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Research Article  |   September 2010
The effect of active selection in human path integration
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Journal of Vision September 2010, Vol.10, 25. doi:10.1167/10.11.25
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      Xiaoang Wan, Ranxiao Frances Wang, James A. Crowell; The effect of active selection in human path integration. Journal of Vision 2010;10(11):25. doi: 10.1167/10.11.25.

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Abstract

Path integration refers to the ability to integrate self-motion information to estimate one's current position and orientation relative to the origin. To investigate the effect of active selection in path integration, we used a virtual homing task in which participants traveled along hallways and attempted to directly return to the origin. Two groups of participants differed in the voluntary selection of the path structure, but received the same perceptual and motor information. Information about distance traveled was purely visual via optic flow, whereas turnings were specified both visually and through body senses. The active group made free (Experiment 1) or forced (Experiment 2) selections to determine the structure of the outbound path, whereas the passive group followed these outbound paths. We found no facilitation effects of the active selection on homing performance, suggesting that humans' limited path integration abilities cannot be attributed to the nature of the task.

Introduction
Spatial updating is a cognitive process that allows navigators to keep track of the spatial relationship between oneself and surroundings when moving. According to the types of information being used in spatial updating, navigations can be classified into piloting and path integration. Piloting allows navigators to use direct sensory information and landmarks to determine their location and orientation, whereas path integration refers to a phenomenon that navigators integrate information regarding self-motion (e.g., velocity and acceleration information) to estimate their current position and orientation relative to the starting point (Etienne, 1992; Gallistel, 1990; Mittelstaedt & Mittelstaedt, 1982). Information regarding self-motion can be either internal information, such as information from the vestibular, proprioceptive and efferent systems, or external information, such as optic flow. 
Many species show the ability to perform path integration, including insects (Müller & Wehner, 1988, 1994; Wehner & Srinivasan, 1981), birds (Regolin, Vallortigara, & Zanforlin, 1995; von Saint Paul, 1982), and mammals (Etienne, 1992; Mittelstaedt & Mittelstaedt, 1982) including humans (Klatzky et al., 1990; Loomis et al., 1993). Etienne, Berlie, Georgakopoulos, and Maurer (1998) summarized the literature to show that humans, dogs, hamsters, spiders, bees, and ants all showed similar return-to-origin behaviors after traveling along an L-shape outbound route. However, comparing to nonhuman animals, human participants showed limited path integration abilities (Klatzky et al., 1990; Loomis et al., 1993; Passini, Proulx, & Rainville, 1990). Klatzky, Beall, Loomis, Golledge, and Philbeck (1999) argued that one possible reason might be the methodological difference between human and nonhuman path integration studies. Path integration in nonhuman species has been studied in both experimental tasks and natural foraging behaviors in which they are motivated to freely navigate through the environment. In contrast, path integration studies in humans have been focused on experimental tasks, primarily in path completion tasks. In this paradigm, human participants travel along several pre-designed segments and then attempt to directly return to the starting point without the aid of direct perceptual cues of the paths. Human participants seldom had opportunity to freely navigate through the environment or voluntarily determine the structure of the paths. Thus, the effects of active exploration on human path integration remain unknown. 
Previous research has shed some light on the “active” aspects of human path integration by manipulating participants' locomotion mode on their outbound trip, including passive locomotion, externally triggered locomotion, and self-initiated locomotion. In the passive locomotion mode, the participants were transported by the experimenters (Mittelstaedt & Glasauer, 1991; Sholl, 1989; Wiener & Mallot, 2006). In the externally triggered locomotion mode, they walked by themselves when being guided by the experimenters (Klatzky et al., 1990, 1999; Loomis et al., 1993). In the self-initiated locomotion mode, they voluntarily traveled along pre-designed routes (Ellmore & McNaughton, 2004; Kearns, Warren, Duchon, & Tarr, 2002; Péruch, May, & Wartenberg, 1997; Riecke, Veen, & Bülthoff, 2002). The influences of different locomotion modes on path integration were also compared (Allen, Kirasic, Rashotte, & Haun, 2004; Cornell & Greidanus, 2006). However, it should be noted that, in the self-initiated locomotion mode, the participants usually can control their own movements (e.g., speed or direction), but the path structures were pre-determined by the researchers. Therefore, these participants were active in physical movements, but not active in terms of making route decisions. 
In the present study, we investigated the effect of active exploration with an emphasis on active selection of the paths in path integration. We framed our visual homing task as a “golden apple hunting game” and therefore tested path integration in humans in simulated foraging. In two experiments, one group of participants (active group) navigated in a virtual space to look for golden apples, whereas the other group (passive group) traveled through the paths selected by the active group. Both groups controlled their own movements, including using a game pad to control the translations and physically turning their bodies to achieve the rotations. Thus, the two groups were both physically active and received the same perceptual and motor information, but differed in the voluntary selection of the outbound path structure. Both groups were asked to directly return to the origin of the path upon seeing a golden apple, so their path completion performance was compared to examine the influence of active selection on path integration. 
Experiment 1
Method
Participants
Twenty-two students from the University of Illinois at Urbana-Champaign (UIUC) participated in this experiment. 
Apparatus and stimuli
The experiment was conducted in a Virtual Reality Cube that produces stereoscopic imagery at 60 frames/second/eye on its six surfaces, each of which is a 3 m × 3 m rear-projection screen. The position and orientation of the observer was tracked by Ascension MotionStar Wireless tracking system, and the observer used an Intel Wireless Series game pad to interact with the virtual objects. A Stereographics LCD shutter-glass system was used to provide active stereo, while proper binocular images were produced according to each individual's inter-ocular distance. As shown in Figure 1, the stimuli were virtual hallway mazes in which only one hallway (1 m wide, 2.2-m high, and with varied lengths) was presented at a time. Outbound and homing paths were specified by two different wallpapers, brown-and-white ceramic tile and sandy yellow rocky pattern, respectively. 
Figure 1
 
