Original: Inﬂuencing Behavioral Attributions to Robot Motion During Task ExecutionAnonymous Author(s)
Revised: Inﬂuencing Behavioral Attributions to Robot Motion During Task Execution

Original: AfﬁliationAddress email Abstract: Recent literature has proposed algorithms for autonomous generationof robot motion that communicates functional attributes of a robot’s state such asintent or incapability. However, lessis known about how to automate the generation of motion for communicating higher-level behavioral attributes such ascuriosity or competence.
Revised: Abstract: While prior work has shown how to autonomously generate motion that communicates task-related attributes, like intent or capability, we know less about how to automatically generate motion that communicates higher-level behavioral attributes such as curiosity or competence.

Original: We propose a framework thatjointly addresses the challenges of modeling human attributions to robot motion, generating trajectories that elicit attributions, and selecting trajectories that balance attribution and taskcompletion.
Revised: We propose a framework that addresses the challenges of modeling human attributions to robot motion, generating trajectories that elicit attributions, and selecting trajectories that balance attribution and task completion.

Original: The insight underpinning our approach is thatmany attributions canbe traced tosalient features of the robot’s motion.
Revised: The insight underpinning our approach is that attributions can be ascribed to features of the motion that don’t severely impact task performance, and that these features form a convenient basis both for predicting and generating communicative motion.

Original: We illustrate the framework ina coverage task resembling household vacuum cleaning.
Revised: We illustrate the framework in a coverage task resembling household vacuum cleaning.

Original: Through a virtual interface, we collect a dataset of human attributions to robot trajectories during taskexecution and learn a probabilistic model that mapsrobot trajectories to humanattributions.
Revised: Through a virtual interface, we collect a dataset of human attributions to robot trajectories during task execution and learn a probabilistic model that maps trajectories to attributions.

Original: We then incorporate this model into a trajectory generation mechanism that balances between task completion and communication of a desiredbehavioral attribution.
Revised: We then incorporate this model into a trajectory generation mechanism that balances between task completion and communication of a desired behavioral attribute.

Original: Through an online user study on a different household layout, we ﬁnd that our prediction model accurately captures human attribution forcoverage tasks.
Revised: Through an online user study on a different household layout, we ﬁnd that our prediction model accurately captures human attribution for coverage tasks.

Original:  Introduction
Revised:  Introduction

Original: As robots enter households and public spaces it is increasingly important to account for humanperceptions of their behavior [1, 2, 3, 4].
Revised: As robots enter households and public spaces, it is increasingly important to account for human perceptions of their behavior [1, 2, 3, 4].

Original: While a robot’s actions might be driven by unambiguousinternal objectives, solely optimizing such criteria might result inrobot behavior that is difﬁcult tointerpret or disruptive to human onlookers.
Revised: While a robot’s actions might be driven by unambiguous internal objectives, solely optimizing such criteria might result in behavior that is difﬁcult to interpret or disruptive to human onlookers.

Original: For example, a highly articulated robot may follow anon-humanlike trajectory that users attribute caprice to, making observers uncomfortable [5] or ahome robot such as a robot vacuum cleaner can exhibit unpredictable motion that causes observersto perceive the robot as broken, interrupting home activity.
Revised: For example, a highly articulated robot may follow a non-humanlike trajectory that users attribute caprice to, making observers uncomfortable [5] or a home robot such as a robot vacuum cleaner can turn arbitrarily and cause observers to perceive the robot as broken, interrupting home activity.

Original: Accounting for high-level attributions to robot behavior is a complex problem relying on the mechanisms underlying human inference and behavior generation.
Revised: Accounting for high-level attributions to robot behavior is a complex problem relying on the mechanisms underlying human attribution and behavior generation.

Original: In psychology, there is a long history of work on understanding human attribution for behavior explanation or inference of behaviortraits [6, 7].
Revised: In psychology, there is a long history of work on understanding human attribution for behavior explanation or inference of behavior traits [6, 7].

Original: Humans are highly attuned to how their actions are perceived and adapt their behavior to elicit a desired impression from others or adhere to social norms, a concept that is known aspresentation of self [8].
Revised: Humans are highly attuned to how their actions are perceived and adapt their behavior to elicit a desired impression from others or adhere to social norms, a concept that is known as presentation of self [8].

Original: The tendency for humans to attribute even situational behaviors to deepercharacter traits is so pervasive that it is known as “the fundamental attribution error” [9].
Revised: The tendency for humans to attribute even situational behaviors to deeper character traits is so pervasive that it is known as “the fundamental attribution error” [9].

Original: Inspired by these theories, we envision robots that can 1) leverage an understanding of humans’ attribution mechanisms to predict attributions to their motion, 2) generate behaviors that elicit desiredhuman impressions and 3) balance attribution elicitation and task completion.
Revised: Inspired by these theories, we envision robots that can 1) leverage an understanding of humans’ attribution mechanisms to predict attributions to their motion, 2) generate behaviors that elicit desired human impressions and 3) balance attribution elicitation and task completion.

Original: This will increase theacceptance of robots in human spaces by enabling them go about their tasking in a way that is botheffective and sensitive to perceptions.
Revised: This will increase the acceptance of robots in human spaces by enabling them go about their tasking in a way that is both effective and sensitive to perceptions.

Original: We propose a framework that addresses these challenges byextracting the salient features of arobot’s motion and the attributions they elicit from users and integrating them intothe a  generation scheme that enables the ﬂexible tradeoff of task completion and attribution. We illustrate thisframework in a virtual representation of a robot vacuum cleaning task.
Revised: We propose a framework, shown in Fig. 1, that addresses these challenges by integrating a learned model of human attribution into a robot’s trajectory generation process. Our observation is that users rely on local characteristics of the robot’s motion, like short patterns of actions, in combination with global trajectory characteristics, like the amount of redundancy, to infer attributions.

Original: We learn a probabilistic
Revised: These features distinguish otherwise functionally equivalent trajectories and provide a basis for the framework. We

Original: [Figure]
Revised: [Figure]

Original: model that maps a  robot coverage trajectory to the expected distribution of human ratings.
Revised: trace an application of the framework to a virtual robot vacuum cleaning task.

Original: We thenincorporate this model into a trajectory generation scheme that balances task-cost and attributionelicitation objectives. We generate a range of trajectories optimizing for different attributions withvarying cost constraints, demonstrating that the approach produces thematically consistent trajectoriesin both an environment it was trained in and an environment variant. We conduct an online userstudy and verify that attributions to the generated trajectories are well predicted by the model.
Revised: In our evaluation, we see that the resulting model is useful for predicting attributions and for enabling the generation of trajectories that balance task execution and attribution elicitation. Some aspects, such as partial trajectory observation or application to highly articulated robots, remain for future work.

Original:  A Framework for Behavioral Attribution
Revised:  A Framework for Behavioral Attribution

Original: We consider a robot performing a task T in a human environment.
Revised: We consider a robot performing a task G in a human environment.

Original: We denote by s ∈ S the robotstate where S is a state space and deﬁne a robot trajectory as a sequence of states ξ = ( s 0 , . . .
Revised: We denote by s 2 S the robot state where S is a state space, and deﬁne a robot trajectory as a sequence of states ⇠ = ( s 0 , . . .

