Tracking of deforming environmental level sets of dynamic fields by a nonholonomic robot without gradient estimation

The paper presents a sliding mode guidance and control method for tracking of moving and deforming environmental level sets by a non-holonomic Dubins-car like vehicle traveling with a constant speed in a plane. The proposed control law steers the vehicle to the set where a scalar unknown and time-varying field distribution assumes a pre-specified value and ensures its subsequent circulation in a close proximity of this set. In doing so, only point-wise measurement of the field value in the vehicle current location is utilized, whereas estimation of the spatial gradient of the field is not required. The proposed algorithm is non-demanding with respect to both computation and motion. Its mathematically rigorous justification is provided. The effectiveness of the proposed guidance law is confirmed by computer simulations.