plays some part in the plans that achieves the task described by g, i.e. the super-agent cannot use the same plans to achieve g if an agent is removed from its composition. This, then, leads to the concept of strong, weak, or optimal teams, depending on if the composition of the super-agent is necessary, sufficient or optimal respectively (note that an optimal team may or may not be a strong team). Definition 2.0a A team T s g = 〈θ,Dθ〉 ∈ τ(g) w.r.t a goal g ∈ G is strong iff 6 ∃φ ∈ θ such that 〈θ \ φ,Dθ\φ〉 ∈ τ(g). A team T g is weak otherwise. Definition 2.0b A team T o g = 〈θ,Dθ〉 ∈ τ(g) w.r.t a goal g ∈ G is optimal iff ∀Θ′ ∈ τ(g), C(π∗ θ) ≤ C(π∗ θ′). This has close ties with concepts of required cooperation and capabilities of teams to solve general planning problems, introduced in (Zhang and Kambhampati 2014), and work on team formation mechanisms and properties of teams (Shoham and Tennenholtz 1992; Tambe 1997). In this paper, we are more concerned about the consequences of such team formations on teaming metrics. So, with these different types of teams we have seen thus far, the question we ask is: What is the relation among the rest of the agents in the environment? How do these different teams interact among and between themselves? Definition 2.1 The set of teams in E are defined by the relation κ : G → R(τ); G ∈ E , where κ(g) ∈ τ(g) denotes the team assigned to the goal g, ∀g ∈ G. This, then, gives rise to the idea of collegiality among agents, due to both inter-team and intra-team interactions. Note that how useful or necessary such interactions are will depend on whether the colleagues can contribute to each other’s goals, or to what extent they influence their respective plans, which leads us to the following two definitions of colleagues based on the concept of teams. Definition 2.2a Let κ(g) = 〈θ1, Dθ1〉, κ(g′) = 〈θ2, Dθ2〉 be two teams in E . An agent φ1 ∈ θ1 is a type-1 colleague to an agent φ2 ∈ θ2 when κ′(g) = 〈θ1 ∪ φ1, Dθ1∪φ1〉 is a weak team w.r.t. the goal g. Definition 2.2b Agents φ1, φ2 ∈ Φ are type-2 colleagues when ∀κ(g) = 〈θ,Dθ〉 s.t. {φ1, φ2} ∩ θ 6= ∅, {φ1, φ2} 6∈ θ ∧ κ′(g) = 〈θ ∪ {φ1, φ2}, Dθ∪{φ1,φ2}〉 is a weak team. Thus type-1 colleagues can potentially contribute to the plans of their colleagues, while type-2 colleagues cannot. Plans of type-2 colleagues can, however, influence each other (for example due to conflicts on usage of shared resources), while type1-colleagues are capable of becoming teammates dynamically during plan execution. Humans in the loop. Instead of a general set of agents, we define the set of agents θ in a super-agent as composition of humans and robots θ = h(θ)∪r(θ) so that the domain model of the super-agent is also a composition of the human and robot capabilities Dθ = ⋃ φ∈h(θ) ⋃ φ∈r(θ)Aφ = h(Dθ) ∪ r(Dθ). We denote the communication actions of the superagent as c(Dθ) ⊆ Dθ. 2 Metrics for Human Robot Interaction At this point we will like to turn our attention to existing metrics for quantifying performance of human-robot teams. 2.1 Metrics for Human Robot Teams We will now ground popular (Olsen Jr. and Goodrich 2003; Steinfeld et al. 2006; Hoffman and Breazeal 2007; Hoffman 2013) metrics for human-robot teams in our current formulation. Task Effectiveness These are the metrics that measure the effectiveness of a team in completing its tasks. • Cost-based Metrics This simply measures the cost ∑ g∈κ−1(Θ) C(π ∗ Θ) of all the (optimal) plans a specific team executes (for all the goals it has been assigned to). • Net Benefit Based Metrics This is based on both plan costs as well as the value of goals and is given by ∑ g∈κ−1(Θ)R(g)− C(π∗ Θ). • Coverage Metrics Coverage metrics for a particular team determine the diversity of its capabilities in terms of the number of goals it can achieve |κ−1(Θ)|. Team Effectiveness These measure the effectiveness of (particularly human-robot) teaming in terms of communication overhead and smoothness of coordination. • Neglect Tolerance This measures how long the robots in a team Θ is able to perform well without human intervention. We can measure this as NT = max{|i − j| s.t. h(Dθ) ⋂ φ∈θ π ∗ Θ(φ)[i : j] = ∅}. • Interaction Time This is given by IT = ∑ |{i | c(Dθ) ∩ π∗ Θ[i] 6= ∅}|, and measures the time spent by a team Θ in communication. • Robot Attention Demand Measures how much attention the robot is demanding and is given by IT IT+NT . • Secondary Task Time This measures the “distraction” to a team, and can be expressed as time not spent on achieving a given goal g, i.e. STT = |{i | π∗ Θ[i] ← ∅ ∧ δ′(s, π∗ Θ) |= g}|. • Free Time FT = 1−RAD is a measure of the fraction of time the humans are not interacting with the robot. • Human Attention Demand HAD = FT − h(STT ) where h(STT ) = |{i | π∗ Θ[i]∩h(Dθ)← ∅∧δ′(s, π∗ Θ) |= g}|/|π∗ Θ| is the time humans spend on the secondary task. • Fan Out This is a measure of the communication load on the humans, and consequently the number of robots that should participate in a human-robot team, and is proportional to FO ∝ |h(θ)|/RAD. • Interaction Time Measures how quickly and effectively interaction takes places as IT = NT (1−STT ) STT . • Robot Idle Time Captures inconsistency or irregularity in coordination from the point of view of the robotic agent, and can be measured as the amount of time the robots are idle, i.e. RIT = |{i | r(Dθ) ∩ π∗ Θ[i] = ∅|. • Concurrent Activity We can talk of concurrency within a team as the time that humans and robots are working concurrently CA1 = |{i | r(Dθ) ∩ h(Dθ) ∩ π∗ Θ[i] 6= ∅}| and also across teams as the maximum time teams are operating concurrently CA2 = max{|{i | πΘ[i] 6= ∅ ∧ πΘ′ [i] 6= ∅}| ∀Θ,Θ′ ∈ R(κ)}. In measuring performance of agents in cohabitation, both as teammates and colleagues, we would still like to reduce interactions times and attentions demand, while simultaneously increasing neglect tolerance and concurrency. However, as we will see in Section 3, these metrics do not effectively capture all the implications of the interactions desired in human-robot cohabitation. So the purpose of the rest of our paper is to establish metrics that can measure the effective behavior of human-robot colleagues, and to see to what extent they can capture desired behaviors of robotic colleagues suggested in existing literature. 2.2 Metrics for Human Robot Colleagues Task Effectiveness The measures for task effectiveness must take into account that agents are not necessarily involved in their assigned team task only. • Altruism This is a measure of how useful it is for a robotic agent r to showcase altruistic behavior in assisting their human colleagues, and is given by the ratio of the gain in utility by adding a robotic colleague to a team Θ to the decrease in utility of plans of the teams r is involved in |π∗ Θ − π∗ 〈θ∪r,Dθ∪r〉|/ ∑ Θ=〈θ,Dθ〉 s.t. r∈θ ∆|π ∗ Θ|. For such a dynamic coalition to be useful, r must be a type-1 colleague to the agents θ ∈ Θ. • Lateral Coverage This measures how deviating from optimal team compositions can achieve global good in terms of number of goals achieved by a team, LT = ∑ Tg=κ(g),∀g∈G {[|κ (Tg)| − |κ−1(T o g )|]/|κ−1(T o g )|} across all the teams that have been formed in E . • Social Good Many times, while planning with humans in the loop, cost optimal plans are not necessarily the optimal plans in the social context. This is useful to measure particularly when agents are interacting outside teams, and the compromise in team utility is compensated by the gain in mutual utility of colleagues. This can be expressed as ∑ g∈G{C(πκ(g))− C(π∗ κ(g))}. Interaction Effectiveness The team effectiveness measures need to be augmented with measures corresponding to interactions among non-team members. While all these metrics are relevant for robotic colleagues as well, they become particularly important in human-robot interactions, where information is often not readily sharable due to higher cognitive mismatch, so as to reduce cognitive demand/overload. • Interaction Time In addition to Interaction Time for human-robot teams, and measures derived from it, we propose two separate components of interaction time for general human-robot cohabitation scenarios. External Interaction Time This is the time spent by agents interacting with type-1 colleagues (EIT1). Extraneous Interaction Time This is the time spent by agents interacting with type-2 colleagues (EIT2). • Compliance This refers to how