Collision-free trajectory planning on Lissajous curves for repeated multi-agent coverage and target detection

This paper proposes a trajectory planning strategy to simultaneously address multiple surveillance objectives such as complete area coverage, periodic surveillance, and guaranteed detection of a rogue element attempting to exit the area of interest. For agents with identical sensing capability, the proposed strategy defines a time-varying multi-agent formation on a Lissajous curve, which completes the aforementioned tasks in finite time with collision free paths for all agents in a 2-D rectangular region. This obviates the need for sensing and communication for collision avoidance among agents. A sufficient upper limit on agent dimensions that ensures collision free motion is derived. An algorithm is developed for choosing the number of agents and optimal Lissajous curve for a prescribed rectangle and agents' sensing capability. The optimal Lissajous curve is chosen to minimize the time period for repeated coverage and maximize the upper bound on agent size. The proposed algorithm is validated through computer simulations and experiments using differential drive robots.