Examples of virtual displays used in Experiments 1 and 2. (A) In Experiment 1, a long hallway appeared in the direction that participants in the active group had selected, while a pair of yellow markers was presented to highlight the minimum allowable distance. (B) In both Experiments 1 and 2, a golden apple appeared at the end of the outbound path accompanied by the change of the wallpaper. (C) In Experiment 2, a long hallway appeared in the direction that participants in the active group had selected, with four green door frames presented to highlight four distance options. (D) In Experiment 2, after the participants had selected a length for the hallway, the long hallway turned into a short one which had the selected length.
Figure 1
 
Examples of virtual displays used in Experiments 1 and 2. (A) In Experiment 1, a long hallway appeared in the direction that participants in the active group had selected, while a pair of yellow markers was presented to highlight the minimum allowable distance. (B) In both Experiments 1 and 2, a golden apple appeared at the end of the outbound path accompanied by the change of the wallpaper. (C) In Experiment 2, a long hallway appeared in the direction that participants in the active group had selected, with four green door frames presented to highlight four distance options. (D) In Experiment 2, after the participants had selected a length for the hallway, the long hallway turned into a short one which had the selected length.
Design and procedure
A between-subjects design was used, and participants were randomly divided into two groups: an active group and a passive group. The active group was informed that their task was to navigate in a virtual space with hidden golden apples scattered around randomly and to find an apple on each trial. At the beginning of each trial, the participants stood in the center of a circular room (with a 0.6-m radius) and chose a random direction to start. A 1000-m long hallway appeared in the selected direction, while a pair of yellow markers (2.2 m high and 0.1 m wide without any depth) was presented at the locations of 2 m to highlight the minimum allowable distance. They faced this hallway and pressed a button on the game pad to drive along at a constant speed of 1.5 m/s. When they decided to stop or were involuntarily stopped at the 10-m maximum distance, whichever occurred first, the hallway disappeared and the same circular room appeared. If a golden apple (0.2 m high and 0.2 m wide) appeared accompanied by the change of the wallpaper, they were asked to directly return to the origin. Otherwise they were instructed to choose another direction to start the next segment for which an angle of any value between 30 and 150 degrees, clockwise or counterclockwise, was allowed, and cross-over between any two segments was also allowable and possible. This process was repeated until a golden apple appeared, then the response stage started in which they were instructed to return to the origin of the path. They first physically turned to face the origin (direction response). For example, if they found the apple at the end of the first segment, the correct response angle would be to turn around 180 degrees. Then a 1000-m long hallway appeared in the selected direction. They pressed the button to drive and stopped when they judged to be at the origin (distance response). 
Unknown to the participants, the appearance of the apple actually was pre-determined on each trial depending on the trial type and how many segments they had traveled. There were four types of trials, with 1-, 2-, 3-, or 4-segment paths, and 8 trials of each type were mixed and randomly presented. For each trial, the golden apple always appeared at the end of the last segment. During their outbound travel, information about distance traveled was purely visual via optic flow, as participants physically remained still and pressed a button to drive along each hallway. Turning angles were specified both visually and through body senses, as participants physically rotated their bodies at the intersections. Participants were given several practice trials until they reported feeling comfortable with the task. No feedback was given anytime. 
The passive group was also asked to travel in a virtual space with hidden golden apples scattered around and to directly return to the origin of the path upon seeing a golden apple. Yet, they were asked to travel along pre-designed paths. They were not informed about how these paths were selected, and they were not informed that the maximum length for each segment was 10 m. Each participant in the passive group was randomly chosen and paired with one participant in the active group, and followed the outbound path chosen by his or her counterpart and completed the same trials. At the beginning of each hallway, a green virtual rod appeared and extended horizontally from the participants' bodies to the wall of the room, initially pointing at the same direction that they were facing. Then the rod started to rotate on the horizontal plane around the center of the room to point toward different directions, and the participants turned their bodies to keep facing the direction the rod was pointing at. When the rod stopped at its final position, a new hallway appeared in that direction with a pair of yellow markers highlighting the nearest allowable position. The participants faced this new hallway and pressed a button to drive along until they were stopped at the same distance their counterparts had traveled, where a circular room appeared. This procedure was repeated until a golden apple appeared. Then they were asked to return to the starting point. 
Analysis
Participant's response times (RTs) to make the direction response and their direction and distance responses were recorded. As can be seen in Figure 2, overall path completion performance was assessed by RTs and position errors which were calculated by the Euclidean distances between the real origins and observed endpoints. Direction responses were assessed by the unsigned angular errors calculated as the unsigned differences between the observed and correct turning angles, while greater values specify less accurate turnings and smaller values specify more accurate turnings. Distance responses were assessed by unsigned linear errors calculated as the unsigned difference between the response and correct distances, while greater values specify less accurate responses and smaller values specify more accurate responses. 
Figure 2
 