much actions of an agent disambiguates its intentions. Though relevant for both, this becomes even more important in absence of teams, when goals or plans are not necessarily sharable. Thus the intention should be to maximize the probability P (Gθ = g | s = δ(πθ[1 : i], Iθ)), κ(g) = 〈θ,Dθ〉,∀g ∈ G given any stage i of plan execution and P (·) is a generic plan recognition algorithm. • External Failure This is the number of times optimal plans fail when resources are contested among colleagues EF = #{δ(π∗ Θ, IΘ) |= ⊥}, ⋃ g∈G Γ(g, κ(g)) 6= ∅. • Stability Of course with continuous interactions, team formations change, so this gives a measure of stability of the system as a whole. If teams κ(g) = 〈θ1, Dθ1〉 and κ(g) = 〈θ2, Dθ2〉 achieves a goal g ∈ G at two different instances, then stability S = ∑ g∈G |θ1 ∩ θ2|/|θ1||θ2|. 3 Discussions and Related Work We will now investigate the usefulness of the proposed metrics in quantifying behavioral traits proposed in existing literature as desirable among cohabiting human and robots. Human-Aware Planning. In (Koeckemann, Pecora, and Karlsson 2014; Cirillo, Karlsson, and Saffiotti 2010) the authors talk of adapting robot plans to suit social norms (e.g. not to vacuum a room while a human is asleep). Clearly, this involves the robots departing from their preferred plans to conform to human preferences. In such cases, involving assistive robots, measures of Altruism and Social Good become particularly relevant, while it is also crucial to reduce unwanted interactions (EIT1 + EIT2). Planning with Resource Conflicts. In (Chakraborti et al. 2015b) we outline an approach for robots sharing resources with humans to compute plans that minimize conflicts in resource usage. Thus, this line of work is aimed at reducing External Failures, while simultaneously increasing Social Good. The paper assumed one-step lookahead on the part of the robot (and zero lookahead on the part of its human colleague), i.e. the robot is responsible for making its plans conform to the human’s intentions, while the human itself is completely aloof of the robot’s plans. However, it may be argued, that humans are rarely completely indifferent about other agents in its environment. Measures of Stability and Compliance become relevant in such cases, to capture evolving beliefs and their consequences on plans. Extraneous Interaction Time is an important measure is such cases, since additional communication is always a proxy to minimizing coordination problems between colleagues. Planning for Serendipity. In (Chakraborti et al. 2015a) we propose a formulation for the robot to produce positive exogenous events during the execution of the human’s plans, i.e. interventions which will be useful to the human regardless of whether he was expecting assistance from the robot. This work particularly looks at planning for Altruism. One major assumption here is that humans, when presented with a positive change to the environment, will always be able to identify that change and exploit its consequences in his plans. Technically, this means that the human does optimal replanning during every step in his plan, which might be too strong an assumption on how humans behave during plan execution. Increasing Compliance in agent behavior can provide better performance in this regard. Further, External Interaction is crucial in such cases for forming such impromptu coalitions among colleagues. 4 Conclusions and Future Work In conclusion, we discussed interaction in human-robot societies involving multiple teams of humans and robots in the capacity of teammates or as colleagues, provided a formal framework for talking about various modes of cooperation, and reviewed existing metrics and proposed new ones that can capture these different modalities of teaming or collegial behavior. Finally we discussed how such metrics can be useful in evaluating existing works in human-robot cohabitation. One line of future inquiry would be to see how such quantitative metrics are complemented by qualitative feedback from human factor studies, to establish what the desired trade-offs are, in order to ensure well-informed design of symbiotic systems involving humans and robots.