Numerous modeling approaches treat active matter through various mathematical analogs. However, most of these approaches do not adequately address the physical interactions between the particles that constitute active matter. In this paper, we propose several models of robot swarm interactions that can be derived using differential equation discovery: a simple model of individual robot motion, a model of single robot motion with interaction forces as external inputs, and a model of the displacement field as a continuous active matter analog. These models can enhance our understanding of the underlying physics of robot swarm interactions today and contribute to future studies of active matter.