Kinematic navigation of a nonholonomic robot for 3D environmental extremum seeking without gradient estimation

We consider a single nonholonomic underactuated robot with a bounded control range. The robot travels in a three-dimensional region supporting an unknown field distribution. A single sensor provides the distribution value at the current robot location. We present a new navigation strategy that drives the robot to the location where the field distribution attains its maximum. This strategy is based on a novel paradigm of kinematic control different from conventionally trying to align the velocity vector with the field gradient. The proposed algorithm does not employ estimation of the field gradient and is non-demanding with respect to both computation and motion. Its mathematically rigorous analysis and justification are provided. Simulation results confirm the applicability and performance of the proposed guidance approach.