A Model of the Sidewalk Salsa

TL;DR

The paper presents a CEI-based model of one-on-one sidewalk interactions to reproduce the sidewalk salsa by combining deterministic plans with probabilistic beliefs about others’ futures. It defines a four-component framework (Plan, Communication, Belief, Risk Perception) and implements it in a 7.0 s horizon with replanning under risk thresholds, tested across five scenarios. Simulations show salsa emergence in symmetric cases and modulation by initial offsets and belief biases, supporting the influence of cultural norms on pass-side conventions. The work offers a foundation for robotics to anticipate human intentions in social navigation, while acknowledging data limitations and proposing future empirical validation and parameter refinement.

Abstract

When two pedestrians approach each other on the sidewalk head-on, they sometimes engage in an awkward interaction, both deviating to the same side (repeatedly) to avoid a collision. This phenomenon is known as the sidewalk salsa. Although well known, no existing model describes how this "dance" arises. Such a model must capture the nuances of individual interactions between pedestrians that lead to the sidewalk salsa. Therefore, it could be helpful in the development of mobile robots that frequently participate in such individual interactions, for example, by informing robots in their decision-making. Here, I present a model based on the communication-enabled interaction framework capable of reproducing the sidewalk salsa. The model assumes pedestrians have a deterministic plan for their future movements and a probabilistic belief about the movements of another pedestrian. Combined, the plan and belief result in a perceived risk that pedestrians try to keep below a personal threshold. In simulations of this model, the sidewalk salsa occurs in a symmetrical scenario. At the same time, it shows behavior comparable to observed real-world pedestrian behavior in scenarios with initial position offsets or risk threshold differences. Two other scenarios provide support for a hypothesis from previous literature stating that cultural norms, in the form of a biased belief about on which side others will pass (i.e. deviating to the left or right), contribute to the occurrence of the sidewalk salsa. Thereby, the proposed model provides insight into how the sidewalk salsa arises.

Figures (5)

• Figure 1: Panel A: a sketch of the situation of interest: two pedestrians approaching each other on a sidewalk. Panel B: a top-down view of the modeled environment. The orange and blue triangles represent the pedestrians' positions and headings. Panel C: a schematic overview of the model. Every pedestrian is assumed to have a deterministic plan for their future trajectory --represented by dots-- and a probabilistic belief about the future trajectory of the other pedestrian, represented by the heat map where orange represents a high and green a low believed probability density. Combined, the plan and belief lead to a perceived risk; if this risk exceeds a personal threshold, pedestrians update their plan to lower it. The belief is based on nonverbal communication (i.e., the movements) from the other pedestrian. Panel D: The belief takes the form of a set of probability distributions over the lateral (x) position of the other pedestrian at a specific longitudinal (y) position. Each slice represents a probability distribution, combining three Gaussian distributions, each representing a specific high-level behavior of the other pedestrian: continuing on their current heading, passing on the ego's right side, and passing on the ego's left side. Each Gaussian distribution is defined by a mean $\mu$ and standard deviation $\sigma$ and is scaled by a weight $\gamma$. The three weights always sum to one.
• Figure 2: A typical interaction in the symmetric scenarios. Triangles indicate the positions and headings of the orange and blue pedestrians. The dots indicate their planned positions until the time horizon ($T=7.0~s$). The lines show their trajectories up to this point. The text above the images indicates the time in the simulation.
• Figure 3: Position traces for all 500 model simulations per scenario, rotated $90\deg$ clockwise (in comparison to figures \ref{['fig:introduction-overview']} and \ref{['fig:example_interaction']}). The colored lines represent the pedestrians' positions up to the point where they pass each other. Thin gray lines represent the remainder of the traces. The colors indicate different trials. The colored triangles in the "Symmetric" plot indicate the starting positions of the orange and blue pedestrians.
• Figure 4: An illustration of how the number of strategy switches is determined, with the orange pedestrian's plan from Figure \ref{['fig:example_interaction']}. A strategy switch is defined as a plan update where the plan changes from moving to one side (e.g., to the left) to moving to the other side (the right). Every pedestrian has a lateral dead band of $+-0.2~m$ (black lines) around their current position (triangles). The mean x-position (circles) of all plan points (histograms) determines this direction. The initial mean x-value lies within the dead band (frame 1). One strategy switch is counted once it moves outside the dead band (frame 4). When the average planned x-position moves to the other side of the dead band, another switch is counted (frame 5). However, if the average x value of the plan stays on that side or moves back inside the dead band, nothing happens (frame 6). Strategy switches are counted up until the moment when pedestrians pass each other. Therefore, pedestrians with zero strategy switches never substantially changed their plans; with one switch, they decided to go left or right and stuck with that, and with more switches, they adjusted their (high-level) plan multiple times.
• Figure 5: The number of strategy switches a single pedestrian made in a single trial per condition. $n=200$ since there are $100$ trials per condition with $2$ pedestrians in each trial.