UAV navigation using predictive vector field control

This paper introduces the predictive vector field controller (PVF). This controller is designed for controlling nonlinear systems with constraints in order to follow artificial vector fields whose integral curves converge to and circulate about a desired path. This is achieved by predicting the state of the system at some future time horizon using a finite set of system inputs by uniformly sampling the configuration space of the system. A cost function relating the vector field and the future state of the system is then evaluated and a continuous mapping between the configuration space and the cost space is computed. The optimal system input with respect to the cost function is determined by minimizing this mapping. To demonstrate the performance of the PVF controller, we compare it to a nonlinear dynamic inversion (NDI) controller for the Dubin´s vehicle model. We show that, for a given path and vector field, the PVF controller provides accurate path following with significantly less control effort when compared to the NDI controller. Additionally, we demonstrate, that due to the predictive nature of the PVF controller, it does not possess the chattering behavior typically associated with other vector field-based techniques. Finally, we demonstrate the robustness of the PVF algorithm relative to the underlying vector field.