An illustration of the path completion task. Participants start from H, travel along two segments (H → A, A → B) and then attempt to directly return to the origin (H). To accurately return to H, they should turn β degree and travel for distance c. However, their actual responses might be to turn β r degree, travel for distance cr, and arrive at a new location Hr. We assessed path completion performance by calculating position errors (Euclidean distances between H and Hr), direction errors (unsigned difference between β r and β), and distance errors (unsigned difference between cr and c).
Figure 2
 
An illustration of the path completion task. Participants start from H, travel along two segments (H → A, A → B) and then attempt to directly return to the origin (H). To accurately return to H, they should turn β degree and travel for distance c. However, their actual responses might be to turn β r degree, travel for distance cr, and arrive at a new location Hr. We assessed path completion performance by calculating position errors (Euclidean distances between H and Hr), direction errors (unsigned difference between β r and β), and distance errors (unsigned difference between cr and c).
Results
We first performed 2 (condition, active or passive) × 4 (number of segments, 1, 2, 3, or 4) Analyses of Variance (ANOVAs) on the data. As shown in Figure 3, the number of segments affected the RTs, position errors, direction errors, and distance errors (all Fs > 9.57, p < .01). The effect of active selection was marginally significant on the direction errors [F(1, 10) = 3.7, p = .083], but not significant on any other measure (all Fs < 1.26, p > .28). The interaction between the active/passive condition and the number of segment was not significant on any measure (all Fs < 2.02, p > .13). Planned pair-wise comparisons suggest that no effects of active selection were significant on any measures after Bonferroni corrections for multiple tests (all ts < 2.3, corrected p > .17). 
Figure 3
 
The results of Experiments 1 and 2. The mean RTs, position errors, direction errors, and distance errors of the active group and passive group in Experiment 1 (free selection) and Experiment 2 (forced choice selection) are shown in Panels A, B, C, and D, respectively. Error bars show standard errors of the mean.
Figure 3
 
The results of Experiments 1 and 2. The mean RTs, position errors, direction errors, and distance errors of the active group and passive group in Experiment 1 (free selection) and Experiment 2 (forced choice selection) are shown in Panels A, B, C, and D, respectively. Error bars show standard errors of the mean.
We also analyzed the outbound paths that the active group selected. On average, they chose 7.2 m (SD = 0.78 m), 7.3 m (SD = 0.74 m), 7.4 m (SD = 0.72 m), and 7.4 m (SD = 0.64 m) to be the lengths of the first, second, third, and fourth segments, respectively. The averaged chosen segment length did not change as a function of the number of the segments or the order of appearance of each segment (both Fs < 1, p > .41). They also chose an average of 89 deg (SD = 12 deg), 85 deg (SD = 10 deg), and 83 deg (SD = 10 deg) as the turning angles at the first, second, and third intersections, respectively. The averaged chosen turning angle did not change as a function of the number of the intersections or the order of appearance of each intersection (both Fs < 2.52, p > .1). As shown in Figure 4, the active group showed a peak at 10 m in length selections and a peak around 90 degrees in turning angle selections, suggesting that the maximum allowable 10-m distance and the right angles (90 degrees) were most frequently chosen when the active group made decisions of their outbound paths. 
Figure 4
 
