  In the literature, a distributed consensus protocol by which a connected
swarm of agents can generate artistic patterns in 2-dimensional space is
proposed. Motivated by this protocol, in this paper, we design the parameters
of this protocol for a 3-agent swarm of non-holonomic robots of finite size
that results in the generation of periodic trochoidal trajectories that satisfy
a set of geometric and speed constraints; this design also includes selecting
the initial positions of the robots. This problem finds applications in
persistent surveillance and coverage, guarding a region of interest, and target
detection. While the trajectories may be self-intersecting, imposing geometric
constraints i. eliminates collisions between robots; ii. ensures minimum and
maximum separation distance between any robot and a fixed point, thus ensuring
the robots are in communication range. Imposing speed constraints ensure that
tracking these trajectories becomes feasible. It is also shown that robots can
be injected to these paths at specific locations, in order to increase the
refresh rate, without violating any of the geometric constraints. The designs
are implemented in an indoor mobile robot platform.
