Psychonomic Bulletin & Review 2008, 15 (6), 1100-1104 doi:10.3758/PBR.15.6.1100

Reaching while walking: Reaching distance costs more than walking distance David A. Rosenbaum

Pennsylvania State University, University Park, Pennsylvania Surprisingly little is known about how people plan and control everyday physical actions, such as walking along and picking up objects. In order to explore this topic, we conducted an experiment in which university students were asked to pick up a common object (a child’s beach bucket) that stood on a table several meters from the participant’s start position. The bucket stood either on the left side, in the middle, or on the right side of the table and, depending on instructions, was to be carried to a farther target whose horizontal position was also varied. The questions were which side of the table the participant would walk along when picking up the bucket and which hand the participant would use to pick up and carry the bucket. Participants, most of whom were righthanded, preferred to walk along the left side of the table and to pick up the bucket with the right hand, although they departed from that preference when the reaching distance across the table was uncomfortable or if the target was too far to the right. The data were well fit with a mathematical model that included a right-hand bias and an estimate of functional distance that expressed the cost of reaching over some distance as approximately twice the cost of walking over the same distance.

Everyday physical tasks are usually so easy to perform that we rarely think about how to perform them. Yet, a moment’s reflection indicates that considerable skill is brought to bear when we move from place to place, pick up and manipulate objects, and so on. Were this not the case, it would not take us years to learn to perform elementary actions. As babies, we would not spill our milk, nor as toddlers would we need help from our parents to get dressed. Robots, too, would be more capable of autonomous planning and control of physical actions than they are today. One way to learn how physical tasks are controlled is to study how adults perform the tasks under a variety of conditions. Variations in the way the tasks are performed can reveal the factors that people take into account when performing them. Such research can help researchers identify possible “grammars of action” (Goodnow & Levine, 1973) or, to use a term rooted in engineering rather than linguistics, optimization criteria underlying action choices (Todorov, 2004). My colleagues and I have pursued this approach in research on object manipulation. We have found that objects are picked up in ways that ensure comfortable or easy-to-control postures when the objects are brought to new positions. For example, in one line of studies, we found that university students picked up a standing toilet plunger at a point along its shaft that was inversely related to the height to which the plunger would be brought: the higher the target height, the lower the grasp height (Cohen & Rosenbaum, 2004; Rosenbaum, Halloran, & Cohen,

2006; Weigelt, Cohen, & Rosenbaum, 2007). This inverse relation between grasp height and target height was interpreted to mean that the final posture adopted when placing the plunger on the target would avoid extreme joint angles. The finding that people pick up objects in ways that reflect what they plan to do with the objects has been obtained in other studies (Claxton, Keen, & McCarty, 2003; Haggard, 1998; Marteniuk, Leavitt, MacKenzie, & Athenes, 1990; Weir, MacDonald, Mallat, Leavitt, & Roy, 1998). For a review of research on this topic, see Rosenbaum, Cohen, Meulenbroek, and Vaughan (2006). Almost all previous research on grasping has focused on situations in which participants sit or stand still while grasping objects of interest. Yet, people often move through the environment while picking up objects. A person in a grocery store, for instance, may grab an apple on the way to the checkout counter; a waiter in a restaurant may pick up a customer’s credit card on the way to the kitchen; and so on. Remarkably little research has been done on the coordination of reaching and walking, despite the fact that reaching and walking are likely to share common neural pathways (Georgopoulos & Grillner, 1989). The few studies that have been done on this topic have focused on fairly detailed features of the relevant arm and leg movements, such as their relative phasing (Carnahan, McFadyen, Cockell, & Halverson, 1996; Cockell, Carnahan, & McFadyen, 1995; Marteniuk & Bertram, 2001) or choice of foot for initiating walks that include reaches to one side or the other some distance away (van der Wel & Rosenbaum, 2007).

D. A. Rosenbaum, [email protected]

Copyright 2008 Psychonomic Society, Inc.

