In the vicinity of humans, it is not only important what a robot does, but also how these actions are performed. Especially in the context of robotic assistants, trajectories should not only be feasible and obstacle-free, but also comply with the user’s preferences. However, preferences over trajectories may vary between users, environments, tasks and also time, which poses challenges to design general cost functions. Instead, it can be beneficial to learn preferences directly from the user.
To learn preferences, input from the user in the form of demonstrations or feedback on candidate trajectories is necessary. Especially for robots with multiple degrees of freedom or for impaired users, providing trajectory demonstrations may be prohibitive. Giving feedback on the robot’s behavior, however, is possible and—especially for relative instead of absolute ratings—does not require expert knowledge.
In order to obtain the human judgment of a trajectory, different modalities such as screen-based rating or speech are conceivable. Brain signals as a feedback modality can be desirable because their measurement does not interfere with the primary task and—especially in the context of robotic assistants for impaired users—can potentially be recorded from users who cannot reliably control robots through other modalities. However, signals measured using non-invasive electroencephalography (EEG) typically have an unfavorable signal-to-noise ratio that makes it challenging to utilize this information based on single brain responses.
In this work, we address the problem of learning trajectory preferences from EEG-based user feedback. For this, we let the user observe multiple trajectory pairs and additionally present a—potentially incorrect—preference statement that indicates which of the observed trajectories was supposedly better. This offers two potentially informative sources for discriminative brain signals: As depicted in Fig. 1
, we classify the user’s brain signals during robot observation and after showing preference statements to predict the actual pairwise preferences of the user and subsequently rank trajectories across pairs using the EEG-based predictions. To facilitate a quantitative evaluation that is comparable across users, we asked them to give feedback according to common target trajectories rather than personal preferences in this work. We compare our approach against explicit user feedback collected from button presses after the preference statements.
Our main contributions are: 1) We propose an approach to estimate user feedback to trajectories by classifying brain signals both during trajectory observation and in reaction to preference statements. 2) We show in experiments withparticipants, who observed videos of real robot trajectories, that these brain signals are informative about trajectory judgment and that our approach enables reliable decoding of the preferred trajectory in pairwise comparisons in an offline manner. 3) We demonstrate that these pairwise preference predictions based on brain signals can be used to successfully identify the target trajectory from the observed ones with a performance that is comparable to explicit feedback in the form of button presses.
2 Related Work
In order for robots to operate successfully and adequately in human environments, motion planning should incorporate the user’s demands. In the past, the modeling of human preferences has been addressed using cost functions Dragan and Srinivasa (2014); Busch et al. (2017) and by integrating hand-crafted costs into planning Mainprice et al. (2011). The use of demonstrations allows to learn reward functions, e.g., from navigation behavior Kretzschmar et al. (2016) or corrective actions for robot manipulators Bajcsy et al. (2017).
Rather than modeling costs manually or demonstrating near-optimal behavior, behavioral feedback can also be used to improve robotic actions. For example, legibility can be optimized by minimizing the time until the user can press a button corresponding to the anticipated goal of the robot Busch et al. (2017). While absolute ratings of robotic actions would be desirable for ranking a set of options, it is easier for human users to give relative feedback by comparing a small set of items. Relative feedback has been used to model, e.g., human perception of “naturalness” of robot configurations Jeon and Dragan (2018) or preferences in simulated driving Sadigh et al. (2017). While many approaches assume label noise in the user feedback Akrour et al. (2014); Sadigh et al. (2017), it is typically small and assumed to vary based on the reward differences. In contrast, strong measurement noise is typically encountered when using EEG signals. Closely related to our setting of using human feedback to a robot’s action is the work by Jain et al. Jain et al. (2015), which aims at learning preferences based on human feedback. However, they utilize screen-based re-ranking of trajectories and kinesthetic teaching as user feedback.
. In reactive attention-based BCIs, discriminative information can be obtained from differing responses—mostly in the form of event-related potentials (ERPs)—to stimulus classes, such as identifying “surprising” outlier stimuli or stimulus changesSchreuder et al. (2011). Due to the low signal-to-noise ratio, prediction is typically limited to binary classification. A large body of different classification approaches specifically tailored to EEG signals exists Lotte et al. (2018). State-of-the-art results increasingly utilize methods from Riemannian geometry Yger et al. (2017); Barachant et al. (2013): Assuming that relevant information about the mental state in a given time interval can be represented by the covariance matrix, the corresponding manifold structure suggests using non-Euclidean distance measures between data points. Generally, classification performance heavily depends on the experimental task—implying the mental states to be classified—and varies from user to user.
