1 Introduction

One of the challenges for autonomous mobile robots operating in public environments is navigating safely around people. A growing variety of robots navigate in environments with people present and people can be very dynamic and unpredictable. This ranges from robots with a social purpose like assisting in elderly care [1] to robots that perform cleaning tasks in dense crowds of people [11]. For all these robots it can be assumed to be important that they understand social conventions when navigating in public environments [21] so that people will feel comfortable being in the same environment as the robot. One important aspect for people when navigating in a public environment is respecting social distances [7], so it is relevant to investigate how this works for robots.

1.1 Human-robot Proxemics

When people are navigating in public environments, they automatically take social rules and distances into account. Proxemics is the field of study in psychology that investigates how people position themselves in relation to each other. In human proxemics, the simple model by Hall [7] is often applied. He distinguished four different circular zones around a person that are used for different kinds of social interactions.

Robot navigation traditionally treated humans as obstacles that need to be circumnavigated with some additional clearance. This is often sufficient in environments with few people or larger spaces. However, in public environments where many people are moving, this is no longer true, and we need to find an accurate and comfortable representation of the distances that people feel comfortable with between them and a robot navigating in the same space. The focus of human-aware navigation is on robot navigation that feels natural, adheres to social conventions and makes the people in the same environment feel comfortable [10]. Several studies aimed to translate knowledge on human proxemics to interactions with robots to be able to use an accurate representation of people and their personal space in navigational models. Some of these studies focus on comfortable approach distances for when a stationary person is approached by a robot [15, 22, 27, 30]. These studies show that there is an optimal distance for approaching a person to start an interaction, albeit there is no consensus over what this distance is. However, approaching too close is considered to be uncomfortable, as is approaching with a distance that is considered to be too large. In a previous study, we considered a situation in which a stationary person is being passed by a robot [17]. In this scenario, there is no optimal distance, as a greater passing distance appears to be related to greater human comfort.

When people are moving, the shape of their personal space also depends on their direction of motion and speed. In pedestrian motion models, personal space around a moving human is often considered to be circular [3, 29]. Therefore, in human-aware navigation algorithms, people could also be represented using a circular form of personal space [6]. To take the future direction of a person into account, this shape can also be extended a bit towards the front [8]. Sisbot et al. [24, 25] developed a model in which people are represented by a cost map, that also takes their orientation into account. Robots navigating in this model encounter higher costs when passing in the back of a person because it is considered to be less comfortable if the robot is not in sight of the person [17]. In the work by Charalampous et al. [2] the actions of people are taken into account in representing their personal space. What is furthermore important to take into account is the context of the navigational scenario [9], for example, the crossing angle between the robot and the person.

1.2 Passing and Crossing Scenarios

In human-aware navigation, it is useful to distinguish different kinds of scenarios, because we see in robot proxemics research differences between approaching and avoiding. We distinguish two specific scenarios in which robots have to plan paths around humans in public spaces: passing a person from opposite directions and crossing paths with a person at a certain angle.

For the passing scenario, we consider a human and a robot starting their paths on opposite sides of each other needing to avoid a collision. In our previous research [16], a robot passed a person at different distances after which people indicated their perceived comfort. We found that perceived comfort increases with distance and that passing at the left or right did not affect perceived comfort. Pacchierotti et al. [20] found similar results, in a study where the robot and human started at a collision course and the robot actively chose a passing distance. A passing distance (center-to-center distance) of 80 cm or higher was found to be acceptable [16]. A very similar distance is found when analysing motion data of pedestrians passing one another [3].

The other scenario for planning paths around moving people is where the robot crosses their paths. This scenario is significantly more challenging, as the environment is more open, and the actors (robot and person) can move in more directions. Either the human or the robot, or both need to change speed and/or trajectory to avoid a collision. The role of personal space in a dynamic scenario such as crossing is not well understood, as most studies looked at a more static situation. Still, some earlier research investigated crossing scenarios. Lo et al. [14] evaluated different crossing strategies for a self-balancing mobile robot. A robot crossed paths with a participant and four different behaviors were compared. The robot would either keep a constant speed and orientation, or it would accelerate, or change its orientation away from the participant, or a combination of these two last adjustments just before crossing paths with the participant. Results indicated that participants rated the robot that used one of the strategies as more comfortable and safe compared to the baseline in which the robot did not change its speed or orientation. However, in this study, no comparison was made between the different avoidance strategies in terms of user comfort or effort. Also, the robot always passed in front of the user and never stopped to let the person pass first. Regarding the latter, Lichtenthaeler et al. [12] showed that stopping or stuttering to let a person pass was the preferred intervention for a teleoperated robot, steered by the participant, whose path was crossed by a confederate. As this was only tested from a bystander perspective, it is unclear whether this robot behaviour is the most desirable from the perspective of the person whose path is crossed.

Humans that cross paths with other humans usually adapt their path based on who arrives first at the crossing point [19]. The first person to arrive increases their speed, and changes their orientation away from the other walker, while the second walker slows down and moves in the opposite direction to prevent a collision. Vassallo et al. [28] found that if a robot uses this strategy, participants behave similarly as when they would encounter a human walker. However, in this study, perceived comfort of participants was not measured and not many other strategies were tested, so it remains unclear whether this strategy is the most comfortable for robots to use when crossing paths with people.

Next to human comfort, effort is another important factor. When two actors try to avoid a collision, the time and energy it takes to reach their goal without a collision both contribute towards the total effort [23]. The walker that arrives last at the crossing point usually contributes the most effort to avoid the collision. Collision avoidance that does not cost a lot of effort is considered to be preferable over collision avoidance that does cost a lot of effort. Effort also encompasses the time it takes to reach the navigation goal and deviation from a straight path.

