Original: Inﬂuencing Behavioral Attributions to Robot Motion During Task Execution
Revised: Inﬂuencing Behavioral Attributions to Robot Motion During Task Execution

Original: 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.
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 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.
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 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.
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 in a 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 task execution and learn a probabilistic model that maps trajectories to attributions.
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 desired behavioral attribute.
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 for coverage 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 human perceptions 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 unambiguous internal objectives, solely optimizing such criteria might result in behavior that is difﬁcult to interpret 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 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.
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 attribution 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 behavior traits [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 as presentation 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 deeper character 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 desired human 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 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.
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, shown in Fig.
Revised: We propose a framework, shown in Fig.

Original: 1, that addresses these challenges by integrating a learned model of human attribution into a robot’s trajectory generation process.
Revised: 1, that addresses these challenges by integrating a learned model of human attribution into a robot’s trajectory generation process.

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

Original: We
Revised: We

Original: [Figure]
Revised: [Figure]

Original: trace an application of the framework to a virtual robot vacuum cleaning task.
Revised: trace an application of the framework to a virtual robot vacuum cleaning task.

Original: 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.
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.

Original: Some aspects, such as partial trajectory observation or application to highly articulated robots, remain for future work.
Revised: 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 G in a human environment.
Revised: We consider a robot performing a task G in a human environment.

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

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

Original: ( ⌅ , A , P , C ) where ⌅ is a space of robot trajectories, A denotes the robot action space, P :
Revised: ( ⌅ , A , P , C ) where ⌅ is a space of robot trajectories, A denotes the robot action space, P :

Original: ⌅ ⇥ A !
Revised: ⌅ ⇥ A !

Original: ⌅ represents a deterministic state transition model, and C : ⌅ !
Revised: ⌅ represents a deterministic state transition model, and C : ⌅ !

Original: R is a trajectory cost.
Revised: 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 time T ) by executing a trajectory ⇠ = ( 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 this trajectory ⇠ is fully observed by a human who is aware of the task speciﬁcation G .
Revised: We assume that this trajectory ⇠ is fully observed by a human who is aware of the task speciﬁcation G .

Original: The observer makes an inference of the form I B : ⌅ ⇥ G !
Revised: The observer makes an inference of the form I B : ⌅ ⇥ G !

Original: 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
Revised: 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

Original: B .
Revised: B .

Original: 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.
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, 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
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 ⇠ : B ⇥ G !
Revised: I ⇠ : B ⇥ G !

Original: ⌅ .
Revised: ⌅ .

Original: In other words, we assume that there is a “way” that a curious—or any other attribution—robot should 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: In practice, we will realize both of these inferences as probabilistic maps.
Revised: In practice, we will realize both of these inferences as probabilistic maps.

Original: 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.
Revised: 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 the form I B , and I ⇠ .
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 communicative effects 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 been shown to enable effective human-robot collaboration in manipulation tasks [10], or smooth robot navigation 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] when the robot can’t complete a task.
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 stylistically distinct 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 of robot 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 vacuum cleaners 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 previous efforts to characterize human perceptions and attributions to 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 implicitly communicative 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 robot motion [10, 11, 23, 13] in that we also incorporate a model of human inference into the robot’s motion 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 communication of task-related attributes, our focus is instead on communicating high-level, behavioral attributes through 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-dimensional discrete 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) 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.
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 ⌅ is the space of all possible 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 A consists of deterministic movements in the cardinal directions.
Revised: The robot action space A consists of deterministic movements in the cardinal directions.

Original: 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.
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: A penalty 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 knowledge for 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 shown in Fig.
Revised: Using the home layout shown in Fig.

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

Original: The ﬁrst factor, which we 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 on the 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 a 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 the items 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 ⇠ as a tuple b = ( b competent , b broken , b curious ) 2 B where the 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 map directly to the space of attributions, so we constructed a low-dimensional space  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: This allows us to describe a trajectory ⇠ as a vector  ⇠ =  ( ⇠ ) 2  .
Revised: This allows us to describe a trajectory ⇠ as a vector  ⇠ =  ( ⇠ ) 2  .

Original: The feature space was inspired by relevant literature on human behavioral attribution to robot motion and enriched with features appearing 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 is listed 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 ⇠ , 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.
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| ⌅ ( b |  ⇠ ) : B !
Revised: B| ⌅ ( b |  ⇠ ) : B !

Original: R .
Revised: R .

Original: 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 |  ⇠ ) =
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 |  ⇠ [Equation]

Original: P
Revised: =

Original: Ci =1 ↵ i (  ⇠ ) k i ( b |  ⇠ ) where ↵ i , i = 1 , . . .
Revised: [Equation] where ↵ i , i = 1 , . . .