Many common BCIs are based solely on the appearance or the identity of an attended visual stimulus, whereas feedback on trajectories requires the decoding of the user’s judgment of an action in a context. Error-related potentials Chavarriaga et al. (2014), i.e., brain responses to committed or observed errors, form one common type of brain responses useful for classification. Error-related potentials are interesting since they are based on judgment of behavior, but typically also require its fast comprehension by the user. Brain activity from time windows that are not time-aligned to specific stimuli can also be informative—e.g., to predict workload Schultze-Kraft et al. (2016) or upcoming task performance Meinel et al. (2016). Although desirable for applications, predictive performance in such asynchronous settings is typically lower than in stimulus-aligned ones.
Recent work has incorporated brain responses to robotic behavior, e.g., for error recognition Salazar-Gomez et al. (2017) or learning gesture mappings with reward signals from EEG Kim et al. (2017). In these contexts, the human judgment of the behavior could be performed near-instantaneously, greatly easing the temporal alignment of EEG signals for classification. However, in the case of observing more complex behavior (e.g., trajectories that have an identical start configuration but continuously deviate thereafter), the temporal alignment—i.e., the time point the human realizes one behavior is superior or inferior—cannot easily be inferred.
3 Decoding Trajectory Preferences from Brain Signals
We consider the problem of identifying a user’s preferred trajectory based on feedback by the user: Given a set of trajectories , we want to find a target trajectory that maximizes the (unknown) reward of a human user in a given environment. In order to estimate , we opt to query the user for relative preference feedback and use this feedback—from EEG or from explicit button presses for comparison—to rank trajectories.
After obtaining feedback, our approach consists of two prediction modules, which are depicted in Fig. 1: First, we propose to classify pairwise feedback to trajectories from brain signals during robot observation and in response to preference statements as described in Section 3.1. We utilize the covariance representations of signals, using methods from Riemannian geometry. Second, we use this feedback to rank trajectories both in an instance-based and a feature-based manner (see Section 3.2). Note that training of both modules is independent, i.e., classifiers for EEG decoding are not specific to different environments or preferences and only depend on the user.
In order to obtain pairwise preference feedback from a user, we
perform a sequence of trajectory comparisons
. Each comparison
consists of two trajectories that
are presented to the user (i.e.,
). To obtain comparative
judgment of the two trajectories, we propose to use preference
statements: After presenting a pair of trajectories, we show a
textual statement to the user in the form of “Path 2 is better than
The correctness of the statement implies a preferred trajectory and should also induce differing decodable mental states. For control, we subsequently ask the user to press a button if she judges this statement to be correct (c.f., Fig. 2). Hence, for each comparison , we observe a behavioral response by the user in response to the statement (i.e., a button press if the statement is correct), which implies the user’s pairwise preference.
3.1 Decoding Pairwise Preferences from Brain Signals
We have two potentially informative sources of user feedback based on brain responses in each comparison: the brain activity during watching the trajectory execution by the robot—the observation setting—and the response to a subsequent statement (e.g., “Path 1 is better than path 2.”). As discussed in Section 2, the latter synchronous case is better suited for classification using brain signals, whereas the former asynchronous one would be desirable to collect information passively during fluent human-robot interaction. We train separate classifiers for both types of signals as well as a combined one. As input, we extract features from fixed-sized windows of the continuous frequency-filtered EEG signal.