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Reaching While Walking     1101 In the present study, we were concerned more with macroscopic variables related to walking and reaching—namely, which side of a table people would walk along to pick up an object standing somewhere on the table, and which hand they would use to pick up the object. The rationale for pursuing this large-scale level of analysis of behavior was to begin to fill the void in the understanding of human perception and performance concerning the rules underlying large-scale action choices. For robotics—to name one field where information about these rules could have practical consequences—knowing the rules for action choices could help robots plan actions more skillfully than they do. In terms of theory, it is interesting to study how people coordinate walking and reaching, because walking costs and reaching costs are quite different, at least on first glance. They use different effector systems, and the spatial scales over which they operate tend to be quite different as well, being large for locomotion and smaller for reaching. Somehow, the nervous system reconciles these two kinds of cost to enable decisions about whole body motion. How it does so is a focus of this investigation. METHOD The setup for the experiment is shown in Figure 1. The participants faced a table with a bucket standing on it. The bucket stood either on the left, in the middle, or on the right of the table’s midsection. Beyond this table was another, long table with targets (pieces of paper numbered 1–7), arranged from left to right. The participants were asked to walk from the start point, pick up the bucket, carry it to a named target, place it on that target, and then return to the start position empty-handed. The questions were which side of the

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Figure 1. Setup for the experiment. From bottom to top are shown the box (tape lines on the floor) where the participant stood at the start of each trial, the table on which the bucket stood at each of three positions, and the table with the targets labeled 1–7, drawn to scale.

table the participant would walk along when picking up the bucket and which hand the participant would use to pick up and carry the bucket to the target. Three hypotheses were considered. All of them concerned the probability of walking along the left side of the table. It was assumed, for the sake of expressing the predictions, that if a participant walked along the left side of the table, he or she would pick up the bucket with the right hand, or if a participant walked along the right side of the table, he or she would pick up the bucket with the left hand. It happened that this assumption was never violated by the data. The three hypotheses were as follows. Walking distance only. For this model, I hypothesized that participants would try to minimize walking distance and would not care how far they reached across the table. The predicted pattern of data is shown in Figure 2A. Reaching distance only. For this model, I hypothesized that participants would try to minimize reaching distance across the table and would not care how far they walked. The predicted pattern of data for this hypothesis is shown in Figure 2B. Walk and reach. For this model, I hypothesized that participants would try to reduce walking distance and reaching distance across the table. The predicted pattern of data for this hypothesis is shown in Figure 2C. Note that the predicted pattern shown in Figure 2C, like the predicted patterns for the other two hypotheses, is merely illustrative of the class it represents. Participants Thirty-eight Penn State undergraduates participated for course credit. The participants ranged in age from 18 to 23 years. All but 3 of the participants were right-handed, as gauged by the Edinburgh handedness inventory (Oldfield, 1971). Thus, 35 of the 38 participants had scores of 8, 9, or 10 out of the possible 10 for right-hand preferences for the tasks in the inventory. Two of the other participants were ambidextrous (only 5 or 6 right-hand preferences), and the other participant was strongly left-handed (10 left-hand preferences). The method was approved by the Penn State Institutional Review Board. Apparatus, Procedure, and Design As shown in Figure 1, a square (30.5 3 30.5 cm) on the floor marked the starting position where the participants stood at the start of each trial. The front edge of the square (i.e., the edge of the square where the participants placed the front of their feet) was 1.22 m from the near end of a table (76.2 cm wide 3 152.4 cm long) on which stood a yellow plastic beach bucket (12.4 cm high, 10.0-cm bottom diameter, 13.7-cm top diameter), which had a blue handle that stood upright and whose peak stood 7.6 cm above the top of the bucket. The bucket could be placed at each of three possible locations, 33.0 cm apart, center to center, along the middle of the length of the table. Small, lightly written numbers on the table helped the experimenter place the bucket on the dot corresponding to the location to be tested in each trial. The experimenter placed the bucket so that its handle was parallel to the long edge of the table. Four rolls of U.S. pennies (50 coins per roll) were kept in the bucket so that the weight of the bucket plus its contents (13⁄8 lbs) was heavy enough to slightly challenge the lifting capacities of all of the participants. The penny rolls did not roll around in the bucket. Penny rolls were used so other researchers could replicate the present setup as closely as possible. The far edge of the bucket-bearing table was 1.22 m from a long table, 76.2 cm wide and 304.8 cm long, whose long edge was centered with respect to the bucket-bearing table. Taped to the top surface of the long table were seven sheets of paper, each 21.6 3 27.9 cm, with the numbers 1–7 each printed in 48-point font on a sheet. The papers were separated by 25.7 cm, center to center, and their numbers increased from left to right, with 4 occupying the center. Each participant was tested in 21 conditions (3 bucket positions 3 7 target positions, in random order for each participant). The instruction given to each participant was to pick up the bucket while walking