Original: , s t )where indices correspond to timesteps following a ﬁxed time parametrization of step size.
Revised: , s t ) where indices correspond to timesteps following a ﬁxed time parametrization.

Original: Let usdeﬁne the task as a tuple T =
Revised: Let us deﬁne the task as a tuple G =

Original: (Ξ , A , P , C ) where Ξ is a space of robot trajectories, A denotes therobot action space, P : Ξ ×A → Ξ represents a deterministic state transition model, and C : Ξ → Ris a trajectory cost.
Revised: ( ⌅ , A , P , C ) where ⌅ is a space of robot trajectories, A denotes the robot action space, P : ⌅ ⇥ A ! ⌅ represents a deterministic state transition model, and C : ⌅ ! R is a trajectory cost.

Original: We assume that the robot starts from an initial state s 0 and reaches a terminal state s T at the endof the task execution (time T ) by executing a trajectory ξ = ( s 0 , . . .
Revised: We assume that the robot starts from an initial state s 0 and reaches a terminal state s T (at time T ) by executing a trajectory ⇠ = ( s 0 , . . .

Original: , s T ) .
Revised: , s T ) .

Original: We assume that thistrajectory ξ is fully observable by a humanobserver who is aware of the task speciﬁcation T .
Revised: We assume that this trajectory ⇠ is fully observed by a human who is aware of the task speciﬁcation G .

Original: Theobserver makes an inference of the form I B : Ξ × T → B , where Ξ is a space of trajectories and Bis a space of behavioral attributions.
Revised: The observer makes an inference of the form I B : ⌅ ⇥ G ! B , mapping their observation from the space of trajectories ⌅ , along with the context of the task speciﬁcation G 2 G , into a space of behavioral attributions B .

Original: The form of B will vary, but should be selected to capture therange, combinations, and intensities of attributions that the robot should be sensitive to.
Revised: The form of B will vary, but should be selected to capture the range, combinations, and intensities of attributions that the robot should be sensitive to.

Original: Conversely,  given a behavioral attribution b from a space of behavioral attributions B and a task T , the observer expects to see a trajectory ξ b ∈ Ξ , corresponding to an inference of the form
Revised: Conversely, we can imagine that a robot, given a behavioral attribution b 2 B and a task G , infers a trajectory ⇠ b 2 ⌅ that exempliﬁes the attribution, corresponding to an inference of the form

Original: I ξ : B × T → Ξ .
Revised: I ⇠ : B ⇥ G !

Revised: ⌅ .

Original: In other words, we assume that there is a “way” that a curious—or any otherattribution—robot would be expected to execute a particular task.
Revised: In other words, we assume that there is a “way” that a curious—or any other attribution—robot should execute a particular task.

Original: Equivalently, we assume thatthere is a set of trajectories that the observer could more often imagine to be consistent with someattribution.
Revised: In practice, we will realize both of these inferences as probabilistic maps. Rather than solely capturing the best way to look curious for a task, we’ll seek to assign densities to trajectories, allowing the possibility that there are many equally likely alternatives.

Original: In the remainder of paper, we aim to provide a general framework for modeling inferences of theform I B , and I ξ .
Revised: In the remainder of paper, we aim to provide a general framework for modeling inferences of the form I B , and I ⇠ .

Original: Our goal is to enable robots to understand and account for the communicativeeffects of their motion on human observers.
Revised: Our goal is to enable robots to understand and account for the communicative effects of their motion on human observers.

Original:  Related Work
Revised:  Related Work

Original: Several studies have illustrated the value of robot motion as a communicative modality [10, 11, 12,13, 14, 15].
Revised: Several studies have illustrated the value of robot motion as a communicative modality [10, 11, 12, 13, 14, 15].

Original: Some works propose algorithms for legible robot motion generation, which have beenshown to enable effective human-robot collaboration in manipulation tasks [10], or smooth robotnavigation in close proximity to humans [12, 14].
Revised: Some works propose algorithms for legible robot motion generation, which have been shown to enable effective human-robot collaboration in manipulation tasks [10], or smooth robot navigation in close proximity to humans [12, 14].

Original: Other works focus on conveying higher-level information such as the robot’s objective function [15] or the source of failure [13] in failure cases.
Revised: Other works focus on conveying higher-level information such as the robot’s objective function [15] or the source of failure [13] when the robot can’t complete a task.

Original: Animation principles [16] or movement analysis [17] are often employed to inform the design of expressive robot behaviors.
Revised: Animation principles [16] or movement analysis [17] are often employed to inform the design of expressive robot behaviors.

Original: Finally, related graphics research focuses on the generation of stylisticallydistinct but functionally equivalent motion primitives for walking and other activities [18, 19].
Revised: Finally, related graphics research focuses on the generation of stylistically distinct but functionally equivalent motion primitives for walking and other activities [18, 19].

Original: The complex interplay of embodiment and communicative motion has motivated research on understanding human perceptions of robot behavior.
Revised: The complex interplay of embodiment and communicative motion has motivated research on understanding human perceptions of robot behavior.

Original: For instance, early work looked at the effect ofrobot gaze on human impressions [20].
Revised: For instance, early work looked at the effect of robot gaze on human impressions [20].

Original: Sung et al.
Revised: Sung et al.

Original: [1] study human attitudes towards robot vacuumcleaners and propose design principles aimed at enhancing the acceptance of robots in domestic environments.
Revised: [1] study human attitudes towards robot vacuum cleaners and propose design principles aimed at enhancing the acceptance of robots in domestic environments.

Original: [2] report a relation between robot motion and perceived affect.
Revised: [2] report a relation between robot motion and perceived affect.

Original: Lo et al.
Revised: Lo et al.

Original: [21] and [14]investigate human perceptions of different robot navigation strategies whereas Walker et al.
Revised: [21] and [14] investigate human perceptions of different robot navigation strategies whereas Walker et al.

Original: [22]study human perceptions of robot actions that deviate from the robot’s assigned task.
Revised: [22] study human perceptions of robot actions that deviate from the robot’s assigned task.

Original: Our work draws inspiration from recent work on design and methods for extracting human perceptions and attributions for robot motion [1, 2].
Revised: Our work draws inspiration from previous efforts to characterize human perceptions and attributions to robot motion [1, 2].

Original: However, it moves beyond the problem of understanding and analyzing human perceptions, and focuses on the problem of synthesizing implicitlycommunicative motion.
Revised: However, it moves beyond the problem of understanding and analyzing human perceptions and focuses on the problem of synthesizing implicitly communicative motion.

Original: Our work is closely related to past work on the generation of legible robotmotion [10, 11, 23, 13] in that we also incorporate a model of human inference into the robot’smotion generation pipeline.
Revised: Our work is closely related to past work on the generation of legible robot motion [10, 11, 23, 13] in that we also incorporate a model of human inference into the robot’s motion generation pipeline.

Original: However, unlike these works which emphasize the communicationof task-related attributes, our focus is instead on communicating high-level, behavioral attributesthrough robot motion.
Revised: However, unlike these works which emphasize the communication of task-related attributes, our focus is instead on communicating high-level, behavioral attributes through robot motion.

