Limited Gradient Criterion for Global Source Seeking with Mobile Robots

Abstract

This paper presents a criterion and control scheme based on the assumption of a bound on the gradient of a field distribution which guarantees to find the global extremum of the distribution. Mobile robots move through the search space gathering information at points which are calculated as a minimization problem over part of the search space which is guaranteed to include the global extremum based on the previously gathered measurements. Position control in combination with collision avoidance drives each robot to the next position while communicating its position to the other robots. Upon arrival, the next measurement of the field distribution is performed and the next position reference is calculated by each robot until the robots narrowed the search area to a single location. Previously proposed control schemes can find single points as candidates for the global maximum but struggle to guarantee that this point is the global extremum. Simulation results with robot models show the performance in comparison to a naive approach.