Smooth surveillance using quadrotors for tasks with nonconvex utility functions

In this paper, we target the problem of having a quadrotor navigate in an area for surveillance where the relative importance is an unknown nonconvex function with multiple local optima. Typical techniques often split the task into a planning phase for the trajectory and a control part to track that reference following the calculated waypoints. A problem arising from any planning strategy is that it requires knowledge of the nonconvex utility function which is not assumed in this setup. We propose a technique where a hybrid system designs the trajectory that is passed as the reference of a backstepping nonlinear controller or a differential flatness-based control law. For handling multiple optima, the system integrates a three-state automaton that supports ascent phases, spiral coverage, and random restarts to prevent revisits and facilitate comprehensive exploration. Numerical simulations show that our approach matches Model Predictive Control (MPC) strategies if the function was assumed to be known, yet requiring much less computation and enabling real-time full inspection of large maps without prior utility knowledge.