An illustration of the distribution of the length of each segment (Panel A) and the turning angle at each intersection (Panel B) chosen by the active group in Experiment 1.
Figure 4
 
An illustration of the distribution of the length of each segment (Panel A) and the turning angle at each intersection (Panel B) chosen by the active group in Experiment 1.
Discussion
In this experiment, the active group freely decided the structure of their outbound paths with minimum constraints, whereas the passive group followed the paths selected by the active group. When we compared their return-to-origin behavior, the active group did not show better homing performance than the passive group. Yet, we also found two unresolved issues with this experiment. First, the active group was motivated to freely explore the virtual environments with minimum limitations by pressing a button to “drive”, which simulated the foraging behaviors of nonhuman species in unstructured natural environments. However, in everyday life, humans often navigate in structured environments and drive along natural or artificial roads. Thus, the requirement of free navigation and driving in random directions during this experiment may contradict their everyday experience of driving. Second, the active group chose the distance by voluntarily stopping at some point in a long hallway (unless they had gone further than the maximum allowable distance), whereas the passive group did not know where to stop until their transition was interrupted. This procedure added increased task difficulty and/or working memory load for the active group, as they had to travel along a segment and make decisions at the same time. It also confounded the effects of passive following and of perceptual disruption for the passive group. These confounding factors were ruled out in Experiment 2
The participants' path choices were also further examined in Experiment 2. The preference of 10-m segments in this experiment might suggest that people prefer the longest paths. We examined this hypothesis in Experiment 2 by using four path lengths which were all shorter than 10 m and were equivalent in their perceptual saliency. If participants preferred long paths, they should also choose the longest distance. Alternatively, they should be indifferent in their choices. Moreover, we further examined human path choice preference other than the right-angle turns, so the right angles were not available to choose in Experiment 2
Experiment 2
In this experiment, we asked the active group to make a forced choice among four options to determine the distance and direction of their travel. In particular, after they had made a distance selection, the long hallway they faced turned into a finite hallway of the selected length, so both the active and passive groups were aware of the length of each segment prior to traveling. This improved procedure ruled out the confounding factors of increased task difficulty and/or working memory load for the active group and perceptual disruption for the passive group. It also allowed the experimental condition more comparable to the human wayfinding behaviors in structured environments to avoid the contradiction of the experiments and previous experience. 
Method
Twenty-two UIUC students participated in this experiment. None of them had participated in Experiment 1. The methods of this experiment were the same as those of Experiment 1 except for those specified as follows. Unlike being able to make a free choice in Experiment 1, the active group in this experiment was instructed to choose a distance or direction among four available options. The possible length of each segment was 3 m, 5 m, 7 m, or 9 m, and the possible turning angle at each intersection was left 120 degrees, left 60 degrees, right 60 degrees, or right 120 degrees. At the beginning of each trial, the participants stood at the center of a circular room in which four green vertical bars (2.2 m tall and 0.1 m wide) were evenly distributed around them in these compass directions: 0, 90, 180, and 270 degrees. After they turned to face one green bar and pressed a button, a 1000-m hallway appeared in the selected direction with four green door frames (2.2 m tall, 1 m wide, and 0.5 m deep) presented at the distance of 3 m, 5 m, 7 m, and 9 m. After they pressed a button to choose one of the markers, the selected marker was highlighted in magenta color and the long hallway turned into a short one which had the selected length. The participants pressed a button to drive along this hallway until arriving at the end. If a golden apple appeared, they were told to return to the origin of the path. If there was no apple, four green bars appeared to highlight four possible directions for the next hallway with corresponding turning angles as left 120 degrees, left 60 degrees, right 60 degrees, and right 120 degrees. This process was repeated until a golden apple appeared. In contrast, each participant in the passive group watched that the four options for each segment length and turning angle appear and one option being selected, and then traveled along the selected paths. It should be noted that neither the active group nor the passive group was informed about the specific values of lengths and turns. 
Results
We first performed 2 (condition, active or passive) × 4 (number of segments, 1, 2, 3, or 4) ANOVAs on the data. As can be seen in Figure 3, the number of segments affected the RTs, position errors, direction errors, and distance errors (all Fs > 4.87, p < .01), but neither the RTs nor any of these errors were significantly different between the active and passive conditions (all Fs < .79, p > .39). The interaction between the active/passive condition and the number of segment was not significant on any measures (all Fs < .84, p > .48). Planned pair-wise comparisons suggest that no effects of active selection were significant on any measures after Bonferroni corrections for multiple tests (all ts < 1.26, corrected p > .92). 
