J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group ... based on height, with co-actor heights differing by less than three inches. During.
Studies in Perception & Action XIII J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group, LLC
Behavioral Dynamics of a Joint-Action Object Movement and Passing Task Auriel Washburn1, James Evans2, Maurice Lamb3, Rachel W. Kallen1, Steven J. Harrison4, and Michael J. Richardson1 1
Department of Psychology, Center for Cognition, Action and Perception, University of Cincinnati, 2 Department of Psychology, Northeastern University, 3Department of Philosophy, University of Cincinnati, 4 School of Health, Physical Education and Recreation, University of Nebraska Omaha
When two people load a dishwasher their behaviors are not prescribed in advance. Nonetheless their actions become so coordinated that they come to behave as a single unit rather than a pair of independent individuals. Cohesive yet highly flexible interaction such as this also occurs between friends clearing a table or tidying a room, among athletes on a sports team, and between improvising musicians or dancers. Determining the behavioral dynamics (Warren, 2006) of these multi-agent behaviors requires understanding how the physical, informational and biomechanical properties of the agent-environment task context operate to constrain how, what and when different action possibilities and action mode transitions occur. With this in mind, the aim of the current study was to investigate and model the behavioral dynamics of a jointaction object movement and passing task. Method Twelve University of Cincinnati students (aged 19 to 28 years) were recruited to participate in the experiment. Six participant pairs were formed based on height, with co-actor heights differing by less than three inches. During the experiment, participants were asked to select, move and pass small virtual objects on a virtual tabletop display. A short-throw Viewsonic projector mounted beneath the frosted glass tabletop (70 cm x 150 cm) was used to present the task environment (i.e., objects, appearance and target locations), with this environment visible on the glass tabletop surface. Participants could interact with the environment in real time via hand-held wireless Polhemus Latus motion tracking sensors. These sensors tracked the movements of the participants (~0.2 mm accuracy; 96 Hz sampling rate) and mapped those movements across the tabletop surface. When the coordinates of a participant’s hand intersected the
Studies in Perception & Action XIII J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group, LLC coordinates of a virtual object, the individual was able to select and then move the object. Movement trajectories were also recorded, although no analysis of these trajectories is reported here.
Figure 1: Experimental set-up. Participants stood on either side of the virtual tabletop in symmetrical standing positions (shown), or asymmetrical standing positions (trial-initiation area for each participant indicated with dashed outlines). Participants performed 300 experimental trials. For each trial, participants moved a small blue disc (virtual object) from one of five appearance locations to one of five target (drop-off) locations (Figure 1). A trial began when both participants placed their sensor in a trial-initiation area displayed directly in front of where they were standing for 1 second. The trial-initiation area would then disappear and the disc object, appearance location, and target location would all become visible. A trial ended when the object disk was moved to the target location, at which time the trial-initiation areas would reappear. Before the experiment started, participants were informed that on any given trial they could move the disc object alone or by working together with their co-partner— i.e., by passing the virtual object. They were then provided with a series of instructional/practice trials in order to become comfortable with both actions. Participant standing position with respect to the position of the disc appearance and target locations was manipulated to provide two different locations (see Figure 1). The ‘symmetrical’ standing condition positioned participants directly across from each other, so that both participants were equidistant from the appearance and target locations. In the ‘asymmetrical’ condition, the standing position of each participant was shifted 32 cm to the participant’s right of their centered standing position. This resulted in Participant
Studies in Perception & Action XIII J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group, LLC 1 being closer to the target locations, and Participant 2 being closer to appearance locations. Experimental trials were organized into four blocks, with standing position alternated between blocks.