1.3 Research Aims

The aim of the current study is to compare different crossing strategies for an autonomous mobile robot in a dynamic scenario and evaluate how they affect perceived comfort and walking behaviour. While some navigational methods might allow a robot to adjust its trajectory much sooner to avoid collision with another actor, sometimes humans are not detected early enough for this, either because of limited sensing capabilities or occlusions. In these cases the robots will have to resort to more last-minute avoidance behaviours, and then the risk for collision between a person and robot is much higher. Hence, it is even more important that people feel comfortable with crossing strategies of the robot when they are executed in the last possible moment and therefore we are focusing on these crossing strategies in the current study.

To investigate this, we conducted two experiments. In the first experiment, a humanoid robot crossed paths with participants. We used a controlled environment in which the robot used different crossing strategies varying speed change, crossing angle and arrival at the hypothetical collision point. In the second experiment, an autonomous guided vehicle was used and we selected four main crossing strategies based on the first experiment. We measured perceived comfort and effort and tracked the walking behaviour of our participants in both experiments.

We have formulated several hypotheses to test our research aims. Based on results of human-robot passing scenarios [16, 20], we expected that the minimal distance between the human and the robot is an important parameter for predicting perceived comfort. H1: a larger distance between the two actors would result in higher perceived comfort. Additionally, we expect that the human crossing strategy as defined by Olivier et al. [19] is regarded as the most comfortable because people are used to using this strategy when crossing paths with other humans. H2: If the robot arrives first at the crossing point accelerating and moving away from the participant is the most comfortable scenario, if the robot arrives last, decelerating and moving towards the participant is the most comfortable scenario.

Assuming that people prefer to spend less effort in a crossing scenario, we also expect to find a negative correlation between comfort and effort, i.e. a situation that is perceived to be very comfortable will cost less effort, and vice versa. H3: comfort and effort are negatively correlated. Additionally, based on our earlier research, [17], we expect that if the robot drives faster people feel less comfortable. H4: A higher movement speed correlates with a lower comfort level. Finally, we expect to detect changes in participants’ walking behaviour dependent on the robot crossing strategy. We can not formulate a hypothesis for this, as the nature of this expectation is more exploratory.

1.4 Outline of the Paper

In the next section we describe the first experiment, in which twenty participants crossed paths with a humanoid robot. The robot employed 20 different strategies for crossing paths and participants’ comfort and effort levels are measured. After this we describe the second experiment, in which a non-humanoid robot crossed paths with a participant. The robot used 12 unique crossing strategies and comfort and effort levels of our participants are measured. We additionally tracked their walking behaviour. In the final section the results of both experiments is discussed and compared. Conclusions and recommendations are formulated.

Fig. 1
figure 1

Picture a and schematic overview b of the set-up of the experiment. In a the yellow squares represent the starting and target point of the participant. In b the red dot represents the hypothetical collision point. The green oval represents the point where the robot would start increasing or decreasing its speed and change its angle

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2 Experiment 1

2.1 Method

2.1.1 Participants and Design

Twenty participants (8 females and 12 males, \({M_{age}}\) = 31.9, \({SD_{age}}\) = 18.3, range = 21 to 83) had to walk across a room while a robot crossed their paths. We used a within-subjects design in which we manipulated the crossing strategy of the robot, and measured the perceived Comfort, Effort and Walking behaviour of our participants. The crossing strategies were combinations of the following independent variables: 3 (crossing angle: left, straight or right) x 4 (speed change when crossing: stopped, decreased, constant or increased) x 2 (participant starting delay (after the robot): 7 or 9 s). When the robot stopped, the crossing angle was always straight, which resulted in 20 unique crossing strategies. Each participant experienced each strategy once in a random order. The design of this experiment has been approved by the ethics committee of Eindhoven University of Technology, in agreement with the ethical guidelines as laid down in the declaration of Helsinki [32]. Participants were recruited through the participant database of Eindhoven University of Technology. In this database students and staff of the university are registered, as well as working and retired people living in the area around the university.

2.1.2 Experimental Set-up

The set-up of the experiment is shown in Fig. 1. The participants had to walk to a target position which was directly across the room (same x-coordinate). The robot crossed this path at a right angle if straight-line trajectories are used.

In calculating the required dimensions of the paths of the human and the robot, the moving speeds were taken into account: average human walking speed (1.2 m/s [5]) and the velocity of the robot (minimum: 0.1 m/s, default: 0.25 m/s and maximum: 0.35 m/s). Because of the difference in speed between the human and the robot, the robot always started 9 s or 7 s earlier than the human. This allowed the robot to reach the crossing point slightly before or after the human, respectively, provided that people would adopt the average human walking speed. However, more often than anticipated the order of arriving at the crossing point did not depend on the starting delay of the participant. After the experiment, it was determined that the planned order of arrival was met in about 76% of the cases and that in most cases the human arrived first at the crossing point. In Fig. 2 a histogram of participant arrival times is shown. It is clear that the average arrival time at the collision point of the participants is later with a longer delay (M = 17.6s, SD = 1.59s) compared to a shorter delay (M = 15.3s, SD = 1.56s).

The robot started its crossing strategy 1 m before the crossing point. In the cases where the crossing angle was different than \(0^{\circ }\), the robot would start changing its angle at this point and this is also where the robot would stop or adjust its speed. Due to the average speed of the robot, it took the robot about 3-4 s to reach the crossing point after starting its strategy.

The experiment was conducted with the 1.2-meter tall Pepper robot (Softbank Robotics, Japan). The location of the participant was monitored using two location trackers (PhaseSpace Motion Capture, USA). The trackers were attached to a toy, plastic builder’s helmet that was worn by the participant during the trial. In the lab, twelve cameras were present for locating the trackers on the participant’s head. A speaker was used to signal when the participant was expected to start walking. Unfortunately, because of technical difficulties, we could not track the location of the robot in real time.

Fig. 2
figure 2

Histogram of participant arrival times in seconds at crossing point sorted by participant starting delay

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2.1.3 Measurements

The cameras in the lab tracked the current position of the participant at a frequency of 2 Hz. The path of the robot was measured four times for each crossing scenario before the experiment and the average position was interpolated to be able to draw the approximate path the robot took in all the different trials. The path of the participant was used as input to determine the average Walking Speed and Path Deviation.