Original:  Modeling and Inﬂuencing Attributions
Revised:  Modeling and Inﬂuencing Attributions

Original: We consider a scenario in which a mobile robot performs a coverage task in a two-dimensionaldiscrete workspace while a human is observing from a top-down view.
Revised: We consider a scenario in which a mobile robot performs a coverage task in a two-dimensional discrete workspace while a human is observing from a top-down view.

Original: We employ a virtual environment 1 that resembles a house and stylize the agent as a robot vacuum cleaner (see Fig. 2) sincethe general population is already somewhat familiar 2 with such robots [1, 24], making it easier forparticipants to develop mental models about their motion than that of a manipulator, for example.
Revised: We employ a virtual environment 1 that resembles a house and stylize the agent as a robot vacuum cleaner (see Fig. 2) since the general population is already somewhat familiar 2 with such robots [1, 24], making it easier for participants to develop mental models about their motion than that of a manipulator, for example.

Original: In this scenario, the robot state space is the complete home workspace and Ξ is the space of allpossible trajectories of any length that could be followed in the space.
Revised: In this scenario, the robot state space is the complete home workspace and ⌅ is the space of all possible trajectories of any length that could be followed in the space.

Original: The robot action space Aconsists of  the cardinal directions and actions are deterministic.
Revised: The robot action space A consists of deterministic movements in the cardinal directions.

Original: The cost of a state transition froma state s t to a state s t +1 after having followed a trajectory ξ t is deﬁned as 0 if the state hasn’t beenvisited before, -5 if the state contains a small, traversable obstacle (e.g. a vase), and -1 otherwise.
Revised: The cost of a state transition from a state s t to a state s t +1 after having followed a trajectory ⇠ t is deﬁned as 0 if the state hasn’t been visited before, -5 if the state contains a small, traversable obstacle (e.g. a vase), and -1 otherwise.

Original: Apenalty of 3 times the number of unvisited states from the goal region is applied on termination.
Revised: A penalty of 3 times the number of unvisited states from the goal region is applied on termination.

Original: 4.1 Understanding Behavioral Attribution for Coverage Tasks
Revised: 4.1 Understanding Behavioral Attribution for Coverage Tasks

Original: Through exploratory studies on Amazon Mechanical Turk, we sought to extract domain knowledgefor attributions to robot motion within coverage tasks.
Revised: Through exploratory studies on Amazon Mechanical Turk, we sought to extract domain knowledge for attributions to robot motion within coverage tasks.

Original: Using the home layout of Fig.
Revised: Using the home layout shown in Fig.

Original: 2, we generateda set of trajectories exhibiting qualitatively distinct ways the robot could respond to the prompt to“clean the bedroom,” ranging from a near optimal coverage plan to a trajectory that barely visitedthe target room (see Appendix A for additional details).
Revised: 2, we generated a set of trajectories exhibiting qualitatively distinct ways the robot could respond to the prompt to “clean the bedroom,” ranging from a near optimal coverage plan to a trajectory that barely visited the target room (see Appendix A for additional details).

Original: Each participant viewed videos of a randomselection of three of these trajectories.
Revised: Each participant viewed videos of a random selection of three of these trajectories.

Original: After each video, participants were asked: a) to providethree words to describe the robot’s behavior; b) to rate their agreement that “the robot is ”for a range of adjectives drawn from relevant literature on human attributions [25, 26, 22]; c) to“explain what factors contributed to their strongest ratings.”
Revised: After each video, participants were asked: a) to provide three words to describe the robot’s behavior; b) to rate their agreement that “the robot is ” for a range of adjectives drawn from relevant literature on human attributions [25, 26, 22]; c) to “explain what factors contributed to their strongest ratings.”

Original: In addition to attributions, participantswere asked to use an interactive interface to demonstrate how they would “clean the bedroom ina way that makes the robot look ” where the blank was ﬁlledat random with an adjectivefrom the attribution rating items.
Revised: In addition to attributions, participants were asked to use an interactive interface to demonstrate how they would “clean the bedroom in a way that makes the robot look ” where the blank was ﬁlled with a random adjective from the attribution rating items.

Original: Across all exploratory studies, we collected 375 sets of attributionratings from 115 participants (73 male, 41 female) aged 21-70 ( M = 38.3, SD = 10.7) covering 63trajectories and a total of 193 demonstrations.1 The environment
Revised: Across all exploratory studies, we collected 375 sets of attribution ratings from 115 participants (73 male, 41 female) aged 21-70 ( M = 38.3, SD = 10.7) covering 63 trajectories and a total of 193 demonstrations.

Original: [Table]
Revised: [Table]

Original: 4.1.1 Extracting the Space of Attributions
Revised: 4.1.1 Extracting the Space of Attributions

Original: To understand the inter-correlation of participant adjective ratings, we conducted an exploratoryfactor analysis.
Revised: To understand the inter-correlation of participant adjective ratings, we conducted an exploratory factor analysis.

Original: We selected a three-factor, promax rotation model which explained 74% of theobserved variance due to its parsimony and coherence (see Appendix B).
Revised: We selected a three-factor, promax rotation model which explained 74% of the observed variance due to its parsimony and coherence (see Appendix B).

Original: The ﬁrst factor, whichwe call “competence” for its similarity to the relevant factor described by Carpinella et al.
Revised: The ﬁrst factor, which we call “competence” for its similarity to the relevant factor described by Carpinella et al.

Original: [26]consists of six items (responsible, competent, efﬁcient, reliable, intelligent, focused) centered onthe capability and diligence of the robot.
Revised: [26] consists of six items (responsible, competent, efﬁcient, reliable, intelligent, focused) centered on the capability and diligence of the robot.

Original: The second consists of four items (lost, clumsy, confused,broken) alluding to atemporary or extended negative state, for which we title the factor “brokeness”.
Revised: The second consists of four items (lost, clumsy, confused, broken) alluding to a negative state, for which we title the factor “brokeness”.

Original: The third contains two items (curious, investigative) and matches the curiosity factor examined by Walker et al.
Revised: The third contains two items (curious, investigative) and matches the curiosity factor examined by Walker et al.

Original: The extracted model enables the computation of standardized factor scores roughly in the range[ − 3 , 3] which denote how many standard deviations from the mean a participant’s ratings for theitems are.
Revised: The extracted model enables the computation of standardized factor scores roughly in the range [  3 , 3] which denote how many standard deviations from the mean a participant’s ratings for the items are.

Original: Reﬂecting the format of the component items, a high or low factor score denotes agreement or disagreement that a trajectory expresses an attribution, respectively.
Revised: Reﬂecting the format of the component items, a high or low factor score denotes agreement or disagreement that a trajectory expresses an attribution, respectively.

Original: Based on this model,we represent the attribution for a trajectory ξ as a tuple b = ( b competent , b broken , b curious ) ∈ B wherethe space of attributions is the set B =
Revised: Based on this model, we represent the attribution for a trajectory ⇠ as a tuple b = ( b competent , b broken , b curious ) 2 B where the space of attributions is the set B =

Original: [ − 3 , 3] 3 .
Revised: [  3 , 3] 3 .

