Should Collaborative Robots be Transparent?

We often assume that robots which collaborate with humans should behave in ways that are transparent (e.g., legible, explainable). These transparent robots intentionally choose actions that convey their internal state to nearby humans: for instance, a transparent robot might exaggerate its trajectory to indicate its goal. But while transparent behavior seems beneficial for human-robot interaction, is it actually optimal? In this paper we consider collaborative settings where the human and robot have the same objective, and the human is uncertain about the robot's type (i.e., the robot's internal state). We extend a recursive combination of Bayesian Nash equilibrium and the Bellman equation to solve for optimal robot policies. Interestingly, we discover that it is not always optimal for collaborative robots to be transparent; instead, human and robot teams can sometimes achieve higher rewards when the robot is opaque. In contrast to transparent robots, opaque robots select actions that withhold information from the human. Our analysis suggests that opaque behavior becomes optimal when either (a) human-robot interactions have a short time horizon or (b) users are slow to learn from the robot's actions. We extend this theoretical analysis to user studies across 43 total participants in both online and in-person settings. We find that -- during short interactions -- users reach higher rewards when working with opaque partners, and subjectively rate opaque robots as about equal to transparent robots. See videos of our experiments here: https://youtu.be/u8q1Z7WHUu