Preamble

Spatial Reference Frame Integration Performance Based on Collaborative Tasks
School of Psychology, Nanjing Normal University

This study investigates the representation of individual spatial reference frames through three experiments, exploring the specific conditions that facilitate the integration of these reference frames.

In each experiment, participants first engaged in collaborative learning of a spatial scene and subsequently performed an individual Judgments of Relative Direction (JRD) task. In the learning phase of Experiment 1, the angular disparity between the participant and their collaborator was $90^{\circ}$. In Experiment 2, this angle was $135^{\circ}$. Experiment 3 maintained the same $135^{\circ}$ angle as Experiment 2, but the collaborator left the scene prematurely. The results indicated that:

There are multiple forms of reference frame representation in spatial collaborative tasks, where both single and multiple reference frame representations may emerge. The integration of reference frames during spatial collaboration is significantly influenced by the physical position of the collaborator. Specifically, an orientation where the participant and partner are approximately face-to-face is more conducive to successful reference frame integration compared to standing side-by-side. Furthermore, even when the collaborator's presence is reduced, participants are still capable of completing the integration process. Notably, compared to scenarios where the partner is present throughout, the partner's departure following the restoration phase prompts the participant to form a more profound representation of the partner's perspective.

Keywords

Spatial Reference Frames, Spatial Perspective Taking, Spatial Collaboration, Reference Frame Integration

1. Introduction

1.1 Spatial Reference Frames

In daily life, to facilitate spatial localization and navigation, individuals often establish a mental spatial coordinate system—known as a spatial reference frame—to represent the positions of objects and others within the environment \cite{Shelton2001}. Since its inception, this concept has attracted extensive exploration. Studies primarily focus on two areas: first, the cognitive dominance of egocentric versus allocentric reference frames \cite{Klatzky1998, Mou2008, Mou2009}; and second, how individuals select and construct spatial reference frames under varying conditions \cite{Hatzipanayioti2021}. The former has enriched the theoretical framework of spatial reference frames, while the latter has deepened our understanding of how multiple factors shape spatial representations.

The conditions influencing the construction of spatial reference frames can be categorized into subjective and objective types. Subjective factors, such as spatial reference preferences and the initial viewpoint used when observing a scene, have a significant impact \cite{Christou1999, Mou2007, Simons1998, Valiquette2003}. External factors, such as the intrinsic axes of a scene, object orientation, and the presence of others, also influence the establishment of an individual's spatial reference frame \cite{Freundlieb2017, Mou2011, Shelton2005}.

In many previous studies, participants learned a scene in isolation; such learning was static and lacked social presence. However, real-life behaviors are dynamic and involve interactions with others, often requiring bilateral cooperation. Schober and Bowman (2004) pointed out that the choice of reference frame affects the efficiency of spatial collaboration and is closely related to the requirements of the collaborative task. Currently, research regarding the mechanisms by which individuals establish spatial reference frames during collaborative tasks needs expansion. Identifying which factors in collaborative tasks promote an individual's representation of another person's perspective—and the integration of that reference frame—is the core focus of this study.

1.2 Establishing Reference Frames in Collaboration

Spatial interaction is a dynamic process in which individuals understand, transmit, and share spatial information based on specific goals. This involves multiple cognitive mechanisms, including spatial perspective-taking and spatial reference frames \cite{2019, 2021}. Spatial collaboration—defined as cooperation between two or more parties to complete a spatial task—relies heavily on spatial perspective-taking. By adopting another person's perspective, individuals may establish a shared mental model and construct a corresponding spatial reference frame.

Spatial collaborative tasks are goal-oriented and involve multiple dimensions of interpersonal interaction. Early research by Schober (2009) demonstrated that when subjects were informed that their partner possessed lower spatial abilities, they were more inclined to describe locations from the partner's perspective. Furthermore, Furlanetto (2013) discovered that another person's gaze and action tendencies toward objects can prompt participants to adopt that person's perspective. Freundlieb (2016) indicated that participants only spontaneously adopt the other's perspective when they believe the partner is actively participating in the task.

Task instructions and cues also influence selection. Studies show that if participants know they must provide spatial descriptions to a partner with a different viewpoint, they are more inclined to choose the partner's perspective \cite{Galati2013, Kelly2018, Shelton2004}. Galati and Avraamides (2015) found that when a partner's location was known, participants tended to use the direction of the scene's intrinsic axis as the representational direction, regardless of whether their own perspective aligned with it.

1.3 Problem Statement and Hypotheses

Existing research faces two primary limitations. First, the social nature of experimental contexts is often insufficient; for instance, in some studies, participants did not communicate or their performance was not influenced by the collaboration \cite{Xie2020, Galati2015}. Second, disagreements remain regarding reference cues; some results indicate that participants tend to establish egocentric representations regardless of a partner's presence \cite{Sjolund2014}.

This study designed three experiments using the Judgments of Relative Direction (JRD) paradigm. Experiment 1 investigates how individuals establish reference frames in an adjacent configuration ($90^{\circ}$ disparity). Experiment 2 increases the angular difference to $135^{\circ}$ (face-to-face) to explore if this facilitates integration. Experiment 3 manipulates the timing of the partner's departure to explore its impact on the stability of the integrated representation.

2. Experiment 1: Spatial Reference Frame Selection in the Adjacent Configuration

2.1 Purpose and Background

We modified the McNamara \cite{McNamara2002} paradigm and incorporated elements from Holmes \cite{2018} to create a "spatial puzzle task." Participants and partners separately learn different portions of a scene and then reconstruct the full scene together. To prevent scene structure from biasing results, we used a symmetrical circular layout \cite{Greenauer2008, Greenauer2020}.