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Figure 2. Qualitative predictions concerning the probability of walking on the left side of the table as a function of target position (abscissa) and bucket position (distinguishing feature of curves in each graph). (A) Walking distance matters, but reaching distance does not (all bucket positions superimposed on one curve). (B) Reaching distance matters, but walking distance does not (three lines for the three bucket positions). (C) Walking distance and reaching distance both matter (three curves for the three bucket positions).

RESULTS The data of 2 participants were excluded because these participants did not follow the basic task instructions. The data from the remaining 36 participants are shown in Figure 3, which displays the probability of walking to the left of the table as a function of target location. The three curves correspond to the three bucket placements (left, middle, and right). The probability of walking to the left of the table was high when the bucket stood on the left side of the table and was low when the bucket stood on the right side of the table. When the bucket stood in the middle of the table, the probability of walking to the left was high for left targets and was low for right targets. The statistical transition from walking to the left to walking to the right of the table was between Targets 4 and 5, which was to the right of the midpoint of all of the targets (Target 4). Because all the participants who walked to the left of the table lifted the bucket with the right hand, and vice versa, the only data graph shown here shows the probability of walking to the left of the table. The graph showing the probability of picking up the bucket with the left hand is identical to Figure 3, but flipped about the vertical axis.

DISCUSSION This study was designed to shed light on the factors that are taken into account in the everyday task of walking along and picking up an object. The questions concerned macroscopic behavior: Which side of a table would people walk along and which hand would they use to pick up an object (a slightly loaded beach bucket), depending on where the object stood and where it needed to be carried? Three hypotheses were considered. The first was that participants would make their choices on the basis of 1 .9 .8

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along either side of the table—whichever side seemed easier—and to carry the bucket to the named target. The participants were told to put the bucket down on the named target and then to walk back to the start square. Upon returning to the start square, the participants were told to face away from the tables while the experimenter set up the next trial, after which the experimenter asked the participants to turn around and take a moment to scan the scene before starting to walk. Performance was recorded with a Web camera. The entire experiment, including completion of the informed consent form, completion of all 21 experimental trials, and debriefing, took about 45 min.

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Target Figure 3. Probability of walking to the left of the table as a function of target location when the bucket stood on the left, middle, or right.

Reaching While Walking     1103 walking distance (Figure 2A). The second was that participants would make their choices on the basis of reaching distance (Figure 2B). The third was that participants would make their choices on the basis of walking distance and reaching distance (Figure 2C). Contrary to the first and second hypotheses, participants’ choices depended on the distance to be walked and on the distance to be reached. However, the way in which the participants’ choices were made on the basis of the combination of these factors did not resemble the pattern that was predicted (Figure 2C). It must be recalled, however, that the predicted pattern was qualitative: It represented a class of predictions rather than a specific quantitative prediction. For the class of predictions represented by Figure 2C, the participants should have combined their judgments of walking costs and reaching costs. Because participants were sensitive to both kinds of costs, the challenge is to understand how the probability of going to the left of the table depended on the two costs. One way of expressing this challenge is to say that, for graphical purposes, it would be desirable to have one curve rather than three curves relating the probability of going to the left of the table to the distances that needed to be walked and reached. A way to approach this goal is to note that the three curves of Figure 2C can be turned into one curve by horizontally shifting two of the curves by amounts that allow all three of the curves to be contiguous. Such a curve is shown in Figure 4. Here, the data from Figure 3 are replotted so the data for the bucket on the left are horizontally shifted to the left and the data for the bucket on the right are horizontally shifted to the right; the data for the bucket in the middle are untouched. The shifts of the left bucket and right bucket data sets were designed to maximize the goodness of fit of the logistic function, y 5 1 2 [1/(1 1 x)], where x 5 exp{2a[(t 2 b)/T ]}, t was the array of adjusted target values (i.e., the values shown on the abscissa of Figure 4), T was the maximum 1 Left on table Middle on table Right on table

