  This paper introduces a distributed leaderless swarm formation control
framework to address the problem of collectively driving a swarm of robots to
track a time-varying formation. The swarm's formation is captured by the
trajectory of an abstract shape that circumscribes the convex hull of robots'
positions and is independent of the number of robots and their ordering in the
swarm. For each robot in the swarm, given global specifications in terms of the
trajectory of the abstract shape parameters, the proposed framework synthesizes
a control law that steers the swarm to track the desired formation using the
information available at the robot's local neighbors. For this purpose, we
generate a suitable local reference trajectory that the robot controller tracks
by solving the input-output linearization problem. Here, we select the swarm
output to be the parameters of the abstract shape. For this purpose, we design
a dynamic average consensus estimator to estimate the abstract shape
parameters. The abstract shape parameters are used as the swarm state feedback
to generate a suitable robot trajectory. We demonstrate the effectiveness and
robustness of the proposed control framework by providing the simulation of
coordinated collective navigation of a group of car-like robots in the presence
of robots and communication link failures.