We also combined data from this experiment and Experiment 1 and performed 2 (task, free choice or forced choice) × 2 (condition, active or passive) × 4 (number of segments, 1, 2, 3, or 4) ANOVAs on the data. No effects of active selection were significant on any measures (all Fs < 1.94, p > .18). Task type influenced RTs [F(1, 20) = 15.56, p < .01], as participants showed longer RTs in the free-choice selection task (3.8 s) than in the forced-choice selection task (2.2 s), but no such effect was significant on any other measure (all Fs < .45, p > .51). Path complexity also mattered. When the paths were more complicated (i.e., with more segments), participants showed longer RTs [F(3, 60) = 14.21, p < .01], greater position errors [F(3, 60) = 90.38, p < .01], greater direction errors [F(3, 60) = 54.88, p < .01], and greater distance errors [F(3, 60) = 50.36, p < .01]. The interaction between the number of segments and task was also marginally significant on the RTs [F(3, 60) = 2.69, p = .054] and position errors [F(3, 60) = 2.66, p = .056], but no other interaction effects were significant (all Fs < 1.38, p > .26). In addition, we also compared the outbound paths used in two experiments, and found that the total length of the outbound paths used in Experiment 1 was greater than that in Experiment 2 [F(1, 20) = 5.06, p < .05], but the correct homing distance (the Euclidean distance between the starting and ending points of the paths) was comparable in these two experiments [F(1, 20) = .03, p > .86]. 
Furthermore, we analyzed the outbound paths that the active group selected on the basis of forced choice. On average, they chose 5.8 m (SD = 1.05 m), 5.3 m (SD = 1.16 m), 5.6 m (SD = 1.01 m), and 5.3 m (SD = 1.01 m) to be the lengths of the first, second, third, and fourth segments, respectively. The averaged chosen segment length did not change as a function of the number of the segments or the order of appearance of each segment (both Fs < 2.31, p > .097). They chose 3 m, 5 m, 7 m, and 9 m to be the length of each segment equally often [F(3, 30) = .99, p > .41], but the length they chose for the later segments was influenced by the length they had selected for previous hallway(s) within the same trial. That is, if they chose the length for subsequent segments by chance, the probability that they chose the same length for all the segments within a pathway should be 25%, 6.25%, and 1.56% for 2-, 3-, and 4-segment trials, respectively. However, on 52% of the 2-segment trials, they chose the same length for both segments; on 31% of the 3-segment trials, they chose the same length for all three segments; and on 32% of the 4-segment trials, they chose the same length for all four segments, all of which were greater than chances (all ts > 2.63, p < .05). 
As for turning angle selections, on average they chose 69 deg (SD = 10 deg), 71 deg (SD = 12 deg), and 68 deg (SD = 10 deg) as the turning angles at the first, second, and third intersections, respectively. The averaged chosen turning angle did not change as a function of the number of the intersections or the order of appearance of each intersection (both Fs < .75, p > .48). They chose 60-degree turns (85%) more often than 120-degree (15%) turns [F(1, 10) = 57.09, p < .01], but chose clockwise and counterclockwise turns equally often [F(1, 10) = 2.81, p = .124]. In addition, the turning angles they selected for the later intersections were also influenced by the turning angles they had selected for previous intersection(s) within the same trial. That is, if they chose the turning angles for subsequent intersections by chance, the probability that they chose the same turning angles (including magnitude and direction) for all the intersections within a pathway should be 25% and 6.25% for 3- and 4-segment trials, respectively. However, on 49% of the 3-segment trials, they chose the same turning angles for both intersections; and on 26% of the 4-segment trials, they chose the same turning angles for all three intersections, both of which were greater than chances (all ts > 3.1, p < .05). 
In particular, it should be noted that, when the active participants chose the same length for each segment and the same turning angle at each intersection, their outbound paths might have very special configurations. For example, if the active group chose the same 120-degree turns in the same direction at each intersection and the same length for each segment of the 3-segment trials, the ending points of their outbound paths would be the same as the starting points. However, this particular type of paths was rarely chosen, that is, only one participant chose this path structure in one trial. In addition, we selected all the 3- and 4-segment trials in which the active group chose the same length for each segment and the same turning angle at each intersection, and compared both groups' path completion performance in these trials and in other trials. We performed 2 (path structure, special as mentioned above or not) × 2 (condition, active or passive) × 2 (number of segments, 3, or 4) ANOVAs on the data. However, choosing the same length for each segment and the same turning angle at each intersection did not improve active or passive group's path completion performance (all Fs < .89, p > .40). 
Discussion
In this experiment, the active group was asked to make a forced choice about the length of each segment and the turning angle at each intersection, which simulated free navigation in the structured environments. In addition to the different types of decision making, there were also two other important differences between this experiment and Experiment 1. First, participants in the active group made the distance decisions before they started to travel along the segments, which ruled out the influence of online decision making on the encoding of segments. Second, after the distance was selected, the long hallways turned into short ones that had the selected lengths. Thus, both groups were aware of the length of each segment prior to traveling, which ruled out the influence of perceptual disruption on the encoding of segments in the passive condition. In addition, the shorter hallways also allowed both groups of participants to have a better visual estimate of the distance they would be travelling, which might have improved path integration. We did not find facilitation of active selection on path completion performance, which is consistent with the results of Experiment 1