Next to these objective measurements, two questions were asked to assess the perceived Comfort (“To what extent did you feel comfortable when crossing the robot in order to get to your destination point?”) and Effort (“How much effort did you make to get to the destination point?”) of the participants. Both questions were answered on a 7-point scale, ranging from “extremely uncomfortable” to “extremely comfortable”, and from “extremely low effort” to “extremely high effort”.

2.1.4 Procedure

Upon arrival in the lab, the participants read and signed an informed consent form, after which they answered demographic questions. Before the trials started, the experimental procedure was explained and a practice trial was run. If everything was clear, the trials started in a random order. Participants were instructed to reach their target point and were told that they could perform any action that felt natural given the distance to the robot and its moving behaviour. They were allowed to change their speed or stop and also change their walking trajectory according to that of the robot. After each trial participants filled in the two questions on Comfort and Effort and the next trial was prepared. After all trials were completed, participants were debriefed and thanked for their participation. The total experiment lasted 30 min for which participants were paid €5, or €7 for non-students.

2.2 Results

2.2.1 Perceived Comfort and Effort

Fig. 3
figure 3

Average ratings of Comfort (a) and Effort (b). On the x-axis, the change in speed and crossing angles are depicted. Error bars represent SE

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The average values for Comfort and Effort for each condition are shown in Fig. 3. We hypothesized that the human-crossing strategy by Olivier et al. [19], was the most comfortable. This would mean in our manipulations that with a larger participant delay (and thus the robot arriving early), the robot should increase its speed and move towards the right (away from the participant) and with a smaller participant delay (and thus the robot arriving later), the robot decreases its speed and move towards the left (towards the starting position of the participant).

To first test whether Comfort or Effort were significantly influenced by our three predictors: crossing angle (left, straight or right), speed change when crossing (stopped, decreased, constant or increased) and starting delay (7 or 9 s), we conducted a repeated measures Analysis of Variance (ANOVA) for Comfort and Effort. Contrary to our hypotheses, none of our predictors had a significant effect on either Comfort or Effort (All F’s < 2.96 and all p’s > 0.05), which means that we cannot support our hypothesis. Only the interaction effect between the crossing angle and starting delay on perceived Comfort was approaching significance (F(2,399) = 2.96, \(p =\) 0.05, \(\eta ^2\) = 0.02). A pairwise comparison using a Bonferroni correction revealed that only within the straight crossing angle condition people reported higher Comfort levels when the robot arrived later compared to the other half of the conditions.

In hypothesis 3, we expected that Comfort and Effort were negatively correlated. To test this hypothesis, Pearson’s correlation was run to assess the relationship between Comfort and Effort. We found a strong negative correlation (r(398) = \(-\)0.67, \(p<\) 0.0001).

2.2.2 Walking Trajectories

We analysed the walking trajectories of the participants to see how the robot’s crossing strategies affected them. The walking trajectories of participants of all trials are depicted in Figs. 4, 5 and 6. The x- and y-axes (in meters) represent the location in the room. The red crosses and blue dots represent the path of the robot. For the red crosses, the starting delay was 9 s, and for the blue dots 7 s. The black lines represent the paths of the participants. The speed change of the robot is shown in the different rows.

Fig. 4
figure 4

Location data for the conditions in which the robot went left

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Fig. 5
figure 5

Location data for the conditions in which the robot went straight

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Fig. 6
figure 6

Location data for the conditions in which the robot went right

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The paths of the participants varied systematically with conditions. From the plotted paths, it becomes clear that some walking trajectories deviate from a straight path at the crossing point. Also, the direction and amount of deviations appear to depend on the condition. For this reason, we decided to look at the deviation from a straight line of the participant when passing the robot’s straight-line trajectory per condition. This value is determined by the x-coordinate of the walking trajectory at the time when the y-coordinate is equal to that of the collision point. This y-coordinate is similar to the starting location of the robot, assuming that it drives a right line. Since the sampled coordinates are never exactly equal to that of the crossing point, we interpolated between the two closest points. We refer to this new variable as Deviation.

The average Deviations per condition are depicted in Fig. 7. We conducted a repeated measures ANOVA to see whether Deviation was significantly influenced by our three predictors.

Fig. 7
figure 7

Average Deviation per condition. On the x-axis, the change of speed and crossing angles are depicted. Error bars represent SE

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We found a significant main effect of crossing angle on Deviation (F(2,38) = 9.72, \(p = \) 0.0004, \(\eta ^2\) = 0.34). From comparing Figs. 4, 5 and 6, it is suggested that people are more inclined to deviate towards the left when the crossing angle of the robot is towards the left, compared to the other two angles. We also found a significant main effect of speed change on Deviation (F(3,57) = 5.86, \(p =\)0.0018, \(\eta ^2\) = 0.23). In Fig. 7 the average Deviation in the different conditions of speed change appears to be higher in the increased and constant speed conditions. Additionally, we found a significant main effect of delay on Deviation (F(1,19) = 5.86, \(p = \)0.026, \(\eta ^2\) = 0.24). To explain this effect, we look at Fig. 7 and see that in most cases the delay of 9 s (when the robot arrives earlier) has a higher deviation than the delay of 7 s. We found a small significant interaction effect between delay and crossing angle (F(2,399) = 3.19, \(p =\).043, \(\eta ^2\) = 0.03). In Fig. 7 we see that the difference between mean Deviation in the different delay conditions is bigger for a straight angle compared to the other crossing angles.

Fig. 8
figure 8

Average comfort levels (a) and effort levels (b) depicted against average deviation in meters. Every point represents a singular crossing strategy. Error bars represent SE

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To try to explain this significant finding, we also tested whether the average deviation can predict Effort and Comfort. In Fig. 8 the relation between deviation and Comfort, and Deviation and Effort is shown. It is clear that the measures of comfort and effort do not differ much across conditions. Based on a first visual inspection of those figures, we notice a small negative correlation for comfort in Fig. 8a, and a small positive correlation for effort in Fig. 8b.