Segmentation and Labeling of Brain Signals
For the observation setting, we use a
window temporally centered in the trajectory execution, leading to feature vectorsfor trajectory in comparison (). Here, denotes the number of channels in the recording and the duration of the window in samples. The temporal centering encodes our hypothesis that the user judgment evolves, with increasing confidence, during the observation and—with a high uncertainty of the user at the start and a low one at the end—intermediate signals might capture discriminative mental states. We assume supervision in the form of a training dataset for which the user’s preference—the target trajectory —is known. While we aim to infer the pairwise preference in each comparison, such a comparative judgment is only possible after having observed both trajectories. Hence, comparative labels are not applicable for observation windows. Instead, we opt to use the similarity between observed candidate trajectories and the target trajectory. As a trajectory similarity measure, we use a geometric distance: For trajectory , we temporally normalize trajectory durations to
and interpolate trajectory waypoints using cubic splines to get a trajectory representation, which we use to calculate the distance
Equipped with this distance, we can calculate for each trajectory in our training data. We obtain binary labels for windows by thresholding on the median of all distances in the training data. Other absolute trajectory metrics or ratings could be used alternatively. Given the predicted distance class for each of the two trajectories in comparison (), we derive the pairwise-preferred trajectory based on the smaller of the two.
For the statement response, we extract a window for each comparison , starting with the onset of the statement. As a label, we use the correctness of each statement based on of the trajectories. Since the statements are comparative, the predicted correctness implies the pairwise-preferred trajectories . In the rare cases in which the behavioral response of the user did not correspond to our label (i.e., the button press implied a preference for the trajectory further away from the target), we assumed that the user’s brain state also reflected the behavioral judgment and consequently corrected these labels.
We also combine both feedback types in addition to classifying observation and statement windows separately. For this, we concatenate the predictions for the statement and the observation windows on the comparison level (), where each prediction is the output of the separately trained classifiers for each window type. Note that we order the observation-based predictions such that the first coincides with the supposedly better trajectory in the statement. For the combined setting, we use the labels
from the corresponding statements to train a logistic regression classifier.
Feature Extraction and Classification of Brain Signals
We use covariance-based features for the classification of both observation and statement windows. Since we expect time-locked event-related potentials only after the statement (c.f., Section 2), we perform baselining and augmentation for these windows: We baseline each of the statement windows by subtracting the channel-wise average activity in the preceding the window and augment them with prototype responses Barachant and Congedo (2014). As prototypes , we use the mean response for each class in the training data. Additionally, we reduce the channel count by projecting the data using obtained by selecting the top three components per class from an xDAWN decomposition Rivet et al. (2009). This leads to augmented statement windows .
For both feedback types ( or ), we calculate window-wise covariances using a Ledoit-Wolf regularization. To account for the symmetric positive-definiteness and the corresponding undesirable properties of the Euclidean distance Yger et al. (2017), we project each of the covariance representations into the corresponding tangent space at the Frechét mean of the training samples of the corresponding window type (c.f., Kolkhorst et al. (2018); Barachant et al. (2013)):
denotes the logarithm of a diagonalizable matrix (i.e., the logarithm of each element of the diagonal after the corresponding decomposition). The upper triangular entries of these projected covariancesare used as input to the classifier. Due to the typically small number of training samples that are available per user, we use -regularized logistic regression classifiers.
3.2 Trajectory Ranking based on Noisy Pairwise Preferences
In order to rank a set of trajectories based on pairwise preferences, we follow two conceptual approaches: In the instance-based setting, ranking is performed solely based on the identity of the compared trajectories (i.e., the index ), disregarding any additional (geometric) information about the trajectory. Alternatively, learning to rank can be based on (e.g., geometric) trajectory features . While only the latter feature-based approach allows to rank trajectories for which no user feedback has been observed, it depends on the expressiveness of the feature representations . Hence, we propose both an instance-based and a feature-based ranking approach for combining the pairwise predictions to identify preferred trajectories.
For instance-based ranking solely based on the pairwise comparison outcome, we use a modified Borda counting method Shah and Wainwright (2018): For each trajectory (which is a candidate in the comparisons ), we count the number of comparisons in which is the predicted pairwise preference, yielding . Here denotes the indicator function that returns 1 iff the argument is true. While conceptually simple, the method is asymptotically optimal for retrieving the most highly ranked items from noisy user observations Shah and Wainwright (2018)
. However, in the case of EEG-based pairwise preferences, we also have to account for substantial noise in the predictions, which typically differs between comparisons yet should be correlated to the classifier’s predicted probability
. We propose a heuristic extension to the Borda counting that weighs comparisons based on the confidence:
Hence, the goal is to find a such that a pairwise preference of over in comparison implies . Consequently, we want the projected feature differences to be positive and can use them to train a binary classifier Joachims (2002). As labels, we use the predicted pairwise preference relations based on the brain signals of the user (c.f., Section 3.1).
