Source Seeking With a Nonholonomic Vehicle in Static and Dynamic Spatial Fields

In this paper, a novel source seeking strategy is presented. A single autonomous vehicle is modeled as a kinematic unicycle moving in two-dimensional space within a spatial field. The proposed control scheme allows the vehicle to reach a neighborhood of the source of the spatial field in finite time. In this work, the spatial field can be static, translating or dynamically evolving. The control strategy, based on the definition of a reference trajectory and on a second order sliding mode extremum seeking approach, exploits only a point measurement at the vehicle position, and does not require knowledge or an estimate of the spatial gradient of the phenomenon of interest. Explicit bounds on the reference trajectory parameters are introduced in order to guarantee finite time convergence to a neighborhood of the source. The approach is tested in simulation on static and dynamic spatial fields.