Hierarchical goal effects on center of mass velocity and eye fixations during gait

The purpose of this study was to determine the effect of hierarchical goal structure of a yet-to-be performed task on gait and eye fixation behavior while walking to the location of where the task was to be performed. Subjects performed different goal-directed tasks representing three hierarchical levels of planning. The first level of planning consisted of having the subject walk to a bookcase on which an object (a cup) was located in the middle of a shelf. The second level of planning consisted of walking to the bookcase and picking up the cup which was in the middle, on the right side, or on the left side of the bookcase shelf. The third level of planning consisted of walking to the bookcase, picking up the cup which was located in the middle of the bookcase shelf, and moving it to a higher shelf. Findings showed that hierarchal goals do affect center of mass velocity and eye fixation behavior. Center of mass velocity to the bookcase increased with an increase in the number of goals. Subjects decreased gait velocity as they approached the bookcase and adjusted their last steps to accommodate picking up the cup. The findings also demonstrated the important role of vision in controlling gait velocity in goal-directed tasks. Eye fixation duration was more important than the number of eye fixations in controlling gait velocity. Thus, the amount of information gained through object fixation duration is of greater importance than the number of fixations on the object for effective goal achievement.


Introduction
Goal-directed gait is a frequent activity of daily living (Bieńkiewicz et al. 2014;Mlinac and Feng 2016). Despite this, a few studies have investigated how gait is affected by to be performed goals. Rosenbaum et al. (2012) demonstrated that the goals of the performer can be inferred by the way which they interact with an object for task performance, and this will allow an examination of the influence of goals on task performance. For example, it has been found that subjects tend to grasp a horizontally placed bar differently depending on which end will be placed in the downward position when the rod is moved vertically (Rosenbaum et al. 1990). According to Rosenbaum, complex planning is a hierarchy in which each subsequent plan interacts with the previous plan in the hierarchy. Researchers (Kaller et al. 2004;McKinlay et al. 2008;Ward and Allport 1997;Potts et al. 2018;van der Wel and Rosenbaum 2007) have identified goal hierarchy as a characteristic that can affect a problem's difficulty.
Before initiating goal-directed gait, the central nervous system forms a motor plan (Winter and Eng 1995;Bucklin et al. 2019;Glover 2004) along with a set of motor commands which are predicted to accomplish task-specific goals. Kaller et al. (2004) found that correct trials correlated with longer preplanning times and shorter movement execution times. An inverse relationship between preplanning and execution of the task indicates that thoroughly planned tasks are performed faster. In addition, online planning has been demonstrated to be important for goal-directed gait (Ariani and Diedrichsen 2019;Sun et al. 2017). Online planning during goal-directed gait may be achieved using visual as Communicated by Francesco Lacquaniti. well as other sources of information such as working memory (Nadkarni et al. 2010;Rosenbaum 2009) to inform the motor system of adjustments necessary for the achievement of the desired goal. Previous studies on visually guided gait demonstrated that subjects change their gait and eye fixation behavior during the performance of either time (Cinelli et al. 2009) or path constrained tasks (Cutting et al. 1995;Fajen and Warren 2004;Higuchi 2013;Marigold and Patla 2007;Matthis et al. 2018;Panchuk and Vickers 2011). Tracking eye fixations during goal-directed gait not only gives insight into where the individual looks as they approach a target, but also indicates where they are overtly attending at any given point in time. Eye fixations also allow one to calculate the location of environmental cues used in the regulation of gait (Fowler and Sherk 2003). While earlier studies demonstrated the synchrony of eye fixations and gait in different environmental contexts, they were not designed to systematically study the influence of a hierarchical goal structure on gait. The empirical literature, therefore, assessing how the hierarchical goal structure of a task influences gait is scarce. The purpose of this study was to determine the effect of hierarchical goal structure (Rosenbaum et al. 2012) of a yet-to-be performed task on gait (Center of Mass Velocity, COM V ; Step Length; Step Time) and eye fixation (Fixation Duration; Number of Fixations) behavior while walking in an unconstrained manner to the location of where the task was to be performed.
To address the effect of goal complexity on gait and eye fixation behavior, subjects in the present study performed five different goal-directed tasks representing three levels of task goal complexity. The structure of tasks used was influenced by the hierarchical framework for goals described by Rosenbaum (2012). Accordingly, the first-order planning consisted of having the subject walk to a bookcase on which an object (a cup) was located in the middle of a shelf. Second-order planning consisted of having the subject walk to the bookcase and pick up the cup. Three tasks were performed for this level of planning. After walking to the bookcase, subjects picked up the cup which was in the middle of the shelf, on the left side of the shelf, or on the right side of the shelf. Third-order planning was to walk to the bookcase, pick up the cup located in the middle of the shelf, and move the cup to the middle of a higher shelf. The hierarchical orders of planning were comprised of one, two, or three separate plans. The first plan was to walk to the bookcase, the second plan was to pick up the cup, and the third plan was to move the cup to the higher shelf. If subjects used these plans independent of one another to perform a task, we would not expect a difference in gait and eye fixation behavior during the walk to the bookcase across the first-, second-, and third-order planning conditions. This is because the performance of the second and third plans would not interact with performance in the first plan. Alternatively, the participant may have integrated the three plans to perform the tasks (Land et al. 2013;Lashley 1951;Rosenbaum et al. 2011). In this case, we would expect to find a difference in gait and eye fixation behavior during the walk to the bookcase across the first-, second-, and third-order planning conditions. This is because the overall difficulty of the first plan would be increased by the additive effects of the second and third plans. The change in gait associated with this strategy may be the result of increasing demand for attentional resources (Nadkarni et al. 2010). In this case, an increase in task difficulty would result in an increase in time to perform the task. Alternatively, there is evidence that effort to perform a task increases with task difficulty, resulting in a decrease in time to perform a task, and this relationship has become known as the "goal difficulty-performance relation" (Locke and Latham 2002). Croxson et al. (2009) found that activity in the striatum, including the putamen, correlated with the anticipated effort for an action. Furthermore, the putamen was identified by Kurniawan et al. (2010) as being responsible for the evaluation of effort cost. That is, whether or not a goal is worth the effort to attain it.