For the feature representation we include geometric information on the robot movement and on the environment interaction: For the movement, we include the end effector’s mean squared velocity, mean squared acceleration and mean and maximal squared jerk as well as mean and maximal joint velocities over the trajectory. For the environment interactions, we use the features proposed in Jain et al. (2015) (e.g., minimal distances to scene objects and distance from the goal), yielding a total of features. Note that also other—potentially more discriminative—feature representations could easily be used instead. We train a -regularized logistic regression classifier on this data and use the classifier predictions to rank trajectories.
In order to evaluate our approach for learning trajectory preferences from brain signals, we assessed the performance of different feedback types for predicting pairwise preferences as well the inference of target trajectories based on combining these predictions into a ranking. We performed the evaluation using data from experiments with participants. Specifically, we wanted to answer the following questions: (1) Are brain signals as a feedback modality—passively during trajectory observation or reactively after a preference statement—informative about user preferences? (2) Is it possible to classify responses to single comparisons in order to predict the pairwise-preferred trajectory? (3) Can we use these predictions to select a trajectory that is close to the user’s target trajectory?
The evaluation design requires a balancing of the diversity of (preference) trajectories against reproducibility, reduction of confounders and comparability across participants. To have identical trajectory execution for all participants, we opted to record videos of a Kuka iiwa robotic arm executing trajectories and showed these videos to the participants. While there is a mismatch between watching videos and observing a robot in the scene, we believe that directly observing the robot would likely be more immersive, and thus might lead to even stronger brain responses. Preference statements could also easily be presented by the robot similar to our setting (e.g., using speech). The recording quality of EEG in the proximity of a robot still allows successful decoding Kolkhorst et al. (2018).
While it would be desirable to let participants give feedback according to their personal preference trajectories, this can lead to infeasible desired target trajectories (especially for novice users) and differing class distributions in the pairwise preference prediction task, hindering performance comparability. Crucially, a geometric representation is not available for personal preference trajectories, which precludes a quantitative evaluation of the predicted preference trajectory based on geometric proximity to the ground truth. Therefore, we presented reference trajectories to the participants and instructed them to give preference feedback according to these references. To validate the adequacy of the references, we also asked participants to rate the personal agreement with the reference trajectories.
4.1 Experimental Setup
Each experiment session consisted of preference tasks with differing target trajectories. With nine comparisons per target trajectory, each participant observed a total of videos in comparisons. We recorded videos in four different environments with differing objects (resembling assembly or dinner settings as depicted in Fig. 3). In each environment, there were two different pairs of initial and final end-effector poses. For each of these pairs, two reference trajectories—each the target of a single preference task—were selected from different homotopy classes. Hence, all trajectories in a task had identical initial and final end-effector poses and only differed in the intermediate configurations. The trajectory videos had a mean duration of . In order to resemble a realistic robotic setup, a minority of videos also contained “failures” (e.g., the arm touches scene objects or an item is dropped from the gripper). We sampled candidate trajectories using RRT-Connect Kuffner and LaValle (2000)
and selected a subset to assure variance within tasks.
For each preference task (i.e., a block with a single target trajectory), we first showed the reference trajectory. Subsequently, we performed nine comparisons, each consisting of two videos, followed by a preference statement as depicted in Fig. 2. We only prompted for the button response after the appearance of the statement to reduce a possible influence of motor activity on the brain response. The order of trajectories in the statement was randomized and statements were balanced with respect to the expected behavioral response of the participants. Including pauses between videos and comparisons, one preference task took approximately 7 minutes.
We acquired the brain signals using a cap holding Ag/AgCl gel-based passive electrodes positioned according to the extended 10-20 system with a nose reference. Channel impedances were kept below . The amplifier sampled the EEG signals at . We used channels whose signals were frequency filtered to a band of to . For the statement responses, we resampled the data to .
We conducted experiment sessions with 14 participants. Following the
declaration of Helsinki, we received approval by the local ethics
committee and obtained written informed consent from participants
prior to the session. Before the first preference task, participants
familiarized themselves with the task in five comparisons that were
not analyzed. In data from three of the sessions, we observed a large
fraction of artifacts after the statements (more than 30% of windows
exceeded a min-max difference of in any
channel), likely caused by eye blinks.