Original: 4.1.2 Low-dimensional Trajectory Representation
Revised: 4.1.2 Low-dimensional Trajectory Representation

Original: The space of possible trajectories in this domain is too large to explore directly, so we constructeda low-dimensional space Φ based on features relevant to the formation of attribution ratings.
Revised: The space of possible trajectories in this domain is too large to map directly to the space of attributions, so we constructed a low-dimensional space  based on features relevant to the formation of attribution ratings.

Original: Thisallows us to describe a trajectory ξ as a vector φ ξ = φ ( ξ ) ∈ Φ .
Revised: This allows us to describe a trajectory ⇠ as a vector  ⇠ =  ( ⇠ ) 2  .

Original: The feature space was inspiredby relevant literature on human behavioral attribution to robot motion and enriched with featuresappearing in participants’ explanations.
Revised: The feature space was inspired by relevant literature on human behavioral attribution to robot motion and enriched with features appearing in participants’ explanations.

Original: The ﬁnal set of 11 features used in further experiments islisted in Table 1.
Revised: The ﬁnal set of 11 features used in further experiments is listed in Table 1.

Original: 4.2 Mapping Trajectories to Attribution Scores
Revised: 4.2 Mapping Trajectories to Attribution Scores

Original: Given a trajectory ξ , an observer’s inference I B of behavioral attribution can be expected to varyboth due to individual differences and as a result of measurement error.
Revised: Given a trajectory ⇠ , an observer’s inference I B of behavioral attribution can be expected to vary both due to individual differences and as a result of measurement error.

Original: For this reason, we model
Revised: For this reason, we model

Original: I B as a conditional probability density f
Revised: I B as a conditional probability density f

Original: B| Ξ ( b | φ ξ ) : 
Revised: B| ⌅ ( b |  ⇠ ) : B !

Original: B → R .
Revised: R .

Original: We observed multimodality in the distribution of factor scores for some trajectories, so we use a Mixture Density Network (MDN) [27] toapproximate each conditional density as a mixture distribution f B| Ξ ( b | φ ξ ) 
Revised: We observed multimodality in the dis- tribution of factor scores for some trajectories, so we use a Mixture Density Network (MDN) [27] to approximate each conditional density as a mixture distribution f B| ⌅ ( b |  ⇠ ) =

Original: [-= (cid:80) Ci =
-]
Revised: [-= (cid:80) Ci =
-]P

Original: α i ( φ ξ ) k i ( b | φ ξ )where α i , i = 1 , . . 
Revised: Ci =1 ↵ i (  ⇠ ) k i ( b |  ⇠ ) where ↵ i , i = 1 , . . .

Original: , C , is a mixing coefﬁcient, and k i is a multivariate Gaussian kernel functionwith mean µ i and covariance Σ i .
Revised: , C , is a mixing coefﬁcient, and k i is a multivariate Gaussian kernel function with mean µ i and covariance ⌃ i .

Original: Note that the mixing coefﬁcients α i and the Gaussian parameters µ i and Σ i are functions of the featurized trajectory φ ξ .
Revised: Note that the mixing coefﬁcients ↵ i and the Gaussian parameters µ i and ⌃ i are functions of the featurized trajectory  ⇠ .

Original: In our models, these functions areimplemented as linear transformations of features produced by a shared multi-layer perceptron.
Revised: In our models, these functions are implemented as linear transformations of features produced by a shared multi-layer perceptron.

Original: To make efﬁcient use of scarce data, we created ensembles of MDNs using bootstrap aggregation, i.e., we trained N models with different data splits and uniformly weight their predictions: 
Revised: To make efﬁcient use of scarce data, we created ensembles of MDNs using bootstrap aggregation, i.e., we trained N models with different data splits and uniformly weight their predictions: f ens

Original: [Equation]
Revised: [Equation]

Original: We studied three different model conﬁgurations; single and four component MDNs, i.e., C = 1 and
Revised: We studied three different model conﬁgurations; single and four component MDNs, i e C = 1 and

Original: C = 4 and an ensemble of 8 MDNs each with four components, i.e., C = 4 , N = 8 .
Revised: C = 4 and an ensemble of 8 MDNs each with four components, i e., C = 4 , N = 8 .

Original: We trainedall models using an average negative log likelihood (NLL) loss function, the Adam optimizer [28],
Revised: We trained all models using an average negative log likelihood (NLL) loss function, the Adam optimizer [

Original: [Table] noise regularization[29], and early stopping.
Revised: , noise regularization and early stopping.

Original: We conﬁgured the input MLP to use a single hiddenlayer with 5 units and a hyperbolic tangent activation.
Revised: We conﬁgured the input MLP to use a single hidden [Table] layer with 5 units and a hyperbolic tangent activation.

Original: We expanded the dataset collected in ourexploratory studies after assessing the sensitivity of the models to increased amounts of data, aprocess described in Appendix C.
Revised: We expanded the dataset collected in our exploratory studies after assessing the sensitivity of the models to increased amounts of data, a process described in Appendix C.

Original: The ﬁnal version of the set includes 126 trajectories with 671attribution ratings.
Revised: The ﬁnal version of the set includes 126 trajectories withattribution ratings.

Original: Table 2 compares the NLL of the models over held-out data.
Revised: Table 2 compares the NLL of the models over held-out data.

Original: The mean indicatesthe typical quality of the prediction and the standard deviation indicates the degree to which thisvaried from sample to sample.
Revised: The mean indicates the typical quality of the prediction and the standard deviation indicates the degree to which this varied from sample to sample.

Original: Both quantities are averaged over 16 random folds and reportedwith bootstrapped 95% conﬁdence intervals.
Revised: Both quantities are averaged over 16 random folds and reported with bootstrapped 95% conﬁdence intervals.

Original: All models perform signiﬁcantly better than a uniformbaseline, which simply assigns equal probability to all outcomes.
Revised: All models perform signiﬁcantly better than a uniform baseline, which simply assigns equal probability to all outcomes.

Original: The ensemble model performsbest and is used in further experiments in the remainder of the paper.
Revised: The ensemble model performs best and is used in further experiments in the remainder of the paper.

Original: 4.3 Generating Trajectories that Elicit Desired Attributions
Revised: 4.3 Generating Trajectories that Elicit Desired Attributions

Original: We represent the behavior speciﬁcation as a one-dimensional Gaussian b ∗ ∼ N ( µ b , σ 2 b ) centered ona desired rating µ b ∈{+
+}
Revised: We represent the behavior speciﬁcation as a one-dimensional Gaussian b ⇤ ⇠ N ( µ b ,  2 b ) centered on a desired rating µ b {+
+}

Original: [ − 3 , 3] for a single attribution dimension where the variance σ b serves as atolerance parameter modeling the acceptable distance from the desired behavioral rating.
Revised: [  3 , 3] for a single attribution dimension where the variance  b serves as a tolerance parameter modeling the acceptable distance from the desired behavioral rating.

Original: We use adensity representation as it more closely matches the output of our model for I B .
Revised: We use a density representation as it more closely matches the output of our model for I B .