To analyse whether these relations were statistically significant, we used a linear regression, which fits a linear relationship between deviation (d) and comfort (c): \(c = \beta _0 + \beta _1 d\). The results showed that Deviation and Comfort are negatively correlated (\(\beta _0 = \) 4.74, \(SE =\) 0.20, \(p < \) 0.0001 and \(\beta _1 = \) \(-\)0.61, \(SE =\) 0.24, \(p = \) 0.012). A significant positive relationship is found between Deviation and Effort (\(\beta _0 = \) 3.30, \(SE =\) 0.23, \(p < \) 0.0001 and \(\beta _1 = \) 0.72, \(SE =\) 0.24, \(p = \) 0.003). This relation means that if participants deviate more from their path, their perceived Comfort is lower and their perceived Effort is higher.

As an additional objective measure, we calculated the average Walking Speed of participants for all crossing strategies, by dividing the total distance from start to end by the time it took them. The values are depicted in Fig. 9. Using a repeated measures ANOVA, we found a significant main effect of crossing angle on walking speed (F(2,38) = 4.34, \(p =\) 0.02, \(\eta ^2\) = 0.19). The walking speed was significantly lower for a crossing angle towards the right compared to the other angles. There is also a significant main effect of speed change on walking speed (F(3,57) = 8.10, \(p =\) 0.0001, \(\eta ^2\) = 0.30). If the robot stopped, participant walking speed was higher compared to the other conditions. Lastly, we found a significant interaction effect between speed change and delay (F(3,399) = 6.69, \(p =\) 0.0002, \(\eta ^2\) = 0.08).

Fig. 9
figure 9

Average walking speed per condition. On the x-axis, the change of speed and crossing angles are depicted. Error bars represent SE

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Fig. 10
figure 10

Average comfort levels (a) and effort levels (b) depicted against average walking speeds in m/s. Every point represents a singular crossing strategy. Error bars represent SE

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Additionally, to investigate the relationship between average Walking Speed and Comfort and Effort we plotted these variables in see Fig. 10. A repeated measures mixed model showed that the effect of average walking speed on comfort is statistically significant with a positive correlation between average walking speed and comfort (\(\beta _0 = \) 4.08, \(SE =\) 0.33, \(p < \) 0.0001 and \(\beta _1 = \) 0.64, \(SE =\) 0.29, \(p = \) 0.03). A significant negative correlation is found between average walking speed and effort (\(\beta _0 = \) 4.08, \(SE =\) 0.29, \(p < \) 0.0001 and \(\beta _1 = \) \(-\)0.76, \(SE =\) 0.29, \(p = \) 0.009). This means that if participants have a higher walking speed, they perceive the crossing strategy as more comfortable and less effortful.

2.3 Discussion

In this experiment, we experimentally compared different crossing strategies in a human-robot crossing scenario with a Pepper robot. The starting delay for participants and a possible speed and orientation change of the robot were manipulated. The average perceived Comfort and Effort were similar across conditions. However, when analysing the amount of deviation from a straight line, we found that participants deviated more when the robot kept a constant speed or increased speed, compared to when the robot decreased its speed or stopped. Also, Deviation was higher when participant delay was longer. Finally, this deviation was more towards the robot for when the robot drove away from the participant or straight compared to a crossing angle where the robot approached the participant. Additionally, there was a small but significant relation between the deviation and walking speed and the self-reported measures of Comfort and Effort.

Although the starting delay had a clear effect on the time at which participants arrived at the collision point, it was not always an accurate prediction of who arrived first at the collision point, mainly because the participants tended to arrive first. This could have impacted our perceived Effort measure. According to Silva et al. [23], the effort is minimal when the walking trajectory does not deviate from a straight path and the preferred velocity. Additionally, the effort is less for the person arriving first at the crossing location. In light of this, it might seem strange that we found no effect of participant starting delay on perceived effort. However, [23] used a numerical value of effort based on their crossing angles, time of collision and speed, and in the current experiment a measure of perceived effort is used, which could explain why we did not find the same effect. Additionally, the difference in perceived effort may be too small to be perceived as such and perhaps a Likert scale is not the best tool for measuring such fine-grained differences. Therefore, it would be better to evaluate a more objective measurement of Effort, such as Walking Speed and Path Deviation. Additionally, the power of this experiment was perhaps not high enough, because of the many conditions, which also can explain why we did not find a significant effect on perceived effort.

We also did not find a significant effect of crossing strategies on perceived comfort. This is unexpected, because in [14] it is found that people rate strategies such as accelerating and changing orientation as more comfortable compared to if the robot does not use any strategy. Furthermore, people prefer robots that are using similar crossing strategies as humans [28]. We did see a clear effect on the walking trajectories of participants. Given that people had the possibility to adjust their own walking path, a possible explanation could be that by deviating from their path, people try to control their perceived comfort level, rather than letting them be influenced by the robot manipulations.

We expected that the human crossing method as described by Olivier et al. [19] would also be the most comfortable to be used by a robot. We did not find any effect on the comfort measures, but we did see that people had to deviate further from their path if the robot did not adhere to this general guidelines. For example, if the robot arrived earlier but moved towards the participant instead of away from them, people had to deviate further from their path.

We decided to use both subjective as well as objective measures in this study, which is a valued method within the field Human-Robot Interaction [26]. As one of the objective measures, we defined participant path deviation. The data showed that people deviate more from their path if the robot increases its speed, or keeps a constant speed, compared to when it decreases or stops. When the robot turns its orientation away from the participant or does not change its orientation, the average deviation is further towards the right (towards the original location of the robot), compared to when the robot orients itself toward the participant. These findings match the hypotheses we had for comfort, albeit the comfort values themselves were not significant. Still, the deviation variable was a significant predictor of comfort and effort, but this effect was very small. It makes sense that more deviation leads to less perceived comfort and more perceived effort since deviating from the path costs more effort than walking a straight line [23].