Subjects
Eight normally sighted college students (mean age ± standard deviation: 21.4 ± 1.4 years, six female) participated in the study. All subjects completed the Edinburgh Handedness Inventory (Oldfield 1971), and were right-hand (score 86.1 ± 13.2) and right-foot dominant. None of the subjects had a history of neurological, musculoskeletal disorders, or other disorders that would limit mobility at the time of participation, according to self-report. The Institutional Review Board of Indiana University Bloomington approved the study. All subjects gave informed consent before participation in the study.

Equipment
This experiment used two Microsoft Kinect cameras. Several studies have evaluated the Kinect sensors against a gold standard motion capture system concerning the accuracy of tracked landmark movements (Clark et al. 2012;Dutta 2012;Galna et al. 2014) and found a good-to-excellent agreement between the two motion-registration systems for spatiotemporal gait parameters and time. A customized visual studio C + + application based on the Kinect SDK 2.0 was developed and used to detect, track, and record human pose and motion for post-analysis. The application tracked and recorded the 3D locations, i.e., the x, y, and z coordinates (X = Mediolateral, Y = Vertical, Z = Anteroposterior), of 25 body parts and joints based on an RGB-D sensor at 30 Hz. The operating field of view for the Kinect V2 had a range of 0.5-4.5 m and a 70° horizontal and 60° vertical view angle (Microsoft, Inc.). Because our goal-directed gait task was 7.5 m in length (see "Procedures", Fig. 1), a Multiple-Kinect system was used to cover a longer distance. To convert a subject's two skeletons into one, which arose from using multiple cameras, a geometric transformation was used (Horn 1987) with customized MATLAB code (MathWorks, Inc. Natick, MA). For calibration, subjects were asked to stand stationary in three points (10 s for each), and the body parts were recorded by the multi-Kinect system.
Subjects' gaze was tracked using a Pupil Labs 1 headmounted eye tracker. The eye tracker has a gaze accuracy of 0.6° and the field of view of the scene camera was 100° diagonal. The eye tracker included three miniature video cameras: two "eye" cameras (one for each eye) which captured the image of the subject's eye at 200 Hz, and one "scene" camera which captured the image scene that the subject was viewing at 120 Hz. For this study, the eye-tracking software developed by Pupil Labs (Kassner et al. 2014) was used. After subjects put on the eye tracker, a nine-point calibration was performed whereby an experimenter held a printed calibration marker 2 m in front of the subject. Subjects were required to follow the marker with their eyes while holding their head still. A nine-point calibration was used, because this calibration method covered the entire field of view of the subject's scene camera. After calibration, subjects were instructed to look at certain areas of the room, and if there were differences between the subject's gaze (in the software) and the area points in the room, the calibration procedure was repeated. Figure 1 shows the experimental set-up. Subjects stood barefoot with both feet at the start position. The start position was 7.50 m from and directly opposite the 1.84 m (height) × 0.90 m (width) × 0.22 m (depth) bookcase with two shelves. The lower shelf was 0.88 m and the upper shelf was 1.23 m above the ground. An empty 16 oz cup (the "target") measuring 15.87 cm in height and 8.30 cm in diameter and weighing 275.23 g was located in the middle of the lower shelf. Subjects received an auditory "ready" signal followed by an auditory "go" signal. Upon receiving the go signal, subjects walked to the bookcase at a self-selected pace. They performed one of the five tasks when they arrived at the bookcase.

