Integrating Vector Field Approach and Input-to-State Stability Curved Path Following for Unmanned Aerial Vehicles

In this paper, a curved path following scheme with the aid of the vector field (VF) and the notion of input-to-state stable (ISS) for a fixed-wing unmanned aerial vehicle (UAV) is developed. The VF strategy is a robust and valid guidance method and its stability is proved using ISS properties. Many existing path following algorithms for fixed-wing UAVs are only proposed for straight-lines and orbits. However, the path required to be followed is always in approximate curves rather than straight-lines and orbits in many high-level missions, such as obstacle avoidance, search, and surveillance. The nonlinear-theoretic notion of ISS is playing a central role in the control law design and stability analysis. The error kinematics are converted into two interconnected subsystems with proven ISS properties, which yield the overall system that is globally asymptotically stable, i.e., and the along-track error and the cross-track error asymptotically approach zeros from any initial position in the space. The followed path is defined in terms of the arc-length parameter, and it can be expanded according to the waypoint fitting without the need to obtain a global function representation. The singularity of multiple closest points on the path is eliminated by constructing a speed profile of a virtual point on the path. The scheme is validated with a semi-physical experiment combined by an actual autopilot, ground station and the X-Plane flight simulator. Flight tests using a small fixed-wing UAV show excellent tracking performance of the curved path following.