The findings in this study are related to the legibility of the robot, which is defined as the ability to correctly predict the future actions of the robot [13]. We assume that if people are more unsure about the behaviour of the robot and its future location, and thereby the risk of a possible collision, this results in more deviation to prevent a collision. If the robot stops or slows down, the assessed risk of collision is probably lower, which is why it is less necessary to deviate from the path. Similarly, it is easier to predict the risk of collision with a robot that arrives later at the collision point, so less need to deviate. For a robot that moves away from the participant, people will predict that deviating towards the robot has the least chance of collision, while for a robot that moves towards the person deviating in the opposite direction is probably a better option.

Another objective measure was the average walking speed of participants during the trials. Results indicated that if the robot moves towards the participant the average walking speed was higher. When the robot arrived later, the average walking speed was also higher. In this case, walking speed could also have something to do with the legibility of the robot. A lower walking speed of the participant could represent more doubt about the prediction of the path of the robot, which could be why a person slows down or stops more often. However, this is just speculation without more research.

To conclude, the data of the current experiment show that to maximize the efficiency (for example a smaller path deviation) and thereby comfort of the person sharing the environment with the robot, robots should decrease their speed or stop, and give priority to the person, allowing them to cross first.

3 Experiment 2

The first experiment gave interesting insights into how people prefer to cross paths with a humanoid robot. However, since earlier research in human-robot proxemics shows different results for different robots [27, 30], we wanted to compare the results of this experiment with a similar experiment that would use a non-humanoid robot. Especially since it is preferred to be able to generalize the results over different circumstances. Additionally, the Pepper robot has a friendly appearance, which might have had an effect on the risk of collision, assessed by our participants. This is why we used a different robot in the second experiment.

In the previous experiment, the robot velocity was limited to a maximum speed of 0.35 m/s. We did find an effect of acceleration on deviation; showing that a constant or increased speed gives higher deviations than a decreased speed or when the robot stopped. We hypothesized that the speed of the robot has a big effect on human comfort since robot speed also had a clear effect on comfort in a passing scenario [17].

Furthermore, in the previous experiment, we could not test the effect of minimum distance on comfort, since we did not track the location of the robot simultaneously with the participant. In the current experiment, we tested this hypothesis by tracking both actors and calculating their minimum distance.

Fig. 11
figure 11

Picture (a) and schematic overview (b) of the setting of the experiment. In (a) the robot and a participant are shown, both with the location trackers. In (b) the red dot represents the hypothetical collision point. The green oval represents the point where the robot stops in one of the four main crossing strategies

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3.1 Method

3.1.1 Participants and Design

Twenty-four participants (13 females and 11 males, \({M_{age}}\) = 28.0, \({SD_{age}}\) = 11.4, range = 20 to 59) participated in a 4 (crossing strategy: straight, stop, left, and right) x 3 (speed: 0.55 m/s, 0.70 m/s, and 0.85 m/s) within-subjects design. Each trial was done three times in random order, for a total of thirty-six trials per participant. For two participants the robot had technical issues which is why we decided to not include their data, leaving us with the usable data of twenty-two participants. The design of this experiment has been approved by the ethics committee of Eindhoven University of Technology, in agreement with the ethical guidelines as laid down in the declaration of Helsinki [32]. Participants were recruited through the participant database of Eindhoven University of Technology. In this database students and staff of the university are registered, as well as working and retired people living in the area around the university.

3.1.2 Experimental Set-up

The set-up of the experiment is shown in Fig. 11. We roughly used the same setup as in the first experiment, with a few changes.

The participants started on one side of the room, and they first had to walk to the starting position. This first walking trajectory was used for determining their average walking speed and basing the start time of the robot on this speed. Next participants had to walk to a target position which was directly across the room. The robot always crossed this path at a right angle.

A significant improvement to the set-up of the first experiment was the starting time of the robot. Because we could calculate the average walking speed of the participant in the first part of their walking trajectory, the starting time of the robot was more accurately tuned. Hereby it was arranged that the two actors would arrive at the collision point at the same time if none of them would change their speed or trajectory. The robot started its crossing strategy again at 1 m before the crossing point, where it would either drive straight, stop, or diverge towards the left or the right, depending on the condition.

The experiment was conducted with a custom-made Autonomous Guided Vehicle (AGV). This robot has the following dimensions, L: 730 mm, W: 650 mm, H: 900 mm. The location of the participant and the robot was monitored using location trackers (PhaseSpace Motion Capture, USA). During the trajectory, the body of the robot rotated to follow the intended line. Two trackers were attached to a toy, plastic builder’s helmet that was worn by the participant during the trial. The robot was tracked using six trackers, four on the corners and two on the top in the middle of the robot. In the lab, twelve cameras were present for locating the trackers.

3.1.3 Measurements

In this experiment, we improved the accuracy of the location data by tracking the position of the participant and the robot simultaneously with a frequency of at least 20 Hz. This data could be used to determine the path deviation of the participant, the walking speed of the participant and the distance between the robot and the participant during the trials, more accurately than in Experiment 1.

Next to these objective measurements, two questions were asked to assess the perceived Comfort (“How comfortable did you feel during the last encounter?”) and Effort (“How much effort did it cost to prevent collision with the robot?”) of the participants. Both questions were answered on a 7-point scale, ranging from “very uncomfortable” to “very comfortable”, and from “very effortless” to “very effortful”.

3.1.4 Procedure

The procedure was mostly similar to Experiment 1, they had the same order of events, and the instructions given to participants were also similar. The total length of this experiment was 15 min longer, and of course, the robot and the trials differed from those of the first experiment. For completeness, we describe the procedure of this Experiment.

Upon arrival in the lab, the participants disinfected their hands, which was part of the then applicable COVID-19 measures, and read and signed an informed consent form. At the start of the experiment, they answered some demographic questions. Before the trials started, the experimental procedure was explained. If everything was clear, the trials started and were presented in random order. Participants were instructed to reach their target point and were told that they could perform any action that felt natural given the distance to the robot and its moving behaviour. They were allowed to change their speed or stop and also change their walking trajectory according to that of the robot. After each trial participants filled in the two questions on comfort and effort and the next trial was prepared. After all trials participants were debriefed and thanked for their participation. The total experiment lasted 45 min for which participants were paid €7,50, or €9,50 for non-students to compensate for travel costs.