While the EEG data of these sessions still contains discriminative information, classification would likely primarily be based on muscular artifacts rather than brain signals. Hence, we only kept data from the other participants. We did not reject any data of the remaining participants, enabling identical sample counts and ranking tasks. We trained separate classifiers for each participant and evaluated them in a chronological 5-fold cross-validation.
4.2 Results for Pairwise Preference Prediction
Before analyzing ranking performance, we discuss the intermediate pairwise preference prediction. We evaluated it based on the comparison accuracy using the trajectory with a smaller as the ground truth, which assures identical labels for all participants. Hence, also the behavioral response of the participants did not achieve a perfect score (which is in line with the assumption of noisily rational behavior). Nevertheless, the mean accuracy based on button presses (, see Fig. 5) indicated that the participants followed the task. We asked the last nine participants after the experiment to indicate whether the reference paths agreed with their personal preference. On a visual analog scale from “little” () to “much” (), participants marked an average of , with seven of nine indicating a tendency to agree (upper half of scale). When asked after each task, participants stated that reference trajectory matched their preference in of cases ( “agree” and “strong agree”).
Electrophysiology of Statement Responses
As an introspection into the signals used for classification,
Fig. 4 shows the classwise average potential in
a fronto-central channel of all participants in response to the
preference statements (which is better suited for visualization due to
the stimulus alignment).
The visually evoked responses after the statement’s appearance are similar for both classes until approximately . However, we observed a second positive deflection only for erroneous statements approximately after the statement. Such a response is plausible since the early response will mainly depend on the visual appearance of the stimulus and not upon the content of the text. The discriminative response could be observed relatively early considering the need for language processing. However, due to the repetitive nature of the comparisons, participants likely did not have to parse the language of the statement, but rather look for which trajectory number was mentioned first. The signal differences in the later part of the time window (approximately to ) might not solely be explained by the statement stimulus, but could also be influenced by the preparation of motor activity for the button press. However, the earliest occurrence of button presses was after the statement (mean across all participants), and results from a different experimental paradigm indicate that the decoding performance in judgment tasks does not rely solely on button press activity and that it can be improved when reducing motor-related signal components Kolkhorst et al. (2019).
EEG-based Classification of Pairwise Preferences
Inspecting the classification results for individual comparisons (as depicted in the left half of Fig. 5), we achieved a mean accuracy of when using the windows time-aligned to the preference statements. In the more difficult asynchronous observation setting—where we had no temporal alignment to specific stimuli—we still achieved an accuracy of . This is especially interesting since such information could potentially be recorded during regular interaction with the robot, with increasing confidence after repeated observations.
To check our expectations about the suitability of windows centered in the trajectory (c.f., Section 3.1), we also evaluated two additional window alignments during observation: Extracting time windows relative to the start or end of trajectories rather than the center performs worse, with accuracies of and , respectively.
Combining classifier output from both window types (accuracy of ) yielded improvements over only using the statement response. Note that in our evaluation setting (using identical target trajectories across all participants), “non-conforming” perception by the participant (indicated by a button accuracy of less than 1) is possible. This likely also affected the decodable brain states and therefore the corresponding accuracies for these trajectories.
Answering our first two questions, (1) brain signals both during trajectory observation and after preference statements were informative about user preferences and (2) this translated into an accuracy of on a single comparison level using combined observation and statement responses.
4.3 Results for Trajectory Ranking
Evaluating the identification of target trajectories from pairwise preferences, we examined 176 preference learning tasks, each consisting of nine pairwise comparisons. The pairwise preferences were estimated from brain signals or—for comparison with behavioral feedback—from button presses. Our experiment design allowed us to evaluate the ranking performance using geometric distances since we had the ground-truth target trajectories available. For this, we used as defined in Equation 1 in order to calculate the difference between the obtained and the best possible distance to the preference. In addition to this absolute score, we also report the normalized discounted cumulative gain (nDCG), which has a range from to and shows the relative performance based on the best possible obtainable ranking. As the relevance
for nDCG calculation, we used the negative distance from the preference, shifted by the maximum. We denote the nDCG of the top-ranked item with nDCG@1 and use nDCG@3 for the metric calculated based on the three highest-ranked trajectories. As a baseline method, we compared our ranking approaches to the trajectory preference perceptron proposed by Jain et al.Jain et al. (2015), using identical features for all methods (c.f., Section 3.2).