Procedures
Subjects performed each task three times in a blocked order. Subjects were informed which of the five tasks they were to perform before each of the 15 trials. The five tasks performed by subjects were: 1. walk to the bookcase (WTB); 2. walk to the bookcase and pick up the cup which was in the middle of the lower shelf of the bookcase (PC-M); 3. walk to the bookcase and pick up the cup which was on the left side of the lower shelf of the bookcase (PC-L); 4. walk to the bookcase and pick up the cup which was on the right side of the lower shelf of the bookcase (PC-R); 5. walk to the bookcase and pick up the cup and move the cup to the upper shelf from the middle of the lower shelf of the bookcase (MCU); The above tasks are consistent with three hierarchically ordered plans. The first task (WTB) represented one level of planning by which the subject walked to the bookcase and stopped in front of the cup. The second, third, and fourth tasks (PC-M, PC-L, and PC-R) represented two plans. In addition to the first plan, the second plan consisted of reaching and picking up the cup. The second plan had three levels represented by the cup being located in the middle of the shelf (PC-M), on the right side of the shelf (PC-R), or on the left side of the shelf (PC-L). The fifth task (MCU) represented three levels of planning where in addition to plans one and two, moving the cup to the upper shelf was the third plan.

Travel time
The travel time for each trial was calculated between the start time and end time. The start time was defined as the foot center local velocity minimum immediately preceding the foot center velocity first exceeding a threshold of + 0.1 m/s in the anterior-posterior plane (Clark et al. 2013). The end time was defined as the time at which the subject completed their walk to the bookcase, and stood still in front of the bookcase with both feet on the ground. Each trial was normalized as a percentage of its total duration and divided into five equal segments (see Fig. 2).

Kinematics
The center of mass (COM) of a human in a uniform gravitational field is the point where all the masses of the human body are centralized. Translation of the COM from one place to another is a fundamental objective of walking. The position of each subject's COM was found by calculating the weighted average of the position of each body segment based on anthropometric data reported by Drillis et al. (1964) and Winter (2009). An automated algorithm with a customized Matlab code was employed to extract various spatiotemporal features of the COM. The X COM defines the position of the subject relative to the stand position (X = 0). The Velocity of COM (COM V ) was calculated as COM V =Ẋ COM where the dot notation indicates the rate of change (i.e., ̇u = du dt ). The kinematic data at 6 Hz were low-pass filtered.
The rate of change of the optic field of view was also calculated using the method of Yilmaz and Warren (1995).
Step length and step time were also calculated for each subject on each trial for each of the five tasks. Specifically, as described by Dolatabadi et al. (2016), step time was computed as the number of seconds that elapsed between the double support phase of one foot and a single support phase of the same foot.
Step length was computed as the displacement, in milli meters, of the ankle of one foot along the z-axis during stance phase to the ankle of the opposite foot on the previous stance phase.