Original: , C , is a mixing coefﬁcient, and k i is a multivariate Gaussian kernel function with mean µ i and covariance ⌃ 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 ↵ i and the Gaussian parameters µ i and ⌃ i are functions of the featurized trajectory  ⇠ .
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 are implemented 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: f ens
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 trained all models using an average negative log likelihood (NLL) loss function, the Adam optimizer [ , noise regularization  and early stopping.
Revised: We trained all models using an average negative log likelihood (NLL) loss function, the Adam optimizer [28], noise regularization [29], and early stopping.

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

Original: 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.
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 withattribution ratings.
Revised: The ﬁnal version of the set includes 126 trajectories with [Table] attribution 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 indicates the typical quality of the prediction and the standard deviation indicates the degree to which this varied 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 reported with 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 uniform baseline, 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 performs best 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 ,  2 b ) centered on a 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  b serves as a tolerance 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 a density 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
Revised: Together with the task requirements as described by the cost function C , we realize the inference

Original: I ⇠ as an optimization of the form:
Revised: 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 | ⌅ |  ( ⇠ ) 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 how suboptimal 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 or to ﬁt in power constraints—the robot designer need only set w to express the hard bound.
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 illustrated in 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: The search 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 the attribution 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, and 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 the divergence 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 after a 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: A detailed 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 new trajectories.
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 data collection, 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 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.
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 target distribution 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 questions used 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 corresponding to 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-ended question 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 balanced attribution 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 15 minute 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 distributed amongst 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: The 95% 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 uniform model, indicating that the model was able to meaningfully predict attributions in the layout it 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 II was signiﬁcantly lower than the uniform model, indicating that the model remains informative even under modiﬁcations to the environment 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 brokenness factor scores, suggesting that the trajectory generation method was effective at eliciting progressively 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 indicated a 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: As shown 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 the competence 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 well as 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, coverage outside 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 of competence.
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 in 
Revised: Some emphasized that time spent not cleaning the bedroom was “wasted movement in the wrong room” (Exp.

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

Original: [Figure]
Revised: [Figure]

Original: Curiosity
Revised: Curiosity

Original: Brokenness Competence
Revised: [Figure]

Original: Curiosity
Revised: Curiosity

Original: Experiment I
Revised: Experiment I

Original: Experiment II
Revised: Experiment II

Original: Competence
Revised: [Figure] [Figure]

Original: Brokenness

Original: [Table]
Revised: [Figure]

Original: Competence

Original: Brokenness
Revised: Brokenness

Original: Curiosity 1x 2.51  (
Revised: Curiosity 1x 2.51 (0.69) 2.44 (0.76) 2.37 (

Original: [Table]
Revised: [Table]

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

Original: [Table]
Revised: [Table]

Original: 12x
Revised: 05) 2x 2.76 (

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

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

Original: [Table]
Revised: [Table]

Original: the wrong room” (Exp.
Revised: 4x 2.98 (

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

Original: I-Competence).
Revised: [Table]

Original: 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).
Revised: [Table] [Table] [Table] 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 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.
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 the prevalence of people that would appreciate the additional coverage of the environment, as indicated by 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 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.
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 ultimately devolving 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 seemed overwrought, “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 the predictive 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, overlapping motion, 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: 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).
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 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.
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 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.
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 envision a lively stable of related instances stretching across domains from delivery service robots to robot arms 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 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.
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 the coverage domain, others like the shape of the acceleration proﬁle may need to be added to capture perceptions 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 of trajectories, using the attribution features to guide the process—something that may have a pronounced impact in a higher dimensional planning space.
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: We haven’t yet addressed some important aspects of behavioral attribution.
Revised: We haven’t yet addressed some important aspects of behavioral attribution.

Original: 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.
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: 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.
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: Further research should evaluate data collection techniques and environments that account for variability in observer perspectives.
Revised: Further research should evaluate data collection techniques and environments that account for variability in observer perspectives.

Original: 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.
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: 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.
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: Acknowledgments
Revised: Acknowledgments

Original: 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 Laboratory CCDC, Amazon, and Honda Research Institute USA.
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 Laboratory CCDC, Amazon and Honda Research Institute USA.

Original: Thiswork was partially supported by the This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant #
Revised: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant #1762114.

Revised: We thank the scientiﬁc Python Community for developing the core set of tools that enabled this work, including NumPy [30], SciPy [31], Pingouin [32], PyTorch [33] and Matplotlib [34].