Unlike in Experiment 1, participants in this experiment did not show any preference for the longest distance, but chose equally among the four path length options. These results are inconsistent with the hypothesis that people prefer longer segments. Instead, the preference for the 10-m segment in Experiment 1 appeared to be a result of certain strategy. A further analysis revealed one strategy that is consistent with participants' behavior in both experiments, that is, to select the same lengths and turning angles (including magnitude and direction) over multiple segments. In Experiment 2, participants chose the same length/turning angle much more frequently than predicted by random selection. In Experiment 1, since the active group knew that they would always be involuntarily stopped upon arriving at the 10-m maximum distance, it would be the easiest strategy to keep moving until being stopped to make sure that the length of each segment was the same. Thus, participants in Experiment 1 also effectively selected the same length and turning angles (90 degrees) across segments of the path. These analyses suggested that participants in both experiments were likely using the same strategy by repeatedly choosing the same segment length and the same turning angle. In addition, the active group in this experiment showed strong preference on small angles (60 degrees) than large angles (120 degrees) without any preference on clockwise or counterclockwise turns. This preference on 60-degree turns might be due to that smaller body rotations intuitively appeared to be more easily encoded and remembered. Some empirical studies showed that 60-degree turns were better reproduced than 120-degree turns (Klatzky et al., 1990; Wan, Wang, & Crowell, in preparation). 
General discussion
In the current study, participants traveled in virtual hallway-mazes and attempted to directly return to the origin upon seeing a golden apple. Half of the participants (active group) were instructed to perform this golden apple hunting game while they had the opportunity to select their paths to navigate in a virtual world full of hidden golden apples, which simulated the foraging behavior that some non-human animals performed in nature. In contrast, the other half of the participants (passive group) followed the identical outbound pathways selected by their counterparts, which is the more usual task in human path integration studies. Therefore, the two groups received the same perceptual and motor information but differed in the voluntary selection of the path structure. We also manipulated the type of the virtual environment. That is, the virtual world in Experiment 1 was less structured, and the active group was allowed to navigate with minimal limitations; whereas the virtual world in Experiment 2 was more structured, and the active group was only allowed to make a forced choice among a few available options. In both experiments, we found no facilitation effect of active selection on homing performance, in terms of the RTs to point to the direction of the origin, position errors (Euclidean distance between the real starting points and the observed ending points of the paths), direction errors, and distance errors. 
These findings cast doubt on the hypothesis that different path integration abilities that humans and nonhuman species have shown in previous studies (Klatzky et al., 1990; Loomis et al., 1993; Passini et al., 1990) are due to the methodological difference of the studies. In the literature, path integration in nonhuman species was tested in both pre-designed path completion tasks and free navigation, whereas humans were mainly tested in path completion tasks. The VR Cube used in the current study provided a very suitable virtual environment to test human path integration in simulated foraging behaviors. In addition to providing the sense of “presence,” good image quality, and wide field of views, the VR cube allowed the participants to freely navigate in the environment with 360 degree turns if needed. Moreover, only one hallway was presented at a time, so they navigated in a hallway maze which provided strong optic flow information without other visual cues about the environment. This also allows us to compare the current study to the literature of path integration in other species in which similar maze was also used. Our findings do not support Klatzky et al.'s (1999) speculations about this methodological difference, as the difference between the path integration abilities of humans and nonhumans cannot be simply attributed to that humans did not have the opportunity to select their paths in the tests of path integration. Indeed, the active group in the current study had the opportunity to freely navigate, or even “forage for food” in a simulated task, but their path completion performance was no better than the passive group who completed the typical experimental task by following paths selected by others. That is, having the opportunity to choose the structure of the outbound paths might not improve humans' path completion performance. 
These findings also provide some empirical evidence about other factors that have been shown to influence path integration. In both Experiments 1 and 2, participants showed longer RTs and greater errors when the outbound paths consisted of more segments, suggesting that the path integration might be impaired when more segments were included in the outbound paths. This finding is well in line with several studies (Klatzky et al., 1990; Loomis et al., 1993). However, it should be noted that path completion performance might depend on not only the number of segment but also the total length of the path. Wiener and Mallot (2006) showed that, when the total length was kept constant and only the number of segment was changed, the participants showed longer RTs and greatest directions errors (unsigned) for 2-segment trials. In the current study, participants showed longer RTs in Experiment 1 than in Experiment 2. Given that the total length of the outbound paths was greater in Experiment 1 than in Experiment 2, it is likely that the longer RTs in Experiment 1 were due to the longer overall path length. However, in the current study, these factors were largely confounded with each other (e.g., the paths with more segments were also generally longer overall) and with other factors (e.g., the visual appearance of the path and the decision types were different in the two experiments). Future research is needed to separate the relative contribution of different factors. 