3.2 Results

3.2.1 Perceived Comfort and Effort

In hypothesis 3, we expected that Comfort and Effort were negatively correlated. Therefore, we check the relationship between them with a Pearson’s correlation. Just as in the first experiment, there was a strong negative correlation (r(860) = \(-\)0.75, \(p<\) 0.0001).

Fig. 12
figure 12

Average Comfort levels (a) and Effort levels (b) for each condition. Error bars represent SE

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Because we want to know whether crossing strategy or speed influenced perceived Comfort in order to determine a comfortable crossing strategy, we analysed perceived Comfort for each condition. The average Comfort values per condition can be seen in Fig. 12a. We conducted a repeated measures ANOVA (rANOVA) where we included speed and strategy and evaluated their effect on Comfort. There was a significant main effect of crossing strategy on Comfort (F(3,63) = 14.57, \(p<\) 0.0001, \(\eta ^2\) = 0.41). The robot diverging towards the left resulted in the lowest Comfort ratings (M = 3.49, SD = 2.09), followed by diverging towards the right (M = 4.84, SD = 1.71). Stopping was rated more comfortable (M = 5.37, SD = 1.57) compared to driving straight (M = 5.15, SD = 1.56). All pairwise comparisons were significant (all t’s > 1.98, all p’s < 0.05). This shows that stopping and driving straight is more comfortable than diverging from a straight path.

Additionally, there was a significant main effect of robot speed on perceived Comfort (F(2,42) = 14.50, \(p<\) 0.0001, \(\eta ^2\) = 0.41) which supported hypothesis 4. The lowest movement speed of 0.55 m/s was rated the most comfortable (M = 5.05, SD = 1.66), followed by a speed of 0.7 m/s (M = 4.86, SD = 1.90) and 0.85 m/s (M = 4.24, SD = 1.94). Pairwise comparisons using a Bonferroni correction show that the difference between the two lowest speeds is not significant, but both differ significantly from the highest speed. There was no significant interaction effect between crossing strategy and speed on Comfort.

We were also interested in the effect of our predictors on perceived effort. The average Effort values can be seen in Fig. 12b. There was a significant main effect of crossing strategy on Effort (F(3,63) = 12.67, \(p<\) 0.0001, \(\eta ^2\) = 0.38). If the robot diverged towards the left this costed participants the most effort (M = 4.30, SD = 1.99), and if the robot stopped this costed participants the least amount of effort (M = 2.37, SD = 1.41). Going right (M = 3.14, SD = 1.70) or straight (M = 2.96, SD = 1.63) resulted in similar effort ratings, which is the only pair that did not differ significantly from each other in a pairwise comparison. There was also a significant main effect of robot speed on perceived effort (F(2,42) = 3.69, p = 0.033, \(\eta ^2\) = 0.15). The highest speed of 0.85 m/s resulted in significantly higher Effort ratings (M = 3.45, SD = 1.94) compared to 0.7 m/s (M = 3.05, SD = 1.80) or 0.55 m/s (M = 3.08, SD = 1.73). The latter two did not differ significantly. Additionally, there was a small but significant interaction effect between crossing strategy and speed on Effort (F(6,654) = 2.71, p = 0.013, \(\eta ^2\) = 0.02). This is probably because the effect of speed is mainly visible for the crossing strategy in which the robot goes left, as shown in Fig. 12b.

3.2.2 Walking Trajectories

Fig. 13
figure 13

Location data per condition. The x- and y-axes (in meters) represent the location in the room. The black lines represent the path of the robot. The yellow and green paths represent the path of the participant. The yellow paths mean that the participant took priority over the robot, and the green paths mean that the participant yielded priority to the robot. The speed of the robot is shown in the different rows per condition: 0.55 m/s, 0.7 m/s and 0.85 m/s. The crossing strategy of the robot is shown in the different subfigures: stopping (a), left (b), straight (c) and right (d)

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Just as in the first experiment, we combined subjective and objective measures. The walking behaviour of our participants can likely give us a good insight into what crossing strategies of the robot work well. Therefore, we now focus on the location data of the second experiment. As in the first experiment, we started by plotting the location data to check the variance. The result can be shown in Fig. 13. We noticed when analysing the data that the crossing strategy determined whether people took priority over the robot or yielded priority to the robot, which is indicated in Fig. 13, indicated by green (yielding) and yellow (not yielding) colours.

Some robots might need to take priority, so it is interesting to find out whether the crossing strategy of the robot influences who has priority. We tested with a chi-square test of independence whether crossing strategy significantly predicts the chance of being first to arrive at the crossing point, and therefore taking priority. We tested whether the number of cases where the robot took priority over the person was significantly different from an equal distribution, and it was significant (\(\chi ^2\)(3) = 255.811, \(p<\) 0.0001). When the robot moves straight or right, most people yield priority to the robot, but when the robot moves left towards the participant or stops, most people take priority. The speed of the robot was no significant predictor of priority (\(\chi ^2\)(2) = 0.07, p = 0.97).

We want to compare the findings on Deviation of the current experiment with those of the previous experiment, and therefore we calculated the deviation from a straight line of the participant when passing the collision point. Just as in experiment 1, we determined the value by taking the difference between the starting x-coordinate and the measured x-coordinate of the participant at the starting y-coordinate of the robot. The average deviations per condition are shown in Fig. 14a. We conducted a repeated measures ANOVA to see whether Deviation is influenced by the condition.