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Adjusted Target Location (cm) Figure 4. Fit of the walk-and-reach model to the obtained probabilities of walking to the left of the table as a function of adjusted target location when the bucket stood on the left, middle, or right.

value of t, b was the mean of t (i.e., the value of t where y switched from less than .5 to greater than or equal to .5), and a was a scale factor. In order to fit the function, two parameters were estimated: a, defined above; and s, the horizontal shift of the data for the bucket on the left. The horizontal shift of the data for the bucket on the right was 22s. The best-fitting values of a and s were 18 and 270, respectively. The percentage of variance accounted for was 98.05%. Given this outcome, it is worth interpreting the bestfitting parameters. The value of 18 for a is a fairly large number, corresponding to a steep transition from values near 1 to values near 0. The steepness of the transition indicates that participants were decisive about which side of the table to pass and which hand to use. The best-fitting value of s (viz., 270 cm) is important because of how large it is. Had the best-fitting value of s been 0 cm, one could have said that participants did not care where the bucket stood. Indeed, a best-fitting value of s equal to or close to 0 cm was predicted by the walking distance only model (Figure 2A). The value of 270 cm gives a numerical estimate of just how reluctant participants were to reach across the table. The estimate can be interpreted to mean that participants were willing to walk an extra 70 cm for each 33-cm shift in the horizontal position of the bucket away from the nearest edge of the table on which the participant stood. Because 70 cm divided by 33 cm equals 2.12, one can say that reaching distance was judged to be 2.12 times more costly than walking distance. A final inference based on the parameters of the bestfitting model relates to b, the mean value of t. This value was 23.33 cm. Had b been 0, one could have said that there was no rightward or leftward bias, but because b was positive, there was a bias to walk to the left of the table or, equivalently, to use the right hand. This bias was alluded to earlier in this report. Such biases have been documented before, albeit in tasks performed while seated (e.g., Bryden & Roy, 2006; Doyen & Carlier, 2002). The foregoing observations point to a simple decision model. The model has two steps, at least for the present participants, the majority of whom were right-handed and had good mobility (of both the arms and the legs): (1) By default, plan to walk to the left and pick up the bucket with the right hand. (2) If the functional distance for reaching with the right hand exceeds the functional distance for reaching with the left hand, switch to the left hand and to the corresponding side (the right side) of the table. Regarding Step 2, the functional distance of reaching with the right hand can be defined as 2.12 times the righthand reaching distance plus the remaining walking distance. The functional distance of reaching with the left hand can be defined as 2.12 times the left-hand reaching distance plus the remaining walking distance plus 23.33 cm. Relying on this simple decision model, one would expect choice probabilities of 1 and 0. The observed departures of the choice probabilities from 1 and 0 can be ascribed to uncertainty in the distance estimation or judgment processes within participants and variation in the transition point among participants.

1104     Rosenbaum CONCLUSION The results from the present study support a simple decision model for reaching while walking. The model was based on the quantitative fit of a psychophysical model, the parameters of which were undoubtedly related to the particular features of the setup used here. Presumably, the parameters of the model would change if the features of the setup were varied. Thus, if the weight of the bucket were altered, participants’ reluctance to lean over to pick up the bucket would probably change as well. Other factors that might affect the decision making include the possible positions of the bucket, the walking distances to the targets, the orientations of the bucket handle, and so on. A more comprehensive version of the present model should incorporate these factors. Features of the participants might also affect their decision making. Handedness would be expected to affect the results (more data would be needed to test this); short participants would probably be less willing to lean over a long distance than would taller participants; weaker participants would be less willing to generate the forces and torques needed to lift a heavier bucket; and so on. Acknowledging these possibilities paves the way for elaborating the model. Finally, one would expect decision making in this task to be carried out with respect to body-scaled measures of the environment, not to centimeters (cf. Marteniuk & Bertram, 2001). Centimeters were used here for convenience. Further work with this method should also focus on more precise timing and on other detailed features of participants’ behavior. For example, no attempt was made to quantify the amount of time participants spent picking up the bucket, nor was an attempt made to characterize the walking paths that participants followed. These are matters that can be pursued if one wishes to obtain a more detailed picture of performance in this task. It is gratifying, nonetheless, that insights can be gained without these more detailed measures. Simple behavioral experiments, requiring little more than paper, pencil, some tables, and a beach bucket, can still help one get at useful truths about the planning and control of physical action. AUTHOR NOTE The author is indebted to the Penn State undergraduates who helped carry out this experiment for independent study credit: Michael Brach, Nurcan Cile, Carrie Gager, and Cassie Kennedy. The author also thanks Pamela Bryden, Jeffrey Eder, Ruud Meulenbroek, Joseph Santamaria,