Mean ranking performance
Inspecting the results of instance-based ranking with incorporated confidences (i.e., using ) for different feedback types (see Fig. 5 and Table 1), we observed that it is indeed possible to successfully learn trajectory preferences from EEG-based user feedback. For this, the use of the statement or combined EEG features is needed. The latter achieved a mean of for the top-ranked trajectory.
Considering the three highest-ranked trajectories, the use of statement windows yielded an nDCG@3 of , compared to for the combined features. Limited by the lower performance on the comparison level, the ranking based on the observation setting performed substantially worse ( of and nDCG@3 of ).
Interestingly, the ranking based on combined EEG signals achieved a similar performance as the ranking obtained by explicit button presses (nDCG@1 of for combined EEG vs. for button and nDCG@3 of vs. , respectively). Note that the improvements (which might appear counter-intuitive at first) were due to taking into account confidence values from the EEG classifiers, which were not available for the button press (c.f., instance-based results without confidences in Table 1). One possible explanation for this is that for comparisons without a clear preference, this ambivalence results in non-discriminative brain signals whereas the button press forces an arbitrary choice.
|traj. perceptron Jain et al. (2015)|
Using our feature-based trajectory ranking approach (, where training labels are based on user feedback), we could observe that for low label noise (i.e., button presses), it outperformed all other ranking settings (mean of and a mean nDCG@1 of ). Since label uncertainty in the form of comparison confidences is, however, not incorporated in this approach, it performed worse than the instance-based ranking when utilizing the less accurate EEG-based feedback. In the adequate comparison with the instance-based approach without confidences, the feature-based ranking performed better. As shown in Table 1, our feature-based approach outperformed the trajectory preference perceptron proposed in Jain et al. (2015) in all feedback settings.
Analysis of Results for Individual Participants and Preferences
Performing identical experiments with all participants allowed us to gain insight into the influence of different tasks and users on the ranking performance. The heat maps in Fig. 6 indicate the performance of participants for the different preference tasks. Looking at the button results with low feedback noise in the top two matrices, the similarities within each individual column show that performance variations were systematic and depended on the set of trajectories and targets.
Specifically, we observed comparatively low performance for target trajectories 3 and 13. Here, also the button feedback accuracy (not shown) is lower for most participants, indicating “harder” comparisons that also translated into worse EEG-based decoding and ranking performance. While behavioral performance is similar across most participants, we observed a higher variance in the EEG-based setting due to the inherent inter-person variability in EEG measurements. However, a recovery of preferences was possible in most of the preference tasks for all participants.
Answering question (3), ranking based on EEG-based predictions was possible both in the instance-based and the feature-based setting. Moreover, we found that utilizing EEG-based confidence values in addition to the pairwise preference prediction allowed a ranking performance based on brain signals that is comparable to results obtained by button presses.
In this work, we presented a novel approach to learn user preferences for trajectories from brain signals based on pairwise comparisons. Our approach predicts pairwise preferences from EEG data both during passive observation of trajectories and in response to explicit statements. We utilize these predictions to rank observed trajectories.
In extensive experiments, we demonstrated that brain signals as a feedback modality were informative about a user’s target trajectory and the latter could be reliably predicted in a pairwise setting. Furthermore, we showed that—despite the low signal-to-noise ratio of EEG signals—ranking trajectories using the EEG-based pairwise preference predictions allowed us to identify the target trajectories with a performance comparable to explicit button presses.
Our results open up paths for future work both on EEG-based active learning of preferencesSadigh et al. (2017); Akrour et al. (2014)—where feedback could also be repeated on demand to reduce measurement noise—and on utilizing brain signals in a passive way during human-robot interaction to improve robotic behavior without explicitly querying the human.
Acknowledgements.The authors would like to thank Robin Burchard for help recording the robot trajectories and Joseline Veit for help conducting the EEG experiments. This work was (partly) supported by BrainLinks-BrainTools, Cluster of Excellence funded by the German Research Foundation (DFG, grant number EXC 1086). Additional support was received from the German Federal Ministry of Education and Research under grant OML, the DFG through INST 39/963-1 FUGG as well as the Ministry of Science, Research and the Arts of Baden-Württemberg for bwHPC.
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