The findings of the current study also shed some light on how navigators choose their pathway. First, when allowed to freely decide the paths, participants more frequently chose the right angles to be the turning angles at the intersections. This preference of the right-angle turns might be due to familiarity, e.g., most road intersections are orthogonal. It is also possible that this orthogonal preference reflects the information processing advantage of making a 90-degree turn (e.g., Loomis et al., 1993). Second, when asked to make choices among non-right-angle turns, participants showed strong preference on smaller angles (60-degree turns) over large angles (120-degree turns) without any preference on clockwise or counterclockwise turns. This preference on 60-degree turns might be due to the fact that smaller body rotations are less effortful. Moreover, smaller turns also have an advantage over larger turns in the path integration process, e.g., some empirical studies showed that 60-degree turns were better reproduced than 120-degree turns (Klatzky et al., 1990; Wan et al., in preparation). Finally, participants in both experiments showed a tendency to choose the same length for each segment and the same turn at each intersection within a path. One possibility is that participants chose the same length and turning angles to reduce the cost of making decisions. That is, they might repeat the same actions so that they didn't need to make a decision every time. In particular, in Experiment 1, they might simply keep moving until being stopped to avoid making their own decisions. An alternative possibility is that participants in both experiments might repeatedly choose the same segment length and same turning angle to make the structure of their outbound paths more easily to encode and remember. That is, if they selected different lengths and turns, they had to encode and remember multiple lengths and turns; if they repeatedly chose the same length and turn, they only had one length and one turn to encode and remember. These two possibilities cannot be distinguished in the current study, and future research is needed. 
Since path integration may rely on different types of information, internal or external information regarding self-motion, one should take cautions to generalize our findings in this study to all types of path integration. Internal information, such as body senses from the vestibular, proprioceptive and efferent systems, has been shown to be sufficient for path integration (Allen et al., 2004; Klatzky et al., 1990; Loomis et al., 1993). In contrast, the adequacy of optic flow only in path integration remains a controversial issue. Some studies suggested that the absence of body senses might impair path integration (Chance, Gaunet, Beall, & Loomis, 1998; Klatzky, Loomis, Beall, Chance, & Golledge, 1998; Péruch et al., 1997; Waller & Greenauer, 2007), whereas other studies showed that humans were able to perform path integration based on optic flow only (Ellmore & McNaughton, 2004; Kearns et al., 2002; Riecke et al., 2002; Wiener & Mallot, 2006). In the present study, information about translation was purely visual via optic flow due to technical limitations, whereas information about rotation was specified both visually and through body senses. Allowing the participants to physically rotate their bodies with resultant optic flow not only reduced possible motion sickness they might experience, but might also facilitate their path integration (Chance et al., 1998; Klatzky et al., 1998). The information basis of path integration should be taken into consideration when any generalization is to be made. 
These findings also expand our understanding of active exploration in its relevance to the literature of piloting and spatial learning. In Péruch, Vercher, and Gauthier (1995) study, participants who were both active in controlling their own movements and in choosing their own routes showed better knowledge of the space than those who passively viewed the same routes, suggesting that active movements and route choice might lead to more efficient spatial learning. However, Wilson, Foreman, Gillett, and Stanton (1997) showed that active choice did not lead to better spatial learning, regardless of whether the participants were able to control their movements in the environments or not. They also failed to replicate Péruch et al.'s (1995) results, regardless of whether participants' attention was focused on the spatial task or not (Wilson, 1999). In the current study, both the active and passive groups received the same perceptual input and were physically active via self-initiated locomotion, but only differed in the active process of making decisions of the routes structures. Although different navigation strategies and different VR were used in our study and Wilson and colleagues' studies, our findings are in line with theirs and added evidence to the lack of facilitation effect of active exploration in navigation. 
To sum up, the current study suggests that actively exploring a virtual environment and voluntarily determining the path structures do not benefit path integration based on optic flow and some body senses, regardless of the type of selection (free or forced choice). As Sholl (1996) suggested, humans rely more on direct visual information about the environment rather than relying on the path integration strategy. In other words, path integration may be a more important navigation strategy to some nonhuman species than to humans, so it is reasonable if humans truly have worse path integration skills than these nonhuman animals. Sighted humans are still able to use path integration, and this navigation strategy might become important and even life-saving in emergencies with smoky environments which is currently investigated in our lab. 
Acknowledgments
Supported by Tsinghua University Initiative Scientific Research Program and NSF Grant BCS 03-17681 to R.F. Wang. Some of the data were presented at Vision Sciences Society 7th Annual Meeting, Sarasota, Florida, 2007. We thank Andrew Wegrzyn, Sonia Stepien, Marvin Richardson, Addison Ellis, Scott Forsman, and Allison Aigner for running some of the experiments. We also thank Hank Kaczmarski and the Integrated Systems Laboratory at the Beckman Institute at the University of Illinois. 
Commercial relationships: none. 
Corresponding author: Xiaoang Wan. 
Email: wanxa@mail.tsinghua.edu.cn. 
Address: Department of Psychology, Tsinghua University, Beijing 100084, China. 
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Figure 1
 
