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In the literature, a distributed consensus protocol by which a connectedswarm of agents can generate artistic patterns in 2-dimensional space isproposed. Motivated by this protocol, in this paper, we design the parametersof this protocol for a 3-agent swarm of non-holonomic robots of finite sizethat results in the generation of periodic trochoidal trajectories that satisfya set of geometric and speed constraints; this design also includes selectingthe initial positions of the robots. This problem finds applications inpersistent surveillance and coverage, guarding a region of interest, and targetdetection. While the trajectories may be self-intersecting, imposing geometricconstraints i. eliminates collisions between robots; ii. ensures minimum andmaximum separation distance between any robot and a fixed point, thus ensuringthe robots are in communication range. Imposing speed constraints ensure thattracking these trajectories becomes feasible. It is also shown that robots canbe injected to these paths at specific locations, in order to increase therefresh rate, without violating any of the geometric constraints. The designsare implemented in an indoor mobile robot platform.

Design of Planar Collision-free Trochoidal Paths for a Multi-robot Swarm