Persistent Monitoring by Multiple Unmanned Aerial Vehicles Using Bernstein Polynomials

A framework for monitoring a target modeled as Dubins car using multiple UAVs is proposed. The UAVs are subject to minimum and maximum speed, maximum angular rate constraints, as well as inter-vehicle safety requirements and no-fly-zones. The problem is formulated as a continuous time nonlinear optimal control problem. This problem is first simplified by using a sequential approach, which significantly reduces its complexity. Then, by defining the desired trajectories to be tracked by the UAVs as Bernstein polynomials, it is transcribed into a nonlinear optimization problem. It is shown through numerical simulations that the present approach is computationally efficient, and thus it is well suited for trajectory planning/re-planning to monitor a target of unknown speed, heading direction and unexpected detours. Moreover, the proposed method guarantees satisfaction of feasibility and safety constraints for the whole planning time period, rather than only at discrete time points.