Examples of virtual displays used in Experiments 1 and 2. (A) In Experiment 1, a long hallway appeared in the direction that participants in the active group had selected, while a pair of yellow markers was presented to highlight the minimum allowable distance. (B) In both Experiments 1 and 2, a golden apple appeared at the end of the outbound path accompanied by the change of the wallpaper. (C) In Experiment 2, a long hallway appeared in the direction that participants in the active group had selected, with four green door frames presented to highlight four distance options. (D) In Experiment 2, after the participants had selected a length for the hallway, the long hallway turned into a short one which had the selected length.
Figure 1
 
Examples of virtual displays used in Experiments 1 and 2. (A) In Experiment 1, a long hallway appeared in the direction that participants in the active group had selected, while a pair of yellow markers was presented to highlight the minimum allowable distance. (B) In both Experiments 1 and 2, a golden apple appeared at the end of the outbound path accompanied by the change of the wallpaper. (C) In Experiment 2, a long hallway appeared in the direction that participants in the active group had selected, with four green door frames presented to highlight four distance options. (D) In Experiment 2, after the participants had selected a length for the hallway, the long hallway turned into a short one which had the selected length.
Figure 2
 
An illustration of the path completion task. Participants start from H, travel along two segments (H → A, A → B) and then attempt to directly return to the origin (H). To accurately return to H, they should turn β degree and travel for distance c. However, their actual responses might be to turn β r degree, travel for distance cr, and arrive at a new location Hr. We assessed path completion performance by calculating position errors (Euclidean distances between H and Hr), direction errors (unsigned difference between β r and β), and distance errors (unsigned difference between cr and c).
Figure 2
 
An illustration of the path completion task. Participants start from H, travel along two segments (H → A, A → B) and then attempt to directly return to the origin (H). To accurately return to H, they should turn β degree and travel for distance c. However, their actual responses might be to turn β r degree, travel for distance cr, and arrive at a new location Hr. We assessed path completion performance by calculating position errors (Euclidean distances between H and Hr), direction errors (unsigned difference between β r and β), and distance errors (unsigned difference between cr and c).
Figure 3
 
The results of Experiments 1 and 2. The mean RTs, position errors, direction errors, and distance errors of the active group and passive group in Experiment 1 (free selection) and Experiment 2 (forced choice selection) are shown in Panels A, B, C, and D, respectively. Error bars show standard errors of the mean.
Figure 3
 
The results of Experiments 1 and 2. The mean RTs, position errors, direction errors, and distance errors of the active group and passive group in Experiment 1 (free selection) and Experiment 2 (forced choice selection) are shown in Panels A, B, C, and D, respectively. Error bars show standard errors of the mean.
Figure 4
 
An illustration of the distribution of the length of each segment (Panel A) and the turning angle at each intersection (Panel B) chosen by the active group in Experiment 1.
Figure 4
 
An illustration of the distribution of the length of each segment (Panel A) and the turning angle at each intersection (Panel B) chosen by the active group in Experiment 1.
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