Since humans and robots often share workspaces and interact with each other to complete tasks cooperatively, as is the case, for example, in automated warehouses and assembly lines, much of the focus has been centered on supporting human interactions with one or a few robots. As the number of robots involved in a task grows large, scalable abstractions are needed to support interactions with larger numbers of robots. Consequently, there has been a growing effort to understand human-swarm interactions (HSIs) and devise abstractions that are amenable to having humans interact with swarms of robots easily and effectively. In this dissertation, we investigate what it means to impose a control structure on a swarm of robots for the purpose of supporting a specific HSI, when such a control structure is suitable for allowing a user to solve a particular task with a swarm of robots, how one can evaluate attention and effort required to interact with a swarm of robots through a particular control structure, how well attention and effort scale as the number of robots in the swarm increases, why some swarms of robots are easier to interact with than others under the same type of control structure, how to select an appropriate swarm size, and how to design new input controllers for interacting with swarm of mobile robots. Consequently, this dissertation provides a comprehensive framework for characterizing, understanding, and designing the control structures of new abstractions that will be amenable to humans interacting with swarms of networked mobile robots, as well as, a number of examples of such old and new abstractions investigated under this framework.

This work presents a new approach to human-swarm interactions, a discipline which addresses the problem of how a human operator can influence the behavior of large groups of robots, providing high-level information understandable by the team. While there exist potential advantages of introducing a human in the control loop of a robot swarm, how the human must be incorporated is not a simple problem. For the intervention of a human operator to be favorable to the performance of the team, the means and form of the information between the human and the robot swarm must be adequately defined: we need to design which device will be provided to the operator to interact with the swarm and how the information will be shaped so that both the human and the robot team understand it. Coordination of multi-robot systems involves the generation of involved motion patterns for the individual agents that result in an overall organized movement. We introduce in this thesis a new human-swarm interaction modality based on music theory, a discipline studied for centuries and capable of creating complex sound structures. In particular, we have focused on understanding how we can apply rules and structures from music theory to an operator's input so that each command both specifies the goal location to be visited and the geometry to be adopted by the swarm. We interpret the sequence of locations to be visited by the swarm as a musical melody, identifying each note with a certain location in the robots' workspace. Once the objective path is defined in the form of a melody, we can apply rules from harmony, a discipline of music theory, to create chords that harmonize the input melody. The interest in using these chords lies fundamentally in that they are structured combinations of pitches, heard simultaneously. These inherent structures will be used to determine the geometry that should be displayed by the team. The developed multi-robot control is applied to a team of differential drive mobile robots through an electronic piano.

The objective of this research is to develop a framework for multi-robot coordination and control with emphasis on human-swarm and inter-agent interactions. We focus on two problems: in the first we address how to enable a single human operator to externally influence large teams of robots. By directly imposing density functions on the environment, the user is able to abstract away the size of the swarm and manipulate it as a whole, e.g., to achieve specified geometric configurations, or to maneuver it around. In order to pursue this approach, contributions are made to the problem of coverage of time-varying density functions. In the second problem, we address the characterization of inter-agent interactions and enforcement of desired interaction patterns in a provably safe (i.e., collision free) manner, e.g., for achieving rich motion patterns in a shared space, or for mixing of sensor information. We use elements of the braid group, which allows us to symbolically characterize classes of interaction patterns. We further construct a new specification language that allows us to provide rich, temporally-layered specifications to the multi-robot mixing framework, and present algorithms that significantly reduce the search space of specification-satisfying symbols with exactness guarantees. We also synthesize provably safe controllers that generate and track trajectories to satisfy these symbolic inputs. These controllers allow us to find bounds on the amount of safe interactions that can be achieved in a given bounded domain.