Original: Together with the task requirements as described by the cost function C , we realize the inference I ξas an optimizationscheme of the form:
Revised: Together with the task requirements as described by the cost function C , we realize the inference I ⇠ as an optimization of the form:

Original: [Equation]
Revised: [Equation]

Original: where D KL denotes the KL divergence, f B i is the density f B | Ξ | φ ( ξ ) marginalized across dimensions other than i , and w is the maximum allowable task cost.
Revised: where D KL denotes the KL divergence, f B i is the density f B | ⌅ |  ( ⇠ ) marginalized across dimensions other than i , and w is the maximum allowable task cost.

Original: Because many applications are conventionally exclusively task-cost driven, this format provides an intuitive “knob” in the form of howsuboptimal the robot is allowed to be.
Revised: Because many applications are conventionally exclusively task-cost driven, this format provides an intuitive “knob” in the form of how suboptimal the robot is allowed to be.

Original: Where performance is critical—perhaps to meet a schedule orto ﬁt in power constraints—the robot designer need only set w to match the need.
Revised: Where performance is critical—perhaps to meet a schedule or to ﬁt in power constraints—the robot designer need only set w to express the hard bound.

Original: Different attributions are expected to be more or less sensitive to the allowable suboptimality, something illustratedin Appendix D.
Revised: Different attributions are expected to be more or less sensitive to the allowable suboptimality, something illustrated in Appendix D.

Original: We implement this optimization using a hill-descending search in the space of trajectories.
Revised: We implement this optimization using a hill-descending search in the space of trajectories.

Original: Thesearch is initialized with a task-optimal trajectory generated via A* search, and progressively samples modiﬁcations to the trajectory.
Revised: The search is initialized with a task-optimal trajectory generated via A* search and progressively samples modiﬁcations to the trajectory.

Original: These modiﬁcations consist of both naive, action-level modiﬁcations to the trajectory as well as changes targeting the activation of the features underlying theattribution model (see Fig. 1).
Revised: These modiﬁcations consist of both naive, action-level modiﬁcations to the trajectory as well as changes targeting the activation of the features underlying the attribution model (see Fig. 1).

Original: Important motion templates, like runs of straight motion, hook patterns,  start-stops are sampled and patched into trajectories.
Revised: Important motion templates, like runs of straight motion, hook patterns, and start-stops are sampled and patched into trajectories.

Original: All modiﬁcations are ranked by thedivergence of their predicted attribution with the behavior speciﬁcation.
Revised: All modiﬁcations are ranked by the divergence of their predicted attribution with the behavior speciﬁcation.

Original: The search terminates aftera ﬁxed duration and the best performing trajectory subject to the task-cost constraint is returned.
Revised: The search terminates after a ﬁxed duration and the best performing trajectory subject to the task-cost constraint is returned.

Original: Adetailed description of the optimization procedure is given in Appendix D.
Revised: A detailed description of the optimization procedure is given in Appendix D.

Original:  Evaluation
Revised:  Evaluation

Original: We conduct a user study to evaluate the efﬁcacy of the framework as a means of producing trajectories that elicit desired attributions.
Revised: We conduct a user study to evaluate the efﬁcacy of the framework as a means of producing trajectories that elicit desired attributions.

Original: Our study is motivated by the following hypotheses:
Revised: Our study is motivated by the following hypotheses:

Original: Hypothesis 1 The model makes accurate predictions about the distribution of attributions to newtrajectories.
Revised: Hypothesis 1 The model makes accurate predictions about the distribution of attributions to new trajectories.

Original: Hypothesis 2 The model makes accurate predictions about the distribution of attributions to trajectories in unseen environments.
Revised: Hypothesis 2 The model makes accurate predictions about the distribution of attributions to trajectories in unseen environments.

Original: Hypothesis 

Revised: Hypothesis

Original: The approach enables the generation of trajectories that elicit desired attributions.
Revised: The approach enables the generation of trajectories that elicit desired attributions.

Original: 5.1 Experiment Design
Revised: 5.1 Experiment Design

Original: In Experiment I, participants observe and rate trajectories in the same home layout used for datacollection, while in Experiment II, trajectories are generated in a modiﬁed home layout.
Revised: In Experiment I, participants observe and rate trajectories in the same home layout used for data collection, while in Experiment II, trajectories are generated in a modiﬁed home layout.

Original: In aneffort to understand the impact of the environment geometry, the modiﬁed layout increases the sizeof the goal region by 100%, varies the placement of items and obstacles, and ﬂips the dominantdirection of the robot’s motion.
Revised: In an effort to understand the impact of the environment geometry, the modiﬁed layout increases the size of the goal region by 100%, varies the placement of items and obstacles, and ﬂips the dominant direction of the robot’s motion.

Original: The experiments are within-subjects, video-based user studies,both instantiated in three parallel sets corresponding to the three attribution dimensions considered.
Revised: The experiments are within-subjects, video-based user studies, both instantiated in three parallel sets corresponding to the three attribution dimensions considered.

Original: For each dimension, we consider four robot trajectories generated by optimizing (1) with a targetdistribution expressed as a Gaussian centered at 1.5 with scale 0.3 and varying task cost thresholds.
Revised: For each dimension, we consider four robot trajectories generated by optimizing (1) with a target distribution expressed as a Gaussian centered at 1.5 with scale 0.3 and varying task cost thresholds.

Original: To ease interpretation, the w values governing the thresholds were set in multiples— 1x , 2x , 4x ,12x —of the cost of the optimal trajectory for the task.
Revised: To ease interpretation, the w values governing the thresholds were set in multiples— 1x , 2x , 4x , 12x —of the cost of the optimal trajectory for the task.

Original: The full set of trajectories is shown in Fig.
Revised: The full set of trajectories is shown in Fig.

Original: In all experiments, participants rate and describe each trajectory using the same items and questionsused in the exploratory studies of Sec. 4.
Revised: In all experiments, participants rate and describe each trajectory using the same items and questions used in the exploratory studies of Sec. 4.

Original: After watching all trajectories in a randomly assigned order,they also respond to additional comparative questions: “which robot seemed the most ” and“which robot seemed the least ”, where the blanks are ﬁlled with the adjective correspondingto the dimension of attribution studied.
Revised: After watching all trajectories in a randomly assigned order, they also respond to additional comparative questions: “which robot seemed the most ” and “which robot seemed the least ”, where the blanks are ﬁlled with the adjective corresponding to the dimension of attribution studied.

Original: Both comparisons are accompanied with an open-endedquestion asking for a brief explanation of the choice.
Revised: Both comparisons are accompanied with an open-ended question asking for a brief explanation of the choice.

Original: No suitable baselines exist for the balancedattribution elicitation task, so our experiments use solely trajectories generated by our approach.
Revised: No suitable baselines exist for the balanced attribution elicitation task, so our experiments use solely trajectories generated by our approach.

Original: Participants A total of 144 participants (76 male, 68 female) aged 20-72 ( M = 38.2, SD =10.9) were recruited via Amazon Mechanical Turk and paid $2 to complete the approximately 15minute task.
Revised: Participants A total of 144 participants (76 male, 68 female) aged 20-72 ( M = 38.2, SD = 10.9) were recruited via Amazon Mechanical Turk and paid $2 to complete the approximately 15 minute task.

Original: 9 had taken part in our earlier exploratory studies.
Revised: 9 had taken part in our earlier exploratory studies.

Original: Participants were equally distributedamongst the six sets of conditions.
Revised: Participants were equally distributed amongst the six sets of conditions.

