Dubins Vehicle Intercept of a Brownian Target on a Sphere

This paper focuses on a navigation of a Dubins vehicle (DV) to intercept a moving target on a sphere. The uncertainty in the target motion is described by a Brownian motion model. An Itô-type stochastic differential equation for the relative motion between DV and the Brownian moving target is derived. This stochastic differential equation is used to formulate an intercept controller as a minimum time optimal controller. The properties of the controller are incorporated into the numerical computations of the controller, which by its construction can intercept a Brownian target. Our numerical simulation results show that the computed controller can intercept both stationary and moving targets on the sphere.