Inter-limb coordination
The number trials for ipsilateral or contralateral inter-limb reach to the cup were recorded from the videos collected by the Kinect cameras. Ipsilateral inter-limb coordination consisted of using the hand on the same side of the body as the leg stepping to the bookcase. Contralateral inter-limb coordination consisted of using the hand on the opposite side of the body as the leg stepping to the bookcase.

Eye fixations
In the current study, a fixation was defined as the subjects' eye angle remaining within 1.6° for a minimum of 100 ms. Our rationale for a 100 ms minimum fixation duration was to ensure that there was enough time for subjects to make an action-related decision (Salthouse and Ellis 1980). Fixations were categorized as falling onto one of three possible fixation locations (environmental objects): (a) target (cup), (b) bookcase, and (c) other. An analysis of fixation duration and the number of fixations in each of the five travel time segments for all subjects, trials, and tasks showed what environmental information subjects used to walk toward the bookcase and to pick up the cup.

Statistical analysis
A 5 (task) × 5 (travel time segment) repeated-measures ANOVA was conducted on COM V to assess how movement behavior changed as a result of the performance of all five tasks (WTB, PC-M, PC-L, PC-R, and MCU). Bonferroni corrected post hoc comparisons were used to further investigate the effect of tasks on COM V .
Univariate linear regressions were performed on gait step length and step time parameters to determine the relationship of these parameters with COM V .
A Chi-square test was used to determine differences in the use of ipsilateral or contralateral inter-limb coordination when reaching for the cup for the four tasks in which subjects picked up the cup (PC-M, PC-L, PC-R, and MCU).
Separate 3 (fixation location) × 5 (task) × 5 (travel time segment) repeated-measures ANOVAs were performed on the number of fixations and fixation duration measures to assess how fixation behavior changed as a result of performance in the five tasks (WTB, PC-M, PC-L, PC-R, and MCU). Bonferroni corrected post hoc comparisons were used to further investigate the effect of the goal-directed tasks on fixation behavior.
Univariate linear regression analyses were performed to find the relation between the COM V and eye fixations on both the target and bookcase across all travel time segments as well as during each of the travel time segments and tasks. Fig. 2 Travel time segments. Each trial was normalized as a percentage of its total duration. Five travel time segments, each consisting of 20% of the trial's duration, were used for analysis For each measure, the three trials within each task for each subject were averaged. All analyses were performed with a customized Matlab code, and Greenhouse-Geisser epsilon was used to control violations of sphericity. An alpha level of .05 was used for all tests. Figure 3 shows COM V across travel time segments for different tasks. The velocity profiles obtained for all five tasks conform to those of many action-gaps (e.g., when reaching); the movement starts at rest, accelerates to peak velocity, and then immediately decelerates to the end of the movement. It can be seen in Fig. 3 that the effect of the goals on gait was noticeable early in the first travel time segment. This effect was an incremental increase in the COM V as the number of goals increased. In addition, at about three steps before reaching the bookcase (as shown with the dashed line in Fig. 3), subjects started to decelerate and adjust their last steps to reach the bookcase. We found that subjects began their deceleration when the rate of change in the optic field of view approximated − 0.5, and that subjects kept this variable constant to have smooth braking.

COM velocity
The analysis of variance performed on the COM V measures confirmed the above observations. Specifically, there were significant main effects for tasks, F(4, 28) = 6.13, p < .01, and for travel time segment, F(4, 28) = 76.55, p < .01. However, the Task × Travel Time Segment interaction, F(16, 112) = 0.702, p = .78, was not significant. Post hoc comparisons showed that during the first and second travel time segments, COM V for the MCU, PC-M, and PC-R and PC-L tasks were significantly faster than the COM V from the WTB task (p < .05). During travel time segment three, the COM V from the MCU task was significantly faster than the COM V for WTB, PC-M, PC-R, and PC-L tasks (p < .05). During travel time segment four, the COM V was significantly faster for the MCU task than the WTB, and PC-M tasks (p < .05). Also, the COM V from the PC-R task was significantly faster than the COM V from the WTB task (p < .05). Table 1 lists the Pearson Correlation Coefficients (r values) obtained from the separate univariate linear regression analyses performed for step length and step time on COM V for all tasks. The obtained r values for step time were smaller than for step length for all tasks. Thus, subjects changed step length to a greater extent than step time to adjust their COM V .