Original: Condition orderings were fully counterbalanced.
Revised: Condition orderings were fully counterbalanced.

Original: 5.2 Results
Revised: 5.2 Results

Original: The predictive performance of the model is illustrated in Fig.
Revised: The predictive performance of the model is illustrated in Fig.

Original: 5 and reported in Table 3.
Revised: 5 and reported in Table 3.

Original: The95% bootstrapped conﬁdence interval on the mean NLL for Experiment I was 2.77 ± .10 ( SD =0.88 ±
Revised: The 95% bootstrapped conﬁdence interval on the mean NLL for Experiment I was 2.77 ± .10 ( SD = 0.88 ±

Original: and 2.87 ± 0.10 ( SD = 0.86 ± .09) for Experiment II.
Revised: and 2.87 ± 0.10 ( SD = 0.86 ± .09) for Experiment II.

Original: Participants’ choices for “most”and “least” trajectories are shown in Fig.
Revised: Participants’ choices for “most” and “least” trajectories are shown in Fig.

Original: Hypothesis 1 was supported; the average NLL of the models was signiﬁcantly lower than a uniformmodel, indicating that the model was able to meaningfully predict attributions in the layoutit was trained in.
Revised: Hypothesis 1 was supported; the average NLL of the models was signiﬁcantly lower than a uniform model, indicating that the model was able to meaningfully predict attributions in the layout it was trained in.

Original: Hypothesis 2 was supported; the average NLL of the attributions observed across Experiment IIwas signiﬁcantly lower than the uniform model, indicating that the model remains informative even under modiﬁcations to the task layout.
Revised: Hypothesis 2 was supported; the average NLL of the attributions observed across Experiment II was signiﬁcantly lower than the uniform model, indicating that the model remains informative even under modiﬁcations to the environment layout.

Original: Hypothesis 3 saw mixed support; Kendall’s tau-b correlation tests (reported in Appendix E) indicate strong positive correlations between the allowable suboptimality and brokennessfactor scores, suggesting that the trajectory generation method was effective at elicitingprogressively higher factor scores.
Revised: Hypothesis 3 saw mixed support; Kendall’s tau-b correlation tests (reported in Appendix E) indicate strong positive correlations between the allowable suboptimality and brokenness factor scores, suggesting that the trajectory generation method was effective at eliciting progressively higher factor scores.

Original: However, tests for the competence conditions indicateda moderate negative correlation, and tests for curiosity conditions were not signiﬁcant.
Revised: However, tests for the competence conditions indicated a moderate negative correlation, and tests for curiosity conditions were not signiﬁcant.

Original: Asshown in Fig.
Revised: As shown in Fig.

Original: 4, while participants found that 12x and 1x were the most and least “ ”for experiments focused on curiosity and brokenness, this relationship was ﬂipped for thecompetence experiments.
Revised: 4, while participants found that 12x and 1x were the most and least “ ” for experiments focused on curiosity and brokenness, this relationship was ﬂipped for the competence experiments.

Original: When optimizing for competence, the model emphasizes over-coverage of the goal region as wellas coverage of the house as a whole (see Fig. 3).
Revised: When optimizing for competence, the model emphasizes over-coverage of the goal region as well as coverage of the house as a whole (see Fig. 3).

Original: Due to the associated task-cost penalty, coverageoutside of the goal begins to appear in the 4x condition of Experiment I and the 12x condition of
Revised: Due to the associated task-cost penalty, coverage outside of the goal begins to appear in the 4x condition of Experiment I and the 12x condition of

Original: Experiment II, and participants’ responses indicate that it is a key driver of negative attributions ofcompetence.
Revised: Experiment II, and participants’ responses indicate that it is a key driver of negative attributions of competence.

Original: Some emphasized that time spent not cleaning the bedroom was “wasted movement 
Revised: Some emphasized that time spent not cleaning the bedroom was “wasted movement in

Revised: Appendix signiﬁcant difference

Original: [Figure]
Revised: [Figure]

Original: Curiosity
Revised: Curiosity

Original: Brokenness Competence
Revised: Brokenness Competence

Original: Curiosity
Revised: Curiosity

Original: Experiment I
Revised: Experiment I

Original: Experiment II
Revised: Experiment II

Original: Competence
Revised: Competence

Revised: Brokenness

Original: [Table]
Revised: [Table]

Original: Competence
Revised: Competence

Original: [Table]
Revised: Brokenness

Original: Curiosity 1x 
Revised: Curiosity 1x 2.51 (

Original: [Table] [Table]
Revised: [Table] [Table]

Original: [Table] [Table]
Revised: [Table] [Table]

Original: 12x
Revised: 12x

Original: [Table]
Revised: [Table]

Original: [Table] [Table] 
Revised: [Table] [Table] [Table]

Original: [Table]
Revised: [Table]

Original: in the wrong room” (Exp.
Revised: the wrong room” (Exp.

Original: I-Competence), while others attributed the deviation to being “lost” or“totally confused” ( Exp.
Revised: I-Competence), while others attributed the deviation to being “lost” or “totally confused” (Exp.

Original: I-Competence).
Revised: I-Competence).

Original: In less extreme conditions, users expressed uncertaintyabout what drove the behavior, saying they were “not sure if robot is cleaning outside the bedroomcause there might be dirt that can be brought in, or just confused as to parameter of bedroom” (Exp. ICompetence, 4x).
Revised: In less extreme conditions, users expressed uncertainty about what drove the behavior, saying they were “not sure if robot is cleaning outside the bedroom cause there might be dirt that can be brought in, or just confused as to parameter of bedroom” (Exp. ICompetence, 4x).

Original: A minority of users thought that the extra motion was worthwhile, marking the12x trajectory as the most competent because it “cleaned more areas in both rooms” or “completedthe entire home from bedroom to kitchen” (Exp.
Revised: A minority of users thought that the extra motion was worthwhile, marking the 12x trajectory as the most competent because it “cleaned more areas in both rooms” or “completed the entire home from bedroom to kitchen” (Exp.

Original: I-Competence).
Revised: I-Competence).

Original: The model overestimated theprevalence of people that would appreciate the additional coverage of the environment, as indicatedby both the “most/least” selections and the NLL.
Revised: The model overestimated the prevalence of people that would appreciate the additional coverage of the environment, as indicated by both the “most/least” selections and the NLL.

Original: We speculate that the format of the experiment—wherein participants view the optimal trajectory and mentally anchor their ratings against it—is acontributing factor; participants may be more inclined to rate the robot as competent when viewingthe optimized trajectories in real-world settings.
Revised: We speculate that the format of the experiment— wherein participants view the optimal trajectory and mentally anchor their ratings against it—is a contributing factor; participants may be more inclined to rate the robot as competent when viewing the optimized trajectories in real-world settings where direct comparison to the task-optimal trajectory is less likely.

Original: Trajectories optimized to look broken progressively cover less of the goal region before ultimatelydevolving into repeated circular motion near the start point (see Fig. 3).
Revised: Trajectories optimized to look broken progressively cover less of the goal region before ultimately devolving into repeated circular motion near the start point (see Fig. 3).