Figure 2. Average frequencies of task actions exhibited by Participant 1 and Participant 2 for each appearance × target location condition, as a function of standing position. Results and Discussion The four potential actions used to complete the object-moving task within a given trial can be defined with respect to one individual’s interaction with the disc: 1) pick up and drop off at target, 2) pick up and pass to co-participant, 3)
Studies in Perception & Action XIII J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group, LLC do nothing, or 4) receive from co-participant and drop off at target. Note that the performance of action 1 or 2 by one participant determines action 3 or 4, respectively, for the other participant. As can be seen in Figure 2, the frequency with which each participant performed actions 1 and 2 (equivalent to the frequencies of the respective complementary actions for the co-participant) on any given trial was almost fully determined by the specific appearance location × drop-off location condition presented. For example, in the symmetrical standing condition Participant 1 is closer to A1, A2, T1 and T2 and therefore was more likely to select and move the objects between these locations alone. However, if the object appeared in A1 or A2 and needed to be moved to T4 or T5, then Participant 1 would more likely select and then pass the object to Participant 2. The influence of the relative distance of co-acting participants to the appearance and target locations is further emphasized by an examination of the asymmetrical standing condition. Consider the data for Participant 2, who in the asymmetric condition was much closer to the appearance locations than Participant 1 (who was closer to the target locations). Accordingly, Participant 2 most often selected objects and passed them to Participant 1. Dynamical Modeling To model the dynamics of this joint-action task, we first defined movingalone and passing as two collective modes of behavior (i.e., the system’s order parameters). These two action modes characterize opposing (orthogonal) directions of behavior, both conceptually and physically, in that actors could either select and move an object alone or select and pass it to their partner. In addition, the two modes interact in a mutually destructive manner (the existence and attractive strength of the two modes covaries). Thus, by representing these two action modes as collective variables, ξ1 and ξ2, respectively, the action selection dynamics exhibited by a given participant in this task can be captured using an adapted version of the behavioral mode transition model developed by Frank, Richardson, Lopresti-Goodman, and Turvey (2009). For each participant, j, this system takes the form ! ! ! 𝜉!! = λ!! 𝜉! − 𝐵𝜉!! 𝜉!! − 𝐶 𝜉!! + 𝜉!! 𝜉!! ! ! ! 𝜉!! = λ!! 𝜉! − 𝐵𝜉!! 𝜉!! − 𝐶(𝜉!! + 𝜉!! )𝜉!!
(1)
where, B and C are positive constants that ensure that the interaction between ξ1 and ξ2 is mutually destructive (for simplicity we fix B = C = 1), and λ1 and λ2 are parameters that determine the growth rates of the amplitudes of ξ1 and ξ2, when ξ1 and ξ2 are close to zero (Frank, et al., 2009; Haken, 1991). Note that for simplicity we only consider ξ1 and ξ2 > 0 and that the order parameters ξ1 and ξ2 only increase from a state equal to zero when their corresponding λ parameter is positive. Accordingly, for a given participant the ‘existence’ of ξ1 or ξ2 as a behavioral mode is dependent on λ1 and λ2 > 0, respectively. Here, the
Studies in Perception & Action XIII J. Weast-Knapp, M. Malone & D. Abney (Eds.) © 2015 Taylor & Francis Group, LLC parameters λ1 and λ2 > 0 can be understood as a mode-relevant projection of a participant’s action capabilities relative to (i) the appearance × target location distances and (ii) their co-actors action capabilities. This projection can be functionalized (Washburn et al., in preparation) such that stable fixed points at 𝜉!!,!" = +
!! !
, 𝜉!!,!" = 0
(2a)
and 𝜉!!,!" = 0 , 𝜉!!,!" = +
!! !
.
(2b)
represent the existence of moving-alone and passing actions, respectively, for each participant. Acknowledgements. This research was supported by the National Institutes of Health (R01GM105045). References Frank, T. D., Richardson, M. J., Lopresti-Goodman, S. M., & Turvey, M. T. (2009). Order parameter dynamics of body-scaled hysteresis and mode transitions in grasping behavior. Journal of biological physics, 35(2), 127147. Haken, H. (Ed.). (1991). Synergetic Computers and Cognition. Springer, Berlin Warren, W. H. (2006). The dynamics of perception and action. Psychological review, 113(2), 358-389. Washburn, A., Evans, J. Kallen, R. W., Harrison, S. J., & Richardson, M. (in preparation). Modeling the Behavioral Dynamics of a Joint-Action Object Movement and Passing Task.