Reaching phase
The Chi-square analysis showed a significant difference in inter-limb coordination (ipsilateral or contralateral) during the reaching phase to pick up the cup (χ 2 = 16.19, p = .001). As shown in Table 2, subjects showed no preference for ipsilateral or contralateral coordination in the tasks for which the cup was in the middle of the bookcase shelf (PC-M and MCU). However, subjects showed a preference for either ipsilateral (for the PC-R task) or contralateral (for the PC-L  Step length (r value) Step task) inter-limb coordination when the cup was not in the middle of the bookcase shelf.  Table 3 lists the Pearson Correlation Coefficients (r values) for eye fixations on the target obtained for the separate univariate linear regression analysis of fixation duration and number of fixations on COM V for all tasks. The correlations between number of fixations and COM V were smaller than the correlations between fixation duration and COM V for all tasks. The correlations between fixation duration on the bookcase and COM V were not significant for all tasks (p > .05). The exception to this was a significant correlation between fixation duration on the bookcase and COM V for the MCU task (r = 0.38,

Relation between eye fixation and gait characteristics
As shown in Fig. 5, a significant correlation was found between overall step length and fixation duration on the target. Significant correlations were also found between fixation duration on the target and step length for the PC-M, PC-L, PC-R, and MCU tasks (p < .05). The correlations between fixation duration on the target and step time were not significant for all tasks (p > .05). In addition, the correlations between the number of fixations on the target and step length and step time were not significant for all tasks (p > .05).

Discussion
The purpose of this study was to determine the effect of goal hierarchy (Rosenbaum et al. 2012) of a yet-to-be performed task on gait (COM V , step length, and step time) and eye fixation (fixation duration and number of fixations) behavior while walking to the location of where the task was to be performed. Even though our study did not constrain subjects in either time or their selected path, our findings are in agreement with previous studies showing that subjects change their gait and eye fixation behavior during the performance of either time constrained tasks (Cinelli et al. 2009) or path constrained tasks (Cutting et al. 1995;Fajen and Warren 2004;Higuchi 2013;Marigold and Patla 2007;Matthis et al. 2018;Panchuk and Vickers 2011).
We believed that gait directed to the performance of a task would be influenced by the hierarchical goal structure of the task to be performed. As can be seen in Fig. 3, this was the case as subjects walked faster during those tasks that comprised of a greater number of goals than the task with only one goal. This suggests that the approach to the bookcase and the execution of the task were governed by integrated hierarchical plans. As a result, our findings also suggest the involvement of the striatum along with the putamen (Croxson et al. 2009;Kurniawan et al. 2010) in the regulation of gait to the bookcase and with task performance. Previous studies using self-paced tasks showed that an increase in cognitive load was effective at increasing working speed and this has been attributed to an increase in effort (Wetter et al. 2012;Muhammed et al. 2018). The results of our study showed that subjects walked faster in self-paced unconstrained tasks which had a greater number of goals.
The change in the gait velocity profile also commenced early and was seen to already start in Travel Time Segment one. This suggests that even in our unconstrained tasks, subjects planned ahead and were able to walk more quickly to complete those tasks comprised of more goals. Therefore, our findings indicate that there was an increase in effort to perform those tasks comprised of a greater number of goals. Planning ahead was the case even when the increase in the number of goals occurred at the end of the task. Specific areas of the central nervous system such as the prefrontal cortex, primary motor area, premotor area, supplementary motor area, and basal ganglia are engaged in the planning and programming of a set of motor commands to perform a task, as well as generating the anticipatory postural adjustments in support of performance (Khanmohammadi et al. 2015;Fujiwara et al. 2012;Jacobs et al. 2010).
From a certain point between Travel Time Segments three and four (shown as the dashed line in Fig. 3), Fixation Duration (ms) Step Length (cm) r = .51, p < .05