2.2 Method

2.2.1 Participants: Using G*Power 3.1, with $\alpha = 0.05$ and power $1 - \beta = 0.9$, a medium effect size ($f = 0.25$) required a specific sample size. We recruited undergraduate students (mean age 22.97 years) with normal vision.

2.2.2 Design: A single-factor within-subjects design was used. The independent variable was the imagined orientation in the JRD task ($0^\circ, 45^\circ, 90^\circ, 135^\circ, 180^\circ, 225^\circ, 270^\circ, 315^\circ$). These were grouped into:
1. Participant’s reference frame ($0^\circ, 180^\circ$) vs. Partner’s reference frame ($90^\circ, 270^\circ$).
2. Four axes: Participant Visual Axis, Partner Visual Axis, Participant Orthogonal Axis, and Partner Orthogonal Axis.

2.2.3 Materials: The scene consisted of nine common objects (pen holder, vase, etc.) on a 1.2m table inside a 3m tent. Each participant learned a partial scene of five objects with some overlap with the partner's scene. The Santa Barbara Sense of Direction Scale (SBSOD) was used as a covariate.

2.2.4 Procedure: Stages included preparation, individual learning, collaborative scene restoration, collaborative learning, scene labeling, and the JRD test. In the restoration phase, the partner (a confederate) placed their objects first, followed by the participant.

2.3 Results

The average accuracy was 90.8%. No speed-accuracy trade-off was found ($r = -0.07$).
Pointing Error: A significant main effect of orientation was found, $F(4.99, 139.77) = 2.98, p = 0.01, \eta_{p}^{2} = 0.10$. The self-perspective ($15.67^\circ$) had significantly lower errors than the partner-perspective ($23.57^\circ, p < 0.001$).
Reaction Time: The main effect was not significant ($F = 1.39, p = 0.25$), though the $0^\circ$ orientation remained faster than others ($ps < 0.01$).

2.4 Discussion

Experiment 1 results align with Sjolund (2014), showing a dominant egocentric reference frame. Although the partner's presence was noted, it did not lead to full integration, possibly because the $90^\circ$ "side-by-side" angle did not necessitate perspective-taking.

3. Experiment 2: The Face-to-Face Configuration

3.1 Method

30 participants (mean age 23.78) were recruited. The partner's perspective was shifted to $135^\circ$ to create a face-to-face orientation. All other procedures remained identical to Experiment 1.

3.2 Results

Accuracy was 93.1%.
Pointing Error: The main effect of orientation was not significant when divided into eight levels or two coordinate systems ($p > 0.05$), suggesting integration. However, the four-axis analysis showed a significant effect ($p < 0.04$).
Reaction Time: A significant main effect was found for the two coordinate systems, $F(1, 28) = 5.03, p = 0.03, \eta_p^2 = 0.15$, with the participant's system ($16.15s$) being faster than the partner's ($18.81s$).

Joint Analysis (Exp 1 & 2): A significant interaction between orientation and experiment was found for pointing errors, $F(5.27, 300.43) = 2.44, p = 0.03, \eta_{p}^{2} = 0.04$. The disadvantage of the partner's orthogonal axis in Exp 1 was significantly reduced in Exp 2.

3.3 Discussion

Increasing the angle to a face-to-face orientation promoted reference frame integration. While pointing errors showed no significant difference between perspectives (accuracy integration), reaction times still favored the egocentric frame, suggesting a "primary-secondary" dual-frame system.

4. Experiment 3: Impact of Partner Departure

4.1 Method

28 participants (mean age 23.14) were analyzed. The partner left the tent immediately after the scene restoration phase. Participants then completed the learning and labeling phases alone.

4.2 Results

Accuracy was 88.3%.
Pointing Error: No significant main effect of orientation was found across any grouping ($F < 1, p > 0.90$), indicating stable integration.
Reaction Time: A significant main effect was found for the eight orientations ($p = 0.01$), where $0^\circ$ remained the fastest. However, the four-axis analysis was not significant ($p = 0.21$).

Joint Analysis (Exp 2 & 3): The interaction between the four axes and the experiments was significant ($p = 0.01$). The advantage of the self-perspective axis observed in Exp 2 disappeared in Exp 3.

4.3 Discussion

The partner's departure did not hinder integration. In fact, the partner's departure seemed to prompt participants to process the partner's perspective more deeply, possibly due to a sense of "social obligation" to maintain the shared representation, leading to the disappearance of the reaction time advantage for the egocentric axis.

5. General Discussion

5.1 Reference Frame Integration

In Experiment 1 (adjacent), participants relied on an egocentric frame. In Experiments 2 and 3 (face-to-face), participants integrated the partner's frame. We propose a "primary-secondary" dual reference frame system where the self-referential axis is primary (faster retrieval) but the partner's axis is equally accurate (integrated representation).

5.2 Influence of Partner Position

Face-to-face orientations ($135^\circ$) are more conducive to integration than side-by-side orientations ($90^\circ$). This may be due to the increased salience of the partner's gaze and location, which triggers spontaneous perspective-taking \cite{Freundlieb2016, Ward2020}.

5.3 Influence of Partner Departure

The partner's departure after collaboration did not disrupt the integrated representation. Instead, it may have deepened the processing of the partner's perspective. This suggests that social interaction factors—such as shared goals and social presence—can fundamentally alter spatial cognitive representations.

6. Conclusion

1. Spatial representations in collaborative tasks can manifest as single or multiple reference frames.
2. Integration is significantly influenced by the partner's position; face-to-face orientations facilitate integration more effectively than side-by-side positions.
3. Integration persists even if the partner leaves the scene prematurely. The departure of a partner after a collaborative phase may even prompt a more profound representation of their perspective.