Dynamic Wildfire Boundary Tracking with Radial Basis Function based Guidance Law

Abstract

This paper presents a radial basis function based vector field controller for a multirotor to track the time-varying wildfire boundary. The wildfire boundary is described as the zero level set of a function approximated with the typical radial basis function thin-plate spline. Its dynamics is modeled by Hamilton-Jacobi equation and solved with the radial basis functions. To guide the multirotor to converge to and patrol along the advancing wildfire boundary, the complex nonlinear dynamics of the multirotor is exploited with differential flatness and it is incorporated with the analytical velocity vector field, which derived from the approximated level set function, to design a nonlinear geometric controller. Computer simulations with a single multirotor have been conducted to evaluate the proposed strategy, and numerical results show that the proposed algorithm can ensure successful tracking of the advancing wildfire boundary regardless of the boundary shape.