Fig. 5
Univariate linear regression analysis between overall step length and fixation duration on the target subjects began to decelerate and this indicates that subjects were also engaged in online planning. This finding is consistent with the subject using information from the optic flow field to evaluate their speed and their distance from the bookcase, from which they began to decelerate and adjust their last steps accordingly (Yilmaz and Warren 1995). Thus, subjects made online velocity adjustments using optic flow information from self-motion (Stanard et al. 1996). This finding is consistent with research done by Lee et al. (1982) who showed that the long-jump run-up requires a similar timing skill. Lee et al.'s (1982) results showed that athletes visually regulated the last two or three steps to the take-off board by adjusting the duration of the steps and their velocity to the board. It is interesting that subjects in our study also began to decelerate about three steps before reaching the bookcase. Neurophysiology studies in humans have clearly pointed to a role for the posterior parietal cortex in the online updating of movements (Buneo and Andersen 2006;Desmurget et al. 1999;Pisella et al. 2000). The result of the study done by Lisi and Morimoto (2015) confirmed that the activity observed in the posterior parietal cortex is associated with the online adaptation of gait. In addition, the consistently higher correlation coefficients found between COM V and step length rather than with step time in the present study (Table 1) suggests that step length played a greater role in the regulation of COM V than step time. These findings are consistent with the recent research done by Wu et al. (2019) who showed that in slow walking, the relationship between gait speed and step length was 26% higher than with step time.
It can be seen in Table 2 that subjects preferred using ipsilateral lower limb support when the cup was on the right side of the bookcase shelf, a finding that is consistent with research performed by Rinaldi and Moraes (2015). However, when the target was on the left side of the shelf, subjects preferred using contralateral lower limb support. Furthermore, there was no preference for lower limb support when the cup was in the middle of the shelf. Our results describing the support limb for the different tasks, therefore, show that normal contralateral gait patterns (swinging lower limbs and upper limbs in opposition) are sometimes violated to accommodate the reach toward an object and that the central nervous system is able to break the upper-lower limb coupling at the appropriate time to exploit the upper limb forward momentum. Recent research (Nakagawa et al. 2016;Debaere et al. 2001) showed that brain activity differs in relation to the performance of ipsilateral and contralateral hand-foot combinations. Debaere et al. (2001) showed that inter-limb coordination affected activity in the supplementary motor area, and that supplementary motor area activity in ipsilateral inter-limb coordination was higher than for contralateral inter-limb coordination.
The current study also determined how vision contributed to the observed movement behaviors. Since our tasks were unconstrained, the pathway chosen by subjects was straight, and given that the cup position for the PC-L and PC-R tasks differed only by about 0.5 m from the PC-M and MCU tasks, it is surprising that the effect of task interacted with eye fixation location and travel time segment for both fixation duration and number of fixations. We found that the number of fixations on the target was high (Fig. 4c), but fixation duration was low (Fig. 4a) for the WTB task in comparison to the other tasks at Travel Time Segment three. After Travel Time Segment three, there was a reduction in the number of fixations and fixation duration on the target for the WTB task. This is evidence that in the absence of a goal hierarchy, subjects performing the WTB task paid less attention to the cup later in the task. This relationship was reversed for the other tasks (PC-M, PC-L, PC-R, and MCU) which had second-and third-level goals. For these tasks, fixation duration on the target was higher and the number of fixations was lower than for the WTB task in Travel Time Segment three. After Travel Time Segment three, fixation duration on the target for the other tasks (PC-M, PC-L, PC-R, and MCU) continued to be significantly higher compared to the WTB task, but the number of fixations was not significantly different from the number of fixations for the WTB task. Thus, subjects paid more attention to the target in these other tasks than in the WTB task. Our finding of different eye fixation behaviors across the different travel time segments between the WTB task and those tasks comprising of more goals demonstrates that subjects planned ahead and that goal hierarchy directly influences how a person surveys their environment and accordingly how they direct their attention.
The noticeable increase in fixation duration and the number of fixations on the bookcase for the MCU task at Travel Time Segment five can be attributed to the third-level goal which required subjects to lift the cup to the second shelf. The other tasks did not have this third-level goal and, therefore, their tasks were completed in Travel Time Segment five. This suggests that subjects in the MCU task were attending to the location of the second shelf, since this was where they would place the cup. Subjects adjusted their eye fixations to finish the task, and this, together with the COM V deceleration findings between Travel Time Segments three and four, indicates that subjects were engaged in online planning. Ballard et al. (1995) referred to this attention as "just in time", because individuals receive information just in time to execute an appropriate movement.
