Spatially-invariant opinion dynamics on the circle

TL;DR

This paper introduces a nonlinear opinion dynamics model for decision-making on circular options, inspired by perceptual processes, with applications in robotic navigation and a focus on spatial invariance and input influence.

Contribution

The paper develops a new theory for opinion formation on the circle with spatially invariant interactions, enabling flexible, distributed decision behaviors in continuous option spaces.

Findings

Model captures opinion dynamics influenced by inputs on circular options

Spatial invariance allows for simplified linearization and analysis

Application demonstrated in robotic navigation in crowded environments

Abstract

We propose and analyze a nonlinear opinion dynamics model for an agent making decisions about a continuous distribution of options in the presence of input. Inspired by perceptual decision-making, we develop new theory for opinion formation in response to inputs about options distributed on the circle. Options on the circle can represent, e.g., the possible directions of perceived objects and resulting heading directions in planar robotic navigation problems. Interactions among options are encoded through a spatially invariant kernel, which we design to ensure that only a small (finite) subset of options can be favored over the continuum. We leverage the spatial invariance of the model linearization to design flexible, distributed opinion-forming behaviors using spatiotemporal frequency domain and bifurcation analysis. We illustrate our model's versatility with an application to robotic navigation in crowded spaces.