Fig. 14
figure 14

Average deviation levels (a), walking speed levels (b) and minimum distance between robot and human (c) for each condition. Error bars represent SE

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A significant main effect of crossing strategy was found (F(3,63) = 10.22, \(p<\) 0.0001, \(\eta ^2\) = 0.33). Figure 14a suggests that people deviated on average further to the right when the robot went right (M = 0.18 m, SD = 0.25 m) or straight (M = 0.18 m, SD = 0.32 m), and more to the left when the robot went left (M = \(-\)0.06 m, SD = 0.48 m) or stopped (M = \(-\)0.05 m, SD = 0.19 m). Furthermore, the standard deviations show that the overall Deviation varied more when the robot went left compared to when it stopped. This matches our findings on priority, namely the robot more often takes priority in the conditions where it moves left.

We also found a significant main effect of robot speed on Deviation (F(2,42) = 3.58, p = 0.0366, \(\eta ^2\) = 0.15). The average deviation was larger for a robot speed of 0.55 m/s (M = 0.09 m, SD = 0.38 m) compared to a speed of 0.7 m/s (M = 0.05 m, SD = 0.34 m) or 0.85 m/s (M = 0.04 m, SD = 0.32 m). This shows most clearly for the conditions where the robot goes straight or right as visible in Fig. 14a, which makes sense, considering those are the conditions where people more often walk behind the robot. If the robot drives slower, people have to deviate further to walk behind it.

To compare with the first experiment and as an objective measurement of effort, we checked for the average walking speed of our participants per trial. We only included the part of the trial where they crossed the room, not the initial part which was used to determine their speed and start the robot. The average levels are indicated in Fig. 14b. We only found a significant main effect of crossing strategy (F(3,63) = 8.32, \(p =\) 0.0001, \(\eta ^2\) = 0.28). Pairwise comparisons using a Bonferroni correction indicated that when the robot stopped, the average walking speed of our participants was higher compared to the other three conditions. There were no other significant main or interaction effects.

As a last objective measurement and to be able to test hypothesis 1, we checked the minimum distance between the robot and participant for each trial, which is indicated in Fig. 14c. We checked whether this differed significantly per condition using a repeated-measures ANOVA. We found a significant main effect of condition (F(3,63) = 7.44, \(p<\) 0.0001, \(\eta ^2\) = 0.58). The minimum distance was largest for the stopping condition (M = 1.37 m, SD = 0.15 m), followed by the robot turning left (M = 1.03 m, SD = 0.27 m), right (M = 0.97 m, SD = 0.39 m) and the smallest minimum distances were found when the robot went straight (M = 0.93 m, SD = 0.30 m). We also found a significant main effect of robot speed (F(2,42) = 8.61, \(p =\) 0.0007, \(\eta ^2\) = 0.29). However, looking at Fig. 14c, we see that this is not consistent over the crossing strategies, which is confirmed by an interaction effect between crossing strategy and robot speed (F(6,646) = 10.19, \(p<\) 0.0001, \(\eta ^2\) = 0.09. When the robot goes right minimum distances are larger for higher speed, and when the robot goes left an opposite effect is observed. For straight and stop there is no clear effect of speed. This makes sense given that when the robot goes right, it drives away from the participant.

Lastly, we checked whether the minimum distance significantly affected the perceived comfort measure. This measurement is especially relevant, because in most robot proxemics studies it is used as the most important predictor of human comfort [16, 20, 27, 31]. In Fig. 15 the distribution of minimal distances can be seen per Comfort rating. The Figure hints to a positive relationship between the two variables. We performed a linear regression which indicated that indeed comfort can be described by minimum distance (\(R^2\) = 0.05, F(1,782) = 41.84). The linear relationship that could describe the fit is \(c = 1.24*d + 3.36\).

Fig. 15
figure 15

Boxplot of minimum distance for each comfort level

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Because this relationship can be highly dependent on condition, we plotted the average minimum distance against the average perceived comfort level in Fig. 16. Clearly, the conditions are more important predictors of comfort level than minimum distance is and the linear relationship between the two factors is less obvious here. For a right crossing strategy, it even appears as if a larger minimum distance is related to less comfort, although probably the speed of the robot is the more important predictor here.

Fig. 16
figure 16

Average minimum distance against average perceived comfort for each condition

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3.3 Discussion

In the second experiment, we investigated different crossing strategies in a human-robot crossing scenario with an AGV. We manipulated the crossing strategy and movement speed of the robot. Results show that the crossing strategy determined the perceived comfort: when the robot stopped participants felt more comfortable than when the robot turned left, right or drove straight. For perceived effort an opposite effect was found, if the robot stopped the perceived effort was less. Also, the movement speed influenced comfort levels: higher movement speeds made people feel less comfortable. Furthermore, higher robot movement speeds resulted in higher effort ratings.

Looking only at the crossing strategies, our results show that stopping or driving straight would be the most comfortable way of crossing paths with a robot, given the comfort ratings. This is not what was found when people cross paths with each other. According to [19] people usually change their trajectory when a collision is imminent. It could be that people are more uncertain and feel more uncomfortable if a robot changes trajectory because this makes it harder to predict its intentions. It is more legible if the front of the robot keeps pointing towards the direction where its goal location [4]. In this scenario, this means the robot should stop or drive straight, and it should not change its orientation. When the robot turns towards the left, people could be confused about its intentions, because they are unsure whether the robot would turn back to the right, or whether it would keep driving in their direction.

In this experiment, we also see an effect of the behaviour of the robot on the behaviour of the participant. The crossing strategy determined whether people in general move in front of or behind the robot. When the robot stops or turns left, most people take priority over the robot, but when the robot moves straight or right, people more often yield priority to the robot. This is also evident in their path deviation: in situations where people take priority over the robot, they tend to towards the left. When they deviate towards the right, they deviate further from a straight walking trajectory, which makes sense, given that the robot is still further away from the crossing point. This is especially the case when the robot drives slowly. Interestingly, a large deviation is not reflected very much in the effort ratings for slow speeds. One would expect that a larger deviation requires more effort from participants. It might be that they considered a slow movement speed as a limitation of the robot, and did not mind taking this into account. In an earlier study, Mead et al. [15] they found that people were willing to accommodate for better speech recognition, and thus allowed a robot to come closer. Perhaps if we relate this to our context, people accommodated the slower movement speed of the robot by deviating a bit further.