Collectively, our findings highlight that the role of vision is to "inform" the motor system about the environmental context (i.e., the relationship of the target's location to the individual's location and the rate of change in this relationship). The number of eye fixations has been associated with visual search (Kit et al. 2014), and the duration of eye fixations has been associated with visual processing (He and McCarley 2010). As shown in Fig. 5, there was a significant correlation between fixation duration and step length. This finding shows the importance of eye fixations in controlling gait to the target, such as controlling step length. Furthermore, unlike previous studies which did not include fixation duration in their analyses (Hsiao and Cottrell 2007;Jacob and Hochstein 2010;Tong et al. 2017), the present study showed that fixation duration played a more important role in controlling a person's gait than the number of fixations. As shown in Table 3, fixation duration explained approximately 32% of the variance in COM V compared to just 12% by the number of fixations. Thus, the information obtained during a fixation informs the motor system, so it can adjust gait to optimize COM V for the individual's approach to the target. Such an adjustment would entail a modification of the step length (and to a lesser degree step time, as suggested by the results reported in Table 1), as well as the selection of the approaching foot and reaching hand coordination when approaching the target.
The implication of the relationship between the gait and vision findings found in this study is that a person must appropriately attend to environmental objects to achieve efficient and safe gait rather than just quickly look at the objects. Thus, the amount of information obtained through the fixation is more important than the fixation itself. Our experiment used a simple and unchanging environment, and so, the performance of our subjects was based on their relative distance to the bookcase and location of the target. Therefore, fixation duration was of more importance than the number of fixations since subjects would not need to visually re-explore a familiar and simple environment as much as their need to visually process pertinent information obtained through their fixations. This relationship might be opposite in studies with a changing environment for which subjects may need more visual searching (greater number of eye fixations) than information processing (longer fixation durations). Several brain regions implicated in the control of eye movements are sensitive to reward probability (Hikosaka et al. 2006). For example, the discharge activity of neurons within the monkey lateral intraparietal area varies according to the expected reward (juice) associated with an eye movement to a visual target. However, fixating a location does not usually elicit a reward in goal-directed gait. Rather, fixation shifts assist the brain to gather relevant details necessary for making a motor decision. Thus, reward alone cannot explain fixation allocation during ongoing, naturalistic behaviors. Foley et al. (2017) showed that certain lateral intraparietal area neurons change firing rates depending on the expected gain in information needed to perform the higher order planning in a two-step decision task, rather than for the expected reward associated with that subsequent action. This highlights the importance of immediate information gain in shaping action decisions.

Conclusion
Our results show hierarchal goals do affect both gait (COM V , step length, and step time) and eye fixations (fixation duration and number of fixations). Specifically, we showed that gait velocity increased as the number of goals in the task increased. We also found that the location of the cup on the bookcase shelf (left side, right side, or middle) rather than the normal contralateral upper-lower limb gait pattern determined whether contralateral or ipsilateral lower limb support was used to pick up the cup. Subjects also not only planned ahead for the next goal during the attainment of a current goal (demonstrated in the present study as the early adoption of increased gait velocity for tasks comprising of more goals), but also utilized online planning. We found that subjects consistently made online velocity adjustments using optic flow information from self-motion as they approached the bookcase.
Our findings also demonstrated the important role that vision plays in controlling gait velocity in goal-directed tasks. We found that fixation behavior changed as a function of goal hierarchy, and that eye fixation duration was more important than the number of eye fixations in controlling gait velocity. Thus, for effective goal achievement, the amount of information gained through object fixation is of greater importance than the number of fixations on the object. Finally, previous studies in this area were not designed to investigate the effect of hierarchical goals on performance, and therefore, their findings may have confounded the effects of variables of interest with the existing task goal structures.