Robrecht van der Wel, Jonathan Vaughan, and an anonymous reviewer for helpful comments. Correspondence concerning this article should be addressed to D. A. Rosenbaum, Department of Psychology, Pennsylvania State University, University Park, PA 16802 (e-mail: [email protected]). REFERENCES Bryden, P. J., & Roy, E. A. (2006). Preferential reaching across regions of hemispace in adults and children. Developmental Psychobiology, 48, 121-136. Carnahan, H., McFadyen, B. J., Cockell, D. L., & Halverson, A. H. (1996). The combined control of locomotion and prehension. Neuroscience Research Communications, 19, 91-100. Claxton, L. J., Keen, R., & McCarty, M. E. (2003). Evidence of motor planning in infant reaching behavior. Psychological Science, 14, 354-356. Cockell, D. L., Carnahan, H., & McFadyen, B. J. (1995). A preliminary analysis of the coordination of reaching, grasping, and walking. Perceptual & Motor Skills, 81, 515-519. Cohen, R. G., & Rosenbaum, D. A. (2004). Where objects are grasped reveals how grasps are planned: Generation and recall of motor plans. Experimental Brain Research, 157, 486-495. Doyen, A.-L., & Carlier, M. (2002). Measuring handedness: A validation study of Bishop’s reaching card test. Laterality, 7, 115-130. Georgopoulos, A. P., & Grillner, S. (1989). Visuomotor coordination in reaching and locomotion. Science, 245, 1209-1210. Goodnow, J. J., & Levine, R. A. (1973). “The grammar of action”: Sequence and syntax in children’s copying. Cognitive Psychology, 4, 82-98. Haggard, P. (1998). Planning of action sequences. Acta Psychologica, 99, 201-215. Marteniuk, R. G., & Bertram, C. P. (2001). Contributions of gait and trunk movement to prehension: Perspectives from world- and bodycentered coordinates. Motor Control, 5, 151-164. Marteniuk, R. G., Leavitt, J. L., MacKenzie, C. L., & Athenes, S. (1990). Functional relationships between grasp and transport components in a prehension task. Human Movement Science, 9, 149-176. Oldfield, R. C. (1971). The assessment and analysis of handedness: The Edinburgh inventory. Neuropsychologia, 9, 97-113. Rosenbaum, D. A., Cohen, R. G., Meulenbroek, R. G., & Vaughan, J. (2006). Plans for grasping objects. In M. Latash & F. Lestienne (Eds.), Motor control and learning over the lifespan (pp. 9-25). New York: Springer. Rosenbaum, D. A., Halloran, E. S., & Cohen, R. G. (2006). Grasping movement plans. Psychonomic Bulletin & Review, 13, 918-922. Todorov, E. (2004). Optimality principles in sensorimotor control. Nature Neuroscience, 7, 907-915. van der Wel, R. P., & Rosenbaum, D. A. (2007). Coordination of locomotion and prehension. Experimental Brain Research, 176, 281-287. Weigelt, M., Cohen, R. G., & Rosenbaum, D. A. (2007). Returning home: Locations rather than movements are recalled in human object manipulation. Experimental Brain Research, 149, 191-198. Weir, P. L., MacDonald, J. R., Mallat, B. J., Leavitt, J.  L., & Roy, E. A. (1998). Age-related differences in prehension: The influence of task goals. Journal of Motor Behavior, 30, 79-89. (Manuscript received May 24, 2008; revision accepted for publication July 11, 2008.)