Original: The majority of users concurred in their assessment of the 12x condition as “defective”, with some remarking that it seemedoverwrought, “a joke version of the robot” (Exp. II-Brokenness).
Revised: The majority of users concurred in their assessment of the 12x condition as “defective”, with some remarking that it seemed overwrought, “a joke version of the robot” (Exp. II-Brokenness).

Original: The model underpredicted the extent of participants’ agreement that the optimal trajectory would be perceived as not broken, but thepredictive performance across all brokenness conditions was still the strongest of the three factors.
Revised: The model underpredicted the extent of participants’ agreement that the optimal trajectory would be perceived as not broken, but the predictive performance across all brokenness conditions was still the strongest of the three factors.

Original: When optimizing for curiosity, the model emphasized over-coverage of the goal region, overlappingmotion, hook-like patterns and visiting penalized states depicted with vases (see Fig. 3).
Revised: When optimizing for curiosity, the model emphasized over-coverage of the goal region, overlapping motion, hook-like patterns and visiting penalized states depicted with vases (see Fig. 3).

Original: Someparticipants highlight the extra coverage as the reason for selecting the 12x as the most curiouscondition, saying the robot “cleans very well but cleaned the same place multiple time, roamingwithout reason” or that  “dawdled around a lot, getting hyper ﬁxated on certain spots” (Exp. IICuriosity).
Revised: Some participants highlight the extra coverage as the reason for selecting the 12x as the most curious condition, saying the robot “cleans very well but cleaned the same place multiple time, roaming without reason” or that it “dawdled around a lot, getting hyper ﬁxated on certain spots” (Exp. IICuriosity).

Original: The same factor is highlighted by participants in less extreme conditions, with onespeculating of the 4x trajectory that “maybe something caught its eye while it was working and it gotso distracted that he totally kept getting off track” (Exp.
Revised: The same factor is highlighted by participants in less extreme conditions, with one speculating of the 4x trajectory that “maybe something caught its eye while it was working and it got so distracted that he totally kept getting off track” (Exp.

Original: I-Curiosity).
Revised: I-Curiosity).

Original: The change in the distributionof curiosity factor scores was expected to be small and the observations bear the predictions out,though it is notable that despite the subtle differences a majority of participants select either 4x or12x as the “most curious” trajectory across both experiments.
Revised: The change in the distribution of curiosity factor scores was expected to be small and the observations bear the predictions out, though it is notable that despite the subtle differences a majority of participants select either 4x or 12x as the “most curious” trajectory across both experiments.

Original:  Discussion
Revised:  Discussion

Original: Our framework is a general approach for endowing robots with a sensitivity to the behavioral attributions their motion elicits.
Revised: Our framework is a general approach for endowing robots with a sensitivity to the behavioral attributions their motion elicits.

Original: We illustrated its application to coverage motions, but we envisiona lively stable of related instances stretching across domains from delivery service robots to robotarms in fulﬁllment centers.
Revised: We illustrated its application to coverage motions, but we envision a lively stable of related instances stretching across domains from delivery service robots to robot arms in fulﬁllment centers.

Original: The process is the same; the robot arm’s designer will build a pool ofvideos and study users’ responses to—and their reasoning about—the motion over a broad set of dimensions, then learn a forward mapping from the features driving their reasoning to the attributionsin their responses.
Revised: The process is the same; the robot arm’s designer will build a pool of videos and study users’ responses to—and their reasoning about—the motion over a broad set of dimensions, then learn a forward mapping from the features driving their reasoning to the attributions in their responses.

Original: While some features such as path length or redundancy may map over from thecoverage domain, others like the shape of the acceleration proﬁle may need to be added to captureperceptions of danger or erraticism.
Revised: While some features such as path length or redundancy may map over from the coverage domain, others like the shape of the acceleration proﬁle may need to be added to capture perceptions of danger or erraticism.

Original: The reverse translation from a desired attribution to a new trajectory can be realized by searching in the space  trajectories, using the attribution features to guidethe process—something that may have a pronounced impact in a higher dimensional planning space.This optimization can be naturally constrained in terms of the maximum permissible task-cost of thetrajectory.
Revised: The reverse translation from a desired attribution to a new trajectory can be realized by searching in the space of trajectories, using the attribution features to guide the process—something that may have a pronounced impact in a higher dimensional planning space.

Original: While our results showed that the framework’s performance transferred to a similar environment,exploring its application to alternative settings is important future work.

Original: In the setting we explored,the observer looks at the robot’s motion from a top-down perspective, but it’s often the case thatan observer will watch a robot’s motion from a different perspective, which may result in differentimpressions. Towards our goal of employing this framework on a real robot, we will explore datacollection techniques and environments that account for variability in observer perspectives. Thefeatures and the learned mappings from features to attributions are speciﬁc to the types of environments and the task considered and would likely need to be augmented to work more broadly. Inthe future, we imagine that robot designers will have access to a wide array of well-studied featureswith which to bootstrap their system, and when human-robot interaction data is abundant, we maysee the rise of learned representations that can power the understanding and generation of motionwith minimal additional supervision.
Revised: We haven’t yet addressed some important aspects of behavioral attribution.

Original: A Initializing a Pool of Trajectories

Original: Our approach suggests beginning with a pool of trajectories, however obtaining this pool can posea bootstrapping problem.

Original: It’s unlikely that a diverse corpus of trajectories—one that would spanthe feasible attribution space and enable a data-driven extraction approach—would already exist.

Original: Inorder to create such a corpus, one would need to be conﬁdent that they have included trajectoriesthat adequately cover the range of attributions that are perceivable in a domain, but the lack of suchinformation is why we want the corpus of trajectories to begin with.

Original: We broke this cycle by referencing existing literature on the perceptions of robot vacuum cleanersto select six adjectives we considered as candidate attributions: curious, broken, energetic, lazy,lost, scared.

Original: We then manually demonstrated six trajectories that we judged to maximally expressthese candidates.

Original: We collected responses to these trajectories and conducted an initial analysis ofwhat aspects of the motion users said contributed to their ratings.

Original: This informed the creation ofan initial subset of the features we would use. Additional trajectories were then generated usinga hill-descending search in the space of trajectories optimizing for incrementally altering individual features ( ± 0.1-0.3) selected at random while holding other features constant. We found thatalternative optimization criteria, like diversity, would lead to degenerate or trivial trajectories whichhappened to have extreme feature values. These new trajectories were posed to users for their ratings.
Revised: While our results showed that the approach’s performance transferred to a similar environment, future work should use more disparate environments to determine the limits of its generalization.

Original: Simultaneously, we asked them to demonstrate how they would “clean the bedroom in a waythat makes the robot look ” for random items fromour questionnaire. This feedback fed backinto analysis and the process was cycled through two more times with a subset of the generated anddemonstrated trajectories, resulting in the ﬁnal exploratory dataset and trajectory featurization. B Loadings The factor loadings of our ﬁnal model, derived via exploratory factor analysis of the exploratorydataset, are shown in Table 4.
Revised: In the setting we explored, the observer looks at the robot’s motion from a top-down perspective, but different perspectives may result in different impressions.

