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