Collaborative design activities are often centered around physical artifacts. Depending on the design activity, this can be the model of a building, paper crafts, carving artwork, or a new circuit to be debugged and evaluated. In a typical setting, collaborators are seated around a table and divide their attention between the design artifact under review, at least one laptop supporting measurements and information foraging, and of course their collaborators. Although these activities involve complex sets of tools and configurations, people can easily work together when they are present in the same space. This is because the physical presence of a partner affords peripheral awareness to inform where the partner's attention is and what they are doing. This peripheral awareness allows collaborators to coordinate actions and manage coupling to achieve a shared task. For example, it is quite easy to know when your partner switches their focus from a breadboard to you as a request to start a face to face discussion.
In environments where multiple robots must coordinate in a shared space, decentralized approaches allow for decoupled planning at the cost of global guarantees, while centralized approaches make the opposite trade-off. These solutions make a range of assumptions -commonly, that all the robots share the same planning strategies. In this work, we present a framework that ensures progress for all robots without assumptions on any robot's planning strategy by (1) generating a partition of the environment into "flow", "open", and "passage" regions and (2) imposing a set of rules for robot motion in these regions. These rules for robot motion prevent deadlock through an adaptively centralized protocol for resolving spatial conflicts between robots. Our proposed framework ensures progress for all robots without a gridlike discretization of the environment or strong requirements on robot communication, coordination, or cooperation. Each robot can freely choose how to plan and coordinate for itself, without being vulnerable to other robots or groups of robots blocking them from their goals, as long as they follow the rules when necessary. We describe our space partition and motion rules, prove that the motion rules suffice to guarantee progress in partitioned environments, and demonstrate several cases in simulated polygonal environments. This work strikes a balance between each robot's planning independence and a guarantee that each robot can always reach any goal in finite time.
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