Abstract—This paper presents an approach to externally influencing a team of robots by means of time-varying density functions. These density functions represent rough references for where the robots should be located. To this end, a continuous-time algorithm is proposed that moves the robots so as to provide optimal coverage given the density functions as they evolve over time. The developed algorithm represents an extension to previous coverage algorithms in that time-varying densities are explicitly taken into account in a provable manner. A distributed approximation to this algorithm is moreover proposed whereby the robots only need to access information from adjacent robots. Simulations and robotic experiments show that the proposed algorithms do indeed exhibit the desired behaviors in practice as well as in theory. Index Terms—Multi-robot teams, coverage, time-varying density functions

Leveraging the abilities of multiple affordable robots as a swarm is enticing because of the resulting robustness and emergent behaviors of a swarm. However, because swarms are composed of many different agents, it is difficult for a hu-man to influence the swarm by managing individual agents. Instead, we propose that human influence should focus on (a) managing the higher level attractors of the swarm system and (b) managing trade-offs that appear in mission-relevant performance. We claim that managing attractors theoret-ically allows a human to abstract the details of individual agents and focus on managing the collective as a whole. Us-ing a swarm model with two attractors, we demonstrate this concept by showing how limited human influence can cause the swarm to switch between attractors. We further claim that using quorum sensing allows a human to manage trade-offs between the scalability of interactions and mitigating the vulnerability of the swarm to agent failures.

Abstract — Many researchers have employed some form of teleoperated leader to influence a robotic swarm; however, the way in which this influence is conveyed has not been well studied. Some researchers employ designated leaders that are known to be leaders by other members of the swarm and hence followed. Others do not impose a leader/follower distinction on the swarm’s algorithms and instead choose to influence the swarm indirectly through controlling one or more of its members. Because the robustness of swarm behavior arises from its many distributed interactions, influence through designated leaders might render it susceptible to noise or disrupt its coherence by overriding these mechanisms. Conversely, limiting human influence to indirect control through the local effects of a leader might prove too sluggish to allow effective human control. This paper compares leader-based methods of each type, designated as consensus (no explicit leader/follower distinction) and flooding (influence propagating from leader takes precedence). Our overall methodology was to compare the two methods, Explicit influence via flooding and Tacit influence via consensus, both in simulation and in experiments with human operators. We compared the two methods for convergence time and properties in noisy and noiseless conditions with static and dynamic graphs. We found that consensus converged much slower than flooding but had slightly better noise tolerance. In the human experiments we compared the ability of operators to maneuver a swarm to goal points using each method, both with and without sensing error. Under flooding each robot matched the speed and direction of the leader (or matched the speed and direction of a neighboring robot already aligned with the leader). Under consensus, robots matched the average speed and direction of neighbors within sensor range. As in simulation, the flooding method was significantly more effective in moving the swarm between goal points. The greater sensitivity of flooding to error found in simulation, however, was not observed in the human experiments. Instead, the error degraded performance equally across the two conditions. Additionally, in the human experiments the consensus method did show advantages in improving overall connectivity and cohesion of the swarm.