Original: [Table]

Original: We investigated the sensitivity of our candidate models’ performance on unseen trajectories to increased amounts of training data. We divided our ﬁnal dataset, holding out 20% of the trajectories,then trained and tested models using varying percentages of the training data, repeating the evaluation with 8 randomized folds of the training data. The results, shown in Fig. 6, indicate diminishingreturns beginning around the use of 50% of the training data.
Revised: Further research should evaluate data collection techniques and environments that account for variability in observer perspectives.

Original: D Trajectory Optimization

Original: We would like to generate trajectories that elicit a particular attribution according to the optimization (1). We have the forward model f B | Ξ | φ ( ξ ) which predicts a distribution over attributions given Train Data Used (%) 2. A v e r a g e
Revised: The features and the learned mappings from features to attributions are speciﬁc to the types of environments and the task considered and would likely need to be augmented to work more broadly.

Original: T e s t

Original: N

Original: LL

Original: C=

Original: C=

Original: Ens C= the featurization of a particular trajectory.

Original: This model affords two routes towards realizing the optimization.

Original: In the ﬁrst, we directly optimize the features to maximize the objective.

Original: However, in thatcase, a further optimization would be needed to ﬁnd a trajectory that has the desired feature vector, and it is possible (and common in practice) that there does not exist a trajectory that producesthe target features.

Original: We instead adopt an alternative approach, in which we search in the space oftrajectories.

Original: This space is large, and ingeneral there is no clear best way to structure the search. Fortunately the features we use have  a clear relationship with patterns of motion, so we can easilysample trajectories that increase the activation of individual features. Given a trajectory, we samplea large set of neighboring trajectories using the following modiﬁcations: Action modiﬁcation : The trajectory is scanned and new trajectories are initialized by individuallywitholding each state s i .
Revised: We imagine that, in the future, robot designers will have access to a wide array of well-studied features with which to bootstrap their system, and when human-robot interaction data is abundant, we may see the rise of learned representations that can power the understanding and generation of motion with minimal additional supervision.

Original: The single removed state is replaced by selecting every validalternative action from s i − 1 and reconnecting the trajectory with a shortest path to s i +1 .

Original: Shortcutting : Sections of the trajectory are deleted uniformly at random and the trajectory isreconnected with a shortest path.

Original: We sample twice as many cuts as there are states inthe trajectory.

Original: Shortcutting is a well established post-processing step in motion planning,helping to uncover shorter or cheaper trajectories that still satisfy the objective. Template Insertion : A sequence of states is patched into the trajectory beginning at each s i . Weused a “straight” template, formed by taking the action used in s i − 1 and repeating it twice,and a “U” template, formed by taking three actions in proceeding clockwise or counterclockwise directions. The trajectory is reconnected with a shortest path to s i +1 .
Revised: Acknowledgments

Original: Bothtemplates were directly motivated by participant feedback highlighting these patterns ascontributing to the appearance of an organized principle to the robot’s motion.

Original: Collision Seeking : The trajectory is scanned and collision-avoiding actions are individually replaced with collision-causing actions if they are available from a state s i . The trajectoryis then reconnected with a shortest path to s i +1 . This sampler was motivated by participant responses highlighting collisions as contributing to their ratings of components of thebrokenness score. These same modiﬁcations are generated by the ”Action modiﬁcation”sampler.
Revised: This work was (partially) funded by the National Science Foundation IIS #2007011, National Science Foundation IIS #1924435 “Program Veriﬁcation and Synthesis for Collaborative Robots,” National Science Foundation DMS (#1839371), the Ofﬁce of Naval Research, US Army Research

Original: We double sample these to reduce the chance that they are dropped in a subsequentsubsampling step.

Original: Overcoverage : A random section of the trajectory s i ..

Original: s j between 3 and 6 states long is selecteduniformly at random and the trajectory is modiﬁed to backtrack this portion by insertingreverse ( s i ..

Original: s j ) followed by s i ..

Original: s j in place of s j .

Original: This modiﬁcation is motivated by participant feedback that highlighted redundant coverage as evidence of attentiveness, explorationor attention to detail.

Original: These samplers, and a good initialization produced by solving the original task using a planner, makesampling-based greedy hill-descending search in the space of trajectories effective.

Original: As practicalconsiderations, we discard sampled trajectories longer than 250 states to prevent the search fromexploding, then we randomly subsample 250 of the modiﬁed trajectories, and we terminate thesearch once 750 steps have been taken.

Original: As illustrated in Fig.

Original: 7, this search process is generally effective at making use of additional allowable suboptimality to produce trajectories that the model predicts to better elicit a desired attribution.

Original: Some non-monotonicity can be observed in one of the brokenness and one of the curiosity plots.

Original: Astrajectories get longer, the pool of neighbors sampled is diluted with many more small changes andour subsampling step can lead the search to randomly discard more fruitful paths.

Original: Factor score 0.

Original: D e n s it y

Original: Competence

Original: Factor score

Original: Brokenness Factor score Curiosity Goal
Revised: Laboratory CCDC, Amazon, and Honda Research Institute USA.

Original: [-Bound 222 2 
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Revised: [-Bound 222 2 
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Original: Suboptimality

Original: K L d i v e

Original: [-r g e n ce 222 2 
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Revised: [-r g e n ce 222 2 
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Original: [-Suboptimality 222 2 
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Revised: [-Suboptimality 222 2 
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Original: Suboptimality (a) Training environment (as used in Experiment I) Factor score 0. D e n s it y Competence
Revised: This work was partially supported by the This material is based upon work supported by the National Science Foundation Graduate

Original: Factor score

Original: Brokenness Factor score Curiosity Goal
Revised: Research Fellowship under Grant #

Original: [-Bound 222 2 
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Revised: [-Bound 222 2 
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Original: Suboptimality

Original: K L d i v e

Original: [-r g e n ce 222 2 
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Revised: [-r g e n ce 222 2 
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Original: [-Suboptimality 222 2 
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Revised: [-Suboptimality 222 2 
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Original: Suboptimality (

Original: [Figure]

Original: E Statistical Results

Original: We conducted one-sample Kolomogorov-Smirnov tests comparing the empirical distribution of factor scores elicited from participants against the distribution predicted by our model.

Original: To account forthe increased likelihood of Type-I errors due to multiple testing, the Holm-Sidak adjustment wasapplied to the resulting p values.

Original: The results of the tests are provided in Table 5.

Original: [Table]

Original: [Table]

Original: For Experiment I, the tests failed to indicate a signiﬁcant difference between the distributions for allbut the Competence-1x condition, suggesting that there is insufﬁcient evidence to support inequivalence between predicted and observed distributions.

Original: For Experiment II, the tests failed to indicate asigniﬁcant difference between the distributions for all conditions, suggesting that there is insufﬁcientevidence to support inequivalence between predicted and observed distributions.

Original: Kendall’s tau-b correlations were run to determine the relationship between the allowable suboptimality of a generated trajectory (1, 2, 4 or 12) and the observed factor scores for the attribution understudy.

Original: The correlation coefﬁcients and p values are reported in Table 6.

Original: The results indicate strongpositive correlations between the allowable suboptimality and brokenness factor scores, suggestingthat the trajectory generation method was effective at eliciting progressively higher factor scores.

Original: However, tests for the competence conditions indicated a moderate negative correlation, and testsfor curiosity conditions were not signiﬁcant.