  This paper proposes trajectory planning strategies for online reconfiguration
of a multi-agent formation on a Lissajous curve. In our earlier work, a
multi-agent formation with constant parametric speed was proposed in order to
address multiple objectives such as repeated collision-free surveillance and
guaranteed sensor coverage of the area with ability for rogue target detection
and trapping. This work addresses the issue of formation reconfiguration within
this context. In particular, smooth parametric trajectories are designed for
the purpose using calculus of variations. These trajectories have been employed
in conjunction with a simple local cooperation scheme so as to achieve
collision-free reconfiguration between different Lissajous curves. A detailed
theoretical analysis of the proposed scheme is provided. These surveillance and
reconfiguration strategies have also been validated through simulations in
MATLAB\reg for agents performing parametric motion along the curves, and by
Software-In-The-Loop simulation for quadrotors. In addition, they are validated
experimentally with a team of quadrotors flying in a motion capture
environment.