We did not find any effects on average walking speed in the second experiment, but the additional objective measure of minimum distance provided some interesting insights. Zhang et al. [33] found that people kept a larger distance from a virtual robot when it was driving with a higher movement speed. In the current experiment, we found no such effect, but we did find an effect of the crossing strategy on minimum distance. The largest minimum distances were found when the robot stopped and the smallest minimum distances were found when the robot went straight. This makes sense since the robot also actively kept its distance from the participant in the stopping conditions. The interaction effect of the crossing strategy and robot moving speed can also be explained by the path of the robot; when the robot goes left but drives slower, the distance between the robot and the participant is larger, than when the robot drives faster. The higher the movement speed of the robot, the faster it approaches the participant. For going right this is the other way around, since going right means driving away from the participant, and a higher speed would reach a larger distance. This shows that the effect that we found, can be explained by the design of the experiment.

We furthermore found that minimum distance affected the comfort levels of our participants, as they showed a small but significant positive linear relationship. In our earlier work [17], we found a strong relationship between passing distances and perceived comfort in the shape of an inverted Gaussian. Upon further inspection, we saw that the difference is related to the crossing strategy, as diverging towards the right shows a negative linear relationship, diverging towards the left shows a positive linear relationship and stopping or driving straight shows no linear relationships. So our previous study [17] is most similar to diverging towards the left. This makes sense because if the robot moves towards the participant, it could be the start of a passing scenario. We found that in a crossing situation, the crossing strategy and movement speed of the robot had a larger effect on the experienced comfort than the minimum distance between the two actors. Since people are able to choose their own path, they can control their own comfort level by adjusting the distance they have to the robot, which would explain why minimum distance is such a poor predictor.

4 General Discussion

In the current paper, we describe two experiments in which different crossing strategies of a robot are compared when crossing paths with a human.

In both experiments, we found clear effects of the crossing strategy on path deviation. Just as in the first experiment, in the second experiment, people tend to deviate from a straight path to the left, if the robot also goes left at the crossing point. When the robot goes straight or right, people deviate from their path to the right. This is according to the way humans cross paths with other people [19], and matches earlier findings that the same strategies are used when crossing paths with robots [28]. However, we found in both experiments that stopping and driving straight is an even more comfortable crossing strategy, leading to the least deviation from a straight path by participants, which is not according to the human-crossing strategy. We believe that this finding can be explained with the notion of predictability. When the robot stops or drives straight, its front is directed towards its end goal, which probably makes it easier for people to detect the intention of the robot.

We found effects of the crossing strategy on our questionnaire items in the second experiment while we did not find any effects on comfort or effort in the first experiment. As we used two different robots in the two experiments, it could be that the (lack of) effect of comfort and effort can be explained by the different robot types. However, this is not consistent with our earlier work [17, 18], where we found similar results on comfort for the two different robot types. It is more likely that the power of the first experiment was not high enough, because of the many conditions and little differences between the conditions. In the second experiment, we compared fewer conditions. This usually makes it easier to detect significant differences.

There were more interesting differences between the two experiments to notice. In the first experiment, most often people took priority over the robot in a crossing scenario. In the second experiment, however, we see that people more often yield priority to the robot. It could be that with a higher movement speed of the robot, people are more hesitant to cross paths in front of the robot. It could also depend on the robot type. The Pepper robot looks more friendly, while the robot used in the second experiment looks more mechanical. Perhaps people felt more threatened by the appearance of the AGV and therefore decided to yield priority more often to be on the safe side. We are unable to state with certainty whether they come from the difference in movement speed of the two robots or the appearance of the two robots. In a future study, it is relevant to compare two different robots with similar movement speeds to further disentangle these differences.

The current experiments were both executed in a smaller lab environment, which limited the space available. If a human and robot would cross paths in a larger room, it could be that a last-moment collision avoidance is unnecessary, because the actors can adapt their path way before any potential collision. However, if the robot for whatever reason cannot start its crossing strategy until the last moment (within 1-2 ms of the human), we expect that the results of the current study will be independent of the room size.

In the current paper two experiments on human-robot crossing are described. Because we executed our experiments in a lab environment, in this study crossing strategies of a robot are compared in a more systematic way than before. The crossing strategies that were compared are a limited selection of often-used strategies, such as stopping, driving straight and turning left/right, and all mainly focused on a last-minute evasion. Still, the results of these experiments contribute to our current understanding of how robots can comfortably avoid a collision with a human, and can be implemented in robots that need to navigate in human environments.

4.1 Limitations and Future Research

Both experiments described in this paper were executed in a lab environment. This allowed us to control for external variance, and focus on comparing different crossing strategies for robots. In the field, a robot can cross paths with a human in an environment where there is more space, or more robots or more people. We believe that the current findings will still be valid, in future research we need to study if and how certain variables in the field would affect the current conclusions.

Future research should also compare robot crossing strategies for different age groups, genders and cultural background, to find whether they differ in their preferences considering robot crossing strategies.

In this study we used external location sensors. If the current experiments are to be replicated in the field, we need to depend on the robot’s ego-centric sensors, such as camera and laser-range finders. This is less precise than the external sensors we used, but it still gives insight in the location of the robot with respect to that of the human.

4.2 Conclusion

In the current study, different crossing strategies for robots were compared on human comfort, effort and walking behaviour. Based on our results we argue that robots should stop if they want to yield priority to a person and drive straight if they want to take priority (provided that they have a high enough speed). The results of our study contribute to our understanding of how human comfort is affected by different robot strategies. We also showed that results from passing studies do not automatically carry over to dynamic interactions where people can control the distance with which they pass a robot. For one it shows that personal space models that are purely based on distance are insufficient for these dynamic interactions. The results can be an indication for developing robot behaviours for mobile robots to cross paths with people in a comfortable and understandable way.