Surveillance Guidance Using Lamé Curve Paths

This paper introduces a new approach for efficient rectangular boundary surveillance guidance for unmanned aerial vehicles (UAVs) using a continuous-curvature path described by a Lamé curve. Curvature and path length characteristics of the Lamé curve paths are analyzed, and conditions are deduced for the Lamé-curve-based circumscription of rectangular boundaries. Given the maximum turn rate capability of the UAV, a comparative study highlights significant reduction in path length as compared to the widely used elliptic circumscription. In conjunction with the desired Lamé curve path, a vector field guidance method is proposed for path-following. The vector field around the path is generated using a commanded heading angle, which encapsulates a tangent vector along the path and an arcsine shaping function of the UAV position error with respect to the desired path. Asymptotically converging behavior of the UAV position error is ascertained, and simulation studies illustrate the accurate following of the desired path for arbitrary UAV initial conditions. Indoor experimental studies utilizing a quadrotor UAV platform present the practical applicability of